Investment Valuation: Tools and Techniques for Determining the Value of Any Asset,

1

CHAPTER 1 INTRODUCTION TO VALUATION Every asset, financial as well as real, has a value. The key to successfully investing in and managing these assets lies in understanding not only what the value is but also the sources of the value. Any asset can be valued, but some assets are easier to value than others and the details of valuation will vary from case to case. Thus, the valuation of a share of a real estate property will require different information and follow a different format than the valuation of a publicly traded stock. What is surprising, however, is not the differences in valuation techniques across assets, but the degree of similarity in basic principles. There is undeniably uncertainty associated with valuation. Often that uncertainty comes from the asset being valued, though the valuation model may add to that uncertainty. This chapter lays out a philosophical basis for valuation, together with a discussion of how valuation is or can be used in a variety of frameworks, from portfolio management to corporate finance. A philosophical basis for valuation It was Oscar Wilde who described a cynic as one who “knows the price of everything, but the value of nothing”. He could very well have been describing some equity research analysts and many investors, a surprising number of whom subscribe to the 'bigger fool' theory of investing, which argues that the value of an asset is irrelevant as long as there is a 'bigger fool' willing to buy the asset from them. While this may provide a basis for some profits, it is a dangerous game to play, since there is no guarantee that such an investor will still be around when the time to sell comes. A postulate of sound investing is that an investor does not pay more for an asset than its worth. This statement may seem logical and obvious, but it is forgotten and rediscovered at some time in every generation and in every market. There are those who are disingenuous enough to argue that value is in the eyes of the beholder, and that any price can be justified if there are other investors willing to pay that price. That is patently absurd. Perceptions may be all that matter when the asset is a painting or a sculpture, but investors do not (and should not) buy most assets for aesthetic or emotional reasons;

2 financial assets are acquired for the cashflows expected on them. Consequently, perceptions of value have to be backed up by reality, which implies that the price paid for any asset should reflect the cashflows that it is expected to generate. The models of valuation described in this book attempt to relate value to the level and expected growth in these cashflows. There are many areas in valuation where there is room for disagreement, including how to estimate true value and how long it will take for prices to adjust to true value. But there is one point on which there can be no disagreement. Asset prices cannot be justified by merely using the argument that there will be other investors around willing to pay a higher price in the future. Generalities about Valuation Like all analytical disciplines, valuation has developed its own set of myths over time. This section examines and debunks some of these myths. Myth 1: Since valuation models are quantitative, valuation is objective Valuation is neither the science that some of its proponents make it out to be nor the objective search for the true value that idealists would like it to become. The models that we use in valuation may be quantitative, but the inputs leave plenty of room for subjective judgments. Thus, the final value that we obtain from these models is colored by the bias that we bring into the process. In fact, in many valuations, the price gets set first and the valuation follows. The obvious solution is to eliminate all bias before starting on a valuation, but this is easier said than done. Given the exposure we have to external information, analyses and opinions about a firm, it is unlikely that we embark on most valuations without some bias. There are two ways of reducing the bias in the process. The first is to avoid taking strong public positions on the value of a firm before the valuation is complete. In far too many cases, the decision on whether a firm is under or over valued precedes the actual

3 valuation1, leading to seriously biased analyses. The second is to minimize the stake we have in whether the firm is under or over valued, prior to the valuation. Institutional concerns also play a role in determining the extent of bias in valuation. For instance, it is an acknowledged fact that equity research analysts are more likely to issue buy rather than sell recommendations,2 i.e., that they are more likely to find firms to be undervalued than overvalued. This can be traced partly to the difficulties they face in obtaining access and collecting information on firms that they have issued sell recommendations and to the pressure that they face from portfolio managers, some of whom might have large positions in the stock. In recent years, this trend has been exacerbated by the pressure on equity research analysts to deliver investment banking business. When using a valuation done by a third party, the biases of the analyst(s) doing the valuation should be considered before decisions are made on its basis. For instance, a self-valuation done by a target firm in a takeover is likely to be positively biased. While this does not make the valuation worthless, it suggests that the analysis should be viewed with skepticism. The Biases in Equity Research The lines between equity research and salesmanship blur most in periods that are characterized by “irrational exuberance”. In the late 1990s, the extraordinary surge of market values in the companies that comprised the new economy saw a large number of equity research analysts, especially on the sell side, step out of their roles as analysts and become cheerleaders for these stocks. While these analysts might have been well meaning in their recommendations, the fact that the investment banks that they worked for were leading the charge on new initial public offerings from these firms exposed them to charges of bias and worse.

1This

is most visible in takeovers, where the decision to acquire a firm often seems to precede the valuation of the firm. It should come as no surprise, therefore, that the analysis almost invariably supports the decision. 2In most years, buy recommendations outnumber sell recommendations by a margin of ten to one. In recent years, this trend has become even stronger.

4 In 2001, the crash in the market values of new economy stocks and the anguished cries of investors who had lost wealth in the crash created a firestorm of controversy. There were congressional hearing where legislators demanded to know what analysts knew about the companies they recommended and when they knew it, statements from the SEC about the need for impartiality in equity research and decisions taken by some investment banking to create at least the appearance of objectivity. At the time this book went to press, both Merrill Lynch and CSFB had decided that their equity research analysts could no longer hold stock in companies that they covered. Unfortunately, the real source of bias – the intermingling of investment banking business and investment advice – was left untouched. Should there be government regulation of equity research? We do not believe that it would be wise, since regulation tends to be heavy handed and creates side costs that seem to quickly exceed the benefits. A much more effective response can be delivered by portfolio managers and investors. The equity research of firms that create the potential for bias should be discounted or, in egregious cases, even ignored. Myth 2: A well-researched and well-done valuation is timeless The value obtained from any valuation model is affected by firm-specific as well as market-wide information. As a consequence, the value will change as new information is revealed. Given the constant flow of information into financial markets, a valuation done on a firm ages quickly, and has to be updated to reflect current information. This information may be specific to the firm, affect an entire sector or alter expectations for all firms in the market. The most common example of firm-specific information is an earnings report that contains news not only about a firm’s performance in the most recent time period but, more importantly, about the business model that the firm has adopted. The dramatic drop in value of many new economy stocks from 1999 to 2001 can be traced, at least partially, to the realization that these firms had business models that could deliver customers but not earnings, even in the long term. In some cases, new information can affect the valuations of all firms in a sector. Thus, pharmaceutical companies that were valued highly in early 1992, on the assumption that the high growth from the eighties would continue into the future, were valued much less in early 1993, as the prospects of

5 health reform and price controls dimmed future prospects. With the benefit of hindsight, the valuations of these companies (and the analyst recommendations) made in 1992 can be criticized, but they were reasonable, given the information available at that time. Finally, information about the state of the economy and the level of interest rates affect all valuations in an economy. A weakening in the economy can lead to a reassessment of growth rates across the board, though the effect on earnings are likely to be largest at cyclical firms. Similarly, an increase in interest rates will affect all investments, though to varying degrees. When analysts change their valuations, they will undoubtedly be asked to justify them. In some cases, the fact that valuations change over time is viewed as a problem. The best response may be the one that Lord Keynes gave when he was criticized for changing his position on a major economic issue: “When the facts change, I change my mind. And what do you do, sir?” Myth 3.: A good valuation provides a precise estimate of value Even at the end of the most careful and detailed valuation, there will be uncertainty about the final numbers, colored as they are by the assumptions that we make about the future of the company and the economy. It is unrealistic to expect or demand absolute certainty in valuation, since cash flows and discount rates are estimated with error. This also means that you have to give yourself a reasonable margin for error in making recommendations on the basis of valuations. The degree of precision in valuations is likely to vary widely across investments. The valuation of a large and mature company, with a long financial history, will usually be much more precise than the valuation of a young company, in a sector that is in turmoil. If this company happens to operate in an emerging market, with additional disagreement about the future of the market thrown into the mix, the uncertainty is magnified. Later in this book, we will argue that the difficulties associated with valuation can be related to where a firm is in the life cycle. Mature firms tend to be easier to value than growth firms, and young start-up companies are more difficult to value than companies with established produces and markets. The problems are not with the valuation models we use, though, but with the difficulties we run into in making estimates for the future.

6 Many investors and analysts use the uncertainty about the future or the absence of information to justify not doing full-fledged valuations. In reality, though, the payoff to valuation is greatest in these firms. Myth 4: .The more quantitative a model, the better the valuation It may seem obvious that making a model more complete and complex should yield better valuations, but it is not necessarily so. As models become more complex, the number of inputs needed to value a firm increases, bringing with it the potential for input errors. These problems are compounded when models become so complex that they become ‘black boxes’ where analysts feed in numbers into one end and valuations emerge from the other. All too often the blame gets attached to the model rather than the analyst when a valuation fails. The refrain becomes “It was not my fault. The model did it.” There are three points we will emphasize in this book on all valuation. The first is the principle of parsimony, which essentially states that you do not use more inputs than you absolutely need to value an asset. The second is that the there is a trade off between the benefits of building in more detail and the estimation costs (and error) with providing the detail. The third is that the models don’t value companies: you do. In a world where the problem that we often face in valuations is not too little information but too much, separating the information that matters from the information that does not is almost as important as the valuation models and techniques that you use to value a firm. Myth 5: To make money on valuation, you have to assume that markets are inefficient Implicit often in the act of valuation is the assumption that markets make mistakes and that we can find these mistakes, often using information that tens of thousands of other investors can access. Thus, the argument, that those who believe that markets are inefficient should spend their time and resources on valuation whereas those who believe that markets are efficient should take the market price as the best estimate of value, seems to be reasonable. This statement, though, does not reflect the internal contradictions in both positions. Those who believe that markets are efficient may still feel that valuation has something to contribute, especially when they are called upon to value the effect of a change in the way a firm is run or to understand why market prices change over time.

7 Furthermore, it is not clear how markets would become efficient in the first place, if investors did not attempt to find under and over valued stocks and trade on these valuations. In other words, a pre-condition for market efficiency seems to be the existence of millions of investors who believe that markets are not. On the other hand, those who believe that markets make mistakes and buy or sell stocks on that basis ultimately must believe that markets will correct these mistakes, i.e. become efficient, because that is how they make their money. This is a fairly self-serving definition of inefficiency – markets are inefficient until you take a large position in the stock that you believe to be mispriced but they become efficient after you take the position. We approach the issue of market efficiency as wary skeptics. On the one hand, we believe that markets make mistakes but, on the other, finding these mistakes requires a combination of skill and luck. This view of markets leads us to the following conclusions. First, if something looks too good to be true – a stock looks obviously under valued or over valued – it is probably not true. Second, when the value from an analysis is significantly different from the market price, we start off with the presumption that the market is correct and we have to convince ourselves that this is not the case before we conclude that something is over or under valued. This higher standard may lead us to be more cautious in following through on valuations. Given the historic difficulty of beating the market, this is not an undesirable outcome. Myth 6: The product of valuation (i.e., the value) is what matters; The process of valuation is not important. As valuation models are introduced in this book, there is the risk of focusing exclusively on the outcome, i.e., the value of the company, and whether it is under or over valued, and missing some valuable insights that can be obtained from the process of the valuation. The process can tell us a great deal about the determinants of value and help us answer some fundamental questions -- What is the appropriate price to pay for high growth? What is a brand name worth? How important is it to improve returns on projects? What is the effect of profit margins on value? Since the process is so

8 informative, even those who believe that markets are efficient (and that the market price is therefore the best estimate of value) should be able to find some use for valuation models. The Role of Valuation Valuation is useful in a wide range of tasks. The role it plays, however, is different in different arenas. The following section lays out the relevance of valuation in portfolio management, acquisition analysis and corporate finance. 1. Valuation and Portfolio Management The role that valuation plays in portfolio management is determined in large part by the investment philosophy of the investor. Valuation plays a minimal role in portfolio management for a passive investor, whereas it plays a larger role for an active investor. Even among active investors, the nature and the role of valuation is different for different types of active investment. Market timers use valuation much less than investors who pick stocks, and the focus is on market valuation rather than on firm-specific valuation. Among security selectors, valuation plays a central role in portfolio management for fundamental analysts and a peripheral role for technical analysts. The following sub-section describes, in broad terms, different investment philosophies and the role played by valuation in each. 1. Fundamental Analysts: The underlying theme in fundamental analysis is that the true value of the firm can be related to its financial characteristics -- its growth prospects, risk profile and cashflows. Any deviation from this true value is a sign that a stock is under or overvalued. It is a long term investment strategy, and the assumptions underlying it are: (a) the relationship between value and the underlying financial factors can be measured. (b) the relationship is stable over time. (c) deviations from the relationship are corrected in a reasonable time period. Valuation is the central focus in fundamental analysis. Some analysts use discounted cashflow models to value firms, while others use multiples such as the priceearnings and price-book value ratios. Since investors using this approach hold a large number of 'undervalued' stocks in their portfolios, their hope is that, on average, these portfolios will do better than the market.

9 2. Franchise Buyer: The philosophy of a franchise buyer is best expressed by an investor who has been very successful at it -- Warren Buffett.

"We try to stick to

businesses we believe we understand," Mr. Buffett writes3. "That means they must be relatively simple and stable in character. If a business is complex and subject to constant change, we're not smart enough to predict future cash flows." Franchise buyers concentrate on a few businesses they understand well, and attempt to acquire undervalued firms. Often, as in the case of Mr. Buffett, franchise buyers wield influence on the management of these firms and can change financial and investment policy. As a long term strategy, the underlying assumptions are that : (a) Investors who understand a business well are in a better position to value it correctly. (b) These undervalued businesses can be acquired without driving the price above the true value. Valuation plays a key role in this philosophy, since franchise buyers are attracted to a particular business because they believe it is undervalued. They are also interested in how much additional value they can create by restructuring the business and running it right. 3. Chartists: Chartists believe that prices are driven as much by investor psychology as by any underlying financial variables. The information available from trading -- price movements, trading volume, short sales, etc. -- gives an indication of investor psychology and future price movements. The assumptions here are that prices move in predictable patterns, that there are not enough marginal investors taking advantage of these patterns to eliminate them, and that the average investor in the market is driven more by emotion rather than by rational analysis. While valuation does not play much of a role in charting, there are ways in which an enterprising chartist can incorporate it into analysis. For instance, valuation can be used to determine support and resistance lines4 on price charts. 3This

is extracted from Mr. Buffett's letter to stockholders in Berkshire Hathaway for 1993. 4On a chart, the support line usually refers to a lower bound below which prices are unlikely to move and the resistance line refers to the upper bound above which prices are unlikely to venture. While these levels are usually estimated using past prices, the range

10 4. Information Traders: Prices move on information about the firm. Information traders attempt to trade in advance of new information or shortly after it is revealed to financial markets, buying on good news and selling on bad. The underlying assumption is that these traders can anticipate information announcements and gauge the market reaction to them better than the average investor in the market. For an information trader, the focus is on the relationship between information and changes in value, rather than on value, per se. Thus an information trader may buy an 'overvalued' firm if he believes that the next information announcement is going to cause the price to go up, because it contains better than expected news. If there is a relationship between how undervalued or overvalued a company is and how its stock price reacts to new information, then valuation could play a role in investing for an information trader. 5. Market Timers: Market timers note, with some legitimacy, that the payoff to calling turns in markets is much greater than the returns from stock picking. They argue that it is easier to predict market movements than to select stocks and that these predictions can be based upon factors that are observable. While valuation of individual stocks may not be of any use to a market timer, market timing strategies can use valuation in at least two ways: (a) The overall market itself can be valued and compared to the current level. (b) A valuation model can be used to value all stocks, and the results from the crosssection can be used to determine whether the market is over or under valued. For example, as the number of stocks that are overvalued, using the dividend discount model, increases relative to the number that are undervalued, there may be reason to believe that the market is overvalued. 6. Efficient Marketers: Efficient marketers believe that the market price at any point in time represents the best estimate of the true value of the firm, and that any attempt to exploit perceived market efficiencies will cost more than it will make in excess profits. They assume that markets aggregate information quickly and accurately, that marginal of values obtained from a valuation model can be used to determine these levels, i.e., the maximum value will become the resistance level and the minimum value will become the support line.

11 investors promptly exploit any inefficiencies and that any inefficiencies in the market are caused by friction, such as transactions costs, and cannot be arbitraged away. For efficient marketers, valuation is a useful exercise to determine why a stock sells for the price that it does. Since the underlying assumption is that the market price is the best estimate of the true value of the company, the objective becomes determining what assumptions about growth and risk are implied in this market price, rather than on finding under or over valued firms. 2. Valuation in Acquisition Analysis Valuation should play a central part of acquisition analysis. The bidding firm or individual has to decide on a fair value for the target firm before making a bid, and the target firm has to determine a reasonable value for itself before deciding to accept or reject the offer. There are also special factors to consider in takeover valuation. First, the effects of synergy on the combined value of the two firms (target plus bidding firm) have to be considered before a decision is made on the bid. Those who suggest that synergy is impossible to value and should not be considered in quantitative terms are wrong. Second, the effects on value, of changing management and restructuring the target firm, will have to be taken into account in deciding on a fair price. This is of particular concern in hostile takeovers. Finally, there is a significant problem with bias in takeover valuations. Target firms may be over-optimistic in estimating value, especially when the takeover is hostile, and they are trying to convince their stockholders that the offer price is too low. Similarly, if the bidding firm has decided, for strategic reasons, to do an acquisition, there may be strong pressure on the analyst to come up with an estimate of value that backs up the acquisition. 3. Valuation in Corporate Finance If the objective in corporate finance is the maximization of firm value5, the relationship among financial decisions, corporate strategy and firm value has to be

5Most

corporate financial theory is constructed on this premise.

12 delineated. In recent years, management consulting firms have started offered companies advice on how to increase value6. Their suggestions have often provided the basis for the restructuring of these firms. The value of a firm can be directly related to decisions that it makes -- on which projects it takes, on how it finances them and on its dividend policy. Understanding this relationship is key to making value-increasing decisions and to sensible financial restructuring. Conclusion Valuation plays a key role in many areas of finance -- in corporate finance, mergers and acquisitions and portfolio management. The models presented in this book will provide a range of tools that analysts in each of these areas will find useful, but the cautionary note sounded in this chapter bears repeating. Valuation is not an objective exercise; and any preconceptions and biases that an analyst brings to the process will find its way into the value.

6The

motivation for this has been the fear of hostile takeovers. Companies have increasingly turned to 'value consultants' to tell them how to restructure, increase value and avoid being taken over.

13 Questions and Short Problems: Chapter 1 1. The value of an investment is A. the present value of the cash flows on the investment B. determined by investor perceptions about it C. determined by demand and supply D. often a subjective estimate, colored by the bias of the analyst E. all of the above 2. There are many who claim that value is based upon investor perceptions, and perceptions alone, and that cash flows and earnings do not matter. This argument is flawed because A. value is determined by earnings and cash flows, and investor perceptions do not matter. B. perceptions do matter, but they can change. Value must be based upon something more stable. C. investors are irrational. Therefore, their perceptions should not determine value. D. value is determined by investor perceptions, but it is also determined by the underlying earnings and cash flows. Perceptions must be based upon reality. 3. You use a valuation model to arrive at a value of $15 for a stock. The market price of the stock is $25. The difference may be explained by A. a market inefficiency; the market is overvaluing the stock. B. the use of the wrong valuation model to value the stock. C. errors in the inputs to the valuation model. D. none of the above E. either A, B, or C.

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CHAPTER 2 APPROACHES TO VALUATION Analysts use a wide range of models to value assets in practice, ranging from the simple to the sophisticated. These models often make very different assumptions about pricing, but they do share some common characteristics and can be classified in broader terms. There are several advantages to such a classification -- it makes it easier to understand where individual models fit into the big picture, why they provide different results and when they have fundamental errors in logic. In general terms, there are three approaches to valuation. The first, discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset. The second, relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable such as earnings, cashflows, book value or sales. The third, contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics. Some of these assets are traded financial assets like warrants, and some of these options are not traded and are based on real assets – projects, patents and oil reserves are examples. The latter are often called real options. There can be significant differences in outcomes, depending upon which approach is used. One of the objectives in this book is to explain the reasons for such differences in value across different models and to help in choosing the right model to use for a specific task. Discounted Cashflow Valuation While discounted cash flow valuation is one of the three ways of approaching valuation and most valuations done in the real world are relative valuations, we will argue that it is the foundation on which all other valuation approaches are built. To do relative valuation correctly, we need to understand the fundamentals of discounted cash flow valuation. To apply option pricing models to value assets, we often have to begin with a discounted cash flow valuation. This is why so much of this book focuses on discounted cash flow valuation. Anyone who understands its fundamentals will be able to analyze and use the other approaches. In this section, we will consider the basis of this approach,

1 a philosophical rationale for discounted cash flow valuation and an examination of the different sub-approaches to discounted cash flow valuation. Basis for Discounted Cashflow Valuation This approach has its foundation in the present value rule, where the value of any asset is the present value of expected future cashflows that the asset generates. t=n

Value =

CF

∑ (1+r)t t t=1

where, n = Life of the asset CFt = Cashflow in period t r = Discount rate reflecting the riskiness of the estimated cashflows The cashflows will vary from asset to asset -- dividends for stocks, coupons (interest) and the face value for bonds and after-tax cashflows for a real project. The discount rate will be a function of the riskiness of the estimated cashflows, with higher rates for riskier assets and lower rates for safer projects. You can in fact think of discounted cash flow valuation on a continuum. At one end of the spectrum, you have the default-free zero coupon bond, with a guaranteed cash flow in the future. Discounting this cash flow at the riskless rate should yield the value of the bond. A little further up the spectrum are corporate bonds where the cash flows take the form of coupons and there is default risk. These bonds can be valued by discounting the expected cash flows at an interest rate that reflects the default risk. Moving up the risk ladder, we get to equities, where there are expected cash flows with substantial uncertainty around the expectation. The value here should be the present value of the expected cash flows at a discount rate that reflects the uncertainty. The Underpinnings of Discounted Cashflow Valuation In discounted cash flow valuation, we try to estimate the intrinsic value of an asset based upon its fundamentals. What is intrinsic value? For lack of a better definition, consider it the value that would be attached to the firm by an all-knowing analyst, who not only knows the expected cash flows for the firm but also attaches the right discount

2 rate(s) to these cash flows and values them with absolute precision. Hopeless though the task of estimating intrinsic value may seem to be, especially when valuing young companies with substantial uncertainty about the future, we believe that these estimates can be different from the market prices attached to these companies. In other words, markets make mistakes. Does that mean we believe that markets are inefficient? Not quite. While we assume that prices can deviate from intrinsic value, estimated based upon fundamentals, we also assume that the two will converge sooner rather than latter. Categorizing Discounted Cash Flow Models There are literally thousands of discounted cash flow models in existence. Oftentimes, we hear claims made by investment banks or consulting firms that their valuation models are better or more sophisticated than those used by

their

contemporaries. Ultimately, however, discounted cash flow models can vary only a couple of dimensions and we will examine these variations in this section. I. Equity Valuation, Firm Valuation and Adjusted Present Value (APV) Valuation There are three paths to discounted cashflow valuation -- the first is to value just the equity stake in the business, the second is to value the entire firm, which includes, besides equity, the other claimholders in the firm (bondholders, preferred stockholders, etc.) and the third is to value the firm in pieces, beginning with its operations and adding the effects on value of debt and other non-equity claims. While all three approaches discount expected cashflows, the relevant cashflows and discount rates are different under each. The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, reinvestment needs, tax obligations and net debt payments (interest, principal payments and new debt issuance), at the cost of equity, i.e., the rate of return required by equity investors in the firm. t=n

Value of Equity = where,

CF to Equity t (1+k e )t t=1

∑

3 CF to Equityt = Expected Cashflow to Equity in period t ke = Cost of Equity The dividend discount model is a specialized case of equity valuation, where the value of the equity is the present value of expected future dividends. The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses, reinvestment needs and taxes, but prior to any payments to either debt or equity holders, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions. t=n

Value of Firm =

CF to Firm

∑ (1+WACC)tt t=1

where, CF to Firm t = Expected Cashflow to Firm in period t WACC = Weighted Average Cost of Capital The value of the firm can also be obtained by valuing each claim on the firm separately. In this approach, which is called adjusted present value (APV), we begin by valuing equity in the firm, assuming that it was financed only with equity. We then consider the value added (or taken away) by debt by considering the present value of the tax benefits that flow from debt and the expected bankruptcy costs. Value of firm = Value of all-equity financed firm + PV of tax benefits + Expected Bankruptcy Costs In fact, this approach can be generalized to allow different cash flows to the firm to be discounted at different rates, given their riskiness. While the three approaches use different definitions of cashflow and discount rates, they will yield consistent estimates of value as long as you use the same set of assumptions in valuation. The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm. In the illustration

4 that follows, we will show the equivalence of equity and firm valuation. Later in this book, we will show that adjusted present value models and firm valuation models also yield the same values. Illustration 2.1: Effects of mismatching cashflows and discount rates Assume that you are analyzing a company with the following cashflows for the next five years. Assume also that the cost of equity is 13.625% and the firm can borrow long term at 10%. (The tax rate for the firm is 50%.) The current market value of equity is $1,073 and the value of debt outstanding is $800. Year

Cashflow to Equity

Interest (1-t)

Cashflow to Firm

1

$ 50

$ 40

$ 90

2

$ 60

$ 40

$ 100

3

$ 68

$ 40

$ 108

4

$ 76.2

$ 40

$ 116.2

5

$ 83.49

$ 40

$ 123.49

Terminal Value

$ 1603.008

$ 2363.008

The cost of equity is given as an input and is 13.625%, and the after-tax cost of debt is 5%. Cost of Debt = Pre-tax rate (1 – tax rate) = 10% (1-.5) = 5% Given the market values of equity and debt, we can estimate the cost of capital. WACC = Cost of Equity (Equity / (Debt + Equity)) + Cost of Debt (Debt/(Debt+Equity)) = 13.625% (1073/1873) + 5% (800/1873) = 9.94% Method 1: Discount CF to Equity at Cost of Equity to get value of equity We discount cash flows to equity at the cost of equity: PV of Equity

= 50/1.13625 + 60/1.136252 + 68/1.136253 + 76.2/1.136254 + (83.49+1603)/1.136255 = $1073

Method 2: Discount CF to Firm at Cost of Capital to get value of firm PV of Firm

= 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 + (123.49+2363)/1.09945 = $1873

5 PV of Equity

= PV of Firm – Market Value of Debt = $ 1873 – $ 800 = $1073

Note that the value of equity is $1073 under both approaches. It is easy to make the mistake of discounting cashflows to equity at the cost of capital or the cashflows to the firm at the cost of equity. Error 1: Discount CF to Equity at Cost of Capital to get too high a value for equity PV of Equity

= 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 + (83.49+1603)/1.09945 = $1248

Error 2: Discount CF to Firm at Cost of Equity to get too low a value for the firm PV of Firm

= 90/1.13625 + 100/1.136252 + 108/1.136253 + 116.2/1.136254 + (123.49+2363)/1.136255 = $1613

PV of Equity

= PV of Firm – Market Value of Debt = $1612.86 – $800 = $813

The effects of using the wrong discount rate are clearly visible in the last two calculations. When the cost of capital is mistakenly used to discount the cashflows to equity, the value of equity increases by $175 over its true value ($1073). When the cashflows to the firm are erroneously discounted at the cost of equity, the value of the firm is understated by $260. We have to point out that getting the values of equity to agree with the firm and equity valuation approaches can be much more difficult in practice than in this example. We will return and consider the assumptions that we need to make to arrive at this result. A Simple Test of Cash Flows There is a simple test that can be employed to determine whether the cashflows being used in a valuation are cashflows to equity or cashflows to the firm. If the cash flows that are being discounted are after interest expenses (and principal payments), they are cash flows to equity and the discount rate that should be used should be the cost of equity. If the cash flows that are discounted are before interest expenses and principal payments, they are usually cash flows to the firm. Needless to say, there are other items that need to be considered when estimating these cash flows, and we will consider them in extensive detail in the coming chapters.

6 II. Total Cash Flow versus Excess Cash Flow Models The conventional discounted cash flow model values an asset by estimating the present value of all cash flows generated by that asset at the appropriate discount rate. In excess return (and excess cash flow) models, only cash flows earned in excess of the required return are viewed as value creating, and the present value of these excess cash flows can be added on to the amount invested in the asset to estimate its value. To illustrate, assume that you have an asset in which you invest $100 million and that you expect to generate $12 million per year in after-tax cash flows in perpetuity. Assume further that the cost of capital on this investment is 10%. With a total cash flow model, the value of this asset can be estimated as follows: Value of asset = $12 million/0.10 = $120 million With an excess return model, we would first compute the excess return made on this asset: Excess return = Cash flow earned – Cost of capital * Capital Invested in asset = $12 million – 0.10 * $100 million = $2 million We then add the present value of these excess returns to the investment in the asset: Value of asset = Present value of excess return + Investment in the asset = $2 million/0.10 + $100 million = $120 million Note that the answers in the two approaches are equivalent. Why, then, would we want to use an excess return model? By focusing on excess returns, this model brings home the point that it is not earning per se that create value, but earnings in excess of a required return. Later in this book, we will consider special versions of these excess return models such as Economic Value Added (EVA). As in the simple example above, we will argue that, with consistent assumptions, total cash flow and excess return models are equivalent. Applicability and Limitations of DCF Valuation Discounted cashflow valuation is based upon expected future cashflows and discount rates. Given these informational requirements, this approach is easiest to use for assets (firms) whose cashflows are currently positive and can be estimated with some reliability for future periods, and where a proxy for risk that can be used to obtain

7 discount rates is available. The further we get from this idealized setting, the more difficult discounted cashflow valuation becomes. The following list contains some scenarios where discounted cashflow valuation might run into trouble and need to be adapted. (1) Firms in trouble: A distressed firm generally has negative earnings and cashflows. It expects to lose money for some time in the future. For these firms, estimating future cashflows is difficult to do, since there is a strong probability of bankruptcy. For firms which are expected to fail, discounted cashflow valuation does not work very well, since we value the firm as a going concern providing positive cashflows to its investors. Even for firms that are expected to survive, cashflows will have to be estimated until they turn positive, since obtaining a present value of negative cashflows will yield a negative1 value for equity or the firm. (2) Cyclical Firms: The earnings and cashflows of cyclical firms tend to follow the economy - rising during economic booms and falling during recessions. If discounted cashflow valuation is used on these firms, expected future cashflows are usually smoothed out, unless the analyst wants to undertake the onerous task of predicting the timing and duration of economic recessions and recoveries. Many cyclical firms, in the depths of a recession, look like troubled firms, with negative earnings and cashflows. Estimating future cashflows then becomes entangled with analyst predictions about when the economy will turn and how strong the upturn will be, with more optimistic analysts arriving at higher estimates of value. This is unavoidable, but the economic biases of the analyst have to be taken into account before using these valuations. (3) Firms with unutilized assets: Discounted cashflow valuation reflects the value of all assets that produce cashflows. If a firm has assets that are unutilized (and hence do not produce any cashflows), the value of these assets will not be reflected in the value obtained from discounting expected future cashflows. The same caveat applies, in lesser degree, to underutilized assets, since their value will be understated in discounted cashflow valuation. While this is a problem, it is not insurmountable. The value of these

1

The protection of limited liability should ensure that no stock will sell for less than zero. The price of such a stock can never be negative.

8 assets can always be obtained externally2, and added on to the value obtained from discounted cashflow valuation. Alternatively, the assets can be valued assuming that they are used optimally. (4) Firms with patents or product options: Firms often have unutilized patents or licenses that do not produce any current cashflows and are not expected to produce cashflows in the near future, but, nevertheless, are valuable. If this is the case, the value obtained from discounting expected cashflows to the firm will understate the true value of the firm. Again, the problem can be overcome, by valuing these assets in the open market or by using option pricing models, and then adding on to the value obtained from discounted cashflow valuation. (5) Firms in the process of restructuring: Firms in the process of restructuring often sell some of their assets, acquire other assets, and change their capital structure and dividend policy. Some of them also change their ownership structure (going from publicly traded to private status) and management compensation schemes. Each of these changes makes estimating future cashflows more difficult and affects the riskiness of the firm. Using historical data for such firms can give a misleading picture of the firm's value. However, these firms can be valued, even in the light of the major changes in investment and financing policy, if future cashflows reflect the expected effects of these changes and the discount rate is adjusted to reflect the new business and financial risk in the firm. (6) Firms involved in acquisitions: There are at least two specific issues relating to acquisitions that need to be taken into account when using discounted cashflow valuation models to value target firms. The first is the thorny one of whether there is synergy in the merger and if its value can be estimated. It can be done, though it does require assumptions about the form the synergy will take and its effect on cashflows. The second, especially in hostile takeovers, is the effect of changing management on cashflows and risk. Again, the effect of the change can and should be incorporated into the estimates of future cashflows and discount rates and hence into value. (7) Private Firms: The biggest problem in using discounted cashflow valuation models to value private firms is the measurement of risk (to use in estimating discount rates), since 2

If these assets are traded on external markets, the market prices of these assets can be used in the valuation. If not, the cashflows can be projected, assuming full utilization of assets, and the value can be

9 most risk/return models require that risk parameters be estimated from historical prices on the asset being analyzed. Since securities in private firms are not traded, this is not possible. One solution is to look at the riskiness of comparable firms, which are publicly traded. The other is to relate the measure of risk to accounting variables, which are available for the private firm. The point is not that discounted cash flow valuation cannot be done in these cases, but that we have to be flexible enough to deal with them. The fact is that valuation is simple for firms with well defined assets that generate cashflows that can be easily forecasted. The real challenge in valuation is to extend the valuation framework to cover firms that vary to some extent or the other from this idealized framework. Much of this book is spent considering how to value such firms. Relative Valuation While we tend to focus most on discounted cash flow valuation, when discussing valuation, the reality is that most valuations are relative valuations. The value of most assets, from the house you buy to the stocks that you invest in, are based upon how similar assets are priced in the market place. We begin this section with a basis for relative valuation, move on to consider the underpinnings of the model and then consider common variants within relative valuation. Basis for Relative Valuation In relative valuation, the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, cashflows, book value or revenues. One illustration of this approach is the use of an industry-average price-earnings ratio to value a firm. This assumes that the other firms in the industry are comparable to the firm being valued and that the market, on average, prices these firms correctly. Another multiple in wide use is the price to book value ratio, with firms selling at a discount on book value, relative to comparable firms, being considered undervalued. The multiple of price to sales is also used to value firms, with the average price-sales ratios of firms with similar characteristics being used for comparison. While these three multiples are among the most widely used, there are others that also play a role in estimated.

10 analysis - price to cashflows, price to dividends and market value to replacement value (Tobin's Q), to name a few. Underpinnings of Relative Valuation Unlike discounted cash flow valuation, which we described as a search for intrinsic value, we are much more reliant on the market when we use relative valuation. In other words, we assume that the market is correct in the way it prices stocks, on average, but that it makes errors on the pricing of individual stocks. We also assume that a comparison of multiples will allow us to identify these errors, and that these errors will be corrected over time. The assumption that markets correct their mistakes over time is common to both discounted cash flow and relative valuation, but those who use multiples and comparables to pick stocks argue, with some basis, that errors made by mistakes in pricing individual stocks in a sector are more noticeable and more likely to be corrected quickly. For instance, they would argue that a software firm that trades at a price earnings ratio of 10, when the rest of the sector trades at 25 times earnings, is clearly under valued and that the correction towards the sector average should occur sooner rather than latter. Proponents of discounted cash flow valuation would counter that this is small consolation if the entire sector is over priced by 50%. Categorizing Relative Valuation Models Analysts and investors are endlessly inventive when it comes to using relative valuation. Some compare multiples across companies, while others compare the multiple of a company to the multiples it used to trade in the past. While most relative valuations are based upon comparables, there are some relative valuations that are based upon fundamentals. I. Fundamentals versus Comparables In discounted cash flow valuation, the value of a firm is determined by its expected cash flows. Other things remaining equal, higher cash flows, lower risk and higher growth should yield higher value. Some analysts who use multiples go back to these discounted cash flow models to extract multiples. Other analysts compare multiples

11 across firms or time, and make explicit or implicit assumptions about how firms are similar or vary on fundamentals. 1. Using Fundamentals The first approach relates multiples to fundamentals about the firm being valued – growth rates in earnings and cashflows, payout ratios and risk. This approach to estimating multiples is equivalent to using discounted cashflow models, requiring the same information and yielding the same results. Its primary advantage is to show the relationship between multiples and firm characteristics, and allows us to explore how multiples change as these characteristics change. For instance, what will be the effect of changing profit margins on the price/sales ratio? What will happen to price-earnings ratios as growth rates decrease? What is the relationship between price-book value ratios and return on equity? 2. Using Comparables The more common approach to using multiples is to compare how a firm is valued with how similar firms are priced by the market, or in some cases, with how the firm was valued in prior periods. As we will see in the later chapters, finding similar and comparable firms is often a challenge and we have to often accept firms that are different from the firm being valued on one dimension or the other. When this is the case, we have to either explicitly or implicitly control for differences across firms on growth, risk and cash flow measures. In practice, controlling for these variables can range from the naive (using industry averages) to the sophisticated (multivariate regression models where the relevant variables are identified and we control for differences.). II. Cross Sectional versus Time Series Comparisons In most cases, analysts price stocks on a relative basis by comparing the multiple it is trading to the multiple at which other firms in the same business are trading. In some cases, however, especially for mature firms with long histories, the comparison is done across time. a. Cross Sectional Comparisons When we compare the price earnings ratio of a software firm to the average price earnings ratio of other software firms, we are doing relative valuation and we are making

12 cross sectional comparisons. The conclusions can vary depending upon our assumptions about the firm being valued and the comparable firms. For instance, if we assume that the firm we are valuing is similar to the average firm in the industry, we would conclude that it is cheap if it trades at a multiple that is lower than the average multiple. If, on the other hand, we assume that the firm being valued is riskier than the average firm in the industry, we might conclude that the firm should trade at a lower multiple than other firms in the business. In short, you cannot compare firms without making assumptions about their fundamentals. b. Comparisons across time If you have a mature firm with a long history, you can compare the multiple it trades today to the multiple it used to trade in the past. Thus, Ford Motor company may be viewed as cheap because it trades at six times earnings, if it has historically traded at ten times earnings. To make this comparison, however, you have to assume that your firm has not changed its fundamentals over time. For instance, you would expect a high growth firm’s price earnings ratio to drop and its expected growth rate to decrease over time as it becomes larger. Comparing multiples across time can also be complicated by changes in the interest rates over time and the behavior of the overall market. For instance, as interest rates fall below historical norms and the overall market increases, you would expect most companies to trade at much higher multiples of earnings and book value than they have historically. Applicability of multiples and limitations The allure of multiples is that they are simple and easy to work with. They can be used to obtain estimates of value quickly for firms and assets, and are particularly useful when there are a large number of comparable firms being traded on financial markets and the market is, on average, pricing these firms correctly. They tend to be more difficult to use to value unique firms, with no obvious comparables, with little or no revenues and negative earnings. By the same token, they are also easy to misuse and manipulate, especially when comparable firms are used. Given that no two firms are exactly similar in terms of risk and

13 growth, the definition of 'comparable' firms is a subjective one. Consequently, a biased analyst can choose a group of comparable firms to confirm his or her biases about a firm's value. An illustration of this is given below. While this potential for bias exists with discounted cashflow valuation as well, the analyst in DCF valuation is forced to be much more explicit about the assumptions which determine the final value. With multiples, these assumptions are often left unstated. Illustration 2.2. The potential for misuse with comparable firms Assume that an analyst is valuing an initial public offering of a firm that manufactures computer software. At the same time, the price-earnings multiples of other publicly traded firms manufacturing software are as follows:3 Firm

Multiple

Adobe Systems

23.2

Autodesk

20.4

Broderbund

32.8

Computer Associates

18.0

Lotus Development

24.1

Microsoft

27.4

Novell

30.0

Oracle

37.8

Software Publishing

10.6

System Software

15.7

Average PE Ratio

24.0

While the average PE ratio using the entire sample listed above is 24, it can be changed markedly by removing a couple of firms from the group. For instance, if the two firms with the lowest PE ratios in the group (Software Publishing and System Software) are eliminated from the sample, the average PE ratio increases to 27. If the two firms with the highest PE ratios in the group (Broderbund and Oracle) are removed from the group, the average PE ratio drops to 21.

3

These were the PE ratios for these firms at the end of 1992.

14 The other problem with using multiples based upon comparable firms is that it builds in errors (over valuation or under valuation) that the market might be making in valuing these firms. In illustration 2.2, for instance, if the market has overvalued all computer software firms, using the average PE ratio of these firms to value an initial public offering will lead to an overvaluation of its stock. In contrast, discounted cashflow valuation is based upon firm-specific growth rates and cashflows, and is less likely to be influenced by market errors in valuation. Asset Based Valuation Models There are some who add a fourth approach to valuation to the three that we describe in this chapter. They argue that you can argue the individual assets owned by a firm and use that to estimate its value – asset based valuation models. In fact, there are several variants on asset based valuation models. The first is liquidation value, which is obtained by aggregating the estimated sale proceeds of the assets owned by a firm. The second is replacement cost, where you evaluate what it would cost you to replace all of the assets that a firm has today. While analysts may use asset-based valuation approaches to estimate value, we do not consider them to be alternatives to discounted cash flow, relative or option pricing models since both replacement and liquidation values have to be obtained using one or more of these approaches. Ultimately, all valuation models attempt to value assets – the differences arise in how we identify the assets and how we attach value to each asset. In liquidation valuation, we look only at assets in place and estimate their value based upon what similar assets are priced at in the market. In traditional discounted cash flow valuation, we consider all assets including expected growth potential to arrive at value. The two approaches may, in fact, yield the same values if you have a firm that has no growth assets and the market assessments of value reflect expected cashflows. Contingent Claim Valuation Perhaps the most significant and revolutionary development in valuation is the acceptance, at least in some cases, that the value of an asset may not be greater than the present value of expected cash flows if the cashflows are contingent on the occurrence or

15 non-occurrence of an event. This acceptance has largely come about because of the development of option pricing models. While these models were initially used to value traded options, there has been an attempt, in recent years, to extend the reach of these models into more traditional valuation. There are many who argue that assets such as patents or undeveloped reserves are really options and should be valued as such, rather than with traditional discounted cash flow models. Basis for Approach A contingent claim or option pays off only under certain contingencies - if the value of the underlying asset exceeds a pre-specified value for a call option, or is less than a pre-specified value for a put option. Much work has been done in the last twenty years in developing models that value options, and these option pricing models can be used to value any assets that have option-like features. The following diagram illustrates the payoffs on call and put options as a function of the value of the underlying asset: Figure 2.1: Payoff Diagram on Call and Put Options

Net Payoff on Call Option Net Payoff on Put Option Break Even Strike price

Maximum Loss

Break Even

Value of Underlying asset

An option can be valued as a function of the following variables - the current value, the variance in value of the underlying asset, the strike price, the time to expiration of the option and the riskless interest rate. This was first established by Black and Scholes (1972) and has been extended and refined subsequently in numerous variants. While the Black-Scholes option pricing model ignored dividends and assumed that options would

16 not be exercised early, it can be modified to allow for both. A discrete-time variant, the Binomial option pricing model, has also been developed to price options. An asset can be valued as an option if the payoffs are a function of the value of an underlying asset. It can be valued as a call option if the payoff is contingent on the value of the asset exceeding a pre-specified level.. It can be valued as a put option if the payoff increases as the value of the underlying asset drops below a pre-specified level. Underpinnings for Contingent Claim Valuation The fundamental premise behind the use of option pricing models is that discounted cash flow models tend to understate the value of assets that provide payoffs that are contingent on the occurrence of an event. As a simple example, consider an undeveloped oil reserve belonging to Exxon. You could value this reserve based upon expectations of oil prices in the future, but this estimate would miss the two nonexclusive facts. 1. The oil company will develop this reserve if oil prices go up and will not if oil prices decline. 2. The oil company will develop this reserve if development costs go down because of technological improvement and will not if development costs remain high. An option pricing model would yield a value that incorporates these rights. When we use option pricing models to value assets such as patents and undeveloped natural resource reserves, we are assuming that markets are sophisticated enough to recognize such options and to incorporate them into the market price. If the markets do not, we assume that they will eventually, with the payoff to using such models comes about when this occurs Categorizing Option Pricing Models The first categorization of options is based upon whether the underlying asset is a financial asset or a real asset. Most listed options, whether they are options listed on the Chicago Board of Options or convertible fixed income securities, are on financial assets such as stocks and bonds. In contrast, options can be on real assets such as commodities, real estate or even investment projects. Such options are often called real options.

17 A second and overlapping categorization is based upon whether the underlying asset is traded on not. The overlap occurs because most financial assets are traded, whereas relatively few real assets are traded. Options on traded assets are generally easier to value and the inputs to the option models can be obtained from financial markets relatively easily. Options on non-traded assets are much more difficult to value since there are no market inputs available on the underlying asset. Applicability of Option Pricing Models and Limitations There are several direct examples of securities that are options - LEAPs, which are long term equity options on traded stocks that you can buy or sell on the American Stock Exchange. Contingent value rights which provide protection to stockholders in companies against stock price declines. and warrants which are long term call options issued by firms. There are other assets that generally are not viewed as options but still share several option characteristics. Equity, for instance, can be viewed as a call option on the value of the underlying firm, with the face value of debt representing the strike price and term of the debt measuring the life of the option. A patent can be analyzed as a call option on a product, with the investment outlay needed to get the project going representing the strike price and the patent life being the time to expiration of the option. There are limitations in using option pricing models to value long term options on non-traded assets. The assumptions made about constant variance and dividend yields, which are not seriously contested for short term options, are much more difficult to defend when options have long lifetimes. When the underlying asset is not traded, the inputs for the value of the underlying asset and the variance in that value cannot be extracted from financial markets and have to be estimated. Thus the final values obtained from these applications of option pricing models have much more estimation error associated with them than the values obtained in their more standard applications (to value short term traded options). Conclusion There are three basic, though not mutually exclusive, approaches to valuation. The first is discounted cashflow valuation, where cashflows are discounted at a risk-adjusted

18 discount rate to arrive at an estimate of value. The analysis can be done purely from the perspective of equity investors, by discounting expected cashflows to equity at the cost of equity, or it can be done from the viewpoint of all claimholders in the firm, by discounting expected cashflows to the firm at the weighted average cost of capital. The second is relative valuation, where the value of the equity in a firm is based upon the pricing of comparable firms relative to earnings, cashflows, book value or sales. The third is contingent claim valuation, where an asset with the characteristics of an option is valued using an option pricing model. There should be a place for each among the tools available to any analyst interested in valuation.

19 Questions and Short Problems: Chapter 2 1. Discounted cash flow valuation is based upon the notion that the value of an asset is the present value of the expected cash flows on that asset, discounted at a rate that reflects the riskiness of those cash flows. Specify whether the following statements about discounted cash flow valuation are true or false, assuming that all variables are constant except for the variable discussed below: A. As the discount rate increases, the value of an asset increases. B. As the expected growth rate in cash flows increases, the value of an asset increases. C. As the life of an asset is lengthened, the value of that asset increases. D. As the uncertainty about the expected cash flows increases, the value of an asset increases. E. An asset with an infinite life (i.e., it is expected to last forever) will have an infinite value. 2. Why might discounted cash flow valuation be difficult to do for the following types of firms? A. A private firm, where the owner is planning to sell the firm. B. A biotechnology firm, with no current products or sales, but with several promising product patents in the pipeline. C. A cyclical firm, during a recession. D. A troubled firm, which has made significant losses and is not expected to get out of trouble for a few years. E. A firm, which is in the process of restructuring, where it is selling some of its assets and changing its financial mix. F. A firm, which owns a lot of valuable land that is currently unutilized. 3. The following are the projected cash flows to equity and to the firm over the next five years: Year

CF to Equity

Int (1-t)

CF to Firm

1

$250.00

$90.00

$340.00

2

$262.50

$94.50

$357.00

3

$275.63

$99.23

$374.85

4

$289.41

$104.19

$393.59

5

$303.88

$109.40

$413.27

Terminal Value

$3,946.50

$6,000.00

(The terminal value is the value of the equity or firm at the end of year 5.)

20 The firm has a cost of equity of 12% and a cost of capital of 9.94%. Answer the following questions: A. What is the value of the equity in this firm? B. What is the value of the firm? 4. You are estimating the price/earnings multiple to use to value Paramount Corporation by looking at the average price/earnings multiple of comparable firms. The following are the price/earnings ratios of firms in the entertainment business. Firm

P/E Ratio

Firm

P/E Ratio

Disney (Walt)

22.09

PLG

23.33

Time Warner

36.00

CIR

22.91

King World Productions

14.10

GET

97.60

New Line Cinema

26.70

GTK

26.00

A. What is the average P/E ratio? B. Would you use all the comparable firms in calculating the average? Why or why not? C. What assumptions are you making when you use the industry-average P/E ratio to value Paramount Communications?

1

CHAPTER 3 UNDERSTANDING FINANCIAL STATEMENTS Financial statements provide the fundamental information that we use to analyze and answer valuation questions. It is important, therefore, that we understand the principles governing these statements by looking at four questions: • How valuable are the assets of a firm? The assets of a firm can come in several forms – assets with long lives such as land and buildings, assets with shorter lives such inventory, and intangible assets that still produce revenues for the firm such as patents and trademarks. • How did the firm raise the funds to finance these assets? In acquiring these assets, firms can use the funds of the owners (equity) or borrowed money (debt), and the mix is likely to change as the assets age. • How profitable are these assets? A good investment, we argued, is one that makes a return greater than the hurdle rate. To evaluate whether the investments that a firm has already made are good investments, we need to estimate what returns we are making on these investments. • How much uncertainty (or risk) is embedded in these assets? While we have not directly confronted the issue of risk yet, estimating how much uncertainty there is in existing investments and the implications for a firm is clearly a first step. We will look at the way accountants would answer these questions, and why the answers might be different when doing valuation. Some of these differences can be traced to the differences in objectives – accountants try to measure the current standing and immediate past performance of a firm, whereas valuation is much more forward looking.

The Basic Accounting Statements There are three basic accounting statements that summarize information about a firm. The first is the balance sheet, shown in Figure 3.1, which summarizes the assets owned by a firm, the value of these assets and the mix of financing, debt and equity, used to finance these assets at a point in time.

1

2 Figure 3.1: The Balance Sheet Assets

Liabilities Fixed Assets

Current Liabilties

Current Assets

Debt

Debt obligations of firm

Investments in securities & assets of other firms

Financial Investments

Other Liabilities

Other long-term obligations

Assets which are not physical, like patents & trademarks

Intangible Assets

Equity

Equity investment in firm

Long Lived Real Assets Short-lived Assets

Short-term liabilities of the firm

The next is the income statement, shown in Figure 3.2, which provides information on the revenues and expenses of the firm, and the resulting income made by the firm, during a period. The period can be a quarter (if it is a quarterly income statement) or a year (if it is an annual report).

2

3

Figure 3.2: Income Statement Gross revenues from sale of products or services

Revenues

Expenses associates with generating revenues

- Operating Expenses

Operating income for the period

= Operating Income

Expenses associated with borrowing and other financing

- Financial Expenses

Taxes due on taxable income

- Taxes

Earnings to Common & Preferred Equity for Current Period

= Net Income before extraordinary items

Profits and Losses not associated with operations

± Extraordinary Losses (Profits)

Profits or losses associated with changes in accounting rules

± Income Changes Associated with Accounting Changes

Dividends paid to preferred stockholders

- Preferred Dividends

= Net Income to Common Stockholders

Finally, there is the statement of cash flows, shown in figure 3.3, which specifies the sources and uses of cash of the firm from operating, investing and financing activities, during a period.

3

4 Figure 3.3: Statement of Cash Flows Net cash flow from operations, after taxes and interest expenses

Cash Flows From Operations

Includes divestiture and acquisition of real assets (capital expenditures) and disposal and purchase of financial assets. Also includes acquisitions of other firms.

+ Cash Flows From Investing

Net cash flow from the issue and repurchase of equity, from the issue and repayment of debt and after dividend payments

+ Cash Flows from Financing

= Net Change in Cash Balance The statement of cash flows can be viewed as an attempt to explain how much the cash flows during a period were, and why the cash balance changed during the period.

Asset Measurement and Valuation When analyzing any firm, we would like to know the types of assets that it owns, the values of these assets and the degree of uncertainty about these values. Accounting statements do a reasonably good job of categorizing the assets owned by a firm, a partial job of assessing the values of these assets and a poor job of reporting uncertainty about asset values. In this section, we will begin by looking at the accounting principles underlying asset categorization and measurement, and the limitations of financial statements in providing relevant information about assets. Accounting Principles Underlying Asset Measurement An asset is any resource that has the potential to either generate future cash inflows or reduce future cash outflows. While that is a general definition broad enough to cover almost any kind of asset, accountants add a caveat that for a resource to be an asset. A firm has to have acquired it in a prior transaction and be able to quantify future benefits with reasonable precision. The accounting view of asset value is to a great extent grounded in the notion of historical cost, which is the original cost of the asset, adjusted upwards for improvements made to the asset since purchase and downwards for the loss in value associated with the aging of the asset. This historical cost is called the book value. While

4

5 the generally accepted accounting principles for valuing an asset vary across different kinds of assets, three principles underlie the way assets are valued in accounting statements. • An Abiding Belief in Book Value as the Best Estimate of Value: Accounting estimates of asset value begin with the book value. Unless a substantial reason is given to do otherwise, accountants view the historical cost as the best estimate of the value of an asset. • A Distrust of Market or Estimated Value: When a current market value exists for an asset that is different from the book value, accounting convention seems to view this market value with suspicion. The market price of an asset is often viewed as both much too volatile and too easily manipulated to be used as an estimate of value for an asset. This suspicion runs even deeper when values are is estimated for an asset based upon expected future cash flows. • A Preference for under estimating value rather than over estimating it: When there is more than one approach to valuing an asset, accounting convention takes the view that the more conservative (lower) estimate of value should be used rather than the less conservative (higher) estimate of value. Thus, when both market and book value are available for an asset, accounting rules often require that you use the lesser of the two numbers. Measuring Asset Value The financial statement in which accountants summarize and report asset value is the balance sheet. To examine how asset value is measured, let us begin with the way assets are categorized in the balance sheet. First, there are the fixed assets, which include the longterm assets of the firm, such as plant, equipment, land and buildings. Next, we have the short-term assets of the firm, including inventory (including raw materials, work in progress and finished goods), receivables (summarizing moneys owed to the firm) and cash; these are categorized as current assets. We then have investments in the assets and securities of other firms, which are generally categorized as financial investments. Finally, we have what is loosely categorized as intangible assets. These include assets, such as patents and trademarks that presumably will create future earnings and cash flows, and also uniquely accounting assets such as goodwill that arise because of acquisitions made by the firm. Fixed Assets Generally accepted accounting principles (GAAP) in the United States require the valuation of fixed assets at historical cost, adjusted for any estimated gain and loss in value from improvements and the aging, respectively, of these assets. While in theory the adjustments for aging should reflect the loss of earning power of the asset as it ages, in 5

6 practice they are much more a product of accounting rules and convention, and these adjustments are called depreciation. Depreciation methods can very broadly be categorized into straight line (where the loss in asset value is assumed to be the same every year over its lifetime) and accelerated (where the asset loses more value in the earlier years and less in the later years). [While tax rules, at least in the United States, have restricted the freedom that firms have on their choice of asset life and depreciation methods, firms continue to have a significant amount of flexibility on these decisions for reporting purposes. Thus, the depreciation that is reported in the annual reports may not, and generally is not, the same depreciation that is used in the tax statements. Since fixed assets are valued at book value and are adjusted for depreciation provisions, the value of a fixed asset is strongly influenced by both its depreciable life and the depreciation method used. Many firms in the United States use straight line depreciation for financial reporting while using accelerated depreciation for tax purposes, since firms can report better earnings with the former1, at least in the years right after the asset is acquired. In contrast, Japanese and German firms often use accelerated depreciation for both tax and financial reporting purposes, leading to reported income which is understated relative to that of their U.S. counterparts. Current Assets Current assets include inventory, cash and accounts receivables. It is in this category that accountants are most amenable to the use of market value, especially in valuing marketable securities. Accounts Receivable Accounts receivable represent money owed by entities to the firm on the sale of products on credit. When the Home Depot sells products to building contractors and gives them a few weeks to make the payment, it is creating accounts receivable. The accounting convention is for accounts receivable to be recorded as the amount owed to the firm, based upon the billing at the time of the credit sale. The only major valuation and accounting issue is when the firm has to recognize accounts receivable that are not collectible. Firms can set aside a portion of their income to cover expected bad debts from credit sales, and accounts receivable will be reduced by this reserve. Alternatively, the bad debts can be recognized as they occur and the firm can reduce the accounts receivable accordingly. There is the danger,

1

Depreciation is treated as an accounting expense. Hence, the use of straight line depreciation (which is lower than accelerated depreciation in the first few years after an asset is acquired) will result in lower expenses and higher income.

6

7 however, that absent a decisive declaration of a bad debt, firms may continue to show as accounts receivable amounts that they know are unlikely to be ever collected. Cash Cash is one of the few assets for which accountants and financial analysts should agree on value. The value of a cash balance should not be open to estimation error. Having said this, we should note that fewer and fewer companies actually hold cash in the conventional sense (as currency or as demand deposits in banks). Firms often invest the cash in interest-bearing accounts or in treasuries, so as to earn a return on their investments. In either case, market value can deviate from book value, especially if the investments are long term. While there is no real default risk in either of these investments, interest rate movements can affect their value. We will examine the valuation of marketable securities later in this section. Inventory Three basis approaches to valuing inventory are allowed by GAAP: FIFO, LIFO and Weighted Average. (a) First-in, First-out (FIFO): Under FIFO, the cost of goods sold is based upon the cost of material bought earliest in the period, while the cost of inventory is based upon the cost of material bought latest in the year. This results in inventory being valued close to the current replacement cost. During periods of inflation, the use of FIFO will result in the lowest estimate of cost of goods sold among the three valuation approaches, and the highest net income. (b) Last-in, First-out (LIFO): Under LIFO, the cost of goods sold is based upon the cost of material bought latest in the period, while the cost of inventory is based upon the cost of material bought earliest in the year. This results in finished goods being valued close to the current production cost. During periods of inflation, the use of LIFO will result in the highest estimate of cost of goods sold among the three valuation approaches, and the lowest net income. (c) Weighted Average: Under the weighted average approach, both inventory and the cost of goods sold are based upon the average cost of all materials bought during the period. When inventory turns over rapidly, this approach will more closely resemble FIFO than LIFO. Firms often adopt the LIFO approach for its tax benefits during periods of high inflation. The cost of goods sold is then higher because it is based upon prices paid towards to the end of the accounting period. This, in turn, will reduce the reported taxable income and net income, while increasing cash flows. Studies indicate that larger firms with rising

7

8 prices for raw materials and labor, more variable inventory growth and an absence of other tax loss carry forwards are much more likely to adopt the LIFO approach. Given the income and cash flow effects of inventory valuation methods, it is often difficult to compare the inventory values of firms that use different methods. There is, however, one way of adjusting for these differences. Firms that choose the LIFO approach to value inventories have to specify in a footnote the difference in inventory valuation between FIFO and LIFO, and this difference is termed the LIFO reserve. It can be used to adjust the beginning and ending inventories, and consequently the cost of goods sold, and to restate income based upon FIFO valuation. Investments (Financial) and Marketable Securities In the category of investments and marketable securities, accountants consider investments made by firms in the securities or assets of other firms, and other marketable securities including treasury bills or bonds. The way in which these assets are valued depends upon the way the investment is categorized and the motive behind the investment. In general, an investment in the securities of another firm can be categorized as a minority, passive investment; a minority, active investment; or a majority, active investment. The accounting rules vary depending upon the categorization. Minority, Passive Investments If the securities or assets owned in another firm represent less than 20% of the overall ownership of that firm, an investment is treated as a minority, passive investment. These investments have an acquisition value, which represents what the firm originally paid for the securities and often a market value. Accounting principles require that these assets be sub-categorized into one of three groups: investments that will be held to maturity, investments that are available for sale and trading investments. The valuation principles vary for each. • For investments that will be held to maturity, the valuation is at historical cost or book value, and interest or dividends from this investment are shown in the income statement under net interest expenses • For investments that are available for sale, the valuation is at market value, but the unrealized gains or losses are shown as part of the equity in the balance sheet and not in the income statement. Thus, unrealized losses reduce the book value of the equity in the firm, and unrealized gains increase the book value of equity. • For trading investments, the valuation is at market value and the unrealized gains and losses are shown in the income statement.

8

9 Firms are allowed an element of discretion in the way they classify investments and, subsequently, in the way they value these assets. This classification ensures that firms such as investment banks, whose assets are primarily securities held in other firms for purposes of trading, revalue the bulk of these assets at market levels each period. This is called marking-to-market and provides one of the few instances in which market value trumps book value in accounting statements. Minority, Active Investments If the securities or assets owned in another firm represent between 20% and 50% of the overall ownership of that firm, an investment is treated as a minority, active investment. While these investments have an initial acquisition value, a proportional share (based upon ownership proportion) of the net income and losses made by the firm in which the investment was made, is used to adjust the acquisition cost. In addition, the dividends received from the investment reduce the acquisition cost. This approach to valuing investments is called the equity approach. The market value of these investments is not considered until the investment is liquidated, at which point the gain or loss from the sale, relative to the adjusted acquisition cost is shown as part of the earnings under extraordinary items in that period. Majority, Active Investments If the securities or assets owned in another firm represent more than 50% of the overall ownership of that firm, an investment is treated as a majority active investment2. In this case, the investment is no longer shown as a financial investment but is instead replaced by the assets and liabilities of the firm in which the investment was made. This approach leads to a consolidation of the balance sheets of the two firms, where the assets and liabilities of the two firms are merged and presented as one balance sheet. The share of the firm that is owned by other investors is shown as a minority interest on the liability side of the balance sheet. A similar consolidation occurs in the financial statements of the other firm as well. The statement of cash flows reflects the cumulated cash inflows and outflows of the combined firm. This is in contrast to the equity approach, used for minority active investments, in which only the dividends received on the investment are shown as a cash inflow in the cash flow statement.

2

Firms have evaded the requirements of consolidation by keeping their share of ownership in other firms below 50%.

9

10 Here again, the market value of this investment is not considered until the ownership stake is liquidated. At that point, the difference between the market price and the net value of the equity stake in the firm is treated as a gain or loss for the period. Intangible Assets Intangible assets include a wide array of assets ranging from patents and trademarks to goodwill. The accounting standards vary across intangible assets. 1. Patents and Trademarks Patents and trademarks are valued differently depending on whether they are generated internally or acquired. When patents and trademarks are generated from internal sources, such as research, the costs incurred in developing the asset are expensed in that period even though the asset might have a life of several accounting periods. Thus, the intangible asset is not usually valued in the balance sheet of the firm. In contrast, when an intangible asset is acquired from an external party, it is treated as an asset. Intangible assets have to be amortized over their expected lives, with a maximum amortization period of 40 years. The standard practice is to use straight-line amortization. For tax purposes, however, firms are not allowed to amortize goodwill or other intangible assets with no specific lifetime. 2. Goodwill Intangible assets are sometimes the by-products of acquisitions. When a firm acquires another firm, the purchase price is first allocated to tangible assets and then allocated to any intangible assets such as patents or trade names. Any residual becomes goodwill. While accounting principles suggest that goodwill captures the value of any intangibles that are not specifically identifiable, it is really a reflection of the difference between the market value of the firm owning the assets and the book value of assets. This approach is called purchase accounting and it creates an intangible asset (goodwill) which has to be amortized over 40 years. Firms, which do not want to see this charge against their earnings, often use an alternative approach called pooling accounting, in which the purchase price never shows up in the balance sheet. Instead, the book values of the two companies involved in the merger are aggregated to create the consolidated balance of the combined firm.3

3

The Financial Accounting Standards Board (FASB) was considering eliminating the use of pooling and reducing the amortization period for goodwill in purchase accounting to 20 years at the time this book went to print.

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11 Illustration 3.1: Asset Values for Boeing and the Home Depot Table 3.1 summarizes asset values, as measured in the balance sheets of Boeing, the aerospace giant, and The Home Depot, a building suppliers retailer, at the end of the 1998 financial year: Table 3.1: Assets: Boeing and the Home Depot Boeing

Home Depot

Net Fixed Assets

$8,589

$8,160

Goodwill

$2,312

$140

$0

$41

$411

$0

Prepaid Pension Expense

$3,513

$0

Customer Financing

$4,930

$0

$542

$191

$2,183

$62

$279

$0

$3,288

$469

$781

$0

Deferred Income Taxes

$1,495

$0

Inventories

$8,349

$4,293

Other Current Assets

$0

$109

Total Current Assets

$16,375

$4,933

$36,672

$13,465

Investments and Notes Receivable Deferred Income Taxes

Other Assets Current Assets Cash Short-term Marketable Investments Accounts Receivables Current Portion of Customer Financing

Total Assets

There are a number of points worth noting about these asset values. 1. Goodwill: Boeing, which acquired Rockwell in 1996 and McDonnell Douglas in 1997, used purchase accounting for the Rockwell acquisition and pooling for McDonnell Douglas. The goodwill on the balance sheet reflects the excess of acquisition value over book value for Rockwell and is being amortized over 30 years. With McDonnell Douglas, there is no recording of the premium paid on the acquisition among the assets. 2. Customer Financing and Accounts Receivable: Boeing often either provides financing to its customers to acquire its planes or acts as the lessor on the planes. Since these contracts tend to run over several years, the present value of the payments due in future years on the financing and the lease payments is shown as customer financing. The current portion of these payments is shown as accounts receivable. The Home Depot provides credit to its customers as well, but all these payments due are shown as accounts receivable, since they are all short term.

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12 3. Inventories: Boeing values inventories using the weighted average cost method, while The Home Depot uses the FIFO approach for valuing inventories. 4. Marketable Securities: Boeing classifies its short term investments as trading investments and records them at market value. The Home Depot has a mix of trading, available-for-sale and held-to-maturity investments and therefore uses a mix of book and market value to value these investments. 5. Prepaid Pension Expense: Boeing records the excess of its pension fund assets over its expected pension fund liabilities as an asset on the balance sheet. Finally, the balance sheet for Boeing fails to report the value of a very significant asset, which is the effect of past research and development expenses. Since accounting convention requires that these be expensed in the year that they occur and not capitalized, the research asset does not show up in the balance sheet. In chapter 9, we will consider how to capitalize research and development expenses and the effects on balance sheets.

Measuring Financing Mix The second set of questions that we would like to answer and accounting statements to shed some light on relates to the current value and subsequently the mixture of debt and equity used by the firm. The bulk of the information about these questions is provided on the liability side of the balance sheet and the footnotes. Accounting Principles Underlying Liability and Equity Measurement Just as with the measurement of asset value, the accounting categorization of liabilities and equity is governed by a set of fairly rigid principles. The first is a strict categorization of financing into either a liability or equity based upon the nature of the obligation. For an obligation to be recognized as a liability, it must meet three requirements: 1. It must be expected to lead to a future cash outflow or the loss of a future cash inflow at some specified or determinable date, 2. The firm cannot avoid the obligation. 3. The transaction giving rise to the obligation has happened already. In keeping with the earlier principle of conservatism in estimating asset value, accountants recognize as liabilities only cash flow obligations that cannot be avoided. The second principle is that the value of both liabilities and equity in a firm are better estimated using historical costs with accounting adjustments, rather than with expected future cash flows or market value. The process by which accountants measure the value of liabilities and equities is inextricably linked to the way they value assets. Since assets are primarily valued at historical cost or at book value, both debt and equity also get

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13 measured primarily at book value. In the section that follows, we will examine the accounting measurement of both liabilities and equity. Measuring the Value of Liabilities and Equities Accountants categorize liabilities into current liabilities, long term debt and long term liabilities that are neither debt nor equity. Next, we will examine the way they measure each of these. Current Liabilities Current liabilities categorizes all obligations that the firm has coming due in the next accounting period. These generally include: 1. Accounts Payable – representing credit received from suppliers and other vendors to the firm. The value of accounts payable represents the amounts due to these creditors. For this item, book and market value should be similar. 2. Short term borrowing – representing short term loans (due in less than a year) taken to finance the operations or current asset needs of the business. Here again, the value shown represents the amounts due on such loans, and the book and market value should be similar, unless the default risk of the firm has changed dramatically since it borrowed the money. 3. Short term portion of long term borrowing – representing the portion of the long term debt or bonds that is coming due in the next year. Here again, the value shown is the actual amount due on these loans, and market and book value should converge as the due date approaches. 4. Other short term liabilities – which is a catch-all component for any other short term liabilities that the firm might have, including wages due to its employees and taxes due to the government. Of all the items on the liability side of the balance sheet, absent outright fraud, current liabilities should be the one for which the accounting estimates of book value and financial estimates of market value are the closest. Long Term Debt Long term debt for firms can take one of two forms. It can be a long-term loan from a bank or other financial institution or it can be a long-term bond issued to financial markets, in which case the creditors are the investors in the bond. Accountants measure the value of long term debt by looking at the present value of payments due on the loan or bond at the time of the borrowing. For bank loans, this will be equal to the nominal value of the loan. With bonds, however, there are three possibilities: When bonds are issued at par value,

13

14 for instance, the value of the long-term debt is generally measured in terms of the nominal obligation created, in terms of principal (face value) due on the borrowing. When bonds are issued at a premium or a discount on par value, the bonds are recorded at the issue price, but the premium or discount to the face value is amortized over the life of the bond. As an extreme example, companies that issue zero coupon debt have to record the debt at the issue price, which will be significantly below the principal (face value) due at maturity. The difference between the issue price and the face value is amortized each period and is treated as a non-cash interest expense that is tax deductible. In all these cases, the book value of debt is unaffected by changes in interest rates during the life of the loan or bond. Note that as market interest rates rise (fall), the present value of the loan obligations should decrease (increase). This updated market value for debt is not shown on the balance sheet. If debt is retired prior to maturity, the difference between book value and the amount paid at retirement is treated as an extraordinary gain or loss in the income statement. Finally, companies which have long term debt denominated in non-domestic currencies have to adjust the book value of debt for changes in exchange rates. Since exchange rate changes reflect underlying changes in interest rates, it does imply that this debt is likely to be valued much nearer to market value than is debt in the home currency. Other Long Term Liabilities Firms often have long term obligations that are not captured in the long term debt item. These include obligations to lessors on assets that firms have leased, to employees in the form of pension fund and health care benefits yet to be paid, and to the government in the form of taxes deferred. In the last two decades, accountants have increasingly moved towards quantifying these liabilities and showing them as long term liabilities. 1. Leases Firms often choose to lease long-term assets rather than buy them. Lease payments create the same kind of obligation that interest payments on debt create, and they must be viewed in a similar light. If a firm is allowed to lease a significant portion of its assets and keep it off its financial statements, a perusal of the statements will give a very misleading view of the company's financial strength. Consequently, accounting rules have been devised to force firms to reveal the extent of their lease obligations on their books. There are two ways of accounting for leases. In an operating lease, the lessor (or owner) transfers only the right to use the property to the lessee. At the end of the lease period, the lessee returns the property to the lessor. Since the lessee does not assume the risk of ownership, the lease expense is treated as an operating expense in the income 14

15 statement and the lease does not affect the balance sheet. In a capital lease, the lessee assumes some of the risks of ownership and enjoys some of the benefits. Consequently, the lease, when signed, is recognized both as an asset and as a liability (for the lease payments) on the balance sheet. The firm gets to claim depreciation each year on the asset and also deducts the interest expense component of the lease payment each year. In general, capital leases recognize expenses sooner than equivalent operating leases. Since firms prefer to keep leases off the books and sometimes to defer expenses they have a strong incentive to report all leases as operating leases. Consequently the Financial Accounting Standards Board has ruled that a lease should be treated as a capital lease if it meets any one of the following four conditions. (a) The lease life exceeds 75% of the life of the asset. (b) There is a transfer of ownership to the lessee at the end of the lease term. (c) There is an option to purchase the asset at a "bargain price" at the end of the lease term. (d) The present value of the lease payments, discounted at an appropriate discount rate, exceeds 90% of the fair market value of the asset. The lessor uses the same criteria for determining whether the lease is a capital or operating lease and accounts for it accordingly. If it is a capital lease, the lessor records the present value of future cash flows as revenue and recognizes expenses. The lease receivable is also shown as an asset on the balance sheet and the interest revenue is recognized over the term of the lease as paid. From a tax standpoint, the lessor can claim the tax benefits of the leased asset only if it is an operating lease, though the revenue code uses slightly different criteria4 for determining whether the lease is an operating lease. 2. Employee Benefits Employers provide pension and health care benefits to their employees. In many cases, the obligations created by these benefits are extensive and a failure by the firm to adequately fund these obligations needs to be revealed in financial statements. a. Pension Plans In a pension plan, the firm agrees to provide certain benefits to its employees, either by specifying a 'defined contribution' (wherein a fixed contribution is made to the plan each year by the employer, without any promises as to the benefits which will be delivered in the

4

The requirements for an operating lease in the revenue code are as follows - (a) the property can be used by someone other than the lessee at the end of the lease term, (b) the lessee cannot buy the asset using a bargain purchase option, (c) the lessor has at least 20% of its capital at risk, (d) the lessor has a positive cash flow from the lease independent of tax benefits and (e) the lessee does not have an investment in the

15

16 plan) or a 'defined benefit' (wherein the employer promises to pay a certain benefit to the employee). In the latter case, the employer has to put sufficient money into the plan each period to meet the defined benefits. Under a defined contribution plan, the firm meets its obligation once it has made the pre-specified contribution to the plan. Under a defined-benefit plan, the firm's obligations are much more difficult to estimate, since they will be determined by a number of variables including the benefits that employees are entitled to, the prior contributions made by the employer, the returns the plan have earned, and the rate of return that the employer expects to make on current contributions. As these variables change, the value of the pension fund assets can be greater than, less than or equal to pension fund liabilities (which is the present value of promised benefits). A pension fund whose assets exceed its liabilities is an overfunded plan, whereas one whose assets are less than its liabilities is an under-funded plan and disclosures to that effect have to be included in financial statements, generally in the footnotes. When a pension fund is over-funded, the firm has several options. It can withdraw the excess assets from the fund, it can discontinue contributions to the plan, or it can continue to make contributions on the assumption that the over-funding is a transitory phenomenon that could well disappear by the next period. When a fund is under-funded, the firm has a liability, though accounting standards require that firms reveal only the excess of accumulated5 pension fund liabilities over pension fund assets on the balance sheet. b. Health Care Benefits A firm can provide health care benefits in one of two ways: by making a fixed contribution to a health care plan, without promising specific benefits (analogous to a defined contribution plan), or by promising specific health benefits and setting aside the funds to provide these benefits (analogous to a defined benefit plan). The accounting for health care benefits is very similar to the accounting for pension obligations. The key difference between the two is that firms do not have to report6 the excess of their health care obligations over the health care fund assets as a liability on the balance sheet, though a footnote to that effect has to be added to the financial statement.

lease. 5 The accumulated pension fund liability does not take into account the projected benefit obligation, where actuarial estimates of future benefits are made. Consequently, it is much smaller than the total pension liabilities. 6 While companies might not have to report the excess of their health care obligations over assets as a liability, some firms choose to do so anyway.

16

17 3. Deferred Taxes Firms often use different methods of accounting for tax and financial reporting purposes, leading to a question of how tax liabilities should be reported. Since accelerated depreciation and favorable inventory valuation methods for tax accounting purposes lead to a deferral of taxes, the taxes on the income reported in the financial statements will generally be much greater than the actual tax paid. The same principles of matching expenses to income that underlie accrual accounting suggest that the 'deferred income tax' be recognized in the financial statements. Thus a company which pays taxes of $55,000 on its taxable income based upon its tax accounting, and which would have paid taxes of $75,000 on the income reported in its financial statements, will be forced to recognize the difference ($20,000) as deferred taxes in liabilities. Since the deferred taxes will be paid in later years, they will be recognized as paid. It is worth noting that companies that actually pay more in taxes than the taxes they report in the financial statements create an asset on the balance sheet called a deferred tax asset. This reflects the fact that the firm's earnings in future periods will be greater as the firm is given credit for the deferred taxes. The question of whether the deferred tax liability is really a liability is an interesting one. Firms do not owe the amount categorized as deferred taxes to any entity, and treating it as a liability makes the firm look more risky than it really is. On the other hand, the firm will eventually have to pay its deferred taxes, and treating it as a liability seems to be the conservative thing to do. Preferred Stock When a company issues preferred stock, it generally creates an obligation to pay a fixed dividend on the stock. Accounting rules have conventionally not viewed preferred stock as debt because the failure to meet preferred dividends does not result in bankruptcy. At the same time, the fact the preferred dividends are cumulative makes them more onerous than common equity. Thus, preferred stock is viewed in accounting as a hybrid security, sharing some characteristics with equity and some with debt. Preferred stock is valued on the balance sheet at its original issue price, with any cumulated unpaid dividends added on. Convertible preferred stock is treated similarly, but it is treated as equity on conversion. Equity The accounting measure of equity is a historical cost measure. The value of equity shown on the balance sheet reflects the original proceeds received by the firm when it issued the equity, augmented by any earnings made since (or reduced by losses, if any) and 17

18 reduced by any dividends paid out during the period. While these three items go into what we can call the book value of equity, a few other items also end up in this estimate. 1. When companies buy back stock for short periods, with the intent of reissuing the stock or using it to cover option exercises, they are allowed to show the repurchased stock as treasury stock, which reduces the book value of equity. Firms are not allowed to keep treasury stock on the books for extended periods and have to reduce their book value of equity by the value of repurchased stock in the case of actions such as stock buybacks. Since these buybacks occur at the current market price, they can result in significant reductions in the book value of equity. 2. Firms that have significant losses over extended periods or carry out massive stock buybacks can end up with negative book values of equity. 3. Relating back to our discussion of marketable securities, any unrealized gain or loss in marketable securities that are classified as available-for-sale is shown as an increase or decrease in the book value of equity in the balance sheet. As part of their financial statements, firms provide a summary of changes in shareholders equity during the period, where all the changes that occurred to the accounting (book value) measure of equity value are summarized. Accounting rules still do not seem to have come to grips with the effect of warrants and equity options (such as those granted by many firms to management) on the book value of equity. If warrants are issued to financial markets, the proceeds from this issue will show up as part of the book value of equity. In the far more prevalent case where options are given or granted to management, there is no effect on the book value of equity. When the options are exercised, the cash inflows from the exercise do ultimately show up in the book value of equity and there is a corresponding increase in the number of shares outstanding. The same point can be made about convertible bonds, which are treated as debt until conversion, at which point they become part of equity. In partial defense of accountants, we must note that the effect of options outstanding is often revealed when earnings and book value are computed on a per share basis. Here, the computation is made on two bases, the first on the current number of shares outstanding (primary shares outstanding) and the second on the number of shares outstanding after all options have been exercised (fully diluted shares outstanding). As a final point on equity, accounting rules still seem to consider preferred stock, with its fixed dividend, as equity or near-equity, largely because of the fact that preferred dividends can be deferred or cumulated without the risk of default. To the extent that there can still be a loss of control in the firm (as opposed to bankruptcy), we would argue that

18

19 preferred stock shares almost as many characteristics with unsecured debt as it does with equity. Illustration 3.2: Measuring Liabilities and Equity: Boeing and the Home Depot Table 3.2 summarizes the accounting estimates of liabilities and equity at Boeing and The Home Depot for the 1998 financial year: Table 3.2: Liabilities – Boeing and Home Depot Boeing

Home Depot

Current Liabilities Accounts Payable & other liabilities

$10,733

$1,586

$0

$1,010

$1,251

$0

Taxes payable

$569

$247

Short term debt and Current LT debt

$869

$14

$13,422

$2,857

$4,831

$0

Other Long Term Liabilities

$0

$210

Deferred Income Taxes

$0

$83

$6,103

$1,566

$0

$9

$5,059

$37

$0

$2,891

$7,257

$5,812

$12,316

$8,740

$36,672

$13,465

Accrued Salaries and Expenses Advances in excess of costs

Total Current Liabilities Accrued Health Care Benefits

Long-term Debt

Minority Interests

Shareholder's Equity Par Value Additional Paid-in Capital Retained Earnings Total Shareholder's Equity Total Liabilities

The most significant difference between the companies is the accrued health care liability, representing the present value of expected health care obligations promised to employees in excess of health care assets. The shareholders’ equity for both firms represents the book value of equity and is significantly different from the market value of equity. Table 3.3 summarizes the difference at the end of the 1998. Table 3.3: Book and Market Value of Equity Comparison Boeing Book Value of Equity

$12,316

Home Depot $8,740

19

20 Market Value of Equity

$32,595

$85,668

One final point needs to be made about the Home Depot’s liabilities. The Home Depot has substantial operating leases. Because these leases are treated as operating expenses, they do not show up in the balance sheet. Since they represent commitments to make payments in the future, we would argue that operating leases should be capitalized and treated as part of the liabilities of the firm. We will consider how best to do this later in this book.

Measuring Earnings and Profitability How profitable is a firm? What did it earn on the assets that it invested in? These are the fundamental questions we would like financial statements to answer. Accountants use the income statement to provide information about a firm's operating activities over a specific time period. In terms of our description of the firm, the income statement is designed to measure the earnings from assets in place. In this section, we will examine the principles underlying earnings and return measurement in accounting, and the methods that they are put into practice. Accounting Principles Underlying Measurement of Earnings and Profitability Two primary principles underlie the measurement of accounting earnings and profitability. The first is the principle of accrual accounting. In accrual accounting, the revenue from selling a good or service is recognized in the period in which the good is sold or the service is performed (in whole or substantially). A corresponding effort is made on the expense side to match 7 expenses to revenues. This is in contrast to cash accounting, where revenues are recognized when payment is received and expenses are recorded when they are paid. The second principle is the categorization of expenses into operating, financing and capital expenses. Operating expenses are expenses that, at least in theory, provide benefits only for the current period; the cost of labor and materials expended to create products that are sold in the current period is a good example. Financing expenses are expenses arising from the non-equity financing used to raise capital for the business; the most common example is interest expenses. Capital expenses are expenses that are expected to generate benefits over multiple periods; for instance, the cost of buying land and buildings is treated as a capital expense.

7

If a cost (such as an administrative cost) cannot be easily linked with a particular revenues, it is usually recognized as an expense in the period in which it is consumed.

20

21 Operating expenses are subtracted from revenues in the current period to arrive at a measure of operating earnings from the firm. Financing expenses are subtracted from operating earnings to estimate earnings to equity investors or net income. Capital expenses are written off over their useful life (in terms of generating benefits) as depreciation or amortization. Measuring Accounting Earnings and Profitability Since income can be generated from a number of different sources, generally accepted accounting principles (GAAP) require that income statements be classified into four sections: income from continuing operations, income from discontinued operations, extraordinary gains or losses and adjustments for changes in accounting principles. Generally accepted accounting principles require the recognition of revenues when the service for which the firm is getting paid has been performed in full or substantially and for which it has received in return either cash or a receivable that is both observable and measurable. Expenses linked directly to the production of revenues (like labor and materials) are recognized in the same period in which revenues are recognized. Any expenses that are not directly linked to the production of revenues are recognized in the period in which the firm consumes the services. While accrual accounting is straightforward in firms that produce goods and sell them, there are special cases where accrual accounting can be complicated by the nature of the product or service being offered. For instance, firms that enter into long term contracts with their customers, for instance, are allowed to recognize revenue on the basis of the percentage of the contract that is completed. As the revenue is recognized on a percentage of completion basis, a corresponding proportion of the expense is also recognized. When there is considerable uncertainty about the capacity of the buyer of a good or service to pay for a service, the firm providing the good or service may recognize the income only when it collects portions of the selling price under the installment method. Reverting back to our discussion of the difference between capital and operating expenses, operating expenses should reflect only those expenses that create revenues in the current period. In practice, however, a number of expenses are classified as operating expenses that do not seem to meet this test. The first is depreciation and amortization. While the notion that capital expenditures should be written off over multiple periods is reasonable, the accounting depreciation that is computed on the original historical cost often bears little resemblance to the actual economical depreciation. The second expense is research and development expenses, which accounting standards in the United States classify as

21

22 operating expenses, but which clearly provide benefits over multiple periods. The rationale used for this classification is that the benefits cannot be counted on or easily quantified. Much of financial analysis is built around the expected future earnings of a firm, and many of these forecasts start with the current earnings. It is therefore important that we know how much of these earnings come from the ongoing operations of the firm, and how much can be attributed to unusual or extraordinary events, that are unlikely to recur on a regular basis. From that standpoint, it is useful that firms categorize expenses into operating and nonrecurring expenses, since it is the earnings prior to extraordinary items that should be used in forecasting. Nonrecurring items include the following: a. Unusual or Infrequent items, such as gains or losses from the divestiture of an asset or division and write-offs or restructuring costs. Companies sometimes include such items as part of operating expenses. As an example, Boeing in 1997 took a write-off of $1,400 million to adjust the value of assets it acquired in its acquisition of McDonnell Douglas, and it showed this as part of operating expenses. b. Extraordinary items, which are defined as events that are unusual in nature, infrequent in occurrence and material in impact. Examples include the accounting gain associated with refinancing high coupon debt with lower coupon debt, and gains or losses from marketable securities that are held by the firm. c. Losses associated with discontinued operations, which measure both the loss from the phase out period and the estimated loss on the sale of the operations. To qualify, however, the operations have to be separable separated from the firm. d. Gains or losses associated with accounting changes, which measure earnings changes created by accounting changes made voluntarily by the firm (such as a change in inventory valuation and change in reporting period) and accounting changes mandated by new accounting standards. Illustration 3.3: Measures of Earnings Table 3.4 summarizes the income statements of Boeing and the Home Depot for the 1998 financial year: Table 3.4: Income Statements: Boeing and Home Depot Boeing

Home Depot

(in millions)

(in millons)

Sales & Other Operating Revenues

$56,154.00

$30,219.00

- Operating Costs & Expenses

$51,022.00

$27,185.00

- Depreciation

$1,517.00

$373.00

- Research and Development Expenses

$1,895.00

$0.00

22

23 Operating Income

$1,720.00

$2,661.00

+ Other Income (Includes Interest Income)

$130.00

$30.00

- Interest Expenses

$453.00

$37.00

$1,397.00

$2,654.00

$277.00

$1,040.00

$1,120.00

$1,614.00

Earnings before Taxes - Income Taxes Net Earnings (Loss)

Boeing's operating income is reduced by the research and development expense, which is treated as an operating expense by accountants. The Home Depot’s operating expenses include operating leases. As noted earlier, the treatment of both these items skews earnings and we will consider how best to adjust earnings when such expenses exist, in chapter 9. Measures of Profitability While the income statement allows us to estimate how profitable a firm is in absolute terms, it is just as important that we gauge the profitability of the firm in comparison terms or percentage returns. Two basic gauges measure profitability. One examines the profitability relative to the capital employed to get a rate of return on investment. This can be done either from the viewpoint of just the equity investors, or by looking at the entire firm. Another examines profitability relative to sales, by estimating a profit margin. I. Return on Assets (ROA) & Return on Capital (ROC) The return on assets (ROA) of a firm measures its operating efficiency in generating profits from its assets, prior to the effects of financing. ROA =

EBIT (1 - tax rate ) Total Assets

Earnings before interest and taxes (EBIT) is the accounting measure of operating income from the income statement and total assets refers to the assets as measured using accounting rules, i.e., using book value for most assets. Alternatively, return on assets can be written as: ROA =

Net Income + Interest Expenses (1 - tax rate ) Total Assets

By separating the financing effects from the operating effects, the return on assets provides a cleaner measure of the true return on these assets. ROA can also be computed on a pre-tax basis with no loss of generality, by using the earnings before interest and taxes (EBIT), and not adjusting for taxes -

23

24 Pre - tax ROA =

EBIT Total Assets

This measure is useful if the firm or division is being evaluated for purchase by an acquirer with a different tax rate or structure. A more useful measure of return relates the operating income to the capital invested in the firm, where capital is defined as the sum of the book value of debt and equity. This is the return on capital (ROC). When a substantial portion of the liabilities is either current (such as accounts payable) or non-interest bearing, this approach provides a better measure of the true return earned on capital employed in the business.

After - Tax ROC = Pre - Tax ROC =

EBIT (1 - t ) BV of Debt + BV of Equity

EBIT BV of Debt + BV of Equity

Illustration 3.4: Estimating Return on Capital Table 3.5 summarizes the after-tax return on asset and return on capital estimates for Boeing, the Home Depot and InfoSoft, using both average and beginning measures of capital in 1998: Table 3.5: Return on Capital Boeing

Home Depot

After-tax Operating Income

$1,118

$1,730

BV of Capital - Beginning

$19,807

$8,525

BV of Capital - Ending

$19,288

$10,320

BV of Capital - Average

$19,548

$9,423

ROC (based on average)

5.72%

18.36%

ROC (based on beginning)

5.64%

20.29%

Boeing had a terrible year in terms of after-tax returns. The Home Depot had a much better year. Decomposing Return on Capital The return on capital of a firm can be written as a function of its operating profit margin and its capital turnover ratio.

24

25 EBIT (1-t ) EBIT (1-t ) Sales = X BV of Capital Sales BV of Capital = After -Tax Operating Margin * Capital Turnover Ratio Pre- Tax ROC = Pre -Tax Operating Margin * Capital Turnover Ratio After - Tax ROC =

Thus, a firm can arrive at a high ROC by either increasing its profit margin or more efficiently utilizing its capital to increase sales. There are likely to be competitive constraints and technological constraints on increasing sales, but firms still have some freedom within these constraints to choose the mix of profit margin and capital turnover that maximizes their ROC. The return on capital varies widely across firms in different businesses, largely as a consequence of differences in profit margins and capital turnover ratios.

mgnroc.xls: There is a dataset on the web that summarizes the operating margins, turnover ratios and returns on capital of firms in the United States, classified by industry. II. Return on Equity While the return on capital measures the profitability of the overall firm, the return on equity (ROE) examines profitability from the perspective of the equity investor by relating profits to the equity investor (net profit after taxes and interest expenses) to the book value of the equity investment.

ROE =

Net Income Book Value of Common Equity

Since preferred stockholders have a different type of claim on the firm than do common stockholders, the net income should be estimated after preferred dividends and the book value of common equity should not include the book value of preferred stock. This can be accomplished by using net income after preferred dividends in the numerator and the book value of common equity in the denominator. Determinants of ROE Since the ROE is based upon earnings after interest payments, it is affected by the financing mix the firm uses to fund its projects. In general, a firm that borrows money to finance projects and that earns a ROC on those projects exceeding the after-tax interest rate

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26 it pays on its debt will be able to increase its ROE by borrowing. The ROE can be written as follows8: ROE = ROC +

D (ROC - i(1 - t )) E

where, ROC =

EBIT (1 - t ) BV of Debt + BV of Equity

D BV of Debt = E BV of Equity i=

Interest Expense on Debt BV of Debt

t = Marginal tax rate on ordinary income The second term captures the benefit of financial leverage. Illustration 3.5: ROE Computations Table 3.6 summarizes the return on equity for Boeing and the Home Depot in 1998: Table 3.6: Return on Equity Return Ratios Net Income

Boeing

Home Depot

$1,120

$1,614

BV of Equity- Beginning

$12,953

$7,214

BV of Equity- Ending

$12,316

$8,740

BV of Equity - Average

$12,635

$7,977

ROE (based on average)

8.86%

20.23%

ROE (based on beginning)

8.65%

22.37%

The results again indicate that Boeing had a poor year in 1998, while the Home Depot reported a healthier return on equity. The returns on equity can also be estimated by decomposing into the components specified above (using the adjusted beginning of the year numbers): Boeing After-tax ROC

8

ROC +

Home Depot

5.82%

16.37%

D (ROC - i(1 - t )) = NI + IE(1 - t ) + D  NI + IE(1 - t ) − IE(1 - t ) E D+E E D+E D 

 NI + IE(1 - t ) D  IE(1 - t ) NI IE(1 - t ) IE(1 - t ) NI = = + − = = ROE 1 +  − D + E  E E E E E E 

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27 Debt/Equity Ratio

35.18%

48.37%

Book Interest Rate (1-tax rate)

4.22%

4.06%

ROE

6.38%

22.33%

Note that we used a tax rate of 35% on both the return on capital and the book interest rate. This approach results in a return on equity that is different from the one estimated using the net income and the book value of equity.

rocroe.xls: There is a dataset on the web that summarizes the return on capital, debt equity ratios, book interest rates and returns on equity of firms in the United States, classified by industry.

Measuring Risk How risky are the investments the firm has made over time? How much risk do equity investors in a firm face? These are two more questions that we would like to find the answer to in the course of an investment analysis. Accounting statements do not really claim to measure or quantify risk in a systematic way, other than to provide footnotes and disclosures where there might be risk embedded in the firm. In this section, we will examine some of the ways in which accountants try to assess risk. Accounting Principles Underlying Risk Measurement To the extent that accounting statements and ratios do attempt to measure risk, there seem to be two common themes. a. The first is that the risk being measured is the risk of default, i.e. the risk that a fixed obligation, such as interest or principal due on outstanding debt, will not be met. The broader equity notion of risk, which measures the variance of actual returns around expected returns, does not seem to receive much attention. Thus, an all-equity-financed firm with positive earnings and few or no fixed obligations will generally emerge as a low-risk firm from an accounting standpoint, in spite of the fact that its earnings are unpredictable. b. Accounting risk measures generally take a static view of risk, by looking at the capacity of a firm at a point in time to meet its obligations. For instance, when ratios are used to assess a firm's risk, the ratios are almost always based upon one period's income statement and balance sheet.

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28 Accounting Measures of Risk Accounting measures of risk can be broadly categorized into two groups. The first is disclosures about potential obligations or losses in values that show up as footnotes on balance sheets, which are designed to alert potential or current investors to the possibility of significant losses. The second is the ratios that are designed to measure both liquidity and default risk. Disclosures in Financial Statements In recent years, the number of disclosures that firms have to make about future obligations has proliferated. Consider, for instance, the case of contingent liabilities. These refer to potential liabilities that will be incurred under certain contingencies, as is the case when a firm is the defendant in a lawsuit. The general rule that has been followed is to ignore contingent liabilities which hedge against risk, since the obligations on the contingent claim will be offset9 by benefits elsewhere. In recent periods, however, significant losses borne by firms from supposedly hedged derivatives positions (such as options and futures) have led to FASB requirements that these derivatives be disclosed as part of a financial statement. In fact, pension fund and health care obligations have moved from mere footnotes to actual liabilities for firms. Financial Ratios Financial statements have long been used as the basis for estimating financial ratios that measure profitability, risk and leverage. In the section on earnings, we looked at two of the profitability ratios – return on equity and return on capital . In this section, we will look at some of the financial ratios that are often used to measure the financial risk in a firm. 1. Short-Term Liquidity Risk Short-term liquidity risk arises primarily from the need to finance current operations. To the extent that the firm has to make payments to its suppliers before it gets paid for the goods and services it provides, there is a cash shortfall that has to be met, usually through short-term borrowing. Though this financing of working capital needs is done routinely in most firms, financial ratios have been devised to keep track of the extent of the firm's exposure to the risk that it will not be able to meet its short-term obligations. The two most frequently used to measure short-term liquidity risk are the current ratio and the quick ratio.

9

This assumes that the hedge is set up competently. It is entirely possible that a hedge, if sloppily set up, can end up costing the firm money.

28

29 The current ratio is the ratio of current assets (cash, inventory, accounts receivable) to its current liabilities (obligations coming due within the next period). Current Ratio =

Current Assets Current Liabilities

A current ratio below one, for instance, would indicate that the firm has more obligations coming due in the next year than assets it can expect to turn to cash. That would be an indication of liquidity risk. While traditional analysis suggests that firms maintain a current ratio of 2 or greater, there is a trade-off here between minimizing liquidity risk and tying up more and more cash in net working capital (Net working capital = Current Assets - Current Liabilities). In fact, it can be reasonably argued that a very high current ratio is indicative of an unhealthy firm, which is having problems reducing its inventory. In recent years, firms have worked at reducing their current ratios and managing their net working capital better. Reliance on current ratios has to be tempered by a few concerns. First, the ratio can be easily manipulated by firms around the time of financial reporting dates to give the illusion of safety; second, current assets and current liabilities can change by an equal amount, but the effect on the current ratio will depend upon its level10 before the change. The quick or acid test ratio is a variant of the current ratio. It distinguishes current assets that can be converted quickly into cash (cash, marketable securities) from those that cannot (inventory, accounts receivable).

Quick Ratio =

Cash + Marketable Securities Current Liabilities

The exclusion of accounts receivable and inventory is not a hard and fast rule. If there is evidence that either can be converted into cash quickly, it can, in fact, be included as part of the quick ratio. Turnover ratios measure the efficiency of working capital management by looking at the relationship of accounts receivable and inventory to sales and to the cost of goods sold.

Accounts Receivable Turnover =

10

Sales Average Accounts Receivable

If the current assets and current liabilities increase by an equal amount, the current ratio will go down if

29

30 Inventory Turnover =

Cost of Goods Sold Average Inventory

These ratios can be interpreted as measuring the speed with which the firm turns accounts receivable into cash or inventory into sales. These ratios are often expressed in terms of the number of days outstanding. Days Receivable Outstandin g =

Days Inventory Held =

365 Receivable Turnover

365 Inventory Turnover

A similar pair of ratios can be computed for accounts payable, relative to purchases.

Accounts Payable Turnover =

Purchases Average Accounts Payable

Days Accounts Payable Outstandin g =

365 Accounts Payable Turnover

Since accounts receivable and inventory are assets and accounts payable is a liability, these three ratios (standardized in terms of days outstanding) can be combined to get an estimate of how much financing the firm needs to fund working capital needs.  Days Receivable   Days Inventory   Days Payable  Required Financing Period =   +   +    Outstandin g   Held   Outstandin g 

The greater the financing period for a firm, the greater is its short-term liquidity risk.

wcdata.xls: This is a dataset on the web that summarizes working capital ratios for firms in the United States, classified by industry.

it was greater than one before the increase and go up if it was less than one.

30

31 finratio.xls: This spreadsheet allows you to compute the working capital ratios for a firm, based upon financial statement data. 2. Long-term Solvency and Default risk Measures of long-term solvency attempt to examine a firm's capacity to meet interest and principal payments in the long term. Clearly, the profitability ratios discussed earlier in the section are a critical component of this analysis. The ratios specifically designed to measure long term solvency try to relate profitability to the level of debt payments, to identify the degree of comfort with which the firm can meet these payments. Interest Coverage Ratios The interest coverage ratio measures the capacity of the firm to meet interest payments from pre-debt, pre-tax earnings.

Interest Coverage Ratio =

EBIT Interest Expenses

The higher the interest coverage ratio, the more secure is the firm's capacity to make interest payments from earnings. This argument however has to be tempered by the recognition that earnings before interest and taxes is volatile and can drop significantly if the economy enters a recession. Consequently, two firms can have the same interest coverage ratio but be viewed very differently in terms of risk. The denominator in the interest coverage ratio can be easily extended to cover other fixed obligations such as lease payments. If this is done, the ratio is called a fixed charges coverage ratio. Fixed Chargeds Coverage Ratio =

EBIT + Fixed Charges Fixed Charges

Finally, this ratio, while stated in terms of earnings, can be restated in terms of cash flows, by using earnings before interest, taxes and depreciation (EBITDA) in the numerator and cash fixed charges in the denominator.

Cash Fixed Charges Coverage Ratio =

EBITDA Cash Fixed Charges

Both interest coverage and fixed charge ratios are open to the criticism that they do not consider capital expenditures, a cash flow that may be discretionary in the very short term,

31

32 but not in the long term if the firm wants to maintain growth. One way of capturing the extent of this cash flow, relative to operating cash flows, is to compute a ratio of the two.

Operating Cash flow to Capital Expenditures =

Cash flows from Operations Capital Expenditures

While there are a number of different definitions of cash flows from operations, the most reasonable way of defining it is to measure the cash flows from continuing operations, before interest but after taxes, and after meeting working capital needs. Cash flow from operations = EBIT (1-tax rate) - ∆ Working Capital

covratio.xls: There is a dataset on the web that summarizes the interest coverage and fixed charge coverage ratios for firms in the United States, classified by industry. Illustration 3.6: Interest and Fixed Charge Coverage Ratios Table 3.7 summarizes interest and fixed charge coverage ratios for Boeing and Home Depot in 1998: Table 3.7: Interest and Fixed Charge Coverage Ratios Boeing EBIT

Home Depot

$1,720

$2,661

Interest Expense

$453

$37

Interest Coverage Ratio

3.80

71.92

$1,720

$2,661

Operating Lease Expenses

$215

$290

Interest Expenses

$453

$37

Fixed Charge Coverage Ratio

2.90

9.02

$3,341

$3,034

Cash Fixed Charges

$668

$327

Cash Fixed Charge Coverage

5.00

9.28

Cash Flows from Operations

$2,161

$1,662

Capital Expenditures

$1,584

$2,059

1.36

0.81

EBIT

EBITDA

CF/Cap Ex

32

33 Boeing, based upon its operating income in 1998, looks riskier than the Home Depot on both the interest coverage ratio and fixed charge coverage ratio basis. On a cash flow basis, however, Boeing does look much better. In fact, when capital expenditures are considered, the Home Depot has a lower ratio. For Boeing, the other consideration is the fact that operating income in 1998 was depressed, relative to income in earlier years, and this does have an impact on the ratios across the board. It might make more sense when computing these ratios to look at the average figures over time. finratio.xls: This spreadsheet allows you to compute the interest coverage and fixed charge coverage ratios for a firm, based upon financial statement data. Debt Ratios Interest coverage ratios measure the capacity of the firm to meet interest payments but do not examine whether it can pay back the principal on outstanding debt. Debt ratios attempt to do this, by relating debt to total capital or to equity. The two most widely used debt ratios are:

Debt to Capital Ratio =

Debt Debt + Equity

Debt to Equity Ratio =

Debt Equity

The first ratio measures debt as a proportion of the total capital of the firm and cannot exceed 100%. The second measures debt as a proportion of equity in the firm and can be easily derived from the first.

Debt/Equit y Ratio =

Debt/Capit al Ratio 1 − Debt/Capit al Ratio

While these ratios presume that capital is raised from only debt and equity, they can be easily adapted to include other sources of financing, such as preferred stock. While preferred stock is sometimes combined with common stock under the ‘equity’ label, it is better to keep it separate and to compute the ratio of preferred stock to capital (which will include debt, equity and preferred stock).

33

34 a. Variants on Debt Ratios There are two close variants of debt ratios. In the first, only long-term debt is used rather than total debt, with the rationale that short-term debt is transitory and will not affect the long-term solvency of the firm. Long term Debt to Capital Ratio =

Long term Debt Long term Debt + Equity

Long term Debt to Equity Ratio =

Long term Debt Equity

Given the ease with which firms can roll over short-term debt, and the willingness of many firms to use short-term financing to fund long-term projects, these variants can provide a misleading picture of the firm's financial leverage risk. The second variant of debt ratios uses market value (MV) instead of book value, primarily to reflect the fact that some firms have a significantly greater capacity to borrow than their book values indicate.

Market Value Debt to Capital Ratio =

MV of Debt MV of Debt + MV of Equity

Market Value Debt to Equity Ratio =

MV of Debt MV of Equity

Many analysts disavow the use of market value in their calculations, contending that market values, in addition to being difficult to get for debt, are volatile and hence unreliable. These contentions are open to debate. It is true that the market value of debt is difficult to get for firms which do not have publicly traded bonds, but the market value of equity is not only easy to obtain, it is constantly updated to reflect market-wide and firm-specific changes. Furthermore, using the book value of debt as a proxy for market value in those cases where bonds are not traded does not significantly shift11 most market-value based debt ratios. Illustration 3.7: Book Value Debt Ratios and Variants- Boeing and Home Depot Table 3.8 summarizes different estimates of the debt ratio for Boeing, the Home Depot and InfoSoft, using book values of debt and equity for all three firms: Table 3.8: Book Value Debt Ratios

11

Deviations in the market value of equity from book value are likely to be much larger than deviation for debt and are likely to dominate in most debt ratio calculations.

34

35 Boeing

Home Depot

Long Term Debt

$6,103

$1,566

Short Term Debt

$869

$14

BV of Equity

$12,316

$8,740

LT Debt/Equity

49.55%

17.92%

LT Debt / (LT Debt + Equity)

33.13%

15.20%

Debt/Equity

56.61%

18.08%

Debt/ (Debt + Equity)

36.15%

15.31%

Boeing has a much higher book value debt ratio, both long term and total debt, than the Home Depot.

dbtfund.xls: There is a dataset on the web that summarizes the book value debt ratios and market value debt ratios for firms in the United States, classified by industry.

Other issues in analyzing financial statements Two more issues bear consideration before we conclude this section on financial statements. The first relates to differences in accounting standards and practices and how these differences may color comparisons across companies and the second relates to accounting for acquisitions and how this can affect both the acquisition method and price. Differences in accounting standards and practices Differences in accounting standards across countries affect the measurement of earnings. These differences, however, are not so great as they are made out to be and they cannot explain away radical departures from fundamental principles of valuation12. Choi and Levich, in a survey of accounting standards across developed markets, note that most countries subscribe to basic accounting notions of consistency, realization and historical cost principles in preparing accounting statements. Table 3.9 summarizes accounting standards in eight major financial markets and reveals that the common elements vastly outnumber those areas where there are differences.

12

At the peak of the Japanese market, there were many investors who explained away the price-earnings multiples of 60 and greater in the market, by noting that Japanese firms were conservative in measuring earnings. Even after taking into account the general provisions and excess depreciation used by many of these firms to depress current earnings, the price-earnings multiples were greater than 50 for many firms, suggesting either extraordinary expected growth in the future or overvaluation.

35

36 The two countries that offer the strongest contrast to the United States are Germany and Japan. The key differences and their implications are as follows. First, companies in the United States generally maintain separate tax and financial reporting books, which in turn generates items like deferred taxes to cover differences between the two books. Companies in Germany and Japan do not maintain separate books. Consequently, depreciation methods in financial reports are much more likely to be accelerated and hence to reduce stated income. Second, the requirement that leases be capitalized and shown as a liability is much more tightly enforced in the United States. In Japan, leases are generally treated as operating leases and do not show up as liabilities in the balance sheet. In Germany, firms can capitalize leases, but they have more leeway in classifying leases as operating and capital leases than U.S. companies. Third, goodwill, once created, can be amortized over 40 years in the United States and over much shorter time periods in Germany and Japan, again depressing stated income. Fourth, reserves in the United States can be created only for specific purposes, whereas German and Japanese companies can use general reserves to equalize earnings across periods, leading earnings to be understated during the good years, and overstated during bad years. Most of these differences can be accounted and adjusted for when comparisons are made between companies in the U.S. and companies in other financial markets. Ratios such as price earnings, which use stated and unadjusted earnings, can be misleading when accounting standards vary widely across the companies being compared.

Summary Financial statements remain the primary source of information for most investors and analysts. There are differences, however, in how accounting and financial analysis approach answering a number of key questions about the firm. We examine these differences in this chapter. The first question that we examined related to the nature and the value of the assets owned by a firm. Categorizing assets into investments already made (assets in place) and investments yet to be made (growth assets), we argued that accounting statements provide a substantial amount of historical information about the former and very little about the latter. The focus on the original price of assets in place (book value) in accounting statements can lead to significant differences between the stated value of these assets and their market value. With growth assets, accounting rules result in low or no values for assets generated by internal research. The second issue that we examined was the measurement of profitability. The two principles that seem to govern how profits are measured are accrual accounting – revenues

36

37 and expenses are shown in the period where transactions occur rather than when the cash is received or paid – and the categorization of expenses into operating, financing and capital expenses. Operating and financing expenses are shown in income statements. Capital expenditures take the form of depreciation and amortization and are spread over several time periods. Accounting standards miscategorize operating leases and research and development expenses as operating expenses (when the former should be categorized as financing expenses and the latter as capital expenses). In the last part of the chapter, we examine how financial statements deal with shortterm liquidity risk and long-term default risk. While the emphasis in accounting statements is on examining the risk that firms may be unable to make payments that they have committed to make, there is very little focus on risk to equity investors.

37

38

Problems Coca Cola’s balance sheet for December 1998 is summarized below (in millions of dollars) for problems 1 through 9: Cash & Near Cash 1648 Accounts Payable 3141 Marketable Securities 159 Short term Borrowings 4462 Accounts Receivable 1666 Other Short term liabilities 1037 Other Current Assets 2017 Current Liabilities 8640 Current Assets 6380 Long term Borrowings 687 Long term investments 1863 Other long term Liabilities 1415 Depreciable Fixed Assets 5486 Non-current liabilities 2102 Non-depreciable Fixed Assets 199 Accumulated Depreciation 2016 Share Capital (Paid-in) 3060 Net Fixed Assets 3669 Retained Earnings 5343 Other Assets 7233 Shareholder Equity 8403 Total Assets 19145 Total Liabilities & Equity 19145 1. Consider the assets on Coca Cola’s balance sheet and answer the following questions: a. Looking at the assets that Coca Cola has on its balance sheet, which assets are likely to be assessed closest to market value? Explain. b. Coca Cola has net fixed assets of $3,669 million. Can you estimate how much Coca Cola paid for these assets? Is there any way to know the age of these assets? c. Coca Cola seems to have far more invested in current assets, rather than fixed assets. Is this significant? Explain. d. In the early 1980s, Coca Cola sold off its bottling operations, with the bottlers becoming independent companies. How would this action have impacted the assets on Coca Cola’s balance sheet? (The manufacturing plants are most likely to be part of the bottling operations) 2. Examine the liabilities on Coca Cola’s balance sheet. a. Based upon the balance sheet, how much interest-bearing debt does Coca Cola have outstanding. (You can assume that other short term liabilities represent sundry payables, and other long term liabilities represent health care and pension obligations.) b. Based upon the balance sheet, how much did Coca Cola obtain in equity capital when it issued stock originally to the financial markets? c. Is there any significance to the fact that retained earnings is much larger than the original paid-in capital?

38

39 d. The market value of Coca Cola’s equity is $140 billion. What is the book value of equity in Coca Cola? Why is there such a large difference between the market value of equity and the book value of equity? 3. Coca Cola’s most valuable asset is its brand name. Where in the balance sheet do you see its value? Is there any way to adjust the balance sheet to reflect the value of this asset? 4. Assume that you have been asked to analyze Coca Cola’s working capital management. a. Estimate the net working capital and non-cash working capital for Coca Cola. b. Estimate the firm’s current ratio. c. Estimate the firm’s quick ratio. d. Would you draw any conclusions about the riskiness of Coca Cola as a firm by looking at these numbers? Why or why not? Coca Cola’s income statements for 1997 and 1998 are summarized below (in millions of dollars): 1997 1998 Net Revenues $18,868 $18,813 Cost of Goods Sold 6,105 5,562 Selling, G & A Expenses 7,852 8,284 Earnings before interest and taxes 5,001 4,967 Interest Expenses 258 277 Non-operating Gains 1,312 508 Income Tax Expenses 1,926 1,665 Net Income 4,129 3,533 Dividends

1,387

1,480

The following questions relate to Coca Cola’s income statement. 5. How much operating income did Coca Cola earn, before taxes, in 1998? How does this compare to how much Coca Cola earned in 1997? What are the reasons for the differences? 6. The biggest expense for Coca Cola is advertising, which is part of the selling, general and administrative expenses. A large portion of these expenses are designed to build up Coca Cola’s brand name. Should advertising expenses be treated as operating expenses or are they really capital expenses? If they are to be treated as capital expenses, how would you capitalize them? (Use the capitalization of R&D as a guide.)

39

40 7. What effective tax rate did Coca Cola have in 1998? How does it compare with what they paid in 1997 as an effective tax rate? What might account for the difference? 8. You have been asked to assess the profitability of Coca Cola, as a firm. To that end, estimate the pre-tax operating and net margins in 1997 and 1998 for the firm. Are there any conclusions you would draw from the comparisons across the two years. 9. The book value of equity at Coca Cola in 1997 was $7,274 million. The book value of interest-bearing debt was $3,875 million. Estimate: a. the return on equity (beginning of the year) in 1998 b. the pre-tax return on capital (beginning of the year) in 1998 c. the after-tax return on capital (beginning of the year) in 1998, using the effective tax rate in 1998. 10. SeeSaw Toys reported that it had a book value of equity of $1.5 billion at the end of 1998 and 100 million shares outstanding. During 1999, it bought back 10 million shares at a market price of $40 per share. The firm also reported a net income of $150 million for 1999, and paid dividends of $50 million. a. Estimate the book value of equity at the end of 1999 b. Estimate the return on equity, using beginning book value of equity. c. Estimate the return on equity, using the average book value of equity.

40

41 Table 3.9: International Comparison of Accounting Principles Accounting Principle

UK

1. Consistence – accounting principles and

USA

France

Germany

Netherlands

Sweden

Switzerland

Japan

Yes

Yes

Yes

Yes

Yes

PP

PP

Yes

Yes

Yes

Yes

Yes

Yes

Yes

PP

Yes

financial Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

4. Historical cost convention – departures Yes

Yes

Yes

Yes

Yes

Yes

RF

Yes

Yes

No

Yes

MP

RF

MP

MP

No

MP

No

Yes

No

RF

PP

No

No

Yes

No

Yes

No

Yes

Yes

No

No

MP

Yes

Yes

Yes

M

Yes

MP

Yes

methods are applied on the same basis from period to period 2. Realization – revenue is recognized when realization is reasonably assured 3.

Fair

presentation

of

the

statement is required

from the historical cost convention are disclosed 5. Accounting policies – a change in accounting principles and methods without a change in circumstances is accounted for by a prior year adjustment 6. Fixed assets – revaluation – in historical cost statements, fixed assets are stated at an amount

in

excess of cost

which

is

determined at irregular intervals. 7. Fixed assets – revaluation – when fixed assets

are

stated,

in

historical

cost

statements, at an amount in excess of cost, depreciation based

on

the

revaluation

amount is charged to income. 8. Goodwill amortized

41

42 9. Finance leases capitalized

Yes

Yes

No

No

No

Yes

RF

No

10. Short-term marketablse securities at the

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

13. Inventory costed using FIFO

PP

M

M

M

M

PP

PP

M

14. Long-term debt included maturities

Yes

Yes

Yes

No

Yes

Yes

Yes

Yes

where Yes

Yes

Yes

No

Yes

No

No

Yes

Yes

Yes

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

PP

Yes

20. Unusual and extraordinary gains and Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

No

Yes

No

lower of cost or market value 11. Inventory values at the lower of cost or market value 12. Manufacturing overhead allocated to year-end inventory

longer than one year 15.

Deferred

tax

recognized

accounting income and taxable income arise at different times 16. Total pension fund assets and liabilities excluded from

a

company’s

financial

statements 17. Research and development expensed

18. General purpose (purely discretionary) No reserves allowed 19. Offsetting-assets and liabilities are offset against each other in the balance sheet only when a legal right of offset exists

losses are taken in the income statement 21. Closing rate method of foreign currency

Yes

translation employed

42

43 22. Currency translation gains or losses

Yes

Yes

MP

MP

MP

MP

MP

No

23. Excess depreciation permitted

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

24. Basic statements reflect a historical cost

Yes

Yes

Yes

Yes

M

Yes

Yes

Yes

25. Supplementary inflation – adjusted MP

MP

No

NO

MP

Yes

No

No

arising from trading are reflected in current income

valuation (no price level adjustment)

financial statements adjusted 26. Accounting for long-term investments: (a) less than 20% ownership - cost method

Yes

Yes

Yes

Yes

No

Yes

Yes

Yes

(b) 20 - 50% ownership -equity method

Yes

Yes

Yes

No

Yes

MP

M

Yes

(c) More than 50% full consolidation

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

27. Both domestic and foreign subsidiaries

Yes

Yes

Yes

M

Yes

Yes

MP

Yes

PP

Yes

Yes

Yes

PP

Yes

Yes

consolidated 28. Acquisition accounted for under the PP purchase cost method 29.

Minority

interest

excluded

from Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

excluded

from Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

consolidation income 30.

Minority

interest

consolidated owners’ equity

Key:

PP – Predominant Practice MP – Minority Practice M – Mixed Practice RF – Rarely or not found

43

44

44

1

CHAPTER 4 THE BASICS OF RISK When valuing assets and firms, we need to use discount rates that reflect the riskiness of the cash flows. In particular, the cost of debt has to incorporate a default spread for the default risk in the debt and the cost of equity has to include a risk premium for equity risk. But how do we measure default and equity risk, and more importantly, how do we come up with the default and equity risk premiums? In this chapter, we will lay the foundations for analyzing risk in valuation. We present alternative models for measuring risk and converting these risk measures into “acceptable” hurdle rates. We begin with a discussion of equity risk and present our analysis in three steps. In the first step, we define risk in statistical terms to be the variance in actual returns around an expected return. The greater this variance, the more risky an investment is perceived to be. The next step, which we believe is the central one, is to decompose this risk into risk that can be diversified away by investors and risk that cannot. In the third step, we look at how different risk and return models in finance attempt to measure this non-diversifiable risk. We compare and contrast the most widely used model, the capital asset pricing model, with other models, and explain how and why they diverge in their measures of risk and the implications for the equity risk premium. In the second part of this chapter, we consider default risk and how it is measured by ratings agencies. In addition, we discuss the determinants of the default spread and why it might change over time. By the end of the chapter, we should have a methodology of estimating the costs of equity and debt for any firm. What is risk? Risk, for most of us, refers to the likelihood that in life’s games of chance, we will receive an outcome that we will not like. For instance, the risk of driving a car too fast is getting a speeding ticket, or worse still, getting into an accident. Webster’s dictionary, in fact, defines risk as “exposing to danger or hazard”. Thus, risk is perceived almost entirely in negative terms. In finance, our definition of risk is both different and broader. Risk, as we see it, refers to the likelihood that we will receive a return on an investment that is different from

2 the return we expected to make. Thus, risk includes not only the bad outcomes, i.e, returns that are lower than expected, but also good outcomes, i.e., returns that are higher than expected. In fact, we can refer to the former as downside risk and the latter is upside risk; but we consider both when measuring risk. In fact, the spirit of our definition of risk in finance is captured best by the Chinese symbols for risk, which are reproduced below:

The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity. It illustrates very clearly the tradeoff that every investor and business has to make – between the higher rewards that come with the opportunity and the higher risk that has to be borne as a consequence of the danger. Much of this chapter can be viewed as an attempt to come up with a model that best measures the “danger” in any investment and then attempts to convert this into the “opportunity” that we would need to compensate for the danger. In financial terms, we term the danger to be “risk” and the opportunity to be “expected return”. What makes the measurement of risk and expected return so challenging is that it can vary depending upon whose perspective we adopt. When analyzing Boeing’s risk, for instance, we can measure it from the viewpoint of Boeing’s managers. Alternatively, we can argue that Boeing’s equity is owned by its stockholders and that it is their perspective on risk that should matter. Boeing’s stockholders, many of whom hold the stock as one investment in a larger portfolio, might perceive the risk in Boeing very differently from Boeing’s managers, who might have the bulk of their capital, human and financial, invested in the firm. In this chapter, we will argue that risk in an investment has to be perceived through the eyes of investors in the firm. Since firms like Boeing often have thousands of investors, often with very different perspectives, we will go further. We will assert that risk has to be measured from the perspective of not just any investor in the stock, but of the marginal investor, defined to be the investor most likely to be trading on the stock

3 at any given point in time. The objective in corporate finance is the maximization of firm value and stock price. If we want to stay true to this objective, we have to consider the viewpoint of those who set the stock prices, and they are the marginal investors. Equity Risk and Expected Return To demonstrate how risk is viewed in corporate finance, we will present risk analysis in three steps. First, we will define risk in terms of the distribution of actual returns around an expected return. Second, we will differentiate between risk that is specific to one or a few investments and risk that affects a much wider cross section of investments. We will argue that in a market where the marginal investor is well diversified, it is only the latter risk, called market risk that will be rewarded. Third, we will look at alternative models for measuring this market risk and the expected returns that go with it. I. Defining Risk Investors who buy assets expect to earn returns over the time horizon that they hold the asset. Their actual returns over this holding period may be very different from the expected returns and it is this difference between actual and expected returns that is source of risk. For example, assume that you are an investor with a 1-year time horizon buying a 1-year Treasury bill (or any other default-free one-year bond) with a 5% expected return. At the end of the 1-year holding period, the actual return on this investment will be 5%, which is equal to the expected return. The return distribution for this investment is shown in Figure 4.1.

4 Figure 4.1: Probability Distribution for Riskfree Investment Probability =

The actual return is always equal to the expected return.

Expected

Return

This is a riskless investment. To provide a contrast to the riskless investment, consider an investor who buys stock in Boeing. This investor, having done her research, may conclude that she can make an expected return of 30% on Boeing over her 1-year holding period. The actual return over this period will almost certainly not be equal to 30%; it might be much greater or much lower. The distribution of returns on this investment is illustrated in Figure 4.2.

5 Figure 4.2: Probability Distribution for Risky Investment

This distribution measures the probability that the actual return will be different

Expected Return

Returns

In addition to the expected return, an investor now has to consider the following. First, note that the actual returns, in this case, are different from the expected return. The spread of the actual returns around the expected return is measured by the variance or standard deviation of the distribution; the greater the deviation of the actual returns from expected returns, the greater the variance. Second, the bias towards positive or negative returns is represented by the skewness of the distribution. The distribution in Figure 4.2 is positively skewed, since there is a higher probability of large positive returns than large negative returns. Third, the shape of the tails of the distribution is measured by the kurtosis of the distribution; fatter tails lead to higher kurtosis. In investment terms, this represents the tendency of the price of this investment to jump (up or down from current levels) in either direction. In the special case, where the distribution of returns is normal, investors do not have to worry about skewness and kurtosis. Normal distributions are symmetric (no skewness) and defined to have a kurtosis of zero. Figure 4.3 illustrates the return distributions on two investments with symmetric returns. Figure 4.3: Return Distribution Comparisons

6 Low Variance Investment

High Variance Investment

Expected Return

When return distributions take this form, the characteristics of any investment can be measured with two variables – the expected return, which represents the opportunity in the investment, and the standard deviation or variance, which represents the danger. In this scenario, a rational investor, faced with a choice between two investments with the same standard deviation but different expected returns, will always pick the one with the higher expected return. In the more general case, where distributions are neither symmetric nor normal, it is still conceivable that investors will choose between investments on the basis of only the expected return and the variance, if they possess utility functions1 that allow them to do so. It is far more likely, however, that they prefer positive skewed distributions to negatively skewed ones, and distributions with a lower likelihood of jumps (lower kurtosis) to those with a higher likelihood of jumps (higher kurtosis). In this world, investors will trade off the good (higher expected returns and more positive skewness) against the bad (higher variance and higher kurtosis) in making investments.

1

A utility function is a way of summarizing investor preferences into a generic term called ‘utility’ on the basis of some choice variables. In this case, for instance, we state the investor’s utility or satisfaction as a function of wealth. By doing so, we effectively can answer questions such as – Will an investor be twice as happy if he has twice as much wealth? Does each marginal increase in wealth lead to less additional utility than the prior marginal increase? In one specific form of this function, the quadratic utility function, the entire utility of an investor can be compressed into the expected wealth measure and the standard deviation in that wealth.

7 In closing, we should note that the expected returns and variances that we run into in practice are almost always estimated using past returns rather than future returns. The assumption we are making when we use historical variances is that past return distributions are good indicators of future return distributions. When this assumption is violated, as is the case when the asset’s characteristics have changed significantly over time, the historical estimates may not be good measures of risk. In Practice 4.1: Calculation of standard deviation using historical returns: Boeing and the Home Depot We will use Boeing and the Home Depot as our investments to illustrate how standard deviations and variances are computed. To make our computations simpler, we will look at returns on an annual basis from 1991 to 1998. To begin the analysis, we first estimate returns for each company for each of these years, in percentage terms, incorporating both price appreciation and dividends into these returns:

Return in year n =

Price at the end of year n - Price at beginning of year n + Dividend in year n Price at the beginning of year n

Table 4.1 summarizes returns on the two companies. Table 4.1: Returns on Boeing and the Home Depot: 1991-1998 Return on Boeing

Return on The Home Depot

1991

5.00%

161%

1992

-16%

50.30%

1993

7.80%

-22%

1994

8.70%

16.50%

1995

66.80%

3.80%

1996

35.90%

5.00%

1997

-8.10%

76.20%

1998

-33.10%

107.90%

Sum

67.00%

398.70%

8 We compute the average and standard deviation in these returns for the two firms, using the information in the table (there are 8 years of data): Average Return on Boeing91-98 = 67.00%/8 = 8.38% Average Return on The Home Depot 91-98 = 398.70%/8 = 49.84% The variance is measured by looking at the deviations of the actual returns in each year, for each stock, from the average return. Since we consider both better-than-expected and worse-than-expected deviations in measuring variance, we square the deviations2. Table 4.2: Squared Deviations from the Mean Return on Boeing Return on

The (RB-

(RHD -

Average(RB))2

Home Depot

Average(RHD ))2

1991

5.00%

161%

0.00113906

1.23571014

1992

-16%

50.30%

0.05941406

2.1391E-05

1993

7.80%

-22%

3.3063E-05

0.51606264

1994

8.70%

16.50%

1.0562E-05

0.11113889

1995

66.80%

3.80%

0.34134806

0.21194514

1996

35.90%

5.00%

0.07576256

0.20104014

1997

-8.10%

76.20%

0.02714256

0.06949814

1998

-33.10%

107.90%

0.17201756

0.33712539

0.6768675

2.68254188

Sum

Following the standard practice for estimating the variances of samples, the variances in returns at the two firms can be estimated by dividing the sum of the squared deviation columns by (n-1), where n is the number of observations in the sample. The standard deviations can be computed to be the squared-root of the variances. Boeing

The Home Depot

Variance

0.6768675 = 0.0967 8 -1

2.68254188 = 0.3832 8 -1

Standard Deviation

0.09670.5 = 0.311 or 31.1%

0.38320.5 = 0.619 or 61.9%

2

If we do not square the deviations, the sum of the deviations will be zero.

9 Based upon this data, the Home Depot looks like it was two times more risky than Boeing between 1991 and 1998. What does this tell us? By itself, it provides a measure of how much each these companies’ returns in the past have deviated from the average. If we assume that the past is a good indicator of the future, the Home Depot is a more risky investment than Boeing.

optvar.xls: There is a dataset on the web that summarizes standard deviations and variances of stocks in various sectors in the United States. II. Diversifiable and Non-diversifiable Risk Although there are many reasons that actual returns may differ from expected returns, we can group the reasons into two categories: firm-specific and market-wide. The risks that arise from firm-specific actions affect one or a few investments, while the risk arising from market-wide reasons affect many or all investments. This distinction is critical to the way we assess risk in finance. The Components of Risk When an investor buys stock or takes an equity position in a firm, he or she is exposed to many risks. Some risk may affect only one or a few firms and it is this risk that we categorize as firm-specific risk. Within this category, we would consider a wide range of risks, starting with the risk that a firm may have misjudged the demand for a product from its customers; we call this project risk. For instance, in the coming chapters, we will be analyzing Boeing’s investment in a Super Jumbo jet. This investment is based on the assumption that airlines want a larger airplane and are will be willing to pay a higher price for it. If Boeing has misjudged this demand, it will clearly have an impact on Boeing’s earnings and value, but it should not have a significant effect on other firms in the market. The risk could also arise from competitors proving to be stronger or weaker than anticipated; we call this competitive risk. For instance, assume that Boeing and Airbus are competing for an order from Quantas, the Australian airline. The possibility that Airbus may win the bid is a potential source of risk to Boeing and perhaps a few of its suppliers. But again, only a handful of firms in the market will be

10 affected by it. Similarly, the Home Depot recently launched an online store to sell its home improvement products. Whether it succeeds or not is clearly important to the Home Depot and its competitors, but it is unlikely to have an impact on the rest of the market. In fact, we would extend our risk measures to include risks that may affect an entire sector but are restricted to that sector; we call this sector risk. For instance, a cut in the defense budget in the United States will adversely affect all firms in the defense business, including Boeing, but there should be no significant impact on other sectors, such as food and apparel. What is common across the three risks described above – project, competitive and sector risk – is that they affect only a small sub-set of firms. There is other risk that is much more pervasive and affects many if not all investments. For instance, when interest rates increase, all investments are negatively affected, albeit to different degrees. Similarly, when the economy weakens, all firms feel the effects, though cyclical firms (such as automobiles, steel and housing) may feel it more. We term this risk market risk. Finally, there are risks that fall in a gray area, depending upon how many assets they affect. For instance, when the dollar strengthens against other currencies, it has a significant impact on the earnings and values of firms with international operations. If most firms in the market have significant international operations, it could well be categorized as market risk. If only a few do, it would be closer to firm-specific risk. Figure 4.4 summarizes the break down or the spectrum of firm-specific and market risks.

11 Figure 4.4: A Break Down of Risk Competition may be stronger or weaker than anticipated Projects may do better or worse than expected

Exchange rate and Political risk Interest rate, Inflation & News about Econoomy

Entire Sector may be affected by action

Firm-specific

Actions/Risk that affect only one firm

Market

Affects few firms

Affects many firms

Actions/Risk that affect all investments

Why Diversification reduces or eliminates Firm-specific Risk: An

Intuitive

Explanation As an investor, you could invest your entire portfolio in one asset, say Boeing. If you do so, you are exposed to both firm-specific and market risk. If, however, you expand your portfolio to include other assets or stocks, you are diversifying, and by doing so, you can reduce your exposure to firm-specific risk. There are two reasons why diversification reduces or, at the limit, eliminates firm specific risk. The first is that each investment in a diversified portfolio is a much smaller percentage of that portfolio than would be the case if you were not diversified. Thus, any action that increases or decreases the value of only that investment or a small group of investments will have only a small impact on your overall portfolio, whereas undiversified investors are much more exposed to changes in the values of the investments in their portfolios. The second reason is that the effects of firm-specific actions on the prices of individual assets in a portfolio can be either positive or negative for each asset for any period. Thus, in very large portfolios, this risk will average out to zero and will not affect the overall value of the portfolio. In contrast, the effects of market-wide movements are likely to be in the same direction for most or all investments in a portfolio, though some assets may be affected

12 more than others. For instance, other things being equal, an increase in interest rates will lower the values of most assets in a portfolio. Being more diversified does not eliminate this risk. A Statistical Analysis Of Diversification Reducing Risk We can illustrate the effects of diversification on risk fairly dramatically by examining the effects of increasing the number of assets in a portfolio on portfolio variance. The variance in a portfolio is partially determined by the variances of the individual assets in the portfolio and partially by how they move together; the latter is measured statistically with a correlation coefficient or the covariance across investments in the portfolio. It is the covariance term that provides an insight into why and by how much diversification will reduce risk. Consider a portfolio of two assets. Asset A has an expected return of 2 A

variance in returns of 2 B

returns of

, while asset B has an expected return of

B

A

and a

and a variance in

. The correlation in returns between the two assets, which measures how

the assets move together, is

AB

. The expected returns and variance of a two-asset

portfolio can be written as a function of these inputs and the proportion of the portfolio going to each asset. P

2 P

= w A2

= wA

2 A

A

+ (1 − w A )

+ (1 − w A )

2

2 B

B

+ 2 w A (1 − w A )

A

B

AB

where wA = Proportion of the portfolio in asset A

The last term in the variance equation is sometimes written in terms of the covariance in returns between the two assets, which is Cov AB =

A

B

AB

The savings that accrue from diversification are a function of the correlation coefficient. Other things remaining equal, the higher the correlation in returns between the two assets, the smaller are the potential benefits from diversification. Why is the marginal investor assumed to be diversified?

13 The argument that diversification reduces an investor’s exposure to risk is clear both intuitively and statistically, but risk and return models in finance go further. The models look at risk through the eyes of the investor most likely to be trading on the investment at any point in time, i.e. the marginal investor. They argue that this investor, who sets prices for investments, is well diversified; thus, the only risk that he or she cares about is the risk added on to a diversified portfolio or market risk. This argument can be justified simply. The risk in an investment will always be perceived to be higher for an undiversified investor than for a diversified one, since the latter does not shoulder any firm-specific risk and the former does. If both investors have the same expectations about future earnings and cash flows on an asset, the diversified investor will be willing to pay a higher price for that asset because of his or her perception of lower risk. Consequently, the asset, over time, will end up being held by diversified investors. This argument is powerful, especially in markets where assets can be traded easily and at low cost. Thus, it works well for a stock traded in the United States, since investors can become diversified at fairly low cost. In addition, a significant proportion of the trading in US stocks is done by institutional investors, who tend to be well diversified. It becomes a more difficult argument to sustain when assets cannot be easily traded, or the costs of trading are high. In these markets, the marginal investor may well be undiversified and firm-specific risk may therefore continue to matter when looking at individual investments. For instance, real estate in most countries is still held by investors who are undiversified and have the bulk of their wealth tied up in these investments. III. Models Measuring Market Risk While most risk and return models in use in corporate finance agree on the first two steps of the risk analysis process, i.e., that risk comes from the distribution of actual returns around the expected return and that risk should be measured from the perspective of a marginal investor who is well diversified, they part ways when it comes to measuring non-diversifiable or market risk. In this section, we will discuss the different models that exist in finance for measuring market risk and why they differ. We will begin with what still is the standard model for measuring market risk in finance – the capital asset pricing model (CAPM) – and then discuss the alternatives to this model that have developed over

14 the last two decades. While we will emphasize the differences, we will also look at what they have in common. A. The Capital Asset Pricing Model (CAPM) The risk and return model that has been in use the longest and is still the standard in most real world analyses is the capital asset pricing model (CAPM). In this section, we will examine the assumptions made by the model and the measures of market risk that emerge from these assumptions. Assumptions While diversification reduces the exposure of investors to firm specific risk, most investors limit their diversification to holding only a few assets. Even large mutual funds rarely hold more than a few hundred stocks and many of them hold as few as ten to twenty. There are two reasons why investors stop diversifying. One is that an investor or mutual fund manager can obtain most of the benefits of diversification from a relatively small portfolio, because the marginal benefits of diversification become smaller as the portfolio gets more diversified. Consequently, these benefits may not cover the marginal costs of diversification, which include transactions and monitoring costs. Another reason for limiting diversification is that many investors (and funds) believe they can find under valued assets and thus choose not to hold those assets that they believe to be fairly or over valued. The capital asset pricing model assumes that there are no transactions costs, all assets are traded and investments are infinitely divisible (i.e., you can buy any fraction of a unit of the asset). It also assumes that everyone has access to the same information and that investors therefore cannot find under or over valued assets in the market place. Making these assumptions allows investors to keep diversifying without additional cost. At the limit, their portfolios will not only include every traded asset in the market but will have identical weights on risky assets

The fact that this diversified portfolio

includes all traded assets in the market is the reason it is called the market portfolio, which should not be a surprising result, given the benefits of diversification and the absence of transactions costs in the capital asset pricing model. If diversification reduces exposure to firm-specific risk and there are no costs associated with adding more assets to

15 the portfolio, the logical limit to diversification is to hold a small proportion of every traded asset in the market. If this seems abstract, consider the market portfolio to be an extremely well diversified mutual fund that holds stocks and real assets, and treasury bills as the riskless asset. In the CAPM, all investors will hold combinations of treasury bills and the same mutual fund3. Investor Portfolios in the CAPM If every investor in the market holds the identical market portfolio, how exactly do investors reflect their risk aversion in their investments? In the capital asset pricing model, investors adjust for their risk preferences in their allocation decision, where they decide how much to invest in a riskless asset and how much in the market portfolio. Investors who are risk averse might choose to put much or even all of their wealth in the riskless asset. Investors who want to take more risk will invest the bulk or even all of their wealth in the market portfolio. Investors, who invest all their wealth in the market portfolio and are still desirous of taking on more risk, would do so by borrowing at the riskless rate and investing more in the same market portfolio as everyone else. These results are predicated on two additional assumptions. First, there exists a riskless asset, where the expected returns are known with certainty. Second, investors can lend and borrow at the same riskless rate to arrive at their optimal allocations. While lending at the riskless rate can be accomplished fairly simply by buying treasury bills or bonds, borrowing at the riskless rate might be more difficult to do for individuals. There are variations of the CAPM that allow these assumptions to be relaxed and still arrive at the conclusions that are consistent with the model. Measuring the Market Risk of an Individual Asset The risk of any asset to an investor is the risk added by that asset to the investor’s overall portfolio. In the CAPM world, where all investors hold the market portfolio, the risk to an investor of an individual asset will be the risk that this asset adds on to the market portfolio. Intuitively, if an asset moves independently of the market

3

The significance of introducing the riskless asset into the choice mix, and the implications for portfolio choice were first noted in Sharpe (1964) and Lintner (1965). Hence, the model is sometimes called the

16 portfolio, it will not add much risk to the market portfolio. In other words, most of the risk in this asset is firm-specific and can be diversified away. In contrast, if an asset tends to move up when the market portfolio moves up and down when it moves down, it will add risk to the market portfolio. This asset has more market risk and less firm-specific risk. Statistically, this added risk is measured by the covariance of the asset with the market portfolio. Measuring the Non-Diversifiable Risk In a world in which investors hold a combination of only two assets – the riskless asset and the market portfolio – the risk of any individual asset will be measured relative to the market portfolio. In particular, the risk of any asset will be the risk that it adds on to the market portfolio. To arrive at the appropriate measure of this added risk, assume that

2 m

is the variance of the market portfolio prior to the addition of the new asset and

that the variance of the individual asset being added to this portfolio is

2 i

. The market

value portfolio weight on this asset is wi , and the covariance correlation in returns between the individual asset and the market portfolio is Covim. The variance of the market portfolio prior to and after the addition of the individual asset can then be written as Variance prior to asset i being added = Variance after asset i is added =

2 m'

2 m

= wi2

2 i

(

+ 1 − wi

)

2

2 m

(

)

+ 2 wi 1 − wi Covim

The market value weight on any individual asset in the market portfolio should be small ( wi is very close to 0) since the market portfolio includes all traded assets in the economy. Consequently, the first term in the equation should approach zero, and the second term should approach

2 m

, leaving the third term (Covim, the covariance) as the measure of the

risk added by individual asset i. Standardizing Covariances The covariance is a percentage value and it is difficult to pass judgment on the relative risk of an investment by looking at this value. In other words, knowing that the

Sharpe-Lintner model.

17 covariance of Boeing with the Market Portfolio is 55% does not provide us a clue as to whether Boeing is riskier or safer than the average asset. We therefore standardize the risk measure by dividing the covariance of each asset with the market portfolio by the variance of the market portfolio. This yields a risk measure called the beta of the asset:

Beta of an asset i =

Covariance of asset i with Market Portfolio Covim = 2 Variance of the Market Portfolio m

Since the covariance of the market portfolio with itself is its variance, the beta of the market portfolio, and by extension, the average asset in it, is one. Assets that are riskier than average (using this measure of risk) will have betas that are greater than 1 and assets that are less riskier than average will have betas that are less than 1. The riskless asset will have a beta of 0. Getting Expected Returns The fact that every investor holds some combination of the riskless asset and the market portfolio leads to the next conclusion: the expected return of an asset is linearly related to the beta of the asset. In particular, the expected return of an asset can be written as a function of the risk-free rate and the beta of that asset. E (Ri ) = R f +

i

(E (R )− R ) m

f

where, E(Ri) = Expected Return on asset i Rf = Risk-free Rate E(Rm) = Expected Return on market portfolio β i= Beta of investment i To use the capital asset pricing model, we need three inputs. While we will look at the estimation process in far more detail in the next chapter, each of these inputs is estimated as follows: •

The riskless asset is defined to be an asset for which the investor knows the expected return with certainty for the time horizon of the analysis.

18 •

The risk premium is the premium demanded by investors for investing in the market portfolio, which includes all risky assets in the market, instead of investing in a riskless asset.

•

The beta, which we defined as the covariance of the asset divided by the variance of the market portfolio, measures the risk added on by an investment to the market portfolio.

In summary, in the capital asset pricing model, all the market risk is captured in the beta, measured relative to a market portfolio, which at least in theory should include all traded assets in the market place held in proportion to their market value. B. The Arbitrage Pricing Model The restrictive assumptions on transactions costs and private information in the capital asset pricing model and the model’s dependence on the market portfolio have long been viewed with skepticism by both academics and practitioners. Ross (1976) suggested an alternative model for measuring risk called the arbitrage pricing model (APM). Assumptions If investors can invest risklessly and earn more than the riskless rate, they have found an arbitrage opportunity. The premise of the arbitrage pricing model is that investors take advantage of such arbitrage opportunities, and in the process, eliminate them. If two portfolios have the same exposure to risk but offer different expected returns, investors will buy the portfolio that has the higher expected returns, sell the portfolio with the lower expected returns and earn the difference as a riskless profit. To prevent this arbitrage from occurring, the two portfolios have to earn the same expected return. Like the capital asset pricing model, the arbitrage pricing model begins by breaking risk down into firm-specific and market risk components. As in the capital asset pricing model, firm specific risk covers information that affects primarily the firm. Market risk affects many or all firms and would include unanticipated changes in a number of economic variables, including gross national product, inflation, and interest rates. Incorporating both types of risk into a return model, we get:

19 R = E (R )+ m +

where R is the actual return, E(R) is the expected return, m is the market-wide component of unanticipated risk and ε is the firm-specific component. Thus, the actual return can be different from the expected return, either because of market risk or firm-specific actions. The Sources of Market-Wide Risk While both the capital asset pricing model and the arbitrage pricing model make a distinction between firm-specific and market-wide risk, they measure market risk differently. The CAPM assumes that market risk is captured in the market portfolio, whereas the arbitrage pricing model allows for multiple sources of market-wide risk and measures the sensitivity of investments to changes in each source. In general, the market component of unanticipated returns can be decomposed into economic factors: R = E (R )+ m +

= R + ( j Fj +

2

F2 + ... +

n

Fn )+

where βj =

Sensitivity of investment to unanticipated changes in factor j

Fj =

Unanticipated changes in factor j

Note that the measure of an investment’s sensitivity to any macro-economic factor takes the form of a beta, called a factor beta. In fact, this beta has many of the same properties as the market beta in the CAPM. The Effects of Diversification The benefits of diversification were discussed earlier, in the context of our break down of risk into market and firm-specific risk. The primary point of that discussion was that diversification eliminates firm-specific risk. The arbitrage pricing model uses the same argument and concludes that the return on a portfolio will not have a firm-specific component of unanticipated returns. The return on a portfolio can be written as the sum of two weighted averages: the anticipated returns in the portfolio and the market factors. R p = (w1 R1 + w2 R2 + ... + wn Rn )+ (w1 R1,1 + w2 R1, 2 + ... + wn R1,n )F1 + + (w2 R2,1 + w2 R2, 2 + ... + wn R2,n )F2 + ...

20 where, wj = Portfolio weight on asset j Rj = Expected return on asset j β i,j = Beta on factor i for asset j Expected Returns and Betas The final step in this process is estimating an expected return as a function of the betas specified above. To do this, we should first note that the beta of a portfolio is the weighted average of the betas of the assets in the portfolio. This property, in conjunction with the absence of arbitrage, leads to the conclusion that expected returns should be linearly related to betas. To see why, assume that there is only one factor and three portfolios. Portfolio A has a beta of 2.0 and an expected return on 20%; portfolio B has a beta of 1.0 and an expected return of 12%; and portfolio C has a beta of 1.5 and an expected return on 14%. Note that the investor can put half of his wealth in portfolio A and half in portfolio B and end up with a portfolio with a beta of 1.5 and an expected return of 16%. Consequently no investor will choose to hold portfolio C until the prices of assets in that portfolio drop and the expected return increases to 16%. By the same rationale, the expected returns on every portfolio should be a linear function of the beta. If they were not, we could combine two other portfolios, one with a higher beta and one with a lower beta, to earn a higher return than the portfolio in question, creating an opportunity for arbitrage. This argument can be extended to multiple factors with the same results. Therefore, the expected return on an asset can be written as E (R ) = R f +

1

[E (R )− R ]+ [E (R )− R ]+ ... + [E (R )− R ] 1

f

2

2

f

n

n

f

where Rf = Expected return on a zero-beta portfolio E(Rj) = Expected return on a portfolio with a factor beta of 1 for factor j and zero for all other factors. The terms in the brackets can be considered to be risk premiums for each of the factors in the model.

21 The capital asset pricing model can be considered to be a special case of the arbitrage pricing model, where there is only one economic factor driving market-wide returns and the market portfolio is the factor. E (R ) = R f +

m

(E (R )− R ) m

f

The APM in Practice The arbitrage pricing model requires estimates of each of the factor betas and factor risk premiums in addition to the riskless rate. In practice, these are usually estimated using historical data on asset returns and a factor analysis. Intuitively, in a factor analysis, we examine the historical data looking for common patterns that affect broad groups of assets (rather than just one sector or a few assets). A factor analysis provides two output measures: 1. It specifies the number of common factors that affected the historical return data 2. It measures the beta of each investment relative to each of the common factors and provides an estimate of the actual risk premium earned by each factor. The factor analysis does not, however, identify the factors in economic terms. In summary, in the arbitrage pricing model, the market risk is measured relative to multiple unspecified macroeconomic variables, with the sensitivity of the investment relative to each factor being measured by a beta. The number of factors, the factor betas and factor risk premiums can all be estimated using the factor analysis. C. Multi-factor Models for risk and return The arbitrage pricing model's failure to identify the factors specifically in the model may be a statistical strength, but it is an intuitive weakness. The solution seems simple: Replace the unidentified statistical factors with specific economic factors and the resultant model should have an economic basis while still retaining much of the strength of the arbitrage pricing model. That is precisely what multi-factor models try to do. Deriving a Multi-Factor Model Multi-factor models generally are determined by historical data, rather than economic modeling. Once the number of factors has been identified in the arbitrage pricing model, their behavior over time can be extracted from the data. The behavior of the

22 unnamed factors over time can then be compared to the behavior of macroeconomic variables over that same period to see whether any of the variables is correlated, over time, with the identified factors. For instance, Chen, Roll, and Ross (1986) suggest that the following macroeconomic variables are highly correlated with the factors that come out of factor analysis: industrial production, changes in default premium, shifts in the term structure, unanticipated inflation, and changes in the real rate of return. These variables can then be correlated with returns to come up with a model of expected returns, with firm-specific betas calculated relative to each variable. E (R ) = R f +

GNP

[E (R )− R ]+ [E (R )− R ]+ ... + [E (R )− R ] GNP

f

I

I

f

∂

∂

f

where β GNP = Beta relative to changes in industrial production E(RGNP) = Expected return on a portfolio with a beta of one on the industrial production factor and zero on all other factors β I = Beta relative to changes in inflation E(RI) = Expected return on a portfolio with a beta of one on the inflation factor and zero on all other factors The costs of going from the arbitrage pricing model to a macroeconomic multifactor model can be traced directly to the errors that can be made in identifying the factors. The economic factors in the model can change over time, as will the risk premia associated with each one. For instance, oil price changes were a significant economic factor driving expected returns in the 1970s but are not as significant in other time periods. Using the wrong factor or missing a significant factor in a multi-factor model can lead to inferior estimates of expected return. In summary, multi-factor models, like the arbitrage pricing model, assume that market risk can be captured best using multiple macro economic factors and betas relative to each. Unlike the arbitrage pricing model, multi factor models do attempt to identify the macro economic factors that drive market risk.

23 D. Regression or Proxy Models All the models described so far begin by defining market risk in broad terms and then developing models that might best measure this market risk. All of them, however, extract their measures of market risk (betas) by looking at historical data. There is a final class of risk and return models that start with the returns and try to explain differences in returns across stocks over long time periods using characteristics such as a firm’s market value or price multiples4. Proponents of these models argue that if some investments earn consistently higher returns than other investments, they must be riskier. Consequently, we could look at the characteristics that these high-return investments have in common and consider these characteristics to be indirect measures or proxies for market risk. Fama and French, in a highly influential study of the capital asset pricing model in the early 1990s, noted that actual returns between 1963 and 1990 have been highly correlated with book to price ratios5 and size. High return investments, over this period, tended to be investments in companies with low market capitalization and high book to price ratios. Fama and French suggested that these measures be used as proxies for risk and report the following regression for monthly returns on stocks on the NYSE:  BV  R t = 1.77% − 0.11 ln (MV )+ 0.35ln    MV 

where MV = Market Value of Equity BV/MV = Book Value of Equity / Market Value of Equity The values for market value of equity and book-price ratios for individual firms, when plugged into this regression, should yield expected monthly returns. A Comparative Analysis of Risk and Return Models Figure 4.5 summarizes all the risk and return models in finance, noting their similarities in the first two steps and the differences in the way they define market risk.

4

A price multiple is obtained by dividing the market price by its earnings or its book value. Studies indicate that stocks that have low price to earnings multiples or low price to book value multiples earn higher returns than other stocks. 5 The book to price ratio is the ratio of the book value of equity to the market value of equity.

24 Figure 4.5: Risk and Return Models in Finance Step 1: Defining Risk The risk in an investment can be measured by the variance in actual returns around an expected return Riskless Investment Low Risk Investment High Risk Investment

E(R) E(R) E(R) Step 2: Differentiating between Rewarded and Unrewarded Risk Risk that is specific to investment (Firm Specific) Risk that affects all investments (Market Risk) Can be diversified away in a diversified portfolio Cannot be diversified away since most assets 1. each investment is a small proportion of portfolio are affected by it. 2. risk averages out across investments in portfolio The marginal investor is assumed to hold a “diversified” portfolio. Thus, only market risk will be rewarded and priced. Step 3: Measuring Market Risk The CAPM If there is 1. no private information 2. no transactions cost the optimal diversified portfolio includes every traded asset. Everyone will hold thismarket portfolio Market Risk = Risk added by any investment to the market portfolio: Beta of asset relative to Market portfolio (from a regression)

The APM If there are no arbitrage opportunities then the market risk of any asset must be captured by betas relative to factors that affect all investments. Market Risk = Risk exposures of any asset to market factors

Multi-Factor Models Since market risk affects most or all investments, it must come from macro economic factors. Market Risk = Risk exposures of any asset to macro economic factors.

Betas of asset relative to unspecified market factors (from a factor analysis)

Betas of assets relative to specified macro economic factors (from a regression)

Proxy Models In an efficient market, differences in returns across long periods must be due to market risk differences. Looking for variables correlated with returns should then give us proxies for this risk. Market Risk = Captured by the Proxy Variable(s) Equation relating returns to proxy variables (from a regression)

As noted in Figure 4.9, all the risk and return models developed in this chapter make some assumptions in common. They all assume that only market risk is rewarded and they derive the expected return as a function of measures of this risk. The capital asset pricing model makes the most restrictive assumptions about how markets work but arrives at the simplest model, with only one factor driving risk and requiring estimation. The arbitrage pricing model makes fewer assumptions but arrives at a more complicated model, at least in terms of the parameters that require estimation. The capital asset pricing model can be considered a specialized case of the arbitrage pricing model, where there is only one underlying factor and it is completely measured by the market index. In general, the CAPM has the advantage of being a simpler model to estimate and to use, but it will underperform the richer APM when an investment is sensitive to economic factors not well represented in the market index. For instance, oil company stocks, which derive most of their risk from oil price movements, tend to have low CAPM betas and low expected

25 returns. Using an arbitrage pricing model, where one of the factors may measure oil and other commodity price movements, will yield a better estimate of risk and higher expected return for these firms6. Which of these models works the best? Is beta a good proxy for risk and is it correlated with expected returns? The answers to these questions have been debated widely in the last two decades. The first tests of the CAPM suggested that betas and returns were positively related, though other measures of risk (such as variance) continued to explain differences in actual returns. This discrepancy was attributed to limitations in the testing techniques. In 1977, Roll, in a seminal critique of the model's tests, suggested that since the market portfolio could never be observed, the CAPM could never be tested, and all tests of the CAPM were therefore joint tests of both the model and the market portfolio used in the tests. In other words, all that any test of the CAPM could show was that the model worked (or did not) given the proxy used for the market portfolio. It could therefore be argued that in any empirical test that claimed to reject the CAPM, the rejection could be of the proxy used for the market portfolio rather than of the model itself. Roll noted that there was no way to ever prove that the CAPM worked and thus no empirical basis for using the model. Fama and French (1992) examined the relationship between betas and returns between 1963 and 1990 and concluded that there is no relationship. These results have been contested on three fronts. First, Amihud, Christensen, and Mendelson (1992), used the same data, performed different statistical tests and showed that differences in betas did, in fact, explain differences in returns during the time period. Second, Kothari and Shanken (1995) estimated betas using annual data, instead of the shorter intervals used in many tests, and concluded that betas do explain a significant proportion of the differences in returns across investments. Third, Chan and Lakonishok (1993) looked at a much longer time series of returns from 1926 to 1991 and found that the positive relationship between betas and returns broke down only in the period after 1982. They also find that betas are a useful guide to risk in extreme market conditions, with the riskiest firms (the

6

Weston and Copeland used both approaches to estimate the cost of equity for oil companies in 1989 and came up with 14.4% with the CAPM and 19.1% using the arbitrage pricing model.

26 10% with highest betas) performing far worse than the market as a whole, in the ten worst months for the market between 1926 and 1991 (See Figure 4.6). Nov 1973

Mar 1980

Oct 1932

Feb 1933

Sep 1937

Apr 1932

May 1932

May 1940

Oct 1987

Mar 1988

Figure 4.6: Returns and Betas: Ten Worst Months between 1926 and 1991

High-beta stocks Whole Market Low-beta stocks

Source: Chan and Lakonishok While the initial tests of the APM suggested that they might provide more promise in terms of explaining differences in returns, a distinction has to be drawn between the use of these models to explain differences in past returns and their use to predict expected returns in the future. The competitors to the CAPM clearly do a much better job at explaining past returns since they do not constrain themselves to one factor, as the CAPM does. This extension to multiple factors does become more of a problem when we try to project expected returns into the future, since the betas and premiums of each of these factors now have to be estimated. Because the factor premiums and betas are themselves volatile, the estimation error may eliminate the benefits that could be gained by moving from the CAPM to more complex models. The regression models that were offered as an alternative also have an estimation problem, since the variables that work best as proxies for market risk in one period (such as market capitalization) may not be the ones that work in the next period.

27 Ultimately, the survival of the capital asset pricing model as the default model for risk in real world applications is a testament to both its intuitive appeal and the failure of more complex models to deliver significant improvement in terms of estimating expected returns. We would argue that a judicious use of the capital asset pricing model, without an over reliance on historical data, is still the most effective way of dealing with risk in modern corporate finance. Models of Default Risk The risk that we have discussed hitherto in this chapter relates to cash flows on investments being different from expected cash flows. There are some investments, however, in which the cash flows are promised when the investment is made. This is the case, for instance, when you lend to a business or buy a corporate bond; the borrower may default on interest and principal payments on the borrowing. Generally speaking, borrowers with higher default risk should pay higher interest rates on their borrowing than those with lower default risk. This section examines the measurement of default risk and the relationship of default risk to interest rates on borrowing. In contrast to the general risk and return models for equity, which evaluate the effects of market risk on expected returns, models of default risk measure the consequences of firm-specific default risk on promised returns. While diversification can be used to explain why firm-specific risk will not be priced into expected returns for equities, the same rationale cannot be applied to securities that have limited upside potential and much greater downside potential from firm-specific events. To see what we mean by limited upside potential, consider investing in the bond issued by a company. The coupons are fixed at the time of the issue and these coupons represent the promised cash flow on the bond. The best case scenario for you as an investor is that you receive the promised cash flows; you are not entitled to more than these cash flows even if the company is wildly successful. All other scenarios contain only bad news, though in varying degrees, with the delivered cash flows being less than the promised cash flows. Consequently, the expected return on a corporate bond is likely to reflect the firmspecific default risk of the firm issuing the bond.

28 The Determinants of Default Risk The default risk of a firm is a function of two variables. The first is the firm’s capacity to generate cash flows from operations and the second is its financial obligations – including interest and principal payments7.

Firms that generate high cash flows

relative to their financial obligations should have lower default risk than firms that generate low cash flows relative to their financial obligations. Thus, firms with significant existing investments, which generate relatively high cash flows, will have lower default risk than firms that do not. In addition to the magnitude of a firm’s cash flows, the default risk is also affected by the volatility in these cash flows. The more stability there is in cash flows the lower the default risk in the firm. Firms that operate in predictable and stable businesses will have lower default risk than will other similar firms that operate in cyclical or volatile businesses. Most models of default risk use financial ratios to measure the cash flow coverage (i.e., the magnitude of cash flows relative to obligations) and control for industry effects to evaluate the variability in cash flows. Bond Ratings and Interest rates The most widely used measure of a firm's default risk is its bond rating, which is generally assigned by an independent ratings agency. The two best known are Standard and Poor’s and Moody’s. Thousands of companies are rated by these two agencies and their views carry significant weight with financial markets. The Ratings Process The process of rating a bond usually starts when the issuing company requests a rating from a bond ratings agency. The ratings agency then collects information from both publicly available sources, such as financial statements, and the company itself and makes a decision on the rating. If the company disagrees with the rating, it is given the

7

Financial obligation refers to any payment that the firm has legally obligated itself to make, such as interest and principal payments. It does not include discretionary cash flows, such as dividend payments or new capital expenditures, which can be deferred or delayed, without legal consequences, though there may be economic consequences.

29 opportunity to present additional information. This process is presented schematically for one ratings agency, Standard and Poors (S&P), in Figure 4.7.

THE RATINGS PROCESS Issuer or authorized representative request rating

Requestor completes S&P rating request form and issue is entered into S&P's administrative and control systems.

S&P assigns analytical team to issue

Final Analytical review and preparation of rating committee presentation

Presentation of the analysis to the S&P rating commitee Discussion and vote to determine rating

Notification of rating decision to issuer or its authorized representative

Does issuer wish to appeal No by furnishing additional information? Yes

Analysts research S&P library, internal files and data bases

Issuer meeting: presentation to S&P personnel or S&P personnel tour issuer facilities

Format notification to issuer or its authorized representative: Rating is released

Presentation of additional information to S&P rating committee: Discussion and vote to confirm or modify rating. The ratings assigned by these agencies are letter ratings. A rating of AAA from Standard and Poor’s and Aaa from Moody’s represents the highest rating granted to firms that are viewed as having the lowest default risk. As the default risk increases, the ratings decrease

30 toward D for firms in default (Standard and Poor’s). A rating at or above BBB by Standard and Poor’s is categorized as investment grade, reflecting the view of the ratings agency that there is relatively little default risk in investing in bonds issued by these firms. Determinants of Bond Ratings The bond ratings assigned by ratings agencies are primarily based upon publicly available information, though private information conveyed by the firm to the rating agency does play a role. The rating assigned to a company's bonds will depend in large part on financial ratios that measure the capacity of the company to meet debt payments and generate stable and predictable cash flows. While a multitude of financial ratios exist, table 4.6 summarizes some of the key ratios used to measure default risk. Table 4.6: Financial Ratios used to measure Default Risk Ratio Pretax Interest Coverage EBITDA Interest Coverage

Funds from Operations / Total

Description

Pretax Income from Continuing Operations + Interest Expense Gross Interest EBITDA Gross Interest

Net Income from Continuing Operations + Depreciation Total Debt

Debt Free Operating Cashflow/ Total Debt

Pretax Return on Permanent Capital

Funds from Operations-Capital Expenditures   -Change in Working Capital  Total Debt Pretax Income from Continuing Operations + Interest Expense  Average of Beginning of the year and End of the year of long and   short term debt, minority interest and Shareholders Equity  )

Operating Income/Sales

Sales-COGS(before depreciation) -Selling Expenses -   Administrative Expenses -R&D Expenses  Sales

31 Long Term Debt Long Term Debt + Equity

Long Term Debt/ Capital

Total Debt Total Debt + Equity

Total Debt/Capitalization

Source: Standard and Poors There is a strong relationship between the bond rating a company receives and its performance on these financial ratios. Table 4.7 provides a summary of the median ratios8 from 1998 to 2000 for different S&P ratings classes for manufacturing firms. Table 4.7: Financial Ratios by Bond Rating: 1998-2000 AAA

AA

A

BBB

BB

B

CCC

17.5

10.8

6.8

3.9

2.3

1.0

0.2

EBITDA interest cov. 21.8

14.6

9.6

6.1

3.8

2.0

1.4

Funds flow/total debt

55.8

46.1

30.5

19.2

9.4

5.8

24.6

15.6

6.6

1.9

–4.5

-14.0

EBIT interest cov. (x)

Free

oper.

105.8

cash 55.4

flow/total debt (%) Return on capital (%)

28.2

22.9

19.9

14.0

11.7

7.2

0.5

Oper.income/sales

29.2

21.3

18.3

15.3

15.4

11.2

13.6

15.2

26.4

32.5

41.0

55.8

70.7

80.3

Total Debt/ Capital 26.9

35.6

40.1

47.4

61.3

74.6

89.4

34

150

234

276

240

23

(%) Long-term debt/capital (%)

(%) Number of firms

10

Source: Standard and Poors Note that the pre-tax interest coverage ratio (EBIT) and the EBITDA interest coverage ratio are stated in terms of times interest earned, whereas the rest of the ratios are stated in percentage terms. Not surprisingly, firms that generate income and cash flows significantly higher than debt payments, that are profitable and that have low debt ratios are more likely to be

32 highly rated than are firms that do not have these characteristics. There will be individual firms whose ratings are not consistent with their financial ratios, however, because the ratings agency does add subjective judgments into the final mix. Thus, a firm which performs poorly on financial ratios but is expected to improve its performance dramatically over the next period may receive a higher rating than is justified by its current financials. For most firms, however, the financial ratios should provide a reasonable basis for guessing at the bond rating.

ratingfins.xls: There is a dataset on the web that summarizes key financial ratios by bond rating class for the United States in the most recent period for which the data is available. Bond Ratings and Interest Rates The interest rate on a corporate bond should be a function of its default risk, which is measured by its rating. If the rating is a good measure of the default risk, higher rated bonds should be priced to yield lower interest rates than would lower rated bonds. In fact, in chapter 5, we will define the difference between the interest rate on a bond with default risk and a default-free government bond to be the default spread. This default spread will vary by maturity of the bond and can also change from period to period, depending on economic conditions. In chapter 7, we will consider how best to estimate these default spreads and how they might vary over time. Summary Risk, as we define it in finance, is measured based upon deviations of actual returns on an investment from its' expected returns. There are two types of risk. The first, which we call equity risk, arises in investments where there are no promised cash flows, but there are expected cash flows. The second, default risk, arises on investments with promised cash flows. On investments with equity risk, the risk is best measured by looking at the variance of actual returns around the expected returns, with greater variance indicating

8

See the Standard and Poor’s online site: http://www.standardandpoors.com/ratings/criteria/index.htm

33 greater risk. This risk can be broken down into risk that affects one or a few investments, which we call firm specific risk, and risk that affects many investments, which we refer to as market risk. When investors diversify, they can reduce their exposure to firm specific risk. By assuming that the investors who trade at the margin are well diversified, we conclude that the risk we should be looking at with equity investments is the market risk. The different models of equity risk introduced in this chapter share this objective of measuring market risk, but they differ in the way they do it. In the capital asset pricing model, exposure to market risk is measured by a market beta, which estimates how much risk an individual investment will add to a portfolio that includes all traded assets. The arbitrage pricing model and the multi-factor model allow for multiple sources of market risk and estimate betas for an investment relative to each source. Regression or proxy models for risk look for firm characteristics, such as size, that have been correlated with high returns in the past and use these to measure market risk. In all these models, the risk measures are used to estimate the expected return on an equity investment. This expected return can be considered the cost of equity for a company. On investments with default risk, risk is measured by the likelihood that the promised cash flows might not be delivered. Investments with higher default risk should have higher interest rates and the premium that we demand over a riskless rate is the default premium. For most US companies, default risk is measured by rating agencies in the form of a company rating; these ratings determine, in large part, the interest rates at which these firms can borrow. Even in the absence of ratings, interest rates will include a default premium that reflects the lenders’ assessments of default risk. These default-risk adjusted interest rates represent the cost of borrowing or debt for a business

34

Problems 1. The following table lists the stock prices for Microsoft from 1989 to 1998. The company did not pay any dividends during the period Year

Price

1989

$

1.20

1990

$

2.09

1991

$

4.64

1992

$

5.34

1993

$

5.05

1994

$

7.64

1995

$

10.97

1996

$

20.66

1997

$

32.31

1998

$

69.34

a. Estimate the average annual return you would have made on your investment. b. Estimate the standard deviation and variance in the annual returns. c. If you were investing in Microsoft today, would you expect the historical standard deviations and variances to continue to hold? Why or why not? 2. Unicom is a regulated utility serving Northern Illinois. The following table lists the stock prices and dividends on Unicom from 1989 to 1998. Year

Price

Dividends

1989

$

36.10

$

3.00

1990

$

33.60

$

3.00

1991

$

37.80

$

3.00

1992

$

30.90

$

2.30

1993

$

26.80

$

1.60

1994

$

24.80

$

1.60

1995

$

31.60

$

1.60

35 1996

$

28.50

$

1.60

1997

$

24.25

$

1.60

1998

$

35.60

$

1.60

a. Estimate the average annual return you would have made on your investment. b. Estimate the standard deviation and variance in the annual returns. c. If you were investing in Unicom today, would you expect the historical standard deviations and variances to continue to hold? Why or why not? 3. The following table summarizes the annual returns you would have made on two companies – Scientific Atlanta, a satellite and data equipment manufacturer, and AT&T, the telecomm giant, from 1988 to 1998. Year

Scientific Atlanta

AT&T

1989

80.95%

58.26%

1990

-47.37%

-33.79%

1991

31%

29.88%

1992

132.44%

30.35%

1993

32.02%

2.94%

1994

25.37%

-4.29%

1995

-28.57%

28.86%

1996

0.00%

-6.36%

1997

11.67%

48.64%

1998

36.19%

23.55%

a. Estimate the average and standard deviation in annual returns in each company. b. Estimate the covariance and correlation in returns between the two companies. c. Estimate the variance of a portfolio composed, in equal parts, of the two investments. 4. You are in a world where there are only two assets, gold and stocks. You are interested in investing your money in one, the other or both assets. Consequently you collect the following data on the returns on the two assets over the last six years.

36 Gold

Stock Market

Average return

8%

20%

Standard deviation

25%

22%

Correlation

-0.4

a. If you were constrained to pick just one, which one would you choose? b. A friend argues that this is wrong. He says that you are ignoring the big payoffs that you can get on gold. How would you go about alleviating his concern? c. How would a portfolio composed of equal proportions in gold and stocks do in terms of mean and variance? d. You now learn that GPEC (a cartel of gold-producing countries) is going to vary the amount of gold it produces with stock prices in the US. (GPEC will produce less gold when stock markets are up and more when it is down.) What effect will this have on your portfolios? Explain. 5. You are interested in creating a portfolio of two stocks – Coca Cola and Texas Utilities. Over the last decade, an investment in Coca Cola stock would have earned an average annual return of 25% with a standard deviation in returns of 36%. An investment in Texas Utilities stock would have earned an average annual return of 12%, with a standard deviation of 22%. The correlation in returns across the two stocks is 0.28. a. Assuming that the average and standard deviation, estimated using past returns, will continue to hold in the future, estimate the average returns and standard deviation of a portfolio composed 60% of Coca Cola and 40% of Texas Utilities stock. b. Estimate the minimum variance portfolio. c. Now assume that Coca Cola’s international diversification will reduce the correlation to 0.20, while increasing Coca Cola’s standard deviation in returns to 45%. Assuming all of the other numbers remain unchanged, answer (a) and (b). 6. Assume that you have half your money invested in Times Mirror, the media company, and the other half invested in Unilever, the consumer product giant. The expected returns and standard deviations on the two investments are summarized below:

Expected Return

Times Mirror

Unilever

14%

18%

37 Standard Deviation

25%

40%

Estimate the variance of the portfolio as a function of the correlation coefficient (Start with –1 and increase the correlation to +1 in 0.2 increments). 7. You have been asked to analyze the standard deviation of a portfolio composed of the following three assets: Investment

Expected Return

Standard Deviation

Sony Corporation

11%

23%

Tesoro Petroleum

9%

27%

Storage Technology

16%

50%

You have also been provided with the correlations across these three investments: Sony

Tesoro

Storage Tech

Sony

1.00

-0.15

0.20

Tesoro

-0.15

1.00

-0.25

Storage Tech

0.20

-0.25

1.00

Estimate the variance of a portfolio equally weighted across all three assets.

9. Assume that the average variance of return for an individual security is 50 and that the average covariance is 10. What is the expected variance of a portfolio of 5, 10, 20, 50 and 100 securities. How many securities need to be held before the risk of a portfolio is only 10% more than the minimum? 10. Assume you have all your wealth (a million dollars) invested in the Vanguard 500 index fund and that you expect to earn an annual return of 12% with a standard deviation in returns of 25%. Since you have become more risk averse, you decide to shift $200,000 from the Vanguard 500 index fund to treasury bills. The T.bill rate is 5%. Estimate the expected return and standard deviation of your new portfolio. 11. Every investor in the capital asset pricing model owns a combination of the market portfolio and a riskless asset. Assume that the standard deviation of the market portfolio is 30% and that the expected return on the portfolio is 15%. What proportion of the following investor’s wealth

38 would you suggest investing in the market portfolio and what proportion in the riskless asset? (The riskless asset has an expected return of 5%) a. an investor who desires a portfolio with no standard deviation b. an investor who desires a portfolio with a standard deviation of 15% c. an investor who desires a portfolio with a standard deviation of 30% d. an investor who desires a portfolio with a standard deviation of 45% e. an investor who desires a portfolio with an expected return of 12% 12. The following table lists returns on the market portfolio and on Scientific Atlanta, each year from 1989 to 1998. Year

Scientific Atlanta

Market Portfolio

1989

80.95%

31.49%

1990

-47.37%

-3.17%

1991

31%

30.57%

1992

132.44%

7.58%

1993

32.02%

10.36%

1994

25.37%

2.55%

1995

-28.57%

37.57%

1996

0.00%

22.68%

1997

11.67%

33.10%

1998

36.19%

28.32%

a. Estimate the covariance in returns between Scientific Atlanta and the market portfolio. b. Estimate the variances in returns on both investments. c. Estimate the beta for Scientific Atlanta. 13. United Airlines has a beta of 1.50. The standard deviation in the market portfolio is 22% and United Airlines has a standard deviation of 66% a. Estimate the correlation between United Airlines and the market portfolio. b. What proportion of United Airlines’ risk is market risk?

39 14. You are using the arbitrage pricing model to estimate the expected return on Bethlehem Steel, and have derived the following estimates for the factor betas and risk premia: Factor

Beta

Risk Premia

1

1.2

2.5%

2

0.6

1.5%

3

1.5

1.0%

4

2.2

0.8%

5

0.5

1.2%

a. Which risk factor is Bethlehem Steel most exposed to? Is there any way, within the arbitrage pricing model, to identify the risk factor? b. If the riskfree rate is 5%, estimate the expected return on Bethlehem Steel. c. Now assume that the beta in the capital asset pricing model for Bethlehem Steel is 1.1 and that the risk premium for the market portfolio is 5%. Estimate the expected return using the CAPM. d. Why are the expected returns different between the two models? 15. You are using the multi-factor model to estimate the expected return on Emerson Electric, and have derived the following estimates for the factor betas and risk premia: Macro-economic Factor

Measure

Beta

Risk Premia (Rfactor-Rf)

Level of Interest rates

T.bond rate

0.5

1.8%

Term Structure

T.bond rate – T.bill rate

1.4

0.6%

Inflation rate

CPI

1.2

1.5%

Economic Growth

GNP Growth rate

1.8

4.2%

With a riskless rate of 6%, estimate the expected return on Emerson Electric. 16. The following equation is reproduced from the study by Fama and French of returns between 1963 and 1990.  BV  R t = 0.0177 − 0.11 ln (MV )+ 0.35ln    MV 

where MV is the market value of equity in hundreds of millions of dollar and BV is the book value of equity in hundreds of millions of dollars. The return is a monthly return.

40 a. Estimate the expected annual return on Lucent Technologies. The market value of equity is $240 billion and the book value of equity is $13.5 billion. b. Lucent Technologies has a beta of 1.55. If the riskless rate is 6%, and the risk premium for the market portfolio is 5.5%, estimate the expected return. c. Why are the expected returns different under the two approaches?

1

CHAPTER 5 OPTION PRICING THEORY AND MODELS In general, the value of any asset is the present value of the expected cash flows on that asset. In this section, we will consider an exception to that rule when we will look at assets with two specific characteristics: •

They derive their value from the values of other assets.

•

The cash flows on the assets are contingent on the occurrence of specific events.

These assets are called options and the present value of the expected cash flows on these assets will understate their true value. In this section, we will describe the cash flow characteristics of options, consider the factors that determine their value and examine how best to value them. Basics of Option Pricing An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (called a strike price or an exercise price) at or before the expiration date of the option. Since it is a right and not an obligation, the holder can choose not to exercise the right and allow the option to expire. There are two types of options: call options and put options. Call and Put Options: Description and Payoff Diagrams A call option gives the buyer of the option the right to buy the underlying asset at a fixed price, called the strike or the exercise price, at any time prior to the expiration date of the option. The buyer pays a price for this right. If at expiration, the value of the asset is less than the strike price, the option is not exercised and expires worthless. If, on the other hand, the value of the asset is greater than the strike price, the option is exercised the buyer of the option buys the asset [stock] at the exercise price. And the difference between the asset value and the exercise price comprises the gross profit on the option investment. The net profit on the investment is the difference between the gross profit and the price paid for the call initially. A payoff diagram illustrates the cash payoff on an option at expiration. For a call, the net payoff is negative (and equal to the price paid for the call) if the value of the

2 underlying asset is less than the strike price. If the price of the underlying asset exceeds the strike price, the gross payoff is the difference between the value of the underlying asset and the strike price and the net payoff is the difference between the gross payoff and the price of the call. This is illustrated in figure 5.1 below: Figure 5.1: Payoff on Call Option Net Payoff on call option

If asset value<strike price, you lose is what you paid for the call Strike Price Price of Underlying Asset

A put option gives the buyer of the option the right to sell the underlying asset at a fixed price, again called the strike or exercise price, at any time prior to the expiration date of the option. The buyer pays a price for this right. If the price of the underlying asset is greater than the strike price, the option will not be exercised and will expire worthless. If on the other hand, the price of the underlying asset is less than the strike price, the owner of the put option will exercise the option and sell the stock a the strike price, claiming the difference between the strike price and the market value of the asset as the gross profit. Again, netting out the initial cost paid for the put yields the net profit from the transaction. A put has a negative net payoff if the value of the underlying asset exceeds the strike price, and has a gross payoff equal to the difference between the strike price and the value of the underlying asset if the asset value is less than the strike price. This is summarized in figure 5.2 below.

3 Figure 5.2: Payoff on Put Option Net Payoff on put

If asset value>strike price, you lose what you paid for the put. Strike Price Price of Underlying Asset

Determinants of Option Value The value of an option is determined by a number of variables relating to the underlying asset and financial markets. 1. Current Value of the Underlying Asset: Options are assets that derive value from an underlying asset. Consequently, changes in the value of the underlying asset affect the value of the options on that asset. Since calls provide the right to buy the underlying asset at a fixed price, an increase in the value of the asset will increase the value of the calls. Puts, on the other hand, become less valuable as the value of the asset increase. 2. Variance in Value of the Underlying Asset: The buyer of an option acquires the right to buy or sell the underlying asset at a fixed price. The higher the variance in the value of the underlying asset, the greater will the value of the option be1. This is true for both calls and puts. While it may seem counter-intuitive that an increase in a risk measure (variance) should increase value, options are different from other securities since buyers of options can never lose more than the price they pay for them; in fact, they have the potential to earn significant returns from large price movements. 3. Dividends Paid on the Underlying Asset: The value of the underlying asset can be expected to decrease if dividend payments are made on the asset during the life of the

4 option. Consequently, the value of a call on the asset is a decreasing function of the size of expected dividend payments, and the value of a put is an increasing function of expected dividend payments. There is a more intuitive way of thinking about dividend payments, for call options. It is a cost of delaying exercise on in-the-money options. To see why, consider an option on a traded stock. Once a call option is in the money, i.e, the holder of the option will make a gross payoff by exercising the option, exercising the call option will provide the holder with the stock and entitle him or her to the dividends on the stock in subsequent periods. Failing to exercise the option will mean that these dividends are foregone. 4. Strike Price of Option: A key characteristic used to describe an option is the strike price. In the case of calls, where the holder acquires the right to buy at a fixed price, the value of the call will decline as the strike price increases. In the case of puts, where the holder has the right to sell at a fixed price, the value will increase as the strike price increases. 5. Time To Expiration On Option: Both calls and puts become more valuable as the time to expiration increases. This is because the longer time to expiration provides more time for the value of the underlying asset to move, increasing the value of both types of options. Additionally, in the case of a call, where the buyer has to pay a fixed price at expiration, the present value of this fixed price decreases as the life of the option increases, increasing the value of the call. 6. Riskless Interest Rate Corresponding To Life Of Option: Since the buyer of an option pays the price of the option up front, an opportunity cost is involved. This cost will depend upon the level of interest rates and the time to expiration on the option. The riskless interest rate also enters into the valuation of options when the present value of the exercise price is calculated, since the exercise price does not have to be paid (received) until expiration on calls (puts). Increases in the interest rate will increase the value of calls and reduce the value of puts.

1 Note, though, that higher variance can reduce the value of the underlying asset. As a call option becomes more in the money, the more it resembles the underlying asset. For very deep in-the-money call options, higher variance can reduce the value of the option.]

5 Table 5.1 below summarizes the variables and their predicted effects on call and put prices. Table 5.1: Summary of Variables Affecting Call and Put Prices Effect on Factor

Call Value

Put Value

Increase in underlying asset’s value

Increases

Decreases

Increase in strike price

Decreases

Increases

Increase in variance of underlying asset

Increases

Increases

Increase in time to expiration

Increases

Increases

Increase in interest rates

Increases

Decreases

Increase in dividends paid

Decreases

Increases

American Versus European Options: Variables Relating To Early Exercise A primary distinction between American and European options is that American options can be exercised at any time prior to its expiration, while European options can be exercised only at expiration. The possibility of early exercise makes American options more valuable than otherwise similar European options; it also makes them more difficult to value. There is one compensating factor that enables the former to be valued using models designed for the latter. In most cases, the time premium associated with the remaining life of an option and transactions costs makes early exercise sub-optimal. In other words, the holders of in-the-money options will generally get much more by selling the option to someone else than by exercising the options. While early exercise is not optimal generally, there are at least two exceptions to this rule. One is a case where the underlying asset pays large dividends, thus reducing the value of the asset, and any call options on that asset. In this case, call options may be exercised just before an ex-dividend date if the time premium on the options is less than the expected decline in asset value as a consequence of the dividend payment. The other exception arises when an investor holds both the underlying asset and deep in-the-money puts on that asset at a time when interest rates are high. In this case, the time premium on the put may be less than the potential gain from exercising the put early and earning interest on the exercise price.

6 Option Pricing Models Option pricing theory has made vast strides since 1972, when Black and Scholes published their path-breaking paper providing a model for valuing dividend-protected European options. Black and Scholes used a “replicating portfolio” –– a portfolio composed of the underlying asset and the risk-free asset that had the same cash flows as the option being valued –– to come up with their final formulation. While their derivation is mathematically complicated, there is a simpler binomial model for valuing options that draws on the same logic. The Binomial Model The binomial option pricing model is based upon a simple formulation for the asset price process in which the asset, in any time period, can move to one of two possible prices. The general formulation of a stock price process that follows the binomial is shown in figure 5.3. Figure 5.3: General Formulation for Binomial Price Path

Su

2

Su Sud S Sd 2

Sd

In this figure, S is the current stock price; the price moves up to Su with probability p and down to Sd with probability 1-p in any time period.

7 Creating A Replicating Portfolio The objective in a replicating portfolio is to use a combination of risk-free borrowing/lending and the underlying asset to create a portfolio that has the same cash flows as the option being valued. The principles of arbitrage apply here and the value of the option must be equal to the value of the replicating portfolio. In the case of the general formulation above, where stock prices can either move up to Su or down to Sd in any time period, the replicating portfolio for a call with strike price K will involve borrowing $B and acquiring

of the underlying asset, where:

∆ = Number of units of the underlying asset bought =

C u − Cd Su - Sd

where, Cu = Value of the call if the stock price is Su Cd = Value of the call if the stock price is Sd In a multi-period binomial process, the valuation has to proceed iteratively, i.e., starting with the last time period and moving backwards in time until the current point in time. The portfolios replicating the option are created at each step and valued, providing the values for the option in that time period. The final output from the binomial option pricing model is a statement of the value of the option in terms of the replicating portfolio, composed of

shares (option delta) of the underlying asset and risk-free

borrowing/lending. Value of the call = Current value of underlying asset * Option Delta - Borrowing needed to replicate the option Illustration 5.1: Binomial Option Valuation Assume that the objective is to value a call with a strike price of 50, which is expected to expire in two time periods, on an underlying asset whose price currently is 50 and is expected to follow a binomial process:

8

Now assume that the interest rate is 11%. In addition, define = Number of shares in the replicating portfolio B = Dollars of borrowing in replicating portfolio The objective is to combine

shares of stock and B dollars of borrowing to replicate the

cash flows from the call with a strike price of 50. This can be done iteratively, starting with the last period and working back through the binomial tree. Step 1: Start with the end nodes and work backwards:

9 Thus, if the stock price is $70 at t=1, borrowing $45 and buying one share of the stock will give the same cash flows as buying the call. The value of the call at t=1, if the stock price is $70, is: Value of Call = Value of Replicating Position = 70∆ − B = (70 )(1)− 45 = 25 Considering the other leg of the binomial tree at t=1,

If the stock price is 35 at t=1, then the call is worth nothing. Step 2: Move backwards to the earlier time period and create a replicating portfolio that will provide the cash flows the option will provide.

In other words, borrowing $22.5 and buying 5/7 of a share will provide the same cash flows as a call with a strike price of $50. The value of the call therefore has to be the same as the value of this position.

10 Value

of

Call

=

Value

of

replicating

position

=

5 5  (Current Stock Price )− 22.5 =  (50 )− 22.5 = 13.21 7 7

The Determinants of Value The binomial model provides insight into the determinants of option value. The value of an option is not determined by the expected price of the asset but by its current price, which, of course, reflects expectations about the future. This is a direct consequence of arbitrage. If the option value deviates from the value of the replicating portfolio, investors can create an arbitrage position, i.e., one that requires no investment, involves no risk, and delivers positive returns. To illustrate, if the portfolio that replicates the call costs more than the call does in the market, an investor could buy the call, sell the replicating portfolio and guarantee the difference as a profit. The cash flows on the two positions will offset each other, leading to no cash flows in subsequent periods. The option value also increases as the time to expiration is extended, as the price movements (u and d) increase, and with increases in the interest rate. While the binomial model provides an intuitive feel for the determinants of option value, it requires a large number of inputs, in terms of expected future prices at each node. As we make time periods shorter in the binomial model, we can make one of two assumptions about asset prices. We can assume that price changes become smaller as periods get shorter; this leads to price changes becoming infinitesimally small as time periods approach zero, leading to a continuous price process. Alternatively, we can assume that price changes stay large even as the period gets shorter; this leads to a jump price process, where prices can jump in any period. In this section, we consider the option pricing models that emerge with each of these assumptions. The Black-Scholes Model When the price process is continuous, i.e. price changes becomes smaller as time periods get shorter, the binomial model for pricing options converges on the BlackScholes model. The model, named after its co-creators, Fischer Black and Myron Scholes, allows us to estimate the value of any option using a small number of inputs and has been shown to be remarkably robust in valuing many listed options.

11 The Model While the derivation of the Black-Scholes model is far too complicated to present here, it is also based upon the idea of creating a portfolio of the underlying asset and the riskless asset with the same cashflows and hence the same cost as the option being valued. The value of a call option in the Black-Scholes model can be written as a function of the five variables: S = Current value of the underlying asset K = Strike price of the option t = Life to expiration of the option r = Riskless interest rate corresponding to the life of the option σ2 = Variance in the ln(value) of the underlying asset The value of a call is then: Value of call = S N (d1) - K e-rt N(d2) where 2  S ln  + ( r + )t K 2 d1 = t

d 2 = d1 −

t

Note that e-rt is the present value factor and reflects the fact that the exercise price on the call option does not have to be paid until expiration. N(d1) and N(d 2) are probabilities, estimated by using a cumulative standardized normal distribution and the values of d 1 and d2 obtained for an option. The cumulative distribution is shown in Figure 5.4:

12 Figure 5.4: Cumulative Normal Distribution N(d 1)

d1 In approximate terms, these probabilities yield the likelihood that an option will generate positive cash flows for its owner at exercise, i.e., when S>K in the case of a call option and when K>S in the case of a put option. The portfolio that replicates the call option is created by buying N(d1) units of the underlying asset, and borrowing Ke-rt N(d2). The portfolio will have the same cash flows as the call option and thus the same value as the option. N(d1), which is the number of units of the underlying asset that are needed to create the replicating portfolio, is called the option delta. A note on estimating the inputs to the Black-Scholes model The Black-Scholes model requires inputs that are consistent on time measurement. There are two places where this affects estimates. The first relates to the fact that the model works in continuous time, rather than discrete time. That is why we use the continuous time version of present value (exp-rt ) rather than the discrete version ((1+r)-t). It also means that the inputs such as the riskless rate have to be modified to make the continuous time inputs. For instance, if the one-year treasury bond rate is 6.2%, the riskfree rate that is used in the Black Scholes model should be Continuous Riskless rate = ln (1 + Discrete Riskless Rate) = ln (1.062) = .06015 or 6.015% The second relates to the period over which the inputs are estimated. For instance, the rate above is an annual rate. The variance that is entered into the model also has to be an

13 annualized variance. The variance, estimated from ln(asset prices), can be annualized easily because variances are linear in time if the serial correlation is zero. Thus, if monthly (weekly) prices are used to estimate variance, the variance is annualized by multiplying by twelve (fifty two).

Illustration 5.2: Valuing an option using the Black-Scholes Model On March 6, 2001, Cisco Systems was trading at $13.62. We will attempt to value a July 2001 call option with a strike price of $15, trading on the CBOT on the same day for $2.00. The following are the other parameters of the options: •

The annualized standard deviation in Cisco Systems stock price over the previous year was 81.00%. This standard deviation is estimated using weekly stock prices over the year and the resulting number was annualized as follows: Weekly standard deviation = 1.556% Annualized standard deviation =1.556%*52 = 81%

•

The option expiration date is Friday, July 20, 2001. There are 103 days to expiration.

•

The annualized treasury bill rate corresponding to this option life is 4.63%.

The inputs for the Black-Scholes model are as follows: Current Stock Price (S) = $13.62 Strike Price on the option = $15.00 Option life = 103/365 = 0.2822 Standard Deviation in ln(stock prices) = 81% Riskless rate = 4.63% Inputting these numbers into the model, we get 2 (0.81)   13.62   ln (0 .2822 )  +  0.0463 + 2   15.00   d1 = = 0.0212 0.81 0.2822

d 2 = 0 .0212 - 0.81 0.2822 = -0.4091

Using the normal distribution, we can estimate the N(d1) and N(d2)

14 N(d1) = 0.5085 N(d2) = 0.3412 The value of the call can now be estimated: Value of Cisco Call = S N (d1) - K e-rt N(d2) = (13.62 )(0.5085 )- 15 e -(0.0463 )(0.2822 )(0.3412 )= 1.87 Since the call is trading at $2.00, it is slightly overvalued, assuming that the estimate of standard deviation used is correct. Implied Volatility The only input on which there can be significant disagreement among investors is the variance. While the variance is often estimated by looking at historical data, the values for options that emerge from using the historical variance can be different from the market prices. For any option, there is some variance at which the estimated value will be equal to the market price. This variance is called an implied variance. Consider the Cisco option valued in the last illustration. With a standard deviation of 81%, we estimated the value of the call option with a strike price of $15 to be $1.87. Since the market price is higher than the calculated value, we tried higher standard deviations and at a standard deviation 85.40%, the value of the option is $2.00. This is the implied standard deviation or implied volatility.. Model Limitations and Fixes The Black-Scholes model was designed to value options that can be exercised only at maturity and on underlying assets that do not pay dividends. In addition, options are valued based upon the assumption that option exercise does not affect the value of the underlying asset. In practice, assets do pay dividends, options sometimes get exercised early and exercising an option can affect the value of the underlying asset. Adjustments exist. While they are not perfect, adjustments provide partial corrections to the BlackScholes model. 1. Dividends The payment of a dividend reduces the stock price; note that on the ex-dividend day, the stock price generally declines. Consequently, call options will become less

15 valuable and put options more valuable as expected dividend payments increase. There are two ways of dealing with dividends in the Black Scholes: •

Short-term Options: One approach to dealing with dividends is to estimate the present value of expected dividends that will be paid by the underlying asset during the option life and subtract it from the current value of the asset to use as S in the model. Modified Stock Price = Current Stock Price – Present value of expected dividends during the life of the option

•

Long Term Options: Since it becomes impractical to estimate the present value of dividends as the option life becomes longer, we would suggest an alternate approach. If the dividend yield (y = dividends/current value of the asset) on the underlying asset is expected to remain unchanged during the life of the option, the Black-Scholes model can be modified to take dividends into account. C = S e-yt N(d1) - K e-rt N(d2)

where S ln  + (r -y + K d1 = t d 2 = d1 −

2

2

)t

t

From an intuitive standpoint, the adjustments have two effects. First, the value of the asset is discounted back to the present at the dividend yield to take into account the expected drop in asset value resulting from dividend payments. Second, the interest rate is offset by the dividend yield to reflect the lower carrying cost from holding the asset (in the replicating portfolio). The net effect will be a reduction in the value of calls estimated using this model. stopt.xls: This spreadsheet allows you to estimate the value of a short term option, when the expected dividends during the option life can be estimated. ltopt.xls: This spreadsheet allows you to estimate the value of an option, when the underlying asset has a constant dividend yield.

16 Illustration 5.3: Valuing a short-term option with dividend adjustments – The Black Scholes Correction Assume that it is March 6, 2001 and that AT&T is trading at $20.50 a share. Consider a call option on the stock with a strike price of $20, expiring on July 20, 2001. Using past stock prices, the variance in the log of stock prices for AT&T is estimated at 60%. There is one dividend, amounting to $0.15, and it will be paid in 23 days. The riskless rate is 4.63%. 0.15

Present value of expected dividend =

1.0463

23 365

= 0.15

Dividend-adjusted stock price = $20.50 - $0.15 = $20.35 Time to expiration = 103/365 = 0.2822 Variance in ln(stock prices) = 0.62=0.36 Riskless rate = 4.63% The value from the Black-Scholes is: d1 = 0.2548

N(d1) = 0.6006

d2 = -0.0639

N(d2) = 0.4745

Value of Call = (20.35)(0.6006 )− (20 )e − (0.0463 )(0.2822 )(0.4745 ) = 2.85 The call option was trading at $2.60 on that day. Illustration 5.4: Valuing a long term option with dividend adjustments - Primes and Scores In recent years, the CBOT has introduced longer term call and put options on stocks. On AT&T, for instance, you could have purchased a call expiring on January 17, 2003, on March 6, 2001. The stock price for AT&T is $20.50 (as in the previous example). The following is the valuation of a call option with a strike price of $20. Instead of estimating the present value of dividends over the next two years, we will assume that AT&T’s dividend yield will remain 2.51% over this period and that the riskfree rate for a two-year treasury bond is 4.85%. The inputs to the Black-Scholes model are: S = Current asset value = $20.50 K = Strike Price = $20.00 Time to expiration = 1.8333 years

17 Standard Deviation in ln(stock prices) = 60% Riskless rate = 4.85% Dividend Yield = 2.51% The value from the Black Scholes is: 2 0 .6   20.50   ln (1.8333)  +  0.0485 - 0.0251 + 2   20.00   d1 = = 0.4894 0.6 1.8333

d 2 = 0.4894 − 0.6 1.8333 = −0.3230

N(d1) = 0.6877

N(d2) = 0.6267

Value of Call= (20.50 )e − (0.0251)(1.8333 )(0.6877 )− (20 )e − (0.0485 )(1.8333 ) = 6.63 The call was trading at $5.80 on March 8, 2001.

2. Early Exercise The Black-Scholes model was designed to value options that can be exercised only at expiration. Options with this characteristic are called European options. In contrast, most options that we encounter in practice can be exercised any time until expiration. These options are called American options. The possibility of early exercise makes American options more valuable than otherwise similar European options; it also makes them more difficult to value. In general, though, with traded options, it is almost always better to sell the option to someone else rather than exercise early, since options have a time premium, i.e., they sell for more than their exercise value. There are two exceptions. One occurs when the underlying asset pays large dividends, thus reducing the expected value of the asset. In this case, call options may be exercised just before an ex-dividend date, if the time premium on the options is less than the expected decline in asset value as a consequence of the dividend payment. The other exception arises when an investor holds both the underlying asset and deep in-the-money puts, i.e., puts with strike prices well above the current price of the underlying asset, on that asset and at a time when interest rates are high. In this case, the time premium on the put may be less than the potential gain from exercising the put early and earning interest on the exercise price. There are two basic ways of dealing with the possibility of early exercise. One is to continue to use the unadjusted Black-Scholes model and regard the resulting value as a

18 floor or conservative estimate of the true value. The other is to try to adjust the value of the option for the possibility of early exercise. There are two approaches for doing so. One uses the Black-Scholes to value the option to each potential exercise date. With options on stocks, this basically requires that we value options to each ex-dividend day and choose the maximum of the estimated call values. The second approach is to use a modified version of the binomial model to consider the possibility of early exercise. In this version, the up and down movements for asset prices in each period can be estimated from the variance and the length of each period2. Approach 1: Pseudo-American Valuation Step 1: Define when dividends will be paid and how much the dividends will be. Step 2:

Value the call option to each ex-dividend date using the dividend-adjusted

approach described above, where the stock price is reduced by the present value of expected dividends. Step 3: Choose the maximum of the call values estimated for each ex-dividend day. Illustration 5.5: Using Pseudo-American option valuation to adjust for early exercise Consider an option, with a strike price of $35 on a stock trading at $40. The variance in the ln(stock prices) is 0.05, and the riskless rate is 4%. The option has a remaining life of eight months, and there are three dividends expected during this period: Expected Dividend

Ex-Dividend Day

$ 0.80

in 1 month

$ 0.80

in 4 months

$ 0.80

in 7 months

The call option is first valued to just before the first ex-dividend date:

2 To illustrate, if σ2 is the variance in ln(stock prices), the up and down movements in the binomial can be estimated as follows:

u=e

2   T  r −    + 2   m   

2  T  m  

2   T  r −    − 2   m   

2  T  m  

d =e

where u and d are the up and down movements per unit time for the binomial, T is the life of the option and m is the number of periods within that lifetime.

19 S = $40

K = $35

t= 1/12

σ2 = 0.05

r = 0.04

The value from the Black-Scholes model is: Value of Call = $5.1312 The call option is then valued to before the second ex-dividend date: Adjusted Stock Price = $40 - $0.80/1.041/12 = $39.20 K = $35

t=4/12

σ2 = 0.05

r = 0.04

The value of the call based upon these parameters is: Value of call = $5.0732 The call option is then valued to before the third ex-dividend date: Adjusted Stock Price = $40 - $0.80/1.041/12 - $0.80/1.044/12 = $38.41 K = $35

t=7/12

σ2 = 0.05

r = 0.04

The value of the call based upon these parameters is: Value of call = $5.1285 The call option is then valued to expiration: Adjusted Stock Price = $40 - $0.80/1.041/12 - $0.80/1.044/12 - $0.80/1.047/12 = $37.63 K = $35

t=8/12

σ2 = 0.05

r = 0.04

The value of the call based upon these parameters is: Value of call = $4.7571 Pseudo-American value of the call = Maximum ($5.1312, $5.0732, $5.1285, $4.7571) = $5.1312 Approach 2: Using the binomial The binomial model is much more capable of handling early exercise because it considers the cash flows at each time period rather than just the cash flows at expiration. The biggest limitation of the binomial is determining what stock prices will be at the end of each period, but this can be overcome by using a variant that allows us to estimate the up and the down movements in stock prices from the estimated variance. There are four steps involved. Step 1: If the variance in ln(stock prices) has been estimated for the Black-Scholes, convert these into inputs for the Binomial

20 u=e

2   r −  2  

d =e

 T    +  m  

T  m  

2   T  r −    −   m  2   

2  T  m  

2

where u and d are the up and down movements per unit time for the binomial, T is the life of the option and m is the number of periods within that lifetime. Step 2: Specify the period in which the dividends will be paid and make the assumption that the price will drop by the amount of the dividend in that period. Step 3: Value the call at each node of the tree, allowing for the possibility of early exercise just before ex-dividend dates. There will be early exercise if the remaining time premium on the option is less than the expected drop in option value as a consequence of the dividend payment. Step 4: Value the call at time 0, using the standard binomial approach. bstobin.xls: This spreadsheet allows you to estimate the parameters for a binomial model from the inputs to a Black-Scholes model.

From Black-Scholes to Binomial The process of converting the continuous variance in a Black-Scholes modesl to a binomial tree is a fairly simple one. Assume, for instance, that you have an asset that is trading at $ 30 currently and that you estimate the standard deviation in the asset value to be 40%; the riskless rate is 5%. For simplicity, let us assume that the option that you are valuing has a one-year life and that each period is a quarter. To estimate the prices at the end of each the four quarters, we begin by first estimating the up and down movements in the binomial: (.4)2 .4 1+(.05 − )1 2

u = exp

−.4

d = exp

= 1.4477

1+(.05−

.402 )1 2

= 0.6505

Based upon these estimates, we can obtain the prices at the end of the first node of the tree (the end of the first quarter): Up price = $ 30 (1.4477) = $ 43.43

21 Down price = $ 40 (0.6505) = $19.52 Progressing through the rest of the tree, we obtain the following numbers: 91.03

62.88

43.43

30

40.90

28.25

19.52

18.38

12.69 8.26

3. The Impact of Exercise On The Value Of The Underlying Asset The Black-Scholes model is based upon the assumption that exercising an option does not affect the value of the underlying asset. This may be true for listed options on stocks, but it is not true for some types of options. For instance, the exercise of warrants increases the number of shares outstanding and brings fresh cash into the firm, both of which will affect the stock price.3 The expected negative impact (dilution) of exercise will decrease the value of warrants compared to otherwise similar call options. The adjustment for dilution in the Black-Scholes to the stock price is fairly simple. The stock price is adjusted for the expected dilution from the exercise of the options. In the case of warrants, for instance: Dilution-adjusted S =

SnS + WnW nS + nW

where S = Current value of the stock

3 Warrants are call options issued by firms, either as part of management compensation contracts or to raise equity. We will discuss them in chapter 16.

22 nw = Number of warrants outstanding W = Value of warrants outstanding ns = Number of shares outstanding When the warrants are exercised, the number of shares outstanding will increase, reducing the stock price. The numerator reflects the market value of equity, including both stocks and warrants outstanding. The reduction in S will reduce the value of the call option. There is an element of circularity in this analysis, since the value of the warrant is needed to estimate the dilution-adjusted S and the dilution-adjusted S is needed to estimate the value of the warrant. This problem can be resolved by starting the process off with an assumed value for the warrant (say, the exercise value or the current market price of the warrant). This will yield a value for the warrant and this estimated value can then be used as an input to re-estimate the warrant’s value until there is convergence. Illustration 5.6: Valuing a warrant with dilution MN Corporation has 1 million shares of stock trading at $50, and it is considering an issue of 500,000 warrants with an exercise price of $60 to raise fresh equity for the firm. The warrants will have a five-year lifetime. The standard deviation in the value of equity has been 20%, and the five-year riskless bond rate is 10%. The stock is expected to pay $1 in dividends per share this year, and is expected to maintain this dividend yield for the next five years. The inputs to the warrant valuation model are as follows: S = (1,000,000 * $50 + 500,000 * $ W )/(1,000,000+500,000) K = Exercise price on warrant = $60 t = Time to expiration on warrant = 5 years σ2 = Variance in value of equity = 0.22 = 0.04 y = Dividend yield on stock = $1 / $50 = 2% Since the value of the warrant is needed as an input to the process, there is an element of circularity in reasoning. After a series of iterations where the warrant value was used to re-estimate S, the results of the Black-Scholes valuation of this option are: d1 = -0.1435

N(d1) = 0.4430

d2 = -0.5907

N(d2) = 0.2774

23 Value of Call= S exp-(0.02) (5) (0.4430) - $60 exp-(0.10)(5) (0.2774) = $ 3.59 Value of warrant = Value of Call * ns /(nw + ns) = $ 3.59 *(1,000,000/1,500,000) = $2.39 Illustration 5.7: Valuing a warrant on Avatek Corporation Avatek Corporation is a real estate firm with 19.637 million shares outstanding, trading at $0.38 a share. In March, 2001, the company had 1.8 million options outstanding, with four years to expiration, with an exercise price of $2.25. The stock paid no dividends, and the standard deviation in ln(stock prices) is 93%. The four-year treasury bond rate was 4.90%. (The warrants were trading at $0.12 apiece at the time of this analysis) The inputs to the warrant valuation model are as follows: S = (0.38 * 19.637 + 0.12* 1.8 )/(19.637+1.8) = 0.3582 K = Exercise price on warrant = 2.25 t = Time to expiration on warrant = 4 years r = Riskless rate corresponding to life of option = 4.90% σ2 = Variance in value of stock = 0.932 y = Dividend yield on stock = 0.00% The results of the Black-Scholes valuation of this option are: d1 = 0.0418

N(d1) = 0.5167

d2 = -1.8182

N(d2) = 0.0345

Value of Warrant= 0.3544 (0.5167) – 2.25 exp-(0.049)(4) (0.0345) = $0.12 The warrant was trading at $0.25. warrant.xls: This spreadsheet allows you to estimate the value of an option, when there is a potential dilution from exercise. The Black-Scholes Model for Valuing Puts The value of a put can be derived from the value of a call with the same strike price and the same expiration date. C – P = S - K e-rt

24 where C is the value of the call and P is the value of the put. This relationship between the call and put values is called put-call parity and any deviations from parity can be used by investors to make riskless profits. To see why put-call parity holds, consider selling a call and buying a put with exercise price K and expiration date t, and simultaneously buying the underlying asset at the current price S. The payoff from this position is riskless and always yields K at expiration t. To see this, assume that the stock price at expiration is S*. The payoff on each of the positions in the portfolio can be written as follows: Position

Payoffs at t if S*>K

Payoffs at t if S*X

Invest in the project: Project has positive net present value

V<X

Do not invest in the project: Project has negative net present value

If the firm does not invest in the project over its life, it incurs no additional cash flows, though it will lose what it invested to get exclusive rights to the project. This relationship can be presented in a payoff diagram of cash flows on this project, as shown in Figure 28.1, assuming that the firm holds out until the end of the period for which it has exclusive rights to the project.

3 Figure 28.1: The Option to Delay a Project PV of Cash Flows

Initial Investment in Project

Project has negative NPV in this range

Present Value of Expected Cash Flows Project's NPV turns positive in this range

Note that this payoff diagram is that of a call option –– the underlying asset is the project, the strike price of the option is the initial investment needed to take the project; and the life of the option is the period for which the firm has rights to the project. The present value of the cash flows on this project and the expected variance in this present value represent the value and variance of the underlying asset. Inputs for Valuing the Option to Delay The inputs needed to apply option pricing theory to value the option to delay are the same as those needed for any option using the Black-Scholes model. We need the value of the underlying asset, the variance in that value, the time to expiration on the option, the strike price, the riskless rate and the equivalent of the dividend yield. Value Of The Underlying Asset In the case of product options, the underlying asset is the project to which the firm has exclusive rights. The current value of this asset is the present value of expected cash flows from initiating the project now, not including the up-front investment. This present value can be obtained by doing a standard investment analysis. There is likely to be a substantial amount of error in the cash flow estimates and the present value, however. Rather than being viewed as a problem, this uncertainty should be viewed as the reason the project delay option has value. If the expected cash flows on the project were

4 known with certainty and were not expected to change, there would be no need to adopt an option pricing framework, since there would be no value to the option. Variance in the value of the asset As noted in the prior section, there is likely to be considerable uncertainty associated with the cash flow estimates and the present value that measures the value of the project now. This is partly because the potential market size for the product may be unknown and partly because technological shifts can change the cost structure and profitability of the product. The variance in the present value of cash flows from the project can be estimated in one of three ways. •

If we have invested in similar projects in the past, the variance in the cash flows from those projects can be used as an estimate. This may be the way that a consumer product company like Gillette might estimate the variance associated with introducing a new blade for its razors.

•

We can assign probabilities to various market scenarios, estimate cash flows and a present value under each scenario and then calculate the variance across present values. Alternatively, the probability distributions can be estimated for each of the inputs into the project analysis - the size of the market, the market share and the profit margin, for instance - and simulations used to estimate the variance in the present values that emerge. This approach tends to work best when there are only one or two sources 1 of significant uncertainty about future cash flows.

•

We can use the variance in the value of firms involved in the same business (as the project being considered) as an estimate of the variance. Thus, the average variance in the value of firms involved in the software business can be used as the variance in present value of a software project. The value of the option is largely derived from the variance in cash flows - the

higher the variance, the higher the value of the project delay option. Thus, the value of an option to invest in a project in a stable business will be less than the value of one in an environment where technology, competition and markets are all changing rapidly.

5 Exercise Price on Option The option to delay a project is exercised when the firm owning the rights to the project decides to invest in it. The cost of making this initial investment is the exercise price of the option. The underlying assumption is that this cost remains constant (in present value dollars) and that any uncertainty associated with the investment is reflected in the present value of cash flows on the product. Expiration of the Option and the Riskless Rate The project delay option expires when the rights to the project lapse. Investments made after the project rights expire are assumed to deliver a net present value of zero as competition drives returns down to the required rate. The riskless rate to use in pricing the option should be the rate that corresponds to the expiration of the option. While expiration dates can be estimated easily when firms have the explicit right to a project (through a license or a patent, for instance), it becomes far more difficult to obtain if the right is less clearly defined. If, for instance, a firm has a competitive advantage on a product or project, the option life can be defined as the expected period over which the advantage can be sustained. Cost of Delay In Chapter 5, we noted that an American option generally will not be exercised prior to expiration. When you have the exclusive rights to a project, though, and the net present value turns positive, you would not want the owner of the rights to wait until the rights expire to exercise the option (invest in the project). Note that there is a cost in delaying investing in a project, once the net present value turns positive. If you wait an additional period, you may gain if the variance pushes value higher but you also lose one period of protection against competition. You have to consider this cost when analyzing the option and there are two ways of estimating it. •

Since the project rights expire after a fixed period and excess profits (which are the source of positive present value) are assumed to disappear after that time as new

1

In practical terms, the probability distributions for inputs like market size and market share can often be obtained from market testing.

6 competitors emerge, each year of delay translates into one less year of valuecreating cash flows.2 If the cash flows are evenly distributed over time and the life of the patent is n years, the cost of delay can be calculated. Annual cost of delay =

1 n

Thus, if the project rights are for 20 years, the annual cost of delay works out to 5% a year for the very first year. Note, though, that this cost of delay rises each year, to 1/19 in year 2, 1/18 in year 3 and so on, making the cost of delaying exercise larger over time. •

If the cash flows are uneven, the cost of delay can be more generally defined in terms of the change in present value that can be expected to occur over the next period as a percent of the present value today. Cost of delay =

Present value next period − Present value Now Present value Now

In either case, the likelihood that a firm will delay investing in a project is higher early in the exclusive rights period rather than later and the cost will increase as the loss in present value from waiting a period increases.

optvar.xls: There is a dataset on the web that summarizes standard deviations in firm value and equity value by industry group in the United States.

Illustration 28.1: Valuing the Option to Delay a Project Assume that you are interested in acquiring the exclusive rights to market a new product that will make it easier for people to access their email on the road. If you do acquire the rights to the product, you estimate that it will cost you $50 million up-front to set up the infrastructure needed to provide the service. Based upon your current projections, you believe that the service will generate only $10 million in after-tax cash

2

A value-creating cashflow is one that adds to the net present value because it is in excess of the required return for investments of equivalent risk.

7 flows each year. In addition, you expect to operate without serious competition for the next 5 years. From a static standpoint, the net present value of this project can be computed by taking the present value of the expected cash flows over the next 5 years. Assuming a discount rate of 15% (based on the riskiness of this project), we obtain the following net present value for the project. = −50 million + 10 million(PV of annuity, 15%, 5 years) NPV of project = −50 million + 33.5 million = −16.5 million

This project has a negative net present value. The biggest source of uncertainty about this project is the number of people who will be interested in the product. While current market tests indicate that you will capture a relatively small number of business travelers as your customers, they also indicate the possibility that the potential market could get much larger over time. In fact, a simulation of the project's cash flows yields a standard deviation of 42% in the present value of the cash flows, with an expected value of $33.5 million. To value the exclusive rights to this project, we first define the inputs to the option pricing model. Value of the Underlying Asset (S) = PV of Cash Flows from Project if introduced now = $ 33.5 million Strike Price (K) = Initial Investment needed to introduce the product = $ 50.0 million Variance in Underlying Asset’s Value = 0.422 = 0.1764 Time to expiration = Period of exclusive rights to product = 5 years Dividend Yield = 1/Life of the patent = 1/5 = 0.20 Assume that the 5-year riskless rate is 5%. The value of the option can be estimated. Call Value = 33.5e(-0.2 )(5 )(0.2250 )− 50.0e(-0.05 )(5 )(0.0451) = $1.019 million The rights to this product, which has a negative net present value if introduced today, is $1.019 million. Note, though, as measured by N(d1) and N(d2), the likelihood is low that this project will become viable before expiration.

8 delay.xls: This spreadsheet allows you to estimate the value of an option to delay an investment.

Arbitrage Possibilities and Option Pricing Models In our discussion of option pricing models in chapter 5, we noted that they are based upon two powerful constructs – the idea of replicating portfolios and arbitrage. Models such as the Black Scholes and the Binomial assume that you can create a replicating portfolio, using the underlying asset and riskless borrowing or lending, that has cashflows identical to those on an option. Furthermore, these models assume that since investors can then create riskless positions by buying the underlying option and selling the replicating portfolio, or vice versa, the value of the call should converge on the cost of creating the replicating portfolio. If it does not, investors should be able to create riskless positions and walk away with guaranteed profits – the essence of arbitrage. This is why the interest rate used in option pricing models is the riskless rate. With listed options on traded stocks or assets, arbitrage is clearly feasible at least for some investors. With options on non-traded assets, it is almost impossible to trade the replicating portfolio though you

can create it on paper. In the illustration above, for

instance, you would need to buy 0.225 units (the option delta) of the underlying project ( a non-traded asset) to create a portfolio that replicates the call option. There are some who argue that the impossibility of arbitrage makes it inappropriate to use option pricing models to value real options, whereas other try to adjust for this limitation by using an interest rate higher than the riskless rate in the option pricing model. We do not think that either of these responses is appropriate. Note that while you cannot trade on the replicating portfolios in many real options, you still can create them on paper (as we did in illustration 28.1) and value the options. The difficulties in creating arbitrage positions may result in prices that deviate by a large amounts from this value, but that is an argument for using real option pricing models and not for avoiding them. Increasing the

9 riskless rate to reflect the higher risk associated with real options may seem like an obvious fix, but doing this will only make call options (such as the one valued in illustration 28.1) more valuable, not less. If you want to be more conservative in your estimate of value for real options to reflect the difficulty of arbitrage, you have two choices. One is to use a higher discount rate in computing the present value of the cash flows that you would expect to make from investing in the project today, thus lowering the value of the underlying asset (S) in the model. In illustration 28.1, using a 20% discount rate rather than a 15% rate would result in a present value of $29.1 million, which would replace the $33.5 million as S in the model. The other is to value the option and then apply an illiquidity discount to it (similar to the one we used in valuing private companies) because you cannot trade it easily. Problems in valuing the Option to Delay While it is quite clear that the option to delay is embedded in many projects, several problems are associated with the use of option pricing models to value these options. First, the underlying asset in this option, which is the project, is not traded, making it difficult to estimate its value and variance. We have argued that the value can be estimated from the expected cash flows and the discount rate for the project, albeit with error. The variance is more difficult to estimate, however, since we are attempting the estimate a variance in project value over time. Second, the behavior of prices over time may not conform to the price path assumed by the option pricing models. In particular, the assumption that value follows a diffusion process and that the variance in value remains unchanged over time, may be difficult to justify in the context of a project. For instance, a sudden technological change may dramatically change the value of a project, either positively or negatively. Third, there may be no specific period for which the firm has rights to the project. Unlike the case of a patent, for instance, in which the firm has exclusive rights to produce the patented product for a specified period, the firm’s rights often are less clearly defined, in terms of both exclusivity and time. For instance, a firm may have significant advantages over its competitors, which may, in turn, provide it with the virtually exclusive rights to a

10 project for a period of time. An example would be a company with strong brand name recognition in retailing or consumer products. The rights are not legal restrictions, however, and will erode over time. In such cases, the expected life of the project itself is uncertain and only an estimate. In the valuation of the rights to the product, in the previous section, we used a life of 5 years for the option, but competitors could in fact enter sooner than we anticipated. Alternatively, the barriers to entry may turn out to be greater than expected and allow the firm to earn excess returns for longer than 5 years. Ironically, uncertainty about the expected life of the option can increase the variance in present value and through it the expected value of the rights to the project. Implications and Extensions of Delay Options Several interesting implications emerge from the analysis of the option to delay a project as an option. First, a project may have a negative net present value currently based upon expected cash flows, but the rights to it may still be valuable because of the option characteristics. Second, a project may have a positive net present value but still not be accepted right away. This can happen because the firm may gain by waiting and accepting the project in a future period, for the same reasons that investors do not always exercise an option that is in the money. A firm is more likely to wait if it has the rights to the project for a long time and the variance in project inflows is high. To illustrate, assume a firm has the patent rights to produce a new type of disk drive for computer systems and building a new plant will yield a positive net present value today. If the technology for manufacturing the disk drive is in flux, however, the firm may delay investing in the project in the hopes that the improved technology will increase the expected cash flows and consequently the value of the project. It has to weigh this benefit against the cost of delaying the project, which will be the cash flows that will be forsaken by not investing in it. Third, factors that can make a project less attractive in a static analysis can actually make the rights to the project more valuable. As an example, consider the effect of uncertainty about the size of the potential market and the magnitude of excess returns. In a static analysis, increasing this uncertainty increases the riskiness of the project and

11 may make it less attractive. When the project is viewed as an option, an increase in the uncertainty may actually make the option more valuable, not less. We will consider two cases, product patents and natural resource reserves, where we believe that the project delay option allows us to estimate value more precisely. Option Pricing Models Once you have identified the option to delay a project as a call option and identified the inputs needed to value the option, it may seem like a trivial task to actually value the option. There are, however, some serious estimation issues that we have to deal with in valuing these options. In Chapter 5, we noted that while the more general model for valuing options is the Binomial model, many practitioners use the Black-Scholes model, which makes far more restrictive assumptions about price processes and early exercise to value options. With listed options on traded assets, options can be exercised early at fairly low cost. With real options, there can be a substantial cost for the following reasons. •

Unlike listed options, real options tend to be exercised early, if they are in the money. While there are ways in which the Black-Scholes can be adjusted to allow for this early exercise, the Binomial allows for much more flexibility.

•

The binomal option pricing model allows for a much wider range of price processes for the underlying asset than the Black-Scholes, which assumes that prices are not only continuous but log-normally distributed. With real options, where the present value of the cashflows is often equivalent to the price, the assumptions of non-normality and continuous distribution may be difficult to sustain.

The biggest problem with the binomial model is that the prices at each node of the binomial tree have to be estimated. As the number of periods expands, this will become more and more difficult to do. You can, however, use the variance estimate to come up with rough measures of the magnitude of the up and down movements, which can be used to obtain the binomial tree. Having made a case for the binomial model, you may find it surprising that we use the Black-Scholes model to value any real options. We do so not only because the model

12 is more compact and elegant to present, but because we believe that it will provide a lower bound on the value in most cases. To provide a frame of reference, we will present the values that we would have obtained using a binomial model in each case. From Black-Scholes to Binomial It is a fairly simple exercise to convert the inputs to the Black-Scholes model into a binomial model. To make the adjustment, you have to assume a multiplicative binomial process, where the magnitude of the jumps, in percent terms, remains unchanged from period to period. If you assume symmetric probabilities, the up (u) and down (d) movements can be estimated as a function of the annualized variance in the price process and how many periods you decide to break each year into (t). 2  dt + r − y −  2 

u= e −

d= e

  dt  

2    dt dt +  r − y −   2  

where dt =

1 number of periods each year

To illustrate, consider the project delay option that we valued in Illustration 28.1. The standard deviation in the value was assumed to be 42%, the riskfree rate was 5% and the dividend yield was 20%. To convert the inputs into a binomial model, we will assume that each year is a time period and estimate the up and down movements. u= e d= e

 0.42 2 0.42 1 +  0.05 − 0.20 −  2 

 1  

 0.422 −0.42 1+ 0.05−0.20−  2 

 1  

= 1.1994 = 0.5178

The value today is $33.5 million. To estimate the end values for the first branch: Value with up movement = $33.5 (1.1994) = $40.20 million Value with down movement = $33.5 (0.5178) = $17.35 million You could use these values then to get the three potential values at the second branch. Note that the value of $17.35 million growing at 19.94% is exactly equal to the value of $40.20 million dropping by 48.22%. The binomial tree for the five periods is shown below in Figure 28.2.

13

Figure 28.2: Binomial tree for delay option 83.14

69.32

57.80 35.89 48.19

40.18

33.5

29.93

24.95

20.80

17.35

15.50

12.92

10.77

8.98

6.69

5.58 4.65 2.89 2.41

1.25

You could estimate the value of the option from this binomial tree to be $1.58 million, slightly higher than the estimate obtained from the Black Scholes model of $1.019 million. The differences will narrow as the option becomes more in the money and the time period used in the binomial model shortens.

14 Valuing a Patent A number of firms, especially in the technology and pharmaceutical sectors, can patent products or services. A product patent provides a firm with the right to develop and market a product and thus can be viewed as an option. Patents as call options The firm will develop a patent only if the present value of the expected cash flows from the product sales exceeds the cost of development, as shown in Figure 28.3. If this does not occur, the firm can shelve the patent and not incur any further costs. If I is the present value of the costs of commercially developing the patent and V is the present value of the expected cash flows from development, then: Payoff from owning a product patent = V - I =0

if V> I if V ≤ I

Thus, a product patent can be viewed as a call option, where the product is the underlying asset. Figure 28.3: Payoff to Introducing Product Net Payoff to introducing product

Cost of product introduction Present value of expected cashflows on product Illustration 28.2: Valuing a Patent: Avonex in 1997 Biogen is a bio-technology firm with a patent on a drug called Avonex, which has received FDA approval for use in treating multiple sclerosis. Assume you are trying to

15 value the patent and that you have the following estimates for use in the option pricing model. •

An internal analysis of the financial viability of the drug today, based upon the potential market and the price that the firm can expect to charge for the drug, yields a present value of cash flows of $3.422 billion, prior to considering the initial development cost.

•

The initial cost of developing the drug for commercial use is estimated to be $2.875 billion, if the drug is introduced today.

•

The firm has the patent on the drug for the next 17 years and the current long-term treasury bond rate is 6.7%.

•

The average variance in firm value for publicly traded bio-technology firms is 0.224.

We assume that the potential for excess returns exists only during the patent life and that competition will eliminate excess returns beyond that period. Thus, any delay in introducing the drug, once it becomes viable, will cost the firm one year of patentprotected returns. (For the initial analysis, the cost of delay will be 1/17, next year it will be 1/16, the year after 1/15 and so on.) Based on these assumptions, we obtain the following inputs to the option pricing model. Present Value of Cash Flows from Introducing the Drug Now = S = $ 3.422 billion Initial Cost of Developing Drug for Commercial Use (today) = K = $ 2.875 billion Patent Life = t = 17 years Riskless Rate = r = 6.7% (17-year Treasury Bond rate) Variance in Expected Present Values =σ2 = 0.224 Expected Cost of Delay = y = 1/17 = 5.89% These yield the following estimates for d and N(d): d1 = 1.1362

N(d1) = 0.8720

d2 = -0.8152 N(d2) = 0.2076 Plugging back into the dividend-adjusted Black-Scholes option pricing model3, we get: Value of the patent = 3,422e(-0.0589 )(17 )(0.8720 )− 2,875e(-0.067 )(17 )(0.2079 ) = $907 million To provide a contrast, the net present value of this project is only $547 million.

16 NPV = $3,422 million - $ 2,875 million = $ 547 million The time premium of $360 million on this option ($907-$547) suggests that the firm will be better off waiting rather than developing the drug immediately, the cost of delay notwithstanding. However, the cost of delay will increase over time and make exercise (development) more likely in future years. To illustrate, we will value the call option, assuming that all of the inputs, other than the patent life, remain unchanged. For instance, assume that there are 16 years left on the patent. Holding all else constant, the cost of delay increases as a result of the shorter patent life. Cost of delay = 1/16 The decline in the present value of cash flows (which is S) and the increase in the cost of delay (y) reduce the expected value of the patent. Figure 28.4 graphs the option value and the net present value of the project each year. Figure 28.4: Patent value versus Net Present value 1000 900 800 Exercise the option here: Convert patent to commercial product 700

Value

600 500 400 300 200 100 0 17

16

15

14

13

12

11

10

9

8

7

6

5

Number of years left on patent Value of patent as option

3

Net present value of patent

With a binomial model, we estimate a value of $915 million for the same option.

4

3

2

1

17 Based upon this analysis, if nothing changes, you would expect Avonex to be worth more as a commercial product than as a patent four years from now, which would also then be the optimal time to commercially develop the product. product.xls: This spreadsheet allows you to estimate the value of a patent.

Competitive Pressures and Option Values In the section above, we have taken the view that a firm is protected from competition for the life of the patent. This is generally true only for the patented product or process, but the firm may still face competition from other firms that come up with their own products to serve the same market. More specifically, Biogen can patent Avonex, but Merck or Pfizer can come up with their own drugs to treat multiple sclerosis and compete with Biogen. What are the implications for the value of the patent as an option? First, the life of the option will no longer be the life of the patent but the lead time that the firm has until a competing product is developed. For instance, if Biogen knows that another pharmaceutical firm is working on a drug to treat MS and where this drug is in the research pipeline (early research or the stage in the FDA approval process), it can use its estimate of how long it will take before the drug is approved for use as the life of the option. This will reduce the value of the option and make it more likely that the drug will be commercially developed earlier rather than later. The presence of these competitive pressures may explain why commercial development is much quicker with some drugs than with others and why the value of patents is not always going to be greater than a discounted cash flow valuation. Generally speaking, the greater the number of competing products in the research pipeline, the less likely it is that the option pricing model will generate a value that is greater than the traditional discounted cash flow model. Valuing a firm with patents If the patents owned by a firm can be valued as options, how can this estimate be incorporated into firm value? The value of a firm that derives its value primarily from

18 commercial products that emerge from its patents can be written as a function of three variables. •

the cash flows it derives from patents that it has already converted into commercial products,

•

the value of the patents that it already possesses that have not been commercially developed and

•

the expected value of any patents that the firm can be expected to generate in future periods from new patents that it might obtain as a result of its research.

Value of Firm = Value of commercial products + Value of existing patents + (Value of New patents that will be obtained in the future – Cost of obtaining these patents) The value of the first component can be estimated using traditional cash flow models. The expected cash flows from existing products can be estimated for their commercial lives and discounted back to the present at the appropriate cost of capital to arrive at the value of these products. The value of the second component can be obtained using the option pricing model described earlier to value each patent. The value of the third component will be based upon perceptions of a firm’s research capabilities. In the special case, where the expected cost of research and development in future periods is equal to the value of the patents that will be generated by this research, the third component will become zero. In the more general case, firms such as Cisco and Pfizer that have a history of generating value from research will derive positive value from this component as well. How would the estimate of value obtained using this approach contrast with the estimate obtained in a traditional discounted cash flow model? In traditional discounted cash flow valuation, the second and the third components of value are captured in the expected growth rate and the expected time in such an expected growth rate in cash flows. Firms such as Cisco are allowed to grow at much higher rates for longer periods because of the technological edge they possess and their research prowess. In contrast, the approach described in this section looks at each patent separately and allows for the option component of value explicitly. The biggest limitation of the option-based approach is the information that is needed to put it in practice. To value each patent separately, you need access to

19 proprietary information that is usually available only to managers of the firm. In fact, some of the information, such as the expected variance to use in option pricing may not even be available to insiders and will have to be estimated for each patent separately. Given these limitations, the real option approach should be used to value small firms with one or two patents and little in terms of established assets. A good example would be Biogen in 1997, which was valued in the last section. For firms such as Cisco and Lucent that have significant assets in place and hundreds of patents, discounted cash flow valuation is a more pragmatic choice. Viewing new technology as options provides insight into Cisco’s successful growth strategy over the last decade. Cisco has been successful at buying firms with nascent and promising technologies (options) and converting them into commercial success (exercising these options). Illustration 28.3: Valuing Biogen as a firm In Illustration 28.2, the patent that Biogen owns on Avonex was valued as a call option and the estimated value was $907 million. To value Biogen as a firm, two other components of value would have to be considered. •

Biogen had two commercial products (a drug to treat Hepatitis B and Intron) at the time of this valuation that it had licensed to other pharmaceutical firms. The license fees on these products were expected to generate $50 million in after-tax cash flows each year for the next 12 years. To value these cash flows, which were guaranteed contractually, the pre-tax cost of debt of 7% of the licensing firms was used.  1   112  Present Value of License Fees = $50 million  1.07  = $397.13 million  0.07     

•

Biogen continued to fund research into new products, spending about $100 million on R&D in the most recent year. These R&D expenses were expected to grow 20% a year for the next 10 years and 5% thereafter. While it was difficult to forecast the specific patents that would emerge from this research, it was assumed

20 that every dollar invested in research would create $1.25 in value in patents4 (valued using the option pricing model described above) for the next 10 years and break even after that (i.e., generate $1 in patent value for every $1 invested in R&D). There was a significant amount of risk associated with this component and the cost of capital was estimated to be 15%.5 The value of this component was then estimated as follows: t =∞

Value of Future Research =

Value of Patents t - R & D t t (1 + r ) t =1

∑

The table below summarizes the value of patents generated each period and the R&D costs in that period. Note that there is no surplus value created after the tenth year. Table 28.1: Value of New Research Year

Value of Patents

R&D Cost Excess Value

Present Value at

generated

4

15%

1

$

150.00

$

120.00

$

30.00

$

26.09

2

$

180.00

$

144.00

$

36.00

$

27.22

3

$

216.00

$

172.80

$

43.20

$

28.40

4

$

259.20

$

207.36

$

51.84

$

29.64

5

$

311.04

$

248.83

$

62.21

$

30.93

6

$

373.25

$

298.60

$

74.65

$

32.27

7

$

447.90

$

358.32

$

89.58

$

33.68

8

$

537.48

$

429.98

$

107.50

$

35.14

9

$

644.97

$

515.98

$

128.99

$

36.67

10

$

773.97

$

619.17

$

154.79

$

38.26

$

318.30

To be honest, this is not an estimate based upon any significant facts other than Biogen’s history of success in coming up with new products. You can estimate this value created from the return and cost of capital for a firm. For instance, if you assume that you can earn a return on capital of 15% in perpetuity with a cost of capital of 10%, you would obtain the following value created for every dollar of investment: Value Created = $ 1 + (ROC – Cost of Capital)/ Cost of Capital = 1 +(.15-.10)/.10 = $ 1.50 5 This discount rate was estimated by looking at the costs of equity of young publicly traded biotechnology firms with little or no revenue from commercial products.

21 The total value created by new research is $318.3 million. The value of Biogen as a firm is the sum of all three components – the present value of cash flows from existing products, the value of Avonex (as an option) and the value created by new research. Value = CF: Commerical products + Value: Undeveloped patents + Value: Future R&D = $ 397.13 million + $ 907 million + $ 318.30 million = $1622.43 million Since Biogen had no debt outstanding, this value was divided by the number of shares outstanding (35.50 million) to arrive at a value per share. Value per share =

$1,622.43 million = $45.70 35.5

Is there life after the patent expires? In our valuations, we assumed that the excess returns are restricted to the patent life and that they disappear the instant the patent expires. In the pharmaceutical sector, the expiration of a patent does not necessarily mean the loss of excess returns. In fact, many firms continue to be able to charge a premium price for their products and earn excess returns even after the patent expires, largely as a consequence of the brand name image that they built up over the project life. A simple way of adjusting for this reality is to increase the present value of the cash flows on the project (S) and decrease the cost of delay (y) to reflect this reality. The net effect is a greater likelihood that firms will delay commercial development, while they wait to collect more information and assess market demand. The other thing that might increase the value of the patent is the capacity that drug companies have shown to lobby legislators to extend the patent life of profitable drugs. If we consider this as a possibility when we value a patent, it will increase the expected life of the patent and its value as an option. Natural Resource Options Natural resource companies, such as oil and mining companies, generate cash flows from their existing reserves but also have undeveloped reserves that they can develop if they choose to do so. They will be much more likely to develop these reserves if the price of the resource (oil, gold, copper) increases and these undeveloped reserves

22 can be viewed as call options. In this section, we will begin by looking at the value of an undeveloped reserve and then consider how we can extend this to look at natural resource companies that have both developed and undeveloped reserves. Undeveloped Reserves as Options In a natural resource investment, the underlying asset is the natural resource and the value of the asset is based upon the estimated quantity and the price of the resource. Thus, in a gold mine, the underlying asset is the value of the estimated gold reserves in the mine, based upon the price of gold. In most such investments, there is an initial cost associated with developing the resource; the difference between the value of the estimated reserves and the cost of the development is the profit to the owner of the resource (see Figure 28.5). Defining the cost of development as X and the estimated value of the resource as V makes the potential payoffs on a natural resource option the following: Payoff on natural resource investment

=V-X

if V > X

=0

if V≤ X

Thus, the investment in a natural resource option has a payoff function similar to a call option. Figure 28.5: Payoff from Developing Natural Resource Reserves Net Payoff on extracting reserve

Cost of Developing reserve Value of estimated reserve of natural resource

23 Inputs for valuing a natural resource option To value a natural resource investment as an option, we need to make assumptions about a number of variables. 1. Available reserves of the resource and estimated value if extracted today: Since this is not known with certainty at the outset, it has to be estimated. In an oil tract, for instance, geologists can provide reasonably accurate estimates of the quantity of oil available in the tract. The value of the reserves is then the product of the estimated reserves and the contribution (market price of the resource – variable cost of extraction) per unit of reserve. 2. Estimated cost of developing the resource: The estimated cost of developing the resource reserve is the exercise price of the option. In an oil reserve, this would be the fixed cost of installing the rigs to extract oil from the reserve. With a mine, it would be the cost associated with making the mine operational. Since oil and mining companies have done this before in a variety of settings, they can use their experience to come up with a reasonable measure of development cost. 3. Time to expiration of the option: The life of a natural resource option can be defined in one of two ways. First, if the ownership of the investment has to be relinquished at the end of a fixed period of time, that period will be the life of the option. In many off-shore oil leases, for instance, the oil tracts are leased to the oil company for a fixed period. The second approach is based upon the inventory of the resource and the capacity output rate, as well as estimates of the number of years it would take to exhaust the inventory. Thus, a gold mine with a reserve of 3 million ounces and a capacity output rate of 150,000 ounces a year will be exhausted in 20 years, which is defined as the life of the natural resource option. 4. Variance in value of the underlying asset: The variance in the value of the underlying asset is determined by the variability in the price of the resource and the variability in the estimate of available reserves. In the special case where the quantity of the reserve is known with certainty, the variance in the underlying asset's value will depend entirely upon the variance in the price of the natural resource. 5. Cost of Delay: The net production revenue is the annual cash flow that will be generated, once a resource reserve has been developed, as a percentage of the market value

24 of the reserve. This is the equivalent of the dividend yield and is treated the same way in calculating option values. An alternative way of thinking about this cost is in terms of a cost of delay. Once a natural resource option is in the money (Value of the reserves > Cost of developing these reserves), by not developing the reserve the firm is costing itself the production revenue it could have generated by doing so. An important issue in using option pricing models to value natural resource options is the effect of development lags on the value of these options. Since oil or gold or any other natural resource reserve cannot be developed instantaneously, a time lag has to be allowed between the decision to extract the resources and the actual extraction. A simple adjustment for this lag is to reduce the value of the developed reserve for the loss of cash flows during the development period. Thus, if there is a one-year lag in development and you can estimate the cash flow you would make over that year, you can estimate the cash flow as a percent of your reserve value and discount the current value of the developed reserve at that rate. This is the equivalent of removing the first year’s cash flow from your investment analysis and lowering the present value of your cash flows. In Practice 28.4: Valuing an Oil Reserve6 Consider an offshore oil property with an estimated oil reserve of 50 million barrels of oil; the cost of developing the reserve is expected to be $600 million, and the development lag is two years. Exxon has the rights to exploit this reserve for the next 20 years, and the marginal value (price per barrel - marginal cost per barrel) per barrel of oil is currently $12 7. Once developed, the net production revenue each year will be 5% of the value of the reserves. The riskless rate is 8%, and the variance in oil prices is 0.03. Given this information, the inputs to the Black-Scholes can be estimated Current Value of the asset = S = Value of the developed reserve discounted back the length of the development lag at the dividend yield =

6

(12)(50) = $544.22 1.05

2

The following is a simplified version of the illustration provided by Siegel, Smith and Paddock to value an offshore oil property. 7 For simplicity, we will assume that while this marginal value per barrel of oil will grow over time, the present value of the marginal value will remain unchanged at $12 per barrel. If we do not make this

25 Exercise Price = Cost of developing reserve = $ 600 million Time to expiration on the option = 20 years Variance in the value of the underlying asset8 = 0.03 Riskless rate =8% Dividend Yield = Net production revenue / Value of reserve = 5% Based upon these inputs, the Black-Scholes model provides the following values. d1 = 1.0359

N(d1) = 0.8498

d2 = 0.2613

N(d2) = 0.6030

Call Value = 544.22e(-0.05 )(20 )(0.8498 )− 600e(-0.08 )(20 )(0.6030 ) = $97.10 million This oil reserve, though not viable at current prices, is still valuable because of its potential to create value if oil prices go up.9 natres.xls: This spreadsheet allows you to estimate the value of an undeveloped natural resource reserve. Multiple Sources of Uncertainty In the example above, we assumed that there was no uncertainty about the quantity of the reserve. Realistically, the oil company has an estimate of the reserve of 50 million barrels but does not know it with certainty. If we introduce uncertainty about the quantity of the reserve into the analysis, there will be two sources of variance and both can affect value. There are two ways we can address this problem. 1. Combine the uncertainties into one value: If we consider the value of the reserves to be the product of the price of oil and the oil reserves, the variance in the value should reflect the combined effect of the variances in each input. In fact, if the variance in the ln(estimated reserve quantity) is σq2 and the variance in ln(oil prices) is σp2 , the variance10 in the value of the reserve can be calculated.

assumption, we will have to estimate the present value of the oil that will be extracted over the extraction period. 8 In this example, we assume that the only uncertainty is in the price of oil and the variance therefore becomes the variance in ln(oil prices). 9 With a binomial model, we arrive at an estimate of value of $99.15 million. 10 This is the variance of a product of two variables. If c = ab, then σ 2 = σ 2+ σ 2+ c a b

26 2

2 res

=

2 q

 # barrels    +  # barrels + price/barrel 

2 p

 price/barrel     # barrels + price/barrel 

2

We are assuming that there is no correlation between the estimated quantity of oil in a reserve and the price per barrel of oil. Thus, in the above example, if we introduced a variance of 0.05 in the estimated reserve of 50 million barrels, we obtain the following estimate for the variance in the value of the reserve. 2

2 res

2

 50   12  = 0.05  + 0.03  = 0.0336  50 + 12   50 + 12 

This would be the variance we would use in the option pricing model to estimate a new value for the reserve. 2. Keep the variances separate and value the option as a rainbow option: A rainbow option allows explicitly for more than one source of variance and allows us to keep the variances separate and still value the option. While option pricing becomes more complicated, you may need to do this if you expect the two sources of uncertainty to evolve differently over time – the variance from one source (say, market conditions) may increase over time whereas the variance from the other source (say, technology) may decrease over time.

Valuing a firm with undeveloped reserves The examples provided above illustrate the use of option pricing theory in valuing individual mines and oil tracts. Since the assets owned by a natural resource firm can be viewed primarily as options, the firm itself can be valued using option pricing models. Individual Reserves versus Aggregate Reserves The preferred approach would be to consider each option separately, value it and cumulate the values of the options to get the value of the firm. Since this information is likely to be difficult to obtain for large natural resource firms, such as oil companies, which own hundreds of such assets, a variant of this approach is to value the entire firm as one option. A purist would probably disagree, arguing that valuing an option on a portfolio of assets (as in this approach) will provide a lower value than valuing a portfolio

27 of options (which is what the natural resource firm really own) because aggregating the assets that are correlated yields a lower variance which will lower the value of the portfolio of the aggregated assets. Nevertheless, the value obtained from the model still provides an interesting perspective on the determinants of the value of natural resource firms. Inputs to option valuation If you decide to apply the option pricing approach to estimate the value of undeveloped reserves, you have to estimate the inputs to the model. In general terms, while the process resembles the process used to value an individual reserve, there are a few differences. Value of underlying asset: You should cumulate all of the undeveloped reserves owned by a company and estimate the value of these reserves, based upon the price of the resource today and the average variable cost of extracting these reserves today. The variable costs are likely to be higher for some reserves and lower for others, and weighting the variable costs at each reserve by the quantity of the resource of that reserve should give you a reasonable approximation of this value. At least hypothetically, we are assuming that the company can decide to extract all of its undeveloped reserves at one time and not affect the price of the resource. Exercise Price: For this input, you should consider what it would cost the company today to develop all of its undeveloped reserves. Again, the costs might be higher for some reserves than for others, and you can use a weighted average cost. Life of the option: A firm will probably have different lives for each of its reserves. As a consequence, you will have to use a weighted average of the lives of the different reserves.11 Variance in the value of the asset: Here, there is a strong argument for looking at only the oil price as the source of variance, since a firm should have a much more precise estimate of its total reserves than it does of any one of its reserves.

11

If you own some reserves in perpetuity, you should cap the life of the reserve at a large value – say, 30 years – in making this estimate.

28 Dividend Yield (cost of delay): As with an individual reserve, a firm with viable reserves will be giving up the cash flows it could receive in the next period from developing these reserves if it delays exercise. This cash flow, stated as a percent of the value of the reserves, becomes the equivalent of the dividend yield. The development lag reduces the value of this option just as it reduces the value of an individual reserve. The logical implication is that undeveloped reserves will be worth more at oil companies that can develop their reserves quicker than at less efficient companies. Illustration 28.5: Valuing an oil company - Gulf Oil in 1984 Gulf Oil was the target of a takeover in early 1984 at $70 per share (It had 165.30 million shares outstanding and total debt of $9.9 billion). It had estimated reserves of 3038 million barrels of oil and the average cost of developing these reserves at that time was estimated to be $30.38 billion dollars (The development lag is approximately two years). The average relinquishment life of the reserves is 12 years. The price of oil was $22.38 per barrel, and the production cost, taxes and royalties were estimated at $7 per barrel. The bond rate at the time of the analysis was 9.00%. If Gulf chooses to develop these reserves, it was expected to have cash flows next year of approximately 5% of the value of the developed reserves. The variance in oil prices is 0.03. Value of underlying asset = Value of estimated reserves discounted back for period of development lag =

(3038)(22.38 - 7 ) = $42,380 million 1.05

2

Note that you could have used forecasted oil prices and estimated cash flows over the production period to estimate the value of the underlying asset, which is the present value of all of these cash flows. We have used as short cut of assuming that the current contribution margin of $15.38 a barrel will remain unchanged in present value terms over the production period. Exercise price = Estimated cost of developing reserves today= $30,380 million Time to expiration = Average length of relinquishment option = 12 years Variance in value of asset = Variance in oil prices = 0.03 Riskless interest rate = 9% Dividend yield = Net production revenue/ Value of developed reserves = 5%

29 Based upon these inputs, the Black-Scholes model provides the following value for the call.12 d1 = 1.6548

N(d1) = 0.9510

d2 = 1.0548

N(d2) = 0.8542

Call Value = 42,380e(-0.05 )(12 )(0.9510 )− 30,380e (-0.09 )(12 )(0.8542 ) = $13,306 million This stands in contrast to the discounted cash flow value of $12 billion that you obtain by taking the difference between the present value of the cash flows of developing the reserve today ($42.38 billion) and the cost of development ($30.38 billion). The difference can be attributed to the option possessed by Gulf to choose when to develop its reserves. This represents the value of the undeveloped reserves of oil owned by Gulf Oil. In addition, Gulf Oil had free cashflows to the firm from its oil and gas production from already developed reserves of $915 million and assume that these cashflows are likely to be constant and continue for ten years (the remaining lifetime of developed reserves). The present value of these developed reserves, discounted at the weighted average cost of capital of 12.5%, yields: 1   9151 10   1.125  = $5,066 Value of already developed reserves = 0.125

Adding the value of the developed and undeveloped reserves of Gulf Oil provides the value of the firm. Value of undeveloped reserves

= $ 13,306 million

Value of production in place

= $ 5,066 million

Total value of firm

= $ 18,372 million

Less Outstanding Debt

= $ 9,900 million

Value of Equity

= $ 8,472 million

Value per share

=

$8,472 = $51.25 165.3

This analysis would suggest that Gulf Oil was overvalued at $70 per share.

12

With a binomial model, we estimate the value of the reserves to be $13.73 billion.

30 Price Volatility and Natural Resource Company Valuation An interesting implication of this analysis is that the value of a natural resource company depends not just on the price of the natural resource but also on the expected volatility in that price. Thus, if the price of oil goes from $25 a barrel to $40 a barrel, you would expect all oil companies to become more valuable. If the price drops back to $25, the values of oil companies may not decline to their old levels, since the perceived volatility in oil prices may have changed. If investors believe that the volatility in oil prices has increased, you would expect an increase in values but the increase will be greatest for companies that derive a higher proportion of their value from undeveloped reserves. If you regard undeveloped reserves as options, discounted cash flow valuation will generally under estimate the value of natural resource companies, because the expected price of the commodity is used to estimate revenues and operating profits. As a consequence, you miss the option component of value. Again, the difference will be greatest for firms with significant undeveloped reserves and with commodities where price volatility is highest. Other Applications While patents and undeveloped reserves of natural resource companies lend themselves best to applying option pricing, there are other assets that we have referenced in earlier chapters that can also be valued as options. •

In Chapter 26, in the context of real estate valuation, we noted that vacant land could be viewed as an option on commercial development.

•

In Chapter 27, we presented an argument that copyrights and licenses could be viewed as options, even if they are not commercially viable today.

The following table presents the inputs you would use to value each of these options in an option pricing model. Table 28.2: Inputs to value other options to delay Undeveloped Land Value of the

Present value of the cash flows

License/ copyright Present value of the

31 underlying asset

that would be obtained from

cashflows that would be

commercial development of

obtained from

land today.

commercially utilizing the license or copyright today.

Variance in value of underlying asset

Variance in the values of

Variance in the present

commercial property in the area values from commercial where the real estate is located.

utilization of copyright or license.

Exercise Price

Cost of commercially

Up-front cost of

developing land today.

commercially utilizing copyright or license today.

Life of the option

If land is under long-term lease,

Period for which you have

you could use the lease period.

rights to copyright or

If not, you should set the

license.

option life equal to the period when the loan that you used to buy the land comes due. Cost of delay

Interest payments you have to

Cashflow you could

make on the loan each year.

generate in next year as a percent of present value of the cash flows today.

Much of what we have said about the other option applications apply here as well. The value is derived from the exclusivity that you have to commercially develop the asset. That exclusivity is obtained by legal sanction in the case of licenses and copyrights and from the scarcity of land in the case of undeveloped land. Summary In traditional investment analysis, we compute the net present value of a project’s cash flows and conclude that firms should not invest in a project with a negative net present value. This is generally good advice, but it does not imply that the rights to this

32 project are not valuable. Projects that have negative net present values today may have positive net present values in the future, and the likelihood of this occurring is directly a function of the volatility in the present value of the cash flows from the project. In this chapter, we valued the option to delay an investment and considered the implications of this option for three valuation scenarios – the value of a firm that derives all or a significant portion of value from patents that have not been commercially exploited yet, the value of a natural resource company with undeveloped reserves of the resource and the value of a real estate firm with undeveloped land. In each case, we showed that using discounted cash flow valuation would result in an understatement of the values for these firms.

33 Problems 1. A company is considering delaying a project which with after-tax cash flows of $25 million but costs $300 million to take (the life of the project is 20 years and the cost of capital is 16%). A simulation of the cash flows leads you to conclude that the standard deviation in the present value of cash inflows is 20%. If you can acquire the rights to the project for the next ten years, what are the inputs for the option pricing model? (The six-month T.Bill rate is 8%, the ten year bond-rate is 12% and the 20-year bond rate is 14%.) 2. You are examining the financial viability of investing in some abandoned copper mines in Chile, which still have significant copper deposits in them. A geologist survey suggests that there might be 10 million pounds of copper in the mines still and that the cost of opening up the mines will be $3 million (in present value dollars). The capacity output rate is 400,000 pounds a year and the price of copper is expected to increase 4% a year. The Chilean Government is willing to grant a twenty-five year lease on the mine. The average production cost is expected to be 40 cents a pound and the current price per pound of copper is 85 cents. (The production cost is expected to grow 3% a year, once initiated.) The annualized standard deviation in copper prices is 25% and the twenty-five year bond rate is 7%. a. Estimate the value of the mine using traditional capital budgeting techniques. b. Estimate the value of the mine based upon an option pricing model. c. How would you explain the difference between the two values? 3. You have been asked to analyze the value of an oil company with substantial oil reserves. The estimated reserves amount to 10,000,000 barrels and the estimated present value of the development cost for each barrel is $12. The current price of oil is $20 per barrel and the average production cost is estimated to be $6 per barrel. The company has the rights to these reserves for the next twenty years and the twenty year bond rate is 7%. The company also proposes to extract 4% of its reserves each year to meet cashflow needs. The annualized standard deviation in the price of the oil is 20%. What is the value of this oil company? 4. You are analyzing a capital budgeting project. The project is expected to have a PV of cash inflows of $250 million and will cost $200 million (in present value dollars) to take on. You have done a simulation of the project cashflows and the

34 simulation yields a variance in present value of cash inflows of 0.04. You have the rights to this project for the next five years, during which period you have to pay $12.5 million a year to retain the project rights. The five-year treasury bond rate is 8%. a. What is the value of project, based upon traditional NPV? b. What is the value of the project as an option? c. Why are the two values different? What factor or factors determine the magnitude of this difference? 5. Cyclops Inc, a high technology company specializing in state-of-the-art visual technology, is considering going public. While the company has no revenues or profits yet on its products, it has a ten-year patent to a product that will enable contact lens users to get no-maintenance lens that will last for years. While the product is technically viable, it is exorbitantly expensive to manufacture and the potential market for it will be relatively small initially. (A cash flow analysis of the project suggests that the present value of the cash inflows on the project, if adopted now, would be $250 million, while the cost of the project will be $500 million.) The technology is rapidly evolving and a simulation of alternative scenarios yields a wide range of present values, with an annualized standard deviation of 60%. To move towards this adoption, the company will have to continue to invest $10 million a year in research. The ten-year bond rate is 6%. a. Estimate the value of this company. b. How sensitive is this value estimate to the variance in project cash flows? What broader lessons would you draw from this analysis?

1

CHAPTER 29 THE OPTIONS TO EXPAND AND ABANDON: VALUATION IMPLICATIONS In the last chapter, we noted that traditional discounted cash flow valuation does not consider the value of the option that many firms have to delay making an investment and consequently understates the value of these firms. In this chapter, we consider two other options that are often embedded in investments (and consequently in the values of the firms that possess them). The first of these is the option to expand an investment, not only in new markets but in new products, to take advantage of favorable conditions. We argue that this option may sometimes make young, start-up firms significantly more valuable than the present value of their expected cash flows. The second option is the option to abandon or scale down investments, which can reduce the risk and downside from large investments and therefore make them more valuable. The Option to Expand Firms sometimes invest in projects because the investments allow them either to make further investments or to enter other markets in the future. In such cases, we can view the initial projects as options allowing the firm to invest in other projects and we should therefore be willing to pay a price for such options. Put another way, a firm may accept a negative net present value on the initial project because of the possibility of high positive net present values on future projects. The Payoff on the Option to Expand The option to expand can be evaluated at the time the initial project is analyzed. Assume that this initial project will give the firm the right to expand and invest in a new project in the future. Assessed today, the expected present value of the cash flows from investing in the future project is V and the total investment needed for this project is X. The firm has a fixed time horizon, at the end of which it has to make the final decision on whether or not to make the future investment. Finally, the firm cannot move forward on this future investment if it does not take the initial project. This scenario implies the option payoffs shown in Figure 29.1.

2 Figure 29.1: The Option to Expand a Project PV of Cash Flows

Cost of Expansion

Expansion has negative NPV in this range

Expansion NPV turns positive in this range

Present Value of Expected Cash Flows

As you can see, at the expiration of the fixed time horizon, the firm will expand into the new project if the present value of the expected cash flows at that point in time exceeds the cost of expansion. Inputs to value the option to expand To understand how to estimate the value of the option to expand, let us begin by recognizing that there are two projects usually that drive this option. The first project generally has a negative net present value and is recognized as a poor investment, even by the firm investing in it. The second project is the potential to expand that comes with the first project. It is the second project that represents the underlying asset for the option. The inputs have to be defined accordingly. •

The present value of the cash flows that you would generate if you were to invest in the second project today (the expansion option) is the value of the underlying asset – S in the option pricing model.

•

If there is substantial uncertainty about the expansion potential, the present value is likely to be volatile and change over time as circumstances change. It is the variance in this present value that you would want to use to value the expansion option. Since projects are not traded, you have to either estimate this variance

3 from simulations or use the variance in values of publicly traded firms in the business. •

The cost that you would incur up front, if you invest in the expansion today, is the equivalent of the strike price.

•

The life of the option is fairly difficult to define, since there is usually no externally imposed exercise period. (This is in contrast to the patents we valued in the last chapter which have a legal life which can be used as the option life.) When valuing the option to expand, the life of the option will be an internal constraint imposed by the firm on itself. For instance, a firm that invests on a small scale in China might impose a constraint that it either will expand within 5 years or pull out of the market. Why might it do so? There may be considerable costs associated with maintaining the small presence or the firm may have scarce resources that have to be committed elsewhere.

•

As with other real options, there may be a cost to waiting, once the expansion option becomes viable. That cost may take the form of cash flows that will be lost on the expansion project if it is not taken or a cost imposed on the firm until it makes its final decision. For instance, the firm may have to pay a fee every year until it makes its final decision.

Illustration 29.1: Valuing an Option to Expand: Ambev and Guarana Guarana is a very popular caffeine-based soft drink in Brazil and Ambev is the Brazilian beverage manufacturer that is the largest producer of Guarana in the world. Assume that Ambev is considering introducing the drink into the United States and that it has decided to do so in two steps. •

Ambev will initially introduce Guarana in just the large metropolitan areas of the United States to gauge potential demand. The expected cost of this limited introduction is $500 million and the estimated present value of the expected cash flows is only $400 million. In other words, Ambev expects to have a negative net present value of $100 million on this first investment.

•

If the limited introduction turns out to be a success, Ambev expects to introduce Guarana to the rest of the U.S. market. At the moment, though, the firm is not

4 optimistic about this expansion potential and believes that while the cost of the full-scale introduction will be $1 billion, the expected present value of the cash flows is only $750 million (making this a negative net present value investment as well). At first sight, investing in a poor project to get a chance to invest in an even poorer project may seem like a bad deal, but the second investment does have a redeeming feature. It is an option and Ambev will not make the second investment (of $1 billion) if the expected present value of the cash flows stays below that number. Furthermore, there is considerable uncertainty about the size and potential for this market and the firm may well find itself with a lucrative investment. To estimate the value of the second investment as an option, we begin by first identifying the underlying asset – the expansion project – and using the current estimate of expected value ($750 million) as the value of the underlying asset. Since the investment needed for the investment of $1 billion is the exercise price, this option is an out-of-themoney option. The two most problematic assumptions relate to the variance in the value of the underlying asset and the life of the option: •

We estimated the average standard deviation of 35% in firm values of small, publicly traded beverage companies in the United States and assumed that this would be a good proxy for the standard deviation in the value of the expansion option.

•

We assumed that Ambev would have a five-year window to make their decision. We admit that this is an arbitrary constraint but, in the real world, it may be driven by any of the following. o financing constraints (loans coming due) o strategic prerogatives (you have to choose where your resources will be invested) o personnel decisions (management has to be hired and put in place).

Based upon these inputs, we had the following inputs to the option pricing model. S = Present value of cash flows from expansion option today = $750 K = Exercise Price = $ 1000 t = 5 years

5 Standard deviation in value = 35% We used a riskless rate of 5% and derived the expected up and down movements from the standard deviation. u = 1.4032 d = 0.6968 The binomial tree is presented in Figure 29.2. Figure 29.2: Binomial Tree – Ambev Expansion Option 4080

2908

2072 2026 1477

1052

750

1444

1029

733

523

1006

717

511

364

500

356 254 248 177

123

6

Using the replicating portfolio framework described in Chapter 5, we estimate the value of the expansion option to be $203 million. This value can be added on to the net present value of the original project under consideration. NPV of limited introduction = -500 + 400 = - $ 100 million Value of Option to Expand = $ 203 million NPV with option to expand = -$ 100 million + $ 203 million = $ 103 million Ambev should go ahead with the limited introduction, even though it has a negative net present value, because it acquires an option of much greater value, as a consequence. Estimating variances from Monte Carlo Simulations We have suggested a couple of times in the last two chapters that the variances to be used in real option pricing models be derived from simulations. A Monte Carlo simulation requires the following steps. 1. You define probability distributions for each of the key inputs that underlie the cash flows and the parameters of the distributions – the average and the standard deviation, if it is a normal distribution, for instance. 2. In each simulation, you draw one outcome from each distribution and estimate the present value of the cash flows based upon these draws. 3. After repeated simulations, you should have a distribution of present values. The mean of this distribution should be the expected value of the project and the standard deviation of the distribution can be used as the variance in the value to value options on the project. While the process of running these simulations is straight forward and there are a number of software packages1 that exist that allow you to do this, we would add the following notes of caution. •

The most difficult step is estimating the probability distributions and parameters for the key variables. It is easier to do when a firm has had experience with similar projects in the past – a retail store considering a new store, for instance – than for a

1

Crystal Ball and @Risk are both add-on packages to Excel that allow you to run simulations.

7 new product or a new market. If the distributions that feed into a simulation are random, the output, impressive though it might look on paper, is meaningless. •

The standard deviation or variance that you want to use in option pricing models is a variance in value over time and not at a point in time. What is the difference, you might ask? Market testing, for instance, provide a distribution for the market potential today and reflect estimation uncertainty. The market itself will evolve over time and it is the variance in that distribution that we would like to estimate. 2

•

You should estimate the standard deviation in the value of the project – the sum of the present value of the cash flows – rather than the standard deviation in annual income or annual cash flows.

expand.xls: This spreadsheet allows you to estimate the value of the option to expand a project to cover new markets or new products, using the Black-Scholes model. Problems in valuing the Option to Expand The practical considerations associated with estimating the value of the option to expand are similar to those associated with valuing the option to delay. In most cases, firms with options to expand have no specific time horizon by which they have to make an expansion decision, making these open-ended options, or, at best, options with arbitrary lives. Even in those cases where a life can be estimated for the option, neither the size nor the potential market for the product may be known and estimating either can be problematic. To illustrate, consider the Ambev example discussed above. While we adopted a period of five years, at the end of which the Ambev has to decide one way or another on its future expansion in United States, it is entirely possible that this time frame is not specified at the time the first store is opened. Futhermore, we have assumed that both the cost and the present value of expansion are known at the time of the initial investment. In reality, the firm may not have good estimates for either input before opening the first store, since it does not have much information on the underlying market.

8 Extensions and Implications of Expansion Options The option to expand can be used by firms to rationalize investing in projects that have negative net present values but provide significant opportunities to enter new markets or to sell new products. The option pricing approach adds rigor to this argument by estimating the value of this option and it also provides insight into those occasions when it is most valuable. The option to expand is clearly more valuable for more volatile businesses with higher returns on projects (such as biotechnology or computer software) than it is for stable businesses with lower returns (such as automobile production). We will consider three cases where the expansion option may yield useful insights – strategic considerations in acquisitions, research and development expenses and multi-stage projects. Strategic Considerations in Acquisitions In many acquisitions or investments, the acquiring firm believes that the transaction will give it competitive advantages in the future. These competitive advantages include: •

Entry into a Large or Growing Market: An investment or acquisition may allow the firm to enter a large or potentially large market much sooner than it otherwise would have been able to do so. A good example of this is the acquisition of a Mexican retail firm by a US firm, with the intent of expanding into the Mexican market.

•

Technological Expertise: In some cases, the acquisition is motivated by the desire to acquire a proprietary technology that will allow the acquirer to either expand its existing market or enter a new market.

•

Brand Name: Firms sometimes pay large premiums over market price to acquire firms with valuable brand names, because they believe that these brand names can be used for expansion into new markets and products in the future.

While all these potential advantages may be used to justify large acquisition premiums, not all of them create valuable options. Even if these advantages can be viewed as valuable

2

You could, for instance, be fairly certain about the size of the market today – the variance would be low or even zero – but be uncertain about what the market will look like a year from now or three years from now. It is the latter variance that determines the value of the option.

9 expansion options, the value has to be greater than the acquisition premium for stockholders to gain. Research, Development and Test Market Expenses Firms that spend considerable amounts of money on research and development and test marketing are often stymied when they try to evaluate these expenses, since the payoffs are in terms of future projects. At the same time, there is the very real possibility that after the money has been spent, the products or projects may turn out not to be viable; consequently, the expenditure must be treated as a sunk cost. In fact, R & D has the characteristics of a call option –– the amount spent on the R&D is the cost of the call option and the projects or products that might emerge from the research provide the payoffs on the options. If these products are viable (i.e., the present value of the cash inflows exceeds the needed investment), the payoff is the difference between the two. If not, the project will not be accepted and the payoff will be zero. Several logical implications emerge from this view of R & D. First, research expenditures should provide much higher value for firms that are in volatile businesses, since the variance in the product or project cash flows is positively correlated with the value of the call option.

Thus, Minnesota Mining and Manufacturing (3M), which

expends a substantial amount on R&D on basic office products, such as the Post-it pad, should receive less value3 for its dollar of research than does Amgen, whose research primarily concerns bio-technology products. Second, the value of research and the optimal amount to be spent on research will change over time as businesses mature. The best example is the pharmaceutical industry - pharmaceutical companies spent most of the 1980s investing substantial amounts in research and earning high returns on new products, as health care costs expanded. In the 1990s, however, as health care costs started leveling off and the business matured, many of these companies found that they were not getting the same payoffs on research and started cutting back. Some companies

3

This statement is based on the assumption that the quality of research is the same at both firm, though the research is in different businesses, and that the only difference is in the volatility of the underlying businesses.

10 moved research dollars from conventional drugs to bio-technology products, where uncertainty about future cash flows remains high. Multi-Stage Projects/Investments When entering new businesses or taking new investments, firms sometimes have the option to move in stages. While doing so may reduce potential upside, it also protects the firm against downside risk, by allowing it at each stage to gauge demand and decide whether to go on to the next stage. In other words, a standard project can be recast as a series of options to expand, with each option being dependent on the previous one. There are two propositions that follow. •

Some projects that are unattractive on a full investment basis may be value creating if the firm can invest in stages.

•

Some projects that look attractive on a full investment basis may become even more attractive if taken in stages.

The gain in value from the options created by multi-stage investments has to be weighed against the cost. Taking investments in stages may allow competitors who decide to enter the market on a full scale to capture the market. It may also lead to higher costs at each stage, since the firm is not taking full advantage of economies of scale. Several implications emerge from viewing this choice between multi-stage and onetime investments in an option framework. The projects where the gains will be largest from making the investment in multiple stages include: •

Projects where there are significant barriers to entry to competitors entering the market and taking advantage of delays in full-scale production: Thus, a firm with a patent on a product or other legal protection against competition pays a much smaller price for starting small and expanding as it learns more about the market.

•

Projects where there is uncertainty about the size of the market and the eventual success of the project: Here, starting small and expanding in stages allows the firm to reduce its losses if the product does not sell as well as anticipated and to learn more about the market at each stage. This information can be useful in both product design and marketing in subsequent stages.

11 •

Projects where there is a substantial investment needed in infrastructure and high operating leverage (fixed costs): Since the savings from doing a project in multiple stages can be traced to the investments needed at each stage, the benefit is likely to be greater in firms where those costs are large. Capital intensive projects as well as projects that require large initial marketing expenses (a new brand name product for a consumer product company), for example, will gain more from the options created by investing in the projects in multiple stages. Sequential and Compound Options: Some Thoughts A compound option is an option on an option. A simple example would be a call

option on a small company that has only one asset – a patent. Last chapter, we argued that a patent could be viewed as an option and thus the call option on the company becomes a compound option. You can also have a sequence of options, where the value of each option is dependent upon whether the previous option is exercised or not. For instance, a five-stage project has sequential options. Whether you reach the fifth stage or not is obviously a function of whether you make it through the first four stages – the value of the fifth option in the sequence is determined by what happens to the first four options. Needless to say, option pricing becomes more complicated when you have sequential and compound options. There are two choices. One is to value these options as simple options and accept the fact that the value that you obtain will be an approximation. The other is to modify the option pricing model to allow for the special characteristics of these options. While we do not consider these models in this book, you can modify both the Black Scholes and binomial models to allow them to price compound and sequential options. When are expansion options valuable? While the argument that some or many investments have valuable strategic or expansion options embedded in them has great allure, there is a danger that this argument can be used to justify poor investments. In fact, acquirers have long justified huge premiums on acquisitions on synergistic and strategic grounds. We need to be more

12 rigorous in our measurement of the value of real options and in our use of real options as justification for paying high prices or making poor investments. Quantitative Estimation When real options are used to justify a decision, the justification has to be in more than qualitative terms. In other words, managers who argue for investing in a project with poor returns or paying a premium on an acquisition on the basis of the real options generated by this investment should be required to value these real options and show that the economic benefits exceed the costs. There will be two arguments made against this requirement. The first is that real options cannot be easily valued, since the inputs are difficult to obtain and often noisy. The second is that the inputs to option pricing models can be easily manipulated to back up whatever the conclusion might be. While both arguments have some basis, an estimate is better than no estimate at all and the process of trying to estimate the value of a real option is, in fact, the first step to understanding what drives it value. Tests for Expansion Option to have Value Not all investments have options embedded in them and not all options, even if they do exist, have value. To assess whether an investment creates valuable options that need to be analyzed and valued, we need to understand three key questions. 1. Is the first investment a pre-requisite for the later investment/expansion? If not, how necessary is the first investment for the later investment/expansion? Consider our earlier analysis of the value of a patent or the value of an undeveloped oil reserve as options. A firm cannot generate patents without investing in research or paying another firm for the patents and it cannot get rights to an undeveloped oil reserve without bidding on it at a government auction or buying it from another oil company. Clearly, the initial investment here (spending on R&D, bidding at the auction) is required for the firm to have the second investment. Now consider the Ambev investment in a limited introduction and the option to expand into the U.S. market later. The initial investment provides Ambev with information about market potential, without which presumably it is unwilling to expand into the larger market. Unlike the patent and undeveloped reserves examples, the initial investment is not a pre-requisite

13 for the second, though management might view it as such. The connection gets even weaker and the option value lower when we look at one firm acquiring another to have the option to be able to enter a large market. Acquiring an internet service provider to have a foothold in the internet retailing market or buying a Chinese brewery to preserve the option to enter the Chinese beer market would be examples of less valuable options. 2. Does the firm have an exclusive right to the later investment/expansion? If not, does the initial investment provide the firm with significant competitive advantages on subsequent investments? The value of the option ultimately derives not from the cash flows generated by the second and subsequent investments, but from the excess returns generated by these cash flows. The greater the potential for excess returns on the second investment, the greater the value of the expansion option in the first investment. The potential for excess returns is closely tied to how much of a competitive advantage the first investment provides the firm when it takes subsequent investments. At one extreme, again, consider investing in research and development to acquire a patent. The patent gives the firm that owns it the exclusive rights to produce that product and, if the market potential is large, the right to the excess returns from the project. At the other extreme, the firm might get no competitive advantages on subsequent investments, in which case, it is questionable as to whether there can be any excess returns on these investments. In reality, most investments will fall in the continuum between these two extremes, with greater competitive advantages being associated with higher excess returns and larger option values. 3. How sustainable are the competitive advantages? In a competitive market place, excess returns attract competitors and competition drives out excess returns. The more sustainable the competitive advantages possessed by a firm, the greater will be the value of the options embedded in the initial investment. The sustainability of competitive advantages is a function of two forces. The first is the nature of the competition; other things remaining equal, competitive advantages fade much more quickly in sectors where there are aggressive competitors. The second is the nature of the competitive advantage. If the resource controlled by the firm is finite and scarce (as is the case with natural resource reserves and vacant land), the competitive

14 advantage is likely to be sustainable for longer periods. Alternatively, if the competitive advantage comes from being the first mover in a market or from having technological expertise, it will come under assault far sooner. The most direct way of reflecting this competitive advantage in the value of the option is its life; the life of the option can be set to the period of competitive advantage and only the excess returns earned over this period counts towards the value of the option. If the answer is yes to all three questions, then the option to expand can be valuable. Applying the last two tests to the Ambev expansion option, you can see the potential problems. While Ambev is the largest producer of Guarana in the world, it does not have a patent on the product. If the initial introduction proves successful, it is entirely possible that Coke and Pepsi could produce their own versions of Guarana for the national market. If this occurs, Ambev will have expended $100 million of its funds to provide market information to its competitors. Thus, if Ambev gets no competitive advantage in the expansion market because of its initial investment, the option to expand ceases to have value and cannot be used to justify the initial investment. Now consider two intermediate scenarios. If Ambev gets a lead time on the expansion investment because of its initial investment, you could build in higher cash flows for that lead time and a fading off to lower cashflows thereafter. This will lower the present value of the cash flows for the expansion and the value of the option. A simpler adjustment would be to cap the present value of the cash flows, the argument being that competition will restrict how large the net present value can become and value the option with the cap. For instance, if you assume that the present value of the cashflows from the expansion option cannot exceed $2 billion, the value of the expansion option drops to $142 million.4 Valuing a firm with the option to expand Is there an option to expand embedded in some firms that can lead to these firms to trade at a premium over their discounted cash flow values? At least in theory, there is a

4

You can value the capped call by valuing the expansion option twice in the Black Scholes model, once with a strike price of $1,000 (yielding the original expansion option value of $218 million) and one with the strike price of $2000 (yielding an option value of $76 million). The difference between the two is the value of the expansion option with a cap on the present value. You could also value it explicitly in the

15 rationale for making this argument for a small, high-growth firm in a large and evolving market. The discounted cash flow valuation is based upon expected cash flows and expected growth and these expectations should reflect the probability that the firm could be hugely successful (or a huge failure). What the expectations might fail to consider is that, in the event of success, the firm could invest more, add new products or expand into new markets and augment this success. This is the real option that is creating the additional value. Relationship to Discounted Cashflow Valuation If the value of this option to expand is estimated, the value of a firm can be written as the sum of two components – a discounted cash flow value based upon expected cash flows and a value associated with the option to expand. Value of firm = Discounted Cash flow Value

+

Option to Expand

The option pricing approach adds rigor to this argument by estimating the value of the option to expand and it also provides insight into those occasions when it is most valuable. In general, the option to expand is clearly more valuable for more volatile businesses with higher returns on projects (such as biotechnology or computer software) than in stable businesses with lower returns (such as housing, utilities or automobile production). Again, though, you have to be careful not to double count the value of the option. If you use a higher growth rate than would be justified based upon expectations because of the option to expand, you have already counted the value of the option in the discounted cash flow valuation. Adding an additional component to reflect the value of the option would be double counting. Inputs for valuing Expansion Option To value a firm with the option to expand, you have to begin by defining the market that the firm has the option to enter and specify the competitive advantages that you believe will give it some degree of exclusivity to make this entry. Once you are

binomial by setting the value to $2,000 whenever it exceeds that number in the binomial tree. [NOTE: The problem calls for a cap on the PV of cash flow or S, not the exercise price.]

16 convinced that there is this exclusivity, you should then estimate the expected cashflows you would get if you entered the market today and the cost of entering that market. Presumably, the costs will exceed the expected cash flows or you would have entered the market already. The cost of entering the market will become the exercise price of the option and the expected cashflows from entering the market today will become the value of the underlying asset. To estimate the variance in the value, you can either run simulations on how the market will evolve over time or use the variances of publicly traded firms that service that market today and assume that this variance is a good proxy for the volatility in the underlying market. You also have to specify a period by which you have to make the decision of whether to enter the market or not – this will become the life of the option. You may tie this assumption to the assumptions you made about competitive advantages. For instance, if you have the exclusive license to enter a market for the next 10 years, you would use 10 years as your option life. Illustration 29.2: Considering the value of the option to expand Rediff.com is an internet portal serving the Indian sub-continent. In June 2000, the firm had only a few million in revenues, but had tremendous growth potential as a portal and electronic marketplace. Using a discounted cashflow model, we valued Rediff.com at $474 million, based upon its expected cash flows in the internet portal business. Assume that in buying Rediff.com, you are in fact buying an option to expand in the online market in India. This market is a small one now, but could potentially be much larger in five or ten years. In more specific terms, assume that Rediff.com has the option to enter the internet retailing business in India in the future. The cost of entering this business is expected to be $1 billion and, based on current expectations, the present value of the cash flows that would be generated by entering this business today is only $500 million. Based upon current expectations of the growth in the Indian e-commerce business, this investment clearly does not make sense. There is substantial uncertainty about future growth in online retailing in India and the overall performance of the Indian economy. If the economy booms and the online

17 market grows faster than expected over the next 5 years, Rediff.com might be able to create value from entering this market. If you leave the cost of entering the online retailing business at $1 billion, the present value of the cash flows would have to increase above this value for Rediff to enter this business and add value. The standard deviation in the present value of the expected cash flows (which is currently $500 million) is assumed to be 50%. The value of the option to expand into internet retailing can now be estimated using an option pricing model, with the following parameters. S = Present Value of the expected cash flows from entering market today = $ 500 million K = Cost of entering the market today = $ 1 billion σ2 = Variance in the present value of expected cash flows = 0.52 = 0.25 r = 5.8% (This is a five year treasury bond rate: the analysis is being done in U.S dollar terms) t = 5 years The value of the option to expand can be estimated. Option to Expand = 500(0.5786 )− 1000e(-0.058 )(5 )(0.1789 ) = $155.47 million Why does the option expire in 5 years? If the online retail market in India expands beyond this point in time, it is assumed that there will be other potential entrants into this market and that Rediff.com will have no competitive advantages and hence no good reason for entering this market. If the online retail market in India expands sooner than expected, it is assumed that Rediff.com, as one of the few recognized names in the market, will be able to parlay its brand name and the visitors to its portal to establish competitive advantages. The value of Rediff.com as a firm can now be estimated as the sum of the discounted cash flow value of $474 million and the value of the option to expand into the retail market ($155 million). It is true that the discounted cash flow valuation is based upon a high growth rate in revenues, but all of this growth is assumed to occur in the internet portal business and not in online retailing. In fact, the option to enter online retailing is only one of several options available to Rediff. Another path it might embark is to become a development exchange for

18 resources - software developers and programmers in India looking for programming work in the United States and other developed markets. The value of this option can also be estimated using an approach similar to the one shown above. expand.xls: This spreadsheet allows you to estimate the value of the option to expand an investment or project. Value of Financial Flexibility When making financial decisions, managers consider the effects of such decisions on their capacity to make new investments or meet unanticipated contingencies in future periods. Practically, this translates into firms maintaining excess debt capacity or larger cash balances than are warranted by current needs to meet unexpected future requirements. While maintaining this financing flexibility has value to firms, it also has a cost; the large cash balances might earn below market returns and excess debt capacity implies that the firm is giving up some value and has a higher cost of capital. Determinants of the Value of Financial Flexibility One reason that a firm maintains large cash balances and excess debt capacity is to have the future option to take unexpected projects with high returns. To value financial flexibility as an option, assume that a firm has expectations about how much it will need to reinvest in future periods, based upon its own past history and current conditions in the industry. Assume also that a firm has expectations about how much it can raise from internal funds and its normal access to capital markets in future periods. There is uncertainty about future reinvestment needs; for simplicity, we will assume that the capacity to generate funds is known with certainty to the firm. The advantage (and value) of having excess debt capacity or large cash balances is that the firm can meet any reinvestment needs, in excess of funds available, using its debt capacity. The payoff from these projects, however, comes from the excess returns the firm expects to make on them. To value financial flexibility on an annualized basis, therefore, we will use the following measures. Input to Model

Measure

S

Expected

Estimation Approach Annual Use

historical

average

of

19 Reinvestment Needs as % Firm Value K

Annual

Net Cap Ex + ∆Non - cash WC Market Value of Firm

Reinvestment If firm does not want to or cannot use

Needs as percent of firm external financing: value that can be raised without

financing

Net Income + Dividend + Depreciation Market Value of Firm

If firm uses external capital (bank debt,

flexibility

bonds or equity) regularly: Net Income + Depreciation + Net External Financing Market Value of Firm

σ2

t

Variance in reinvestment Variance in the reinvestment as percent of needs

firm value (using historical data)

1 year

To get an annual estimate of the value of flexibility

Illustration 29.3: Valuing Financial Flexibility at the Home Depot The Home Depot is a giant retail chain that sells home improvement products, primarily in the United States. This firm traditionally has not been a heavy user of leverage and has also grown at an extraordinary rate over the last decade. To estimate the value of financial flexibility for the Home Depot, we began by estimating reinvestments as a percent of firm value from 1989 to 1998 in Table 29.1. Table 29.1: Reinvestment Needs as percent of firm value Year

Reinvestment Needs Firm Value Reinvestment Needs as

ln(Reinvestment

percent of Firm Value

Needs)

1989

$175

$2,758

6.35%

-2.7574751

1990

$374

$3,815

9.80%

-2.3224401

1991

$427

$5,137

8.31%

-2.4874405

1992

$456

$7,148

6.38%

-2.7520951

1993

$927

$9,239

10.03%

-2.2992354

1994

$1,176

$12,477

9.43%

-2.3617681

20 1995

$1,344

$15,470

8.69%

-2.4432524

1996

$1,086

$19,535

5.56%

-2.8897065

1997

$1,589

$24,156

6.58%

-2.7214279

1998

$1,817

$30,219

6.01%

-2.8112841

Average Reinvestment needs as % of Firm Value = 7.71% Standard Deviation in ln(Reinvestment Needs) = 22.36% We followed up by estimating internal funds as a percent of firm value, using the sum of net income and depreciation as a measure of internal funds. Table 29.2: Internal Funds as percent of firm value Year

Net Income Depreciation Firm Value Internal Funds/Value

1989

$112

$21

$2,758

4.82%

1990

$163

$34

$3,815

5.16%

1991

$249

$52

$5,137

5.86%

1992

$363

$70

$7,148

6.06%

1993

$457

$90

$9,239

5.92%

1994

$605

$130

$12,477

5.89%

1995

$732

$181

$15,470

5.90%

1996

$938

$232

$19,535

5.99%

1997

$1,160

$283

$24,156

5.97%

1998

$1,614

$373

$30,219

6.58%

Internal funds, on average, were 5.82% of firm value between 1989 and 1998. Since the firm uses almost no external debt, the firm made up the difference between its average reinvestment needs (7.71%) and the average internal fund generation (5.82%) by issuing equity. We will assume, looking forward, that the Home Depot will no longer issue new equity. The Home Depot’s current debt ratio is 4.55% and its current cost of capital is 9.51%. Using the cost of capital framework developed in Chapter 15, we estimated its optimal debt ratio to be 20%, and its cost of capital at that debt level is 9.17%. Finally, the Home Depot in 1998, earned a return on capital of 16.37% and we will assume that this is the expected return on new projects, as well.

21 S = Expected Reinvestment Needs as percent of Firm Value = 7.71% K = Reinvestment needs that can be financed without flexibility = 5.82% t = 1 year σ2 = Variance in ln(Net Capital Expenditures) = (.2237)2 = .05 With a riskfree rate of 6%, the option value that we estimate using these inputs is 0.0228 or 2.28%. We then converted this option value into a measure of value over time by multiplying the value by the annual excess return and then assuming that the firm foregoes this excess returns forever5.  Return on Capital - Cost of Capital  = 0.0228  Cost of Capital    0.1637 − 0.0951  Value of Flexibility = 0.0228  0.0951   = 0.0164 = 1.64%

On an annual basis, the flexibility generated by the excess debt capacity is worth 1.64% of firm value at the Home Depot, which is well in excess of the savings (9.51% - 9.17% = 0.34%) in the cost of capital that would be accomplished, if it used up the excess debt capacity. The one final consideration here is that this estimate does not consider the fact that the Home Depot does not have unlimited financial flexibility. In fact, assume that excess debt capacity of the Home Depot (which is 15.45%, the difference between the optimal debt ratio and the current debt ratio) is the upside limit on financial flexibility. We can value the effect of this limit, by valuing a call with the same parameters as the call described above, but with a strike price of 21.27% (15.45% + 5.82%). In this case, the effect of imposing this constraint on the value of flexibility is negligible. finflex.xls: This spreadsheet allows you to estimate the value of financial flexibility as an option.

5

We are assuming that the project that a firm is unable to take because it lacks financial flexibility is lost forever and that the excess returns on this project would also have lost forever. Both assumptions are strong and may result in overstatement of the lost value.

22 Implications of Financial Flexibility Option Looking at financial flexibility as an option yields valuable insights on when financial flexibility is most valuable. Using the approach developed above, for instance, we would argue that: •

Other things remaining equal, firms operating in businesses where projects earn substantially higher returns than their hurdle rates should value flexibility more than those that operate in stable businesses where excess returns are small. This would imply that firms such as Microsoft and Dell, which earn large excess returns on their projects, can use the need for financial flexibility as justification for holding large cash balances and maintaining excess debt capacity.

•

Since a firm’s ability to fund these reinvestment needs is determined by its capacity to generate internal funds, other things remaining equal, financial flexibility should be worth less to firms with large and stable earnings, as a percent of firm value. Firms that have small or negative earnings, and therefore have much lower capacity to generate internal funds, will value flexibility more.

•

Firms with limited internal funds can still get away with little or no financial flexibility if they can tap external markets for capital – bank debt, bonds and new equity issues. Other things remaining equal, the greater the capacity (and the willingness) of a firm to raise funds from external capital markets, the less should be the value of flexibility. This may explain why private or small firms, which have far less access to capital, will value financial flexibility more than larger firms. The existence of corporate bond markets can also make a difference in how much flexibility is valued. In markets where firms cannot issue bonds and have to depend entirely upon banks for financing, there is less access to capital and a greater need to maintain financial flexibility. In the Home Depot example above, a willingness to tap external funds – debt or equity – would reduce the value of flexibility substantially.

•

The need for and the value of flexibility is a function of how uncertain a firm is about future reinvestment needs. Firms with predictable reinvestment needs should value flexibility less than firms in businesses where reinvestment needs are volatile on a period-to-period basis.

23 In our analysis of Home Depot, we considered the firm’s gross debt ratio, which cannot be less than 0%. If we consider a firm’s net debt ratio (gross debt minus cash), it is entirely possible for firms to have negative net debt ratios. Extending the financing flexibility argument, you could argue that in extreme circumstances – low or negative internal cash flows and no access to capital markets – firms will not only not use their debt capacity (thus driving the gross debt ratio to zero) but accumulate cash. This may explain why many emerging market firms and young technology firms use no debt and accumulate large cash balances. The Option to Abandon When investing in new projects, firms worry about the risk that the investment will not pay off and that actual cash flows will not measure up to expectations. Having the option to abandon a project that does not pay off can be valuable, especially on projects with a significant potential for losses. In this section, we examine the value of the option to abandon and its determinants. The Payoff on the Option to Abandon The option pricing approach provides a general way of estimating and building in the value of abandonment. To illustrate, assume that V is the remaining value on a project if it continues to the end of its life and L is the liquidation or abandonment value for the same project at the same point in time. If the project has a remaining life of n years, the value of continuing the project can be compared to the liquidation (abandonment) value. If the value from continuing is higher, the project should be continued; if the value of abandonment is higher, the holder of the abandonment option could consider abandoning the project. The payoffs can be written as: Payoff from owning an abandonment option

=0

if V > L

= L-V if V ≤ L These payoffs are graphed in Figure 29.3, as a function of the expected stock price.

24 Figure 29.3: The Option to Abandon a Projectt PV of Cash Flows from project

Salvage Value from Abandonment

Unlike the prior two cases, the option to abandon takes on the characteristics of a put option. Illustration 29.4: Valuing an Option to Abandon: Airbus and Lear Aircraft Assume that Lear Aircraft is interested in building a small passenger plane and that it approaches Airbus with a proposal for a joint venture. Each firm will invest $500 million in the joint venture and produce the planes. The investment is expected to have a 30-year life. Airbus works through a traditional investment analysis and concludes that their share of the present value of the expected cash flows would be only $480 million. The net present value of the project would therefore be negative and Airbus would not want to be part of this joint venture. On rejection of the joint venture, Lear approaches Airbus with a sweetener, offering to buy out Airbus’s 50% share of the joint venture any time over the next 5 years for $400 million. This is less than what Airbus will invest initially but it puts a floor on their losses and thus gives Airbus an abandonment option. To value this option to Airbus, note that the inputs are as follows. S = Present value of the share of cash flows from the investment today = $ 480 million K = Abandonment value = $ 400 million T = Period for which abandonment option holds = 5 years To estimate the variance, assume that Airbus employs a Monte Carlo simulation on the project analysis and estimates a standard deviation in project value of 25%. Finally, note

25 that since the project is a finite life project, the present value will decline over time, because there will be fewer years of cash flows left. For simplicity, we will assume that this will be proportional to the time left on the project: Dividend yield =

1 1 = = 3.33% Remaining life of the project 30

Inputting these values into the Black-Scholes model and using a 5% riskless rate, we value the put option. Value of abandonment option

= 400e (-0.05 )(5 )(1 - 0.5776 )- 480e (-0.033 )(5 )(1 - 0.7748 ) = $40.09 million

Since this is greater than the negative net present value of the investment, Airbus should enter into this joint venture. On the other hand, Lear needs to be able to generate a positive net present value of at least $40.09 million to compensate for giving up this option.6 abandon.xls: This spreadsheet allows you to estimate the value of the option to abandon an investment. Problems in valuing the Option to Abandon In Illustration 29.4, we assumed, rather unrealistically, that the abandonment value was clearly specified and did not change during the life of the project. This may be true in some very specific cases, in which an abandonment option is built into the contract. More often, however, the firm has the option to abandon and the salvage value from abandonment can only be estimated. Further, the abandonment value may change over the life of the project, making it difficult to apply traditional option pricing techniques. Finally, it is entirely possible that abandoning a project may not bring in a liquidation value but may create costs instead; a manufacturing firm may have to pay severance to its workers, for instance. In such cases, it would not make sense to abandon, unless the cash flows on the project are even more negative.

6

The binomial model yields a value of $34.74 million for this option.

26 Extensions and Implications of Abandonment Option The fact that the option to abandon has value provides a rationale for firms to build the operating flexibility to scale back or terminate projects if they do not measure up to expectations. It also indicates that firms that try to generate more revenues by offering their customers the option to walk away from commitments will have to weigh the higher revenues against the cost of the options that have been granted to these customers. Escape Clauses in Contracts The first and most direct way of creating an abandonment option is to build operating flexibility contractually with other parties that are involved in a project. Thus, contracts with suppliers may be written on an annual basis rather than be long term and employees may be hired on a temporary basis rather than permanently. The physical plant used for a project may be leased on a short term basis rather than bought and the financial investment may be made in stages rather than as an initial lump sum. While there is a cost to building in this flexibility, the gains may be much larger, especially in volatile businesses. Customer Incentives On the other side of the transaction, offering abandonment options to customers and partners in joint ventures can have a negative impact on value. As an example, assume that a firm that sells its products on multi-year contracts offers customers the option to cancel the contract at any time. While this may increase sales, there is likely to be a substantial cost. In the event of a recession, firms that are unable to meet their obligations are likely to cancel their contracts. Any benefits gained by the initial sale (obtained by offering the inducement of cancellation by the buyer) may be offset by the cost of the option provided to customers. Reconciling net present value and real option valuations Why does an investment sometimes have higher value when you value it using real option approaches than with traditional discounted cash flow models? The answer lies in the flexibility that firms have to change the way they invest in and run a project, based

27 upon what they observe in the market. Thus, an oil company will not produce the same amount of oil or drill as many new wells if oil prices go to $15 a barrel as it would if oil prices go up to $ 35 a barrel. In traditional net present value, we consider the expected actions and the cash flow consequences of those actions to estimate the value of an investment. If there is a potential for further investments, expansion or abandonment down the road, all you can do is consider the probabilities of such actions and build it into your cash flows. Analysts often allow for flexibility by using decision trees and mapping out the optimal path, given each outcome. You can then estimate the value of a project today, using the probabilities of each branch and estimating the present value of the cash flows from each branch. For instance, you have a decision tree for a new investment for the Home Depot in the Figure 29.4. Figure 10.9: Decision Tree for The Home Depot Home Shopping t=0 Market Test

t=1 Partial Introduction

t=2 Full Introduction

t=3 Year 1

Invest (2,500) (1000)

0.75

Stop

t=6 Year 4

15,000

18,000 21,000

0.25 8,000

10,000 0.50

12,000 16,000

(2,000)

(4,000)

(6,000) (8,000)

0.50

Stop

t=5 Year 3

Prob 12,000

Invest (15,000)

t=4 Year 2

0.25

NPV

.09375

$23.066

.1875

$7,978

.09375 -$26,252 .375

-$3,222

0.25

-$1000

0.50

0.25

This decision tree does bear a significant resemblance to the binomial tree approach that we use to value real options, but there are two differences. The first is that the probabilities of the outcomes are not used directly to value the real option and the second is that you have only two branches at each node in the binomial tree. Notwithstanding this, you might wonder why the two approaches will yield different values for the project. The answer is surprisingly simple. It lies in the discount rate assumptions we make to compute the value. In the real options approach, you use a replicating portfolio to compute value. In the decision tree above, you used the cost of capital for the project

28 as the discount rate all through the process. If the exposure to market risk, which is what determines the cost of capital, changes at each node, you can argue that using the same cost of capital all the way through is incorrect and that you should be modifying the discount rate as you move through time. If you do, you will obtain the same value with both approaches. The real options approach does allow for far more complexity and is simpler to employ with continuous distributions (as opposed to the discrete outcomes that we assume in decision trees). Summary In this chapter, we consider two options that are embedded in many investments – the option to expand an investment and the option to abandon it. When a firm has an option to expand an investment, the value of this expansion option may sometimes allow it to override the fact that the initial investment has a negative net present value. Extending this concept to firm valuation, you may sometimes add a premium to the value obtained from a discounted cash flow valuation for a firm that has the potential to enter new markets or create new products. This expansion option has maximum value when the firm has the exclusive right to make these investments and the value decreases as the competitive advantages enjoyed by the firm decline. The option to abandon refers to the right that firms often possess to walk away from poor investments. To the extent that this reduces the firm’s exposure to the worst outcomes, it can make the difference between investing in a new project and not.

29 Problems 1. NBC has the rights to televise the Winter Olympics in 2 years and is trying to estimate the value of these rights for possible sale to another network. NBC expects it to cost $40 million (in present value terms) to televise the Olympics and based upon current assessments expects to have a Nielsen rating7 of 15 for the games. Each rating point is expected to yield net revenue of $2 million to NBC (in present value terms). There is substantial variability in this estimate and the standard deviation in the expected net revenues is 30%. The riskless rate is 5%. a. What is the net present value of these rights, based upon current assessments? b. Estimate the value of these rights for sale to another network. 2. You are analyzing Skates Inc., a firm that manufactures skateboards. The firm is currently unlevered and has a cost of equity of 12%. You estimate that Skates would have a cost of capital of 11% at its optimal debt ratio of 40%. The management, however, insists that it will not borrow the money because of the value of maintaining financial flexibility and they have provided you with the following information. •

Over the last 10 years, reinvestments (net capital expenditures + working capital investments) have amounted to 10% of firm value, on an annual basis. The standard deviation in this reinvestment has been 0.30.

•

The firm has traditionally used only internal funding (net income + depreciation) to meet these needs and these have amounted to 6% of firm value.

•

In the most recent year, the firm earned $180 million in net income on a book value of equity of $1 billion and it expects to earn these excess returns on new investments in the future.

•

The riskless rate is 5%.

a. Estimate the value of financial flexibility as a percent of firm value, on an annual basis.

7

There are 99.4 million households in the United States. Each rating point represents 1% of roughly 994,000 households.

30 b. Based upon part a, would you recommend that Skates use its excess debt capacity? 3. Disney is considering entering into a joint venture to build condominiums in Vail, Colorado, with a local real estate developer. The development is expected to cost $1 billion overall and, based on Disney’s estimate of the cashflows, generate $900 million in present value cash flows. Disney will have a 40% share of the joint venture (requiring it to put up $400 million of the initial investment and entitling it to 40% of the cashflows) but it will have the right to sell its share of the venture back to the developer for $300 million. a. If the standard deviation in real estate values in Vail is 30% and the riskless rate is 5%, estimate the value of the abandonment option to Disney. b. Would you advice Disney to enter into the joint venture? c. If you were advising the developer, how much would he need to generate in present value cashflows from the investment to make this a good investment? 4. Quality Wireless is considering making an investment in China. While it knows that the investment will cost $1 billion and generate only $800 million in cashflows (in present value terms), the proponents of expansion are arguing that the potential market is huge and that Quality should go ahead with its investment. a. Under what conditions will the expansion potential have option value? b. Assume now that there is an option value to expansion that exactly offsets the negative net present value on the initial investment. If the cost of the subsequent expansion in 5 years is $2.5 billion, what is your current estimate of the present value of the cash flows from expansion? (You can assume that the standard deviation in the present value of the cashflows is 25% and that the riskless rate is 6%.) 5. Reliable Machinery Inc. is considering expanding its operations in Thailand. The initial analysis of the projects yields the following results. •

The project is expected to generate $85 million in after-tax cash flows every year for the next 10 years.

31 •

The initial investment in the project is expected to be $750 million.

•

The cost of capital for the project is 12%.

If the project generates much higher cash flows than anticipated, you will have the exclusive right for the next 10 years (from a manufacturing license) to expand operations into the rest of South East Asia. A current analysis suggests the following about the expansion opportunity. •

The expansion will cost $2 billion (in current dollars).

•

The expansion is expected to generate $150 million in after tax cash flows each year for 15 years. There is substantial uncertainty about these cash flows and the standard deviation in the present value is 40%.

•

The cost of capital for this investment is expected to be 12% as well. The riskfree rate is 6.5%. a. Estimate the net present value of the initial investment. b. Estimate the value of the expansion option.

1

CHAPTER 30 VALUING EQUITY IN DISTRESSED FIRMS In Chapter 22, we examined how discounted cash flow models could be adapted to value firms with negative earnings. In most of our solutions, we estimated the expected cash flows into the future and assumed that an improvement in margins or earnings would result in positive cash flows and firm value. In the special case where the firm has substantial amounts of debt, we argued that there is a very real possibility of defaulting on the debt and going bankrupt. In these cases, discounted cash flow valuation may be an inadequate tool for estimating value. In this chapter, we look at firms with negative earnings, significant assets in place and substantial debt. We argue that the equity investors in this firm, given limited liability, have the option to liquidate the firm and pay off the debt. This call option on the underlying firm can add value to equity, especially when there is significant uncertainty about the value of the assets. Equity in Highly Levered distressed firms In most publicly traded firms, equity has two features. The first is that the equity investors run the firm and can choose to liquidate its assets and pay off other claim holders at any time. The second is that the liability of equity investors in some private firms and almost all publicly traded firms is restricted to their equity investments in these firms. This combination of the option to liquidate and limited liability allows equity to have the features of a call option. In firms with substantial liabilities and negative earnings, the option value of equity may be in excess of the discounted cash flow value. The Payoff on Equity as an Option The equity in a firm is a residual claim, that is, equity holders lay claim to all cash flows left after other financial claimholders (debt, preferred stock, etc.) have been satisfied. If a firm is liquidated, the same principle applies; equity investors receive the cash that is left in the firm after all outstanding debt and other financial claims have been paid off. With limited liability, if the value of the firm is less than the value of the outstanding debt, equity investors cannot lose more than their investment in the firm. The payoff to equity investors on liquidation can therefore be written as:

2 Payoff to equity on liquidation

=V-D

if V > D

=0

if V ≤ D

where V = Liquidation Value of the firm D = Face Value of the outstanding debt and other external claims Equity can thus be viewed as a call option on the firm, where exercising the option requires that the firm be liquidated and the face value of the debt (which corresponds to the exercise price) be paid off. The firm is the underlying asset and the option expires when the debt comes due. The payoffs are shown in Figure 30.1. Figure 30.1: Payoff on Equity as Option on a Firm Net Payoff on Equity

Face Value of Debt Value of firm

Illustration 30.1: Valuing Equity as an Option Assume that you are valuing the equity in a firm whose assets are currently valued at $100 million; the standard deviation in this asset value is 40%. The face value of debt is $80 million (it is zero coupon debt with 10 years left to maturity). The 10-year treasury bond rate is 10%. We can value equity as a call option on the firm, using the following inputs for the option pricing model. Value of the underlying asset = S = Value of the firm = $ 100 million Exercise price = K = Face Value of outstanding debt = $ 80 million Life of the option = t = Life of zero-coupon debt = 10 years

3 Variance in the value of the underlying asset = σ2 = Variance in firm value = 0.16 Riskless rate = r = Treasury bond rate corresponding to option life = 10% Based upon these inputs, the Black-Scholes model provides the following value for the call. d1 = 1.5994

N(d1) = 0.9451

d2 = 0.3345

N(d2) = 0.6310

Value of the call = 100(0.9451)− 80e(-0.10 )(10 )(0.6310 ) = $75.94 million Since the call value represents the value of equity and the firm value is $100 million, the estimated value of the outstanding debt can be calculated. Value of the outstanding debt = $100 - $75.94 = $24.06 million Since the debt is a 10-year zero coupon bond, the market interest rate on the bond can be calculated. 1

 $80 10 Interest rate on debt =   - 1 = 12.77%  $24.06 

Thus, the default spread on this bond should be 2.77%. The Importance of Limited Liability The argument that equity is a call option holds only if equity has limited liability – i.e., the most that an equity investor can lose is what he or she has invested in a firm. This is clearly the case in publicly traded companies. In private companies, however, the owners often have unlimited liability. If these firms get into financial trouble and are unable to make their debt payments, the owner’s personal assets can be put at risk. You should not value equity as a call option in these cases. Implications of viewing Equity as an Option When the equity in a firm takes on the characteristics of a call option, you have to change the way you think about its value and what determines its value. In this section, we will consider a number of potential implications for equity investors and bondholders in the firm.

4 When will equity be worthless? In discounted cash flow valuation, we argue that equity is worthless if what you own (the value of the firm) is less than what you owe. The first implication of viewing equity as a call option is that equity will have value, even if the value of the firm falls well below the face value of the outstanding debt. While the firm will be viewed as troubled by investors, accountants and analysts, its equity is not worthless. In fact, just as deep outof-the-money traded call options command value because of the possibility that the value of the underlying asset may increase above the strike price in the remaining lifetime of the option, equity commands value because of the time premium on the option (the time until the bonds mature and come due) and the possibility that the value of the assets may increase above the face value of the bonds before they come due. Illustration 30.2: Firm Value and Equity Value Revisiting the preceding example, assume that the value of the firm drops to $50 million, below the face value of the outstanding debt ($80 million). Assume that all the other inputs remain unchanged. The parameters of equity as a call option are as follows: Value of the underlying asset = S = Value of the firm = $ 50 million Exercise price = K = Face Value of outstanding debt = $ 80 million Life of the option = t = Life of zero-coupon debt = 10 years Variance in the value of the underlying asset = σ2 = Variance in firm value = 0.16 Riskless rate = r = Treasury bond rate corresponding to option life = 10% Based upon these inputs, the Black-Scholes model provides the following value for the call. d1 = 1.0515

N(d1) = 0.8534

d2 = -0.2135

N(d2) = 0.4155

Value of the call (equity) = 50 (0.8534) - 80 exp(-0.10)(10) (0.4155) = $30.44 million Value of the bond= $50 - $30.44 = $19.56 million As you can see, the equity in this firm retains value, because of the option characteristics of equity. In fact, equity continues to have value in this example even if the firm value drops to $10 million or below, as shown in Figure 30.2.

5 Value of Equity as Firm Value Changes 80

70

Value of Equity

60

50

40

30

20

10

0 100

90

80

70

60

50

40

30

20

10

Value of Firm ($ 80 Face Value of Debt)

Increasing Risk can increase Equity Value In traditional discounted cash flow valuation, higher risk almost always translates into lower value for equity investors. When equity takes on the characteristics of a call option, you should not expect this relationship to continue to hold. Risk can become your ally, when you are an equity investor in a troubled firm. In essence, you have little to lose and much to gain from swings in firm value. Illustration 30.3: Equity Value and Volatility Let us revisit the valuation in Illustration 30.1. The value of the equity is a function of the variance in firm value, which we assumed to be 40%. If we change this variance, holding all else constant, the value of the equity will change as evidenced in Figure 30.3.

6 Figure 30.3: Equity Value and Standard Deviation in Firm Value 25%

100

90

20%

80

15%

60

50

10%

40

Interest rate on debt

Value of Equity

70

Equity Value Interest rate on debt

30

5%

20

10

0%

0 0%

10%

20%

30%

40%

50%

60%

70%

80%

Standard deviation in firm value

Note that the value of equity increases, if we hold firm value constant, as the standard deviation increases. The interest rate on debt also increases as the standard deviation increases. Probability of Default and Default Spreads One of the more interesting pieces of output from the option pricing model is the risk-neutral probability of default that you can obtain for the firm. In the Black-Scholes model, you can estimate this value from N(d2), which is the risk-neutral probability that S>K, which in this model is the probability that the value of the firm’s asset will exceed the face value of the debt. Risk-neutral probability of default = 1 – N(d2) In addition, the interest rate from the debt allows us to estimate the appropriate default spread to charge on bonds. You can see the potential in applying this model to bank loan portfolios to extract both the probability of default and to measure whether you are charging an interest rate that is high enough on the debt. In fact, there are commercial services that use fairly sophisticated option pricing models to estimate both values for firms.

7 Illustration 30.4: Probabilities of default and Default Spreads We return to Illustration 30.1 and estimate the probability of default as N(d2) and the default spread, measured as the difference between the interest rate on a firm’s debt and the riskfree rate, as a function of the variance. These values are graphed in Figure 30.4. Figure 30.4: Risk Neutral Probability of default and Default spreads 90%

14%

80% 12% 70% 10%

8%

50% 40%

6%

probability of default

Default Spread

60%

Default Spread 1-N(d2)

30% 4% 20% 2% 10% 0%

0% 0%

10%

20%

30%

40%

50%

60%

70%

80%

Standard Deviation in firm value

Note that the probability of default climbs very quickly as the standard deviation in firm value increases and the default spread follows it along. Estimating the Value of Equity as an Option The examples we have used thus far to illustrate the application of option pricing to value equity have included some simplifying assumptions. Among them are the following. 1. There are only two claimholders in the firm - debt and equity. 2. There is only one issue of debt outstanding and it can be retired at face value. 3. The debt has a zero coupon and no special features (convertibility, put clauses, etc.) 4. The value of the firm and the variance in that value can be estimated.

8 Each of these assumptions is made for a reason. First, by restricting the claimholders to just debt and equity, we make the problem more tractable; introducing other claimholders such as preferred stock makes it more difficult to arrive at a result, albeit not impossible. Second, by assuming only one zero-coupon debt issue that can be retired at face value any time prior to maturity, we align the features of the debt more closely to the features of the strike price on a standard option. Third, if the debt is coupon debt, or more than one debt issue is outstanding, the equity investors can be forced to exercise (liquidate the firm) at these earlier coupon dates if they do not have the cash flows to meet their coupon obligations. Finally, knowing the value of the firm and the variance in that value makes the option pricing possible, but it also raises an interesting question about the usefulness of option pricing in equity valuation. If the bonds of the firm are publicly traded, the market value of the debt can be subtracted from the value of the firm to obtain the value of equity much more directly. The option pricing approach does have its advantages, however. Specifically, when the debt of a firm is not publicly traded, option pricing theory can provide an estimate of value for the equity in the firm. Even when the debt is publicly traded, the bonds may not be correctly valued and the option pricing framework can be useful in evaluating the values of debt and equity. Finally, relating the values of debt and equity to the variance in firm value provides some insight into the redistributive effects of actions taken by the firm. Inputs for Valuing Equity as an Option Since most firms do not fall into the neat framework developed above (such as having only one zero-coupon bond outstanding), we have to make some compromises to use this model in valuation. Value of the Firm We can obtain the value of the firm in one of four ways. In the first, we cumulate the market values of outstanding debt and equity, assuming that all debt and equity are traded, to obtain firm value. The option pricing model then reallocates the firm value between debt and equity. This approach, while simple, is internally inconsistent. We start

9 with one set of market values for debt and equity and, using the option pricing model, end up with entirely different values for each. In the second, we estimate the market values of the assets of the firm by discounting expected cash flows at the cost of capital. The one consideration that we need to keep in mind is that the value of the firm in an option pricing model should be the value obtained on liquidation. This may be less than the total firm value, which includes expected future investments and it may also be reduced to reflect the cost of liquidation. If we estimate the firm value using a discounted cash flow model, then this would suggest that only existing investments1 should be considered while estimating firm value. The biggest problem with this approach is that financial distress can affect operating income and thus the value that you obtain by using current operating income may be too low. In the third approach, we estimate a multiple of revenues by looking at healthy firms in the same business and apply this multiple to the revenues of the firm you are valuing. Implicitly, we are assuming that a potential buyer, in the event of liquidation, will pay this value. We can use the third approach for firms that have separable assets that are individually traded. For example, we can value a troubled real estate firm that owns five properties by valuing each property separately and then aggregating the values. Variance in Firm value We can obtain the variance in firm value directly if both stocks and bonds in the firm are traded. Defining σe2 as the variance in the stock price and σd2 as the variance in the bond price, w e as the market-value weight of equity and wd as the market-value weight of debt, we can write the variance in firm value as:2 2 firm

= we2

2 e

+ wd2

2 d

+ 2 we wd

ed

e

d

where ρ ed is the correlation between the stock and the bond prices. When the bonds of the firm are not traded, we can use the variance of similarly rated bonds as the estimate of

1

Technically, this can be done by putting the firm into stable growth and valuing it as a stable growth firm, where reinvestments are used to either preserve or augment existing assets. 2 This is an extension of the variance formula for a two-asset portfolio.

10 σd2 and the correlation between similarly rated bonds and the firm's stock as the estimate of ρ ed. When companies get into financial trouble, this approach can yield misleading results as both its stock prices and its bond prices become more volatile. An alternative that often yields more reliable estimates is to use the average variance in firm value for other firms in the sector. Thus, the value of equity in a deeply troubled steel company can be estimated using the average variance in firm value of all traded steel companies.

optvar.xls: There is a dataset on the web that summarizes standard deviations in equity and firm value, by industry, for firms in the United States. Maturity of the Debt Most firms have more than one debt issue on their books and much of the debt comes with coupons. Since the option pricing model allows for only one input for the time to expiration, we have to convert these multiple bonds issues and coupon payments into one equivalent zero-coupon bond. •

One solution, which takes into account both the coupon payments and the maturity of the bonds, is to estimate the duration of each debt issue and calculate a face-value-weighted average of the durations of the different issues. This valueweighted duration is then used as a measure of the time to expiration of the option.

•

An approximation is to use the face-value weighted maturity of the debt converted to the maturity of the zero-coupon bond in the option pricing model.

Face Value of Debt When a distressed firm has multiple debt issues outstanding, you have three choices when it comes to what you use as the face value of debt: •

You could add up the principal due on all of the debt of the firm and consider it to be the face value of the hypothetical zero coupon bond that you assume that the firm has issued. The limitation of this approach is that it will understate what the

11 firm will truly have to pay out over the life of the debt, since there will be coupon payments and interest payments during the period. •

At the other extreme, you could add the expected interest and coupon payments that will come due on the debt to the principal payments to come up with a cumulated face value of debt. Since the interest payments occur in the near years and the principal payments are due only when the debt comes due, you are mixing cash flows up at different points in time when you do this. This is, however, the simplest approach of dealing with intermediate interest payments coming due.

•

You can consider only the principal due on the debt as the face value of the debt and the interest payments each year, specified as a percent of firm value, can take the place of the dividend yield in the option pricing model. In effect, each year that the firm remains in existence, you would expect to see the value of the firm decline by the expected payments on the debt.

Illustration 30.5: Valuing Equity as an option – Eurotunnel in 1997 Eurotunnel was the firm that was created to build and ultimately profit from the tunnel under the English Channel, linking England and France. While the tunnel was readied for operations in the early 1990s, it was never a commercial success and reported significant losses each year after opening. In early 1998, Eurotunnel had a book value of equity of -£117 million, and in 1997, the firm had reported earnings before interest and taxes of -£3.45 million and net income of -£611 million on revenues of £456 million. By any measure, it was a firm in financial trouble. Much of the financing for the tunnel had come from debt and, at the end of 1997, Eurotunnel had debt obligations in excess of £5,000 million, raised from a variety of bond issues and bank debt. Adding the expected interest payments and coupon payments on the debt brings the total obligations of the firm up to £8,865 million. The following table summarizes the outstanding debt at the firm, with our estimates of the expected duration for each class of debt. Table 30.1: Debt Breakdown for Eurotunnel Debt Type

Face Value (including cumulated coupons)

Duration

Short term

£ 935

0.50

12 10 year

£ 2435

6.7

20 year

£ 3555

12.6

Longer

£ 1940

18.2

£8,865 mil

10.93 years

Total

The firm’s only significant asset is its ownership of the tunnel and we estimated the value of this asset from its expected cash flows and the appropriate cost of capital. The assumptions we made were as follows. 1. Revenues will grow 10% a year for the next 5 years and 3% a year in perpetuity after that. 2. The cost of goods sold which was 72% of revenues in 1997 will drop to 60% of revenues by 2002 in linear increments and stay at that level. 3. Capital spending and depreciation will grow 3% a year for the next 5 years. Note that the net capital expenditure is negative for each of these years – we are assuming that the firm will be able to not make significant reinvestments for the next 5 years. Beyond year 5, capital expenditures will offset depreciation. 4. There are no working capital requirements. 5. The debt ratio, which was 95.35% at the end of 1997, will drop to 70% by 2002. The cost of debt is 10% for the next 5 years and 8% after that. 6. The beta for the stock will be 2.00 for the next five years, and drop to 0.8 thereafter (as the leverage decreases). The long-term bond rate at the time of the valuation was 6% and the tax rate was 35%. Based on these assumptions, we estimated the cash flows in Table 30.2. Table 30.2: Estimated FCFF: Eurotunnel

Revenues - COGS - Depreciation EBIT - EBIT*t EBIT (1-t) + Depreciation - Capital Spending

1 $501.60 $361.15 $141.11 ($0.66) $0.00 ($0.66) $141.11 $46.35

2 $551.76 $380.71 $145.34 $25.70 $9.00 $16.71 $145.34 $47.74

3 $606.94 $400.58 $149.70 $56.65 $19.83 $36.83 $149.70 $49.17

4 $667.63 $420.61 $154.19 $92.83 $32.49 $60.34 $154.19 $50.65

5 $734.39 $440.64 $158.82 $134.94 $47.23 $87.71 $158.82 $52.17

Terminal Year $756.42 $453.85 $163.59 $138.98 $48.64 $90.34 $163.59 $163.59

13 Chg. Working Capital $0.00 $0.00 $0.00 $0.00 $0.00 Free CF to Firm $94.10 $114.31 $137.36 $163.89 $194.36 Terminal Value $2,402.66 Present Value $87.95 $99.86 $112.16 $125.08 $1,852.67 Value of firm = $2,277.73

$0.00 $90.34

The value of the assets of the firm is £2,278 million. The final input we estimated was the standard deviation in firm value. Since there are no directly comparable firms, we estimated the standard deviations in Eurotunnel stock and debt using the data over the previous years. Standard deviation in Eurotunnel stock price (ln) = 41% Standard deviation in Eurotunnel bond price (ln) = 17% We also estimated a correlation of 0.50 between Eurotunnel stock and bond prices and the average market debt to capital ratio during the two-year period was 85%. Combining these inputs, we estimated the standard deviation in firm value to be: 2 firm

= (0.15) (0.41) + (0.85) (0.17 ) + 2(0.15)(0.85)(0.5)(0.41)(0.17 ) = 0.0335 2

2

2

2

In summary, the inputs to the option pricing model were as follows. Value of the underlying asset = S = Value of the firm = £2,278 million Exercise price = K = Face Value of outstanding debt = £8,865 mil Life of the option = t = Weighted average duration of debt = 10.93 years Variance in the value of the underlying asset = σ2 = Variance in firm value = 0.0335 Riskless rate = r = Treasury bond rate corresponding to option life = 6% Based upon these inputs, we estimate the following value for the call: d1 = -0.8582

N(d1) = 0.1955

d2 = -1.4637

N(d2) = 0.0717

Value of the call = 2,278(0.1955) − 8,865e ( -0.06) (10.93) (0.0717) = $116 million Eurotunnel's equity was trading at £150 million in 1997. The option pricing framework, in addition to yielding a value for Eurotunnel equity, yields some valuable insight into the drivers of value for this equity. While it is certainly important that the firm try to bring costs under control and increase operating margins, the two most critical variables determining equity value are the duration of the

14 debt and the variance in firm value. Any action that increases (decreases) the debt duration will have a positive (negative) effect on equity value. For instance, when the French government put pressure on the bankers who had lent money to Eurotunnel to ease restrictions and allow the firm more time to repay its debt, equity investors benefited as their options became more long term. Similarly, an action that increases the volatility of expected firm value will increase the value of the option. equity.xls: This spreadsheet allows you to estimate the value the equity in a troubled firm as an option. Vulture Investing and Option Pricing Vulture investing refers to an investment strategy of buying the securities of firms that are in severe financial distress. In a sense, you are investing in deep out of the money options and hoping that some of these options pay off handsomely. Using the option pricing framework allows us to draw some conclusions about when and how this strategy can pay off. •

As with any portfolio of deep out-of-the-money options, you should expect a considerable proportion of the portfolio to end up worthless. The relatively few investments that do pay off, however, will earn huge returns and you could still end up with a portfolio with impressive returns.

•

You should direct your equity investments to equity in deeply troubled firms in volatile sectors. Risk is your ally when you invest in options; and the equity in these firms should be worth more than equity in deeply troubled stable firms.

•

If you are buying equity in deeply troubled firms, you should direct your investments towards troubled firms with longer term debt rather than shorter tem debt. As the life of the option increases, you will see the value of the option also increase.

•

If you are investing in the debt issued by financially troubled firms, you cannot be a passive bondholder. You have to take an active role in the management and obtain an equity stake in the companies you invest in, perhaps by making the debt convertible.

15 Consequences for decision making Option pricing theory can be applied to illustrate the conflict between stockholders and bondholders when it comes to investment analysis and conglomerate mergers. In this section, we will argue that decisions that make stockholders better off are not necessarily value maximizing for the firm and can hurt bondholders. The Conflict between Bondholders and Stockholders Stockholder and bondholders have different objective functions, and this can lead to agency problems, whereby stockholders expropriate wealth from bondholders. The conflict can manifest itself in a number of ways. For instance, stockholders have an incentive to invest in riskier projects than bondholders and to pay more out in dividends than bondholders would like them to. The conflict between bondholders and stockholders can be illustrated dramatically using the option pricing methodology developed in the previous section. Investing in Risky Projects Since equity is a call option on the value of the firm, other things remaining equal, an increase in the variance in the firm value will lead to an increase in the value of equity. It is therefore conceivable that stockholders can invest in risky projects with negative net present values, which, while making them better off, may make the bonds and the firm less valuable. To illustrate, consider the firm in Illustration 30.1 with a value of assets of $100 million, a face value of zero-coupon ten-year debt of $80 million and a standard deviation in the value of the firm of 40%. The equity and debt in this firm were valued as follows: Value of Equity = $75.94 million Value of Debt = $24.06 million Value of Firm == $100 million Now assume that the stockholders have the opportunity to invest in a project with a net present value of -$2 million; the project is a very risky one that will push up the standard deviation in firm value to 50%. The equity as a call option can then be valued using the following inputs.

16 Value of the underlying asset = S = Value of the firm = $ 100 million - $2 million = $ 98 million (The value of the firm is lowered because of the negative net present value project.) Exercise price = K = Face Value of outstanding debt = $ 80 million Life of the option = t = Life of zero-coupon debt = 10 years Variance in the value of the underlying asset = σ2 = Variance in firm value = 0.25 Riskless rate = r = Treasury bond rate corresponding to option life = 10% Based upon these inputs, the Black-Scholes model provides the following value for the equity and debt in this firm. Value of Equity = $77.71 Value of Debt = $20.29 Value of Firm = $98.00 The value of equity rises from $75.94 million to $ 77.71 million, even though the firm value declines by $2 million. The increase in equity value comes at the expense of bondholders, who find their wealth decline from $24.06 million to $20.29 million. Conglomerate Mergers Bondholders and stockholders may also be affected differently by conglomerate mergers, where the variance in earnings and cash flows of the combined firm can be expected to decline because the merging firms have earning streams that are not perfectly correlated. In these mergers, the value of the combined equity in the firm will decrease after the merger because of the decline in variance; consequently, bondholders will gain. Stockholders can reclaim some or all of this lost wealth by utilizing their higher debt capacity and issuing new debt. To illustrate, suppose you are provided with the following information on two firms, Lube and Auto (auto service) and Gianni Cosmetics (a cosmetics manufacturer) that hope to merge. Lube & Auto

Gianni Cosmetics

Value of the firm

$100 million

$ 150 million

Face Value of Debt

$ 80 million

$ 50 million

Maturity of debt

10 years

10 years

Std. Dev. in firm value

40 %

50 %

(Zero-coupon debt)

17 Correlation between firm cash flows

0.4

The ten-year bond rate is 10%. We calculate the variance in the value of the firm after the acquisition as follows: = we

2

2 e

+ wd

2

2 d

+ 2 we wd

ed

e

d

Variance in combined firm value = (0.4 ) (0.4 ) + (0.6 ) (0.5) + 2(0.4 )(0.6 )(0.4 )(0.4 )(0.5) = 0.154 2

2

2

2

We estimate the values of equity and debt in the individual firms and the combined firm using the option pricing model. Lube & Auto

Gianni

Combined firm

Value of equity in the firm

$75.94

$134.48

$ 207.58

Value of debt in the firm

$24.06

$ 15.52

$ 42.42

Value of the firm

$100.00

$150.00

$ 250.00

The combined value of the equity prior to the merger is $ 210.42 million; it declines to $207.58 million after that. The wealth of the bondholders increases by an equal amount. There is a transfer of wealth from stockholders to bondholders, as a consequence of the merger. Thus, conglomerate mergers that are not followed by increases in leverage are likely to result in a wealth transfer from stockholders to bondholders. Is equity not a call option in every firm? Looking at the framework that we have employed in this chapter, you are probably wondering why equity in every firm cannot be viewed as a call option and why therefore we should not add a premium to discounted cash flow values for all firms. It is true that equity is a call option in every firm, but in most firms, the value of the firm as a going concern will be greater than the value you obtain from a liquidation option. Consider, for instance, a high growth firm with very little in assets in place and a high proportion of value from growth potential. If this firm liquidates, it will get the value of its asset in place – this will become the value of the underlying asset in the option pricing model and determine the value of equity as a call option on the firm. This value will be much lower than the value you would obtain if you valued the firm as a going concern and considered the cash flows from expected growth.

18 Value of equity = Maximum (Equity value as a going concern from a discounted cashflow valuation, Equity value as a call option on liquidation) For some mature firms that derive most of their value coming from assets in place and substantial debt, the call option can be the higher value. For other firms, though, the going concern will be greater. Summary The value of equity in deeply troubled firms - firms with negative earnings and high leverage - can be viewed as a call option. The option rests in the hands of equity investors, who can choose to liquidate the firm and claim the difference between firm value and debt outstanding. With limited liability, they do not have to make up the difference if firm value falls below the value of the outstanding debt. The equity will retain value even when the value of the assets of the firm is lower than the debt outstanding, because of the time premium on the option.

19 Problems 1. Designate the following statements as true or false. a. Equity can be viewed as an option because equity investors have limited liability (limited to their equity investment in the firm). b. Equity investors will sometimes take bad projects (with negative net present value) because they can add to the value of the firm. c. Investing in a good project (with positive NPV) -- which is less risky than the average risk of the firm -- can negatively impact equity investors. d. The value of equity in a firm is an increasing function of the duration of the debt in the firm (i.e., equity will be more valuable in a firm with longer term debt than an otherwise similar firm with short term debt). e. In a merger in which two risky firms merge and do not borrow more money, equity can become less valuable because existing debt will become less risky. 2. XYZ Corporation has $500 million in zero-coupon debt outstanding, due in five years. The firm had earnings before interest and taxes of $40 million in the most recent year (the tax rate is 40%). These earnings are expected to grow 5% a year in perpetuity and the firm paid no dividends. The firm had a cost of equity of 12% and a cost of capital of 10%. The annualized standard deviation in firm values of comparable firms is 12.5%. The fiveyear bond rate is 5%. a. Estimate the value of the firm. b. Estimate the value of equity, using an option pricing model. c. Estimate the market value of debt and the appropriate interest rate on the debt. 3. McCaw Cellular Communications reported earnings before interest and taxes of $850 million in 1993 and had a depreciation allowance of $400 million in that year (which was offset by capital spending of an equivalent amount). The earnings before interest and taxes are expected to grow 20% a year for the next five years and 5% a year after that. The cost of capital is 10%. The firm has $10 billion in debt outstanding with the following characteristics. Duration

Debt

1 year

$2 billion

20 2 years

$4 billion

5 years

$4 billion

The annualized standard deviation in the firm's stock price is 35%, while the annualized standard deviation in the traded bonds is 15%. The correlation between stock and bond prices has been 0.5. The firm has a debt/equity ratio of 50% and the after-tax cost of debt is 6%. (The beta of the stock is 1.50; the 30-year treasury bond rate is 7%.) The threeyear bond rate is 5%. a. Estimate the value of the firm. b. Estimate the value of the equity. c. The stock was trading at $60 and there were 210 million shares outstanding in January 1994. Estimate the implied standard deviation in firm value. d. Estimate the market value of the debt. 4. You have been asked to analyze the value of equity in a company that has the following features. •

The earnings before interest and taxes is $25 million and the corporate tax rate is 40%. There is no net capital expenditures or working capital requirements and the earnings are expected to grow 5% a year in perpetuity. The cost of capital of comparable firms is 10%.

•

The firm has two types of debt outstanding - 2-year zero-coupon bonds with a face value of $250 million and bank debt with ten years to maturity with a face value of $250 million (The duration of this debt is 4 years.).

•

The firm is in two businesses - food processing and auto repair. The average standard deviation in firm value for firms in food processing is 25%, whereas the standard deviation for firms in auto repair is 40%. The correlation between the businesses is 0.5.

•

The riskless rate is 7%.

Use the option pricing model to value equity as an option. 5. You are valuing the equity in a firm with $800 million (face value) in debt with an average duration of 6 years and assets with an estimated value of $400 million. The

21 standard deviation in asset value is 30%. With these inputs (and a riskless rate of 6%) we obtain the following values (approximately) for d1 and d2. d1 = - 0.15

d2 = - 0.90

Estimate the default spread (over and above the riskfree rate) that you would charge for the debt in this firm.

1

CHAPTER 31 VALUE ENHANCEMENT: A DISCOUNTED CASHFLOW VALUATION FRAMEWORK In much of this book, we have taken on the role of a passive investor valuing going concerns. In this chapter, we switch roles and look at valuation from the perspective of those who can make a difference in the way a company is run and hence its value. Our focus is therefore on how actions taken by managers and owners can change the value of a firm. We will use the discounted cash flow framework that we have developed in earlier parts of the book to explore the requirements for an action to be value creating and then go on to examine the different ways in which a firm can create value. In the process, we will also examine the role that marketing decisions, production decisions, and strategic decisions have in value creation. Value Creating and Value Neutral Actions The value of a firm is the present value of the expected cash flows from both assets in place and future growth, discounted at the cost of capital. For an action to create value, it has to do one or more of the following. 1. increase the cash flows generated by existing investments 2. increase the expected growth rate in earnings 3. increase the length of the high growth period 4. reduce the cost of capital that is applied to discount the cash flows Conversely, an action that does not affect cash flows, the expected growth rate, the length of the high growth period or the cost of capital cannot affect value. While this might seem obvious, a number of value-neutral actions taken by firms receive disproportionate attention from both managers and analysts. Consider four examples. •

Stock dividends and stock splits change the number of units of equity in a firm but do not affect cash flows, growth or value. These actions can have price effects, though, because they alter investors’ perceptions of the future of the company.

2 •

Accounting changes in inventory valuation and depreciation methods that are restricted to the reporting statements and do not affect tax calculations have no effect on cash flows, growth or value. In recent years, firms have spent an increasing amount of time on the management and smoothing of earnings and seem to believe that there is a value payoff in doing this.

•

When making acquisitions, firms often try to structure the deals in such a way that they can pool their assets and not show the market premium paid in the acquisition. When they fail and they are forced to show the difference between market value and book value as goodwill, their earnings are reduced by the amortization of the goodwill over subsequent periods. This amortization is not tax deductible, however, and thus does not affect the cash flows of the firm. So, whether a firm adopts purchase or pooling accounting and the length of time it takes to write off the goodwill should not really make any difference to value.

•

In the late 1990s, a number of firms that have issued tracking stock on their highgrowth divisions. Since these divisions remain under the complete control of the parent company, we would argue that the issue of tracking stock, by itself, should not create value. Some would take issue with some of these propositions. When a stock splits or a

firm issues tracking stock, they would argue, the stock price often goes up1 significantly. While this is true, we would emphasize that it is value, not price, that we claim is unaffected by these actions. While paying stock dividends, splitting stock and issuing tracking stock are value neutral actions, they can still be useful tools for a firm that perceives itself to be undervalued by the market. These actions can change market perceptions about growth or cash flows and thus act as signals to financial markets. Alternatively, they might provide more information about undervalued assets owned by the firm and the price may react as a consequence. In some cases, these actions may even lead to changes in operations; tying the compensation of managers to the price of stock tracking the division in which they work may improve efficiency and thus increase cash flows, growth and value.

1

This is backed up empirically. Stock prices do tend to increase, on average, when stocks are split.

3 Ways of Increasing Value The value of a firm can be increased by increasing cash flows from assets in place, increasing expected growth and the length of the growth period and by reducing the cost of capital. In reality, however, none of these is easily accomplished or likely to reflect all the qualitative factors that we, as financial analysts, are often accused of ignoring in valuation. In this section, we will consider how actions taken by a firm on a variety of fronts – marketing, strategic and financial – can have an effect on value.

1. Increase Cash Flows from Existing Investments The first place to look for value is in the firm’s existing assets. These assets represent investments the firm has already made and they generate the current operating income for the firm. To the extent that these investments earn less than their cost of capital or are earning less than they could if optimally managed, there is potential for value creation.

1.1: Poor Investments: Keep, Divest or Liquidate Every firm has some investments that earn less than necessary to break even (the cost of capital) and sometimes even lose money. At first sight, it would seem to be a simple argument to make that investments that do not earn their cost of capital should either be liquidated or divested. If, in fact, the firm could get back the original capital on liquidation, this statement would be true. But that assumption is not generally true and there are three different measures of value for an existing investment that we need to consider. The first is the continuing value and it reflects the present value of the expected cash flows from continuing the investment through the end of its life. The second is the liquidation or salvage value, which is the net cash flow that the firm will receive if it terminated the project today. Finally, there is the divestiture value, which is the price that will be paid by the highest bidder for this investment. Whether a firm should continue with an existing project, liquidate the project, or sell it to someone else will depend upon which of the three is highest. If the continuing value is the highest, the firm should continue with the project to the end of the project

4 life, even though it might be earning less than the cost of capital. If the liquidation or divestiture value is higher than the continuing value, there is potential for an increase in value from liquidation or divestiture. The value increment can then be summarized. If liquidation is optimal: Expected Value Increase = Liquidation Value - Continuing Value If divestiture is optimal: Expected Value Increase = Divestiture Value - Continuing Value How does a divestiture affect a firm’s value? To answer, we compare the price received on the divestiture to the present value of the expected cash flows that the firm would have received from the divested assets. There are three possible scenarios. 1. If the divestiture value is equal to the present value of the expected cash flows, the divestitures will have no effect on the divesting firm’s value. 2. If the divestiture value is greater than the present value of the expected cash flows, the value of the divesting firm will increase on the divestiture. 3. If the divestiture value is less than the present value of the expected cash flows, the value of the firm will decrease on the divestiture. The divesting firm receives cash in return for the assets and can choose to retain the cash and invest it in marketable securities, invest the cash in other assets or new investments, or return the cash to stockholders in the form of dividends or stock buybacks. This action, in turn, can have a secondary effect on value. Illustration 31.1: Potential for value creation from divestiture: Boeing While it is difficult to make judgments about individual investments that firms might have and their capacity to generate continuing value, you can make some observations about the potential for value creation from divestitures and liquidation by looking at the cost of capital and return on capital earned by different divisions of a firm. For instance, Boeing earned a return on capital of 5.82% in 1998, while its cost of capital was 9.18%. Breaking down Boeing’s return, by division, we obtain the numbers in Table 31.1. Table 31.1: Return and Cost of Capital Commercial Aircraft Information, Space &

Firm

Defense Operating Income

$

75

$

1,576

$

1,651

5 Capital Invested

$

After-tax ROC

18,673 0.40%

$

9,721 16.21%

$

28,394 5.82%

At Boeing’s annual meeting in 1999, Phil Condit, Boeing’s CEO, was candid in admitting that 35% of Boeing’s capital was in investments that earned less than the cost of capital. He revealed little, however, about whether it would be feasible to liquidate2 or divest these investments and get more than continuing value from such actions. Assume that Boeing is interested in selling its information, space and defense systems division and that it has found a potential buyer who is willing to pay $11 billion for the division. The division reported cash flows before debt payments, but after reinvestment needs and taxes, of $393 million in the most recent year and the cash flows are expected to grow 5% a year in the long term. The cost of capital for the division is 9%, a little lower than the cost of capital for the entire firm. The division, as a continuing part of Boeing, can be valued. Value of Division =

($393)(1.05) = $10,316 million (0.09 − 0.05)

With the divestiture value of $11 billion, the net effect of the divestiture will be an increase in Boeing’s value of $684 million. Net Effect on Value = Divestiture Value – Continuing Value = $11,000 mil - $10,316 mil = $ 684 million Reasons for Divestitures Why would a firm sell assets or a division? There are at least three reasons. The first is that the divested assets may have a higher value to the buyer of these assets. For assets to have a higher value, they have to either generate higher cash flows for the buyers or result in lower risk (leading to a lower discount rate). The higher cash flows can occur because the buyer is more efficient at utilizing the assets or because the buyer finds synergies with its existing businesses. The lower discount rate may reflect the fact that the owners of the buying firm are more diversified that the owners of the firm selling the

2

In 1999, Lockheed, Boeing’s leading competitor in the sector, announced plans to divest itself of approximately 15% of its assets as a remedy for its poor stock price performance.

6 assets. In either case, both sides can gain from the divestiture and share in the increased value. The second reason for divestitures is less value-driven and more a result of the immediate cash flow needs of the divesting firm. Firms that find themselves unable to meet their current operating or financial expenses may have to sell assets to raise cash. For instance, many leveraged acquisitions in the 1980s were followed by divestitures of assets. The cash generated from these divestitures was used to retire and service debt. The third reason for divestitures relates to the assets not sold by the firm, rather than the divested assets. In some cases, a firm may find the cash flows and values of its core businesses affected by the fact that it has diversified into unrelated businesses. This lack of focus can be remedied by selling assets or businesses that are peripheral to the main business of a firm.

1.2: Improve Operating Efficiency A firm’s operating efficiency determines its operating margin and, thus, its operating income; more efficient firms have higher operating margins, other things remaining equal, than less efficient firms in the same business. If a firm can increase its operating margin on existing assets, it will generate additional value. There are a number of indicators of the potential to increase margins, but the most important is a measure of how much a firm's operating margin deviates from its industry. Firms whose current operating margins are well below their industry average must locate the source of the difference and try to fix it. In most firms, the first step in value enhancement takes the form of cost cutting and layoffs. These actions are value enhancing only if the resources that are pruned do not contribute sufficiently either to current operating income or to future growth. Companies can easily show increases in current operating income by cutting back on expenditures (such as research and training), but they may sacrifice future growth in doing so. Illustration 31.2: Operating Margin Comparisons In Chapter 22, we valued Marks and Spencer in 2000 and noted that its value was depressed because its operating margins had dropped over the previous two years. In

7 Figure 31.1, we compare the after-tax operating margins at Marks and Spencer in 2000 with the average after-tax margin earned by the firm over the previous five years and the average after-tax margin in 2000 for other firms in the sector. Figure 31.1: Marks and Spencer: Margin Comparisons 14.00%

12.00%

10.00%

8.00% Current Five-year average Industry average

6.00%

4.00%

2.00%

0.00% Pre-tax Operating Margin

After-tax Operating Margin

Net Margin

Marks and Spencer’s current margins lag both its own historical levels and the average for the sector. We estimated the effect on value per share, at Marks and Spencer, of improvements in the operating margin from the current level. Figure 31.2 summarizes the effect of these changes.

8 Figure 31.2: Operating Margin and Value per Share: Marks and Spencer 6

5

Value / Share

4

3

2

1

0 3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

11.00%

12.00%

13.00%

14.00%

Pre-tax Operating Margin

While it is not surprising that the value per share is sensitive to changes in the operating margin, you can see that the decline in operating margins from historical levels to the current one have had a significant impact on value. Any value enhancement the firm plans, therefore, has to be centered on improving operating margins. Some Thoughts on Cost Cutting Firms embark on cost cutting with a great deal of fanfare but seem to have trouble carrying through. Cost cutting is often promised by firms, especially after acquisitions or new management comes into the firm, but seldom delivered. We would make the following general conclusions about cost cutting. •

The greater the absolute magnitude of the cost cuts promised, the more likely it is that they will not be delivered.

•

Cost cutting is never painless – not only is the human cost associated with layoffs large, but there is an associated loss of morale that can be just as expensive.

•

The initial phases of cost cuts go much more smoothly than the later phases. Part of the reason for this is that the easy cost cuts come first and the tough ones come later.

9 •

It is far more difficult to separate those costs that do not generate benefits for the firm from those that do than it seems at the outset, especially if we think of benefits in the long term.

•

Cost cutting that is promised in the abstract is less likely to happen than cost cutting that is described in detail – an example would be a bank merger where the branches that will be closed after the merger are specified as opposed to one where the bank just specified that economies of scale will lower costs.

From a valuation perspective, you should first evaluate the credibility of the management that is making the cost cutting claims and, even if you believe the managers, you should phase the costs cuts in over a long period – the larger the firm and the bigger the cost cuts, the longer the period.

1.3: Reduce the Tax Burden The value of a firm is the present value of its after-tax cash flows. Thus, any action that can reduce the tax burden on a firm for a given level of operating income will increase value. Although there are some aspects of the tax code that offer no flexibility to the firm, the tax rate can be reduced over time by doing any or all of the following. •

Multinational firms that generate earnings in different markets may be able to move income from high-tax locations to low-tax or no-tax locations. For instance, the prices that divisions of these firms charge each other for intra-company sales (transfer prices) can allow profits to be shifted from one part of the firm to another3.

•

A firm may be able to acquire net operating losses that can be used to shield future income. In fact, this might be why a profitable firm acquires an unprofitable one.

•

A firm can use risk management to reduce the average tax rate paid on income over time because the marginal tax rate on income tends to rise, in most tax systems, as income increases. By using risk management to smooth income over time, firms can make their incomes more stable and reduce their exposure to the highest marginal tax

3

Taxes are only one aspect of transfer pricing. Brickley, Smith and Zimmerman (1995) look at the broader issue of how to best set transfer prices.

10 rates4. This is especially the case when a firm faces a windfall or supernormal profit taxes. Illustration 31.3: Tax Burden and Valuation In Chapter 22, we valued Daimler Chrysler, using a tax rate of 44%, which is much higher than the tax rates we have used for other companies that we have valued. As a German company, Daimler is clearly much more exposed to high tax rates, but there are two forces that may change this tax rate. •

With the acquisition of Chrysler and the increasing globalization of its business, Daimler Chrysler has far more options when it comes to moving income to lower tax locales.

•

As a result of expected changes in German law, the tax rate in Germany will decline over the next 5 years.

We show the impact on the value of equity at Daimler Chrysler of changes in the tax rate from 0% to 50% in Figure 31.3.

4

Stulz (1996) makes this argument for risk management. He also presents other ways in which risk management can be value enhancing.

11 Figure 31.3: Daimler Chrysler: Tax Rate versus Value of Equity 100,000 DM

90,000 DM

80,000 DM

70,000 DM

Value of Equity

60,000 DM

50,000 DM

40,000 DM

30,000 DM

20,000 DM

10,000 DM

0 DM 0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Tax Rate

The value of equity changes dramatically as the tax rate changes and would triple from the base case value, if the tax rate were zero. This is notwithstanding the fact that the tax benefits from depreciation and interest expenses also decline as the tax rate drops.

1.4: Reduce net capital expenditures on existing investments The net capital expenditures is the difference between capital expenditures and depreciation. As a cash outflow, it reduces the free cash flow to the firm. Part of the net capital expenditure is designed to generate future growth, but part is to maintain existing assets. If a firm can reduce its net capital expenditures on existing assets, it will increase value. During short periods, the capital expenditures can even be lower than depreciation for those assets, creating a cash inflow from net capital expenditures. There is generally a trade off between capital maintenance expenditures and the life of existing assets. A firm that does not make any capital expenditures on its assets will generate much higher after-tax cash flows from these assets, but the assets will have a far shorter life. At the other extreme, a firm that reinvests all the cash flows it gets from depreciation into capital maintenance may be able to extend the life of its assets in place

12 significantly. Firms often ignore this trade-off when they embark on cost cutting and reduce or eliminate capital maintenance expenditures. Although these actions increase current cash flows from existing assets, the firm might actually lose value as it depletes these assets at a faster rate.

1.5: Reduce non-cash Working capital The non-cash working capital in a firm is the difference between non-cash current assets, generally inventory and accounts receivable, and the non-debt portion of current liabilities, generally accounts payable. Money invested in non-cash working capital is tied up and cannot be used elsewhere; thus, increases in non-cash working capital are cash outflows, whereas decreases are cash inflows. For retailers and service firms, non-cash working capital may be a much larger drain on cash flows than traditional capital expenditures. The path to value creation seems simple. Reducing non-cash working capital as a percent of revenues should increase cash flows and therefore, value. This assumes, however, that there are no negative consequences for growth and operating income. Firms generally maintain inventory and provide credit because it allows them to sell more. If cutting back on one or both causes lost sales, the net effect on value may be negative. The availability of updated reliable data has made it easier for firms to plan and reduced the need for inventory and working capital. In fact, the average non-cash working capital as a percent of revenues at major U.S. corporations has dropped from 17.6% in 1988 to 14.5% in 1998. Illustration 31.4: Non-Cash Working Capital: The Home Depot Consider a large retail firm like the Home Depot. It has significant investments in working capital and changes in this input can make a significant difference to the value of equity in the firm. In Figure 31.4, we compare non-cash working capital as a percent of revenues, operating income and book value of capital invested for the Home Depot for 1998 with the previous five years and the average for the sector.

13 Figure 31.4: Home Depot's Working Capital Investment 100.00%

Non-cash Working Capital as % of Revenues

90.00%

80.00%

70.00%

60.00% Current 5-Year Average

50.00%

Industry Average 40.00%

30.00%

20.00%

10.00%

0.00% As % of Operating Income

As % of Revenues

As % of Capital

Due to its economies of scale, the Home Depot carries far less working capital than its competitors and this has a positive effect on both cash flows and value. In 1998, we valued the Home Depot using the following inputs for the valuation.

Length Growth Inputs - Reinvestment Rate - Return on Capital - Expected Growth rate Cost of Capital Inputs - Beta - Cost of Debt - Debt Ratio - Cost of Capital General Information - Tax Rate

Table 31.2: Valuing the Home Depot High Growth Phase Stable Growth Phase 10 years Forever after year 10 88.62% 16.37% 14.51%

35.46% 14.10% 5.00%

0.87 5.80% 4.55% 9.52%

0.87 5.50% 30.00% 7.92%

35%

35%

The value per share that we obtained, which is summarized in Figure 31.5, was $42.55. We looked at the impact on The Home Depot’s value of changing the non-cash working

14 capital as a percent of revenues. As non-cash working capital increases, the value of equity decreases and the results are graphed in Figure 31.6. Figure 31.6: The Home Depot: Working Capital and Value/Share $50.00 $45.00 $40.00 $35.00

Value/Share

$30.00 $25.00 $20.00 $15.00 $10.00 $5.00 $0.00 0%

5%

10%

15%

20%

Non-Cash Working Capital as % of Revenues

As the non-cash working capital increases from 0% to 20% of revenues, the value per share decreases by approximately 20%.

cfbasics.xls: There is a dataset on the web that summarizes operating margins, tax rates and non-cash working capital as a percent of revenues by industry group for the United States.

15

Figure 31.5: The Home Depot: A Valuation Current Cashflow to Firm Reinvestment Rate 88.62% EBIT(1-t) : 1,829 - Nt CpX 1,799 - Chg WC 190 = FCFF Reinvestment Rate =108.75%

Expected Growth in EBIT (1-t) .8862*.1637= .1451 14.51 %

Return on Capital 16.37% Stable Growth g = 5%; Beta = 0.87; D/(D+E) = 30%;ROC=14.1% Reinvestment Rate=35.46%

Terminal Value 10 = 4806 / (.0792-.05) = 164,486 Firm Value: 68,949 + Cash: 62 - Debt: 4,081 =Equity 64,930 -Options 2,021 Value/Share $42.55

EBIT(1-t) 2095 - Reinv 1857 FCFF 238

2747 2434 313

3146 2788 358

3602 3192 410

4125 3655 469

4723 4186 538

5409 4793 616

6194 5489 705

Discount at Cost of Capital (WACC) = 9.79% (0.9555) + 3.77% (0.0445) = 9.52%

Cost of Equity 9.79%

Riskfree Rate : Government Bond Rate = 5%

2399 2126 273

Cost of Debt (5%+ 0.80%)(1-.35) = 3.77%

+

Beta 0.87

Unlevered Beta for Sectors: 0.86

Weights E = 95.55% D = 4.45%

X

Risk Premium 5.5%

Firm’s D/E Ratio: 4.76%

Historical US Premium 5.5%

Country Risk Premium 0%

7092 6285 807

16 2. Increase Expected Growth A firm with low current cash flows can still have high value if it is able to grow quickly. For profitable firms, the growth will be defined in terms of earnings but for money-losing firms, you have to consider the nexus of revenue growth and higher margins.

I. Profitable Firms Higher growth either arises from increases in reinvestment or a higher return on capital. It does not always translate into higher value, though, since higher growth can be offset by changes elsewhere in the valuation. Thus, higher reinvestment rates usually result in higher expected growth but at the expense of lower cash flows, since reinvestment reduces the free cash flows. Higher returns on capital also cause expected growth to increase, but value can still go down if the new investments are in riskier businesses and there is a more than proportionate increase in the cost of capital. The trade off from increasing the reinvestment rate is listed in Table 31.3. The positive effect of reinvesting more, higher growth, has to be compared to the negative effect of reinvesting more, the drop in free cash flows: Table 31.3: Trade off on Reinvestment Rate Negative Effects Positive Effects Reduces free cash flow to firm:

Increases Expected Growth:

FCFF

Expected Growth

= EBIT (1- tax rate) ( 1- Reinvestment = Reinvestment Rate * Return on Capital Rate) We could work through the entire valuation and determine whether the present value of the additional cash flows created by higher growth is greater than the present value of the actual reinvestments made, in cash flow terms. There is, however, a far simpler test to determine the effect on value. Note that the net present value of a project measures the value added by the project to overall firm value and that the net present value is positive only if the internal rate of return on the project exceeds the cost of capital. If we make the assumption that the accounting return on capital on a project is a reasonable estimate for the internal rate of return, then increasing the reinvestment rate will increase value if and

17 only if the return on capital is greater than the cost of capital. If the return on capital is less than the cost of capital, the positive effects of growth will be less than the negative effects of making the reinvestment. Note that the return on capital that we are talking about is the marginal return on capital, i.e., the return on capital earned on the actual reinvestment, rather than the average return on capital. Given that firms tend to accept their most attractive investment first and their less attractive investments later, the average returns on capital will tend to be greater than the marginal returns on capital. Thus, a firm with a return on capital of 18% and a cost of capital of 12% may really be earning only 11% on its marginal projects. In addition, the marginal return on capital will be much lower if the increase in the reinvestment rate is substantial. Thus, we have to be cautious about assuming large increases in the reinvestment rate while keeping the current return on capital constant. A firm that is able to increase its return on capital, while keeping the cost of capital fixed, will increase its value. The increase in growth will increase value, and there are generally no offsetting effects. If, however, the increase in return on capital comes from the firm entering new businesses that are far riskier than its existing business, there might be an increase in the cost of capital that offsets the increase in growth. The general rule for value creation remains simple, however. As long as the projects, no matter how risky they are, have a marginal return on capital that exceeds their cost of capital, they will create value. Using the comparison between return on capital and cost of capital, a firm that earns a return on capital that is less than its cost of capital can get an increase in value by accepting higher return investments, but it would get an even greater increase in value by not investing at all and returning the cash to the owners of the business. Liquidation or partial liquidation might be the most value enhancing strategy for firms trapped in businesses where it is impossible to earn the cost of capital. Illustration 31.5: Reinvestment Rates, Return on Capital and Value In 1998, Boeing earned a return on capital of 6.59% and had a reinvestment rate of 65.98%. If you assume a cost of capital of 9.17% for the firm, you would value the equity in the firm at $13.14 a share. In the same year, the Home Depot had a return on

18 capital of 16.38%, a reinvestment rate of 88.62% and a cost of capital of 9.51%, resulting in a value per share of $42.55. Table 31.4: Value per Share Boeing The Home Depot Cost of Capital

9.17%

9.51%

Return on Capital

6.59%

16.38%

Reinvestment Rate

65.98%

88.62%

Expected Growth Rate

4.35%

14.51%

Value Per Share

$13.14

$42.55

If the Home Depot could increase its reinvestment rates, without affecting its returns on capital, the effect on value will be positive, because it is earning excess returns. For Boeing, the effect of increasing the reinvestment rate at the current return on capital will be negative, since the firm’s return on capital is less than its cost of capital. In Figure 31.7, we summarize the impact on the value of equity of changing the reinvestment rate at both firms, keeping the cost of capital.

19 Figure 31.7: Effect of Changes in the Reinvestment Rate on the Value of Equity 30.00%

Change in Value of Equity

20.00%

10.00%

0.00% -20%

-10%

10%

20%

-10.00%

-20.00%

-30.00% Change in Reinvestment Rate Boeing

The Home Depot

To illustrate, we reduced the reinvestment rate at Boeing from 65.98% to 45.98% and examined the percentage effect on value of equity; the change was + 4.49%. The effects of a similar change at the Home Depot was negative. The effect of changes in the reinvestment rate were dramatic at the Home Depot, because the high growth period lasts 10 years. fundgrEB.xls: There is a dataset on the web that summarizes returns on capital and reinvestment rates by industry group for the United States.

II. Negative Earnings Firms For the negative earnings firms in the analysis – Amazon, Ariba and Rediff.com – expected future cash flows are derived from assumptions made about three variables – the expected growth rate in revenues, the target operating margin and the sales to capital ratio. The first two variables determine the operating earnings in future years and the last variable determines reinvestment needs. Figure 31.8 summarizes the impact of each of these variables on the cash flows.

20 Figure 31.8: Determinants of Growth

Revenue Growth

Free Cashflow to Firm (FCFF)

=

Target Operating Margin

EBIT (1 - tax rate)

-

Reinvestment Needs

Sales to Capital Ratio

Other things remaining equal, the expected cash flows in future years will be higher if any of the three variables – revenue growth, target margins and sales to capital ratios – increase. Increasing revenue growth and target margins will increase operating earnings, while increasing the sales to capital ratio will reduce reinvestment needs. In reality, though, firms have to make a trade off between higher revenue growth and higher margins. When firms increase prices for their products, they improve operating margins but reduce revenue growth. Michael Porter, one of the leading thinkers in corporate strategy, suggests that when it comes to pricing strategy, there are two basic routes a firm can take5. It can choose to be a volume leader, reducing price and hoping to increase revenues sufficiently to compensate for the lower margins. For this strategy to work, the firm needs a cost advantage over its competitors to prevent pricing wars that may make all firms in the industry worse off. Alternatively, it can attempt to be a price leader, increasing prices and hoping that the effect on volume will be smaller than the increased margins. The extent to which revenue growth will drop depends upon how elastic the demand for the product is and how competitive the overall product market is. The net effect will determine value. While a higher sales to capital ratio reduces reinvestment needs and increases cash flow, there are both internal and external constraints on the process. As the sales to capital ratio increases, the return on capital on the firm in future years will also increase. If the return on capital substantially exceeds the cost of capital, new competitors will

5

“Competitive Strategy”, Michael Porter

21 enter the market, making it more difficult to sustain the expected operating margins and revenue growth. Illustration 31.6: Revenue Growth, Operating Margins and Sales to Capital Ratios In Chapter 23, we valued Commerce One, a firm with an operating loss of $529 million and only $537 million in revenues. Using a compounded revenue growth rate of 40.24%, a target operating margin of 14.72% in ten years and a sales to capital ratio of 2.20, we estimated a value for the firm of $4.8 billion and value per share of $19.26. Changes in these inputs can have a dramatic effect on the value of the firm, as we noted in Chapter 23. As you would expect, higher revenue growth translates into higher values per share. Figure 31.9 graphs the change in value per share for Commerce One as a function of the change in expected growth rate in revenues over the next decade. Figure 31.9: Revenue Growth and Value per share $35.00

$30.00

Value per share

$25.00

$20.00

$15.00

$10.00

$5.00

$0.00 5%

10%

15%

20%

25%

30%

35%

40%

45%

Compounded Revenue Growth - Next 10 years

Thus, Commerce One’s value per share increases by 50% if the compounded revenue growth over the next 10 years is 45% instead of 40%. By the same token, the value per share drops by a third if the growth rate is 35%.

22 While higher revenue growth clearly increases value, we assumed that the target margin would remain unchanged as we change the growth rate. The target margin is just as important, if not more so, than revenue growth in determining value. In Figure 31.10, we estimate the value per share, holding revenue growth at 40.24% and changing the target margin. Figure 31.10: Value per share and Sustainable Margins $25.00

Value per share

$20.00

$15.00

$10.00

$5.00

$0.00 10%

11%

12%

13%

14%

15%

16%

Pre-tax operating margin

Every 1% change in the target operating margin changes the value by approximately $3 per share. The trade off between revenue growth and margins is made more explicit in Table 31.5, which shows value per share as a function of both variables. Table 31.5: Margin versus Revenue Growth: Commerce One Target Pre-tax Operating Margin in 10 years 8% 10% 12% 14%

16%

10%

$0.00

$0.00

$0.00

$0.47

$1.08

20%

$0.00

$0.18

$1.46

$2.91

$4.29

30%

$0.02

$2.98

$5.74

$8.47

$11.18

Compounded Revenue Growth over next 10 years

23 next 10 years

40%

$3.51

$8.94

$14.36

$19.77

$25.17

50%

$10.31

$20.74

$31.16

$41.56

$51.97

Commerce One’s value varies widely depending upon the combination of revenue growth and margins that you assume. In practical terms, this also provides the firm with a sense of the trade off between higher revenue growth and lower target margins. Finally, a higher sales to capital ratio (which translates into a higher return on capital in 10 years) leads to a higher value per share, because it determines both how much Commerce One has to reinvest to generate its expected growth rate. Figure 31.11 presents the effects on value per share of changing the sales to capital ratio over the high growth period for Commerce One. As we change the sales to capital ratio, we also change the return on capital in stable growth – it increases as the sales to capital ratio increases. Figure 31.11: Value per Share versus Sales to Capital $30.00

$25.00

Value per Share

$20.00

$15.00

$10.00

$5.00

$0.00 1.60

1.80

2

2.2

2.4

2.6

Sales to Capital Ratio

As the sales to capital ratio (and the terminal return on capital) increases, the value per share of Commerce One also increases.

24 3. Lengthen the Period of High Growth Every firm, at some point in the future, will become a stable growth firm, growing at a rate equal to or less than that of the economy in which it operates. In addition, growth creates value only if the firm earns excess returns on its investments. With excess returns, the longer the high growth period lasts, other things remaining equal, the greater the value of the firm. No firm should be able to earn excess returns for any length of time in a competitive product market, since competitors will be attracted to the business by the excess returns. Thus, implicit in the assumption that there will be high growth with excess returns is the assumption that there also exist some barriers to entry that prevent competing firms from entering the market and eliminating the excess returns that prevail. One way firms can increase value is by increasing existing barriers to entry and erecting new ones. Another way to express this idea is that companies earning excess returns have significant competitive advantages. Nurturing these advantages can increase value.

3.1: The Brand Name Advantage As we noted earlier in the book, the inputs to the traditional discounted cash flow valuation incorporate the effects of brand name. In particular, firms with more valuable brand names are either able to charge higher prices than the competition for the same products (leading to higher margins) or sell more than the competitors at the same price (leading to higher turnover ratios). They usually have higher returns on capital and greater value than their competitors in the industry. Creating a brand name is a difficult and expensive process that may take years to achieve, but firms can often build on existing brand names and make them valuable. Brand management and advertising can contribute in value creation. Consider the extraordinary success that Coca Cola has had in increasing its market value over the last two decades. Some attribute its success to its high return on equity or capital, yet these returns are not the cause of its success but the consequence of it. The high returns can be traced to the

25 company's relentless focus on making its brand name more valuable globally6. Conversely, the managers of a firm who take over a valuable brand name and then dissipate its value will reduce the values of the firm substantially. The near-death experience of Apple Computers in 1996 and 1997 and the travails of Quaker Oats after the Snapple acquisition suggest that managers can quickly squander the advantage that comes from valuable brand names.

3.2: Patents, Licenses and Other Legal Protection The second competitive advantage that companies can possess is a legal one. Firms may enjoy exclusive rights to produce and market a product because they own the patent rights on the product, as is often the case in the pharmaceutical industry. Alternatively, firms may have exclusive licensing rights to service a market, as is the case with utilities in the United States. The key to value enhancement is not just to preserve but to increase any competitive advantages that the firm possesses. If the competitive advantage comes from its existing patents, the firm has to work at developing new patents that allow it to maintain this advantage over time. While spending more money on research and development (R&D) is clearly one way, the efficiency of reinvestment also applies here. The companies that have the greatest increases in value are not necessarily those that spend the most on R&D, but those that have the most productive R&D departments not only in generating patents but also in converting patents into commercial products. The competitive advantage from exclusive licensing or a legal monopoly is a mixed blessing and may not lead to value enhancement. When a firm is granted these rights by another entity, say the government, that entity usually preserves the right to control the prices charged and margins earned through regulation. In the United States, for instance, much of the regulation of power and phone utilities was driven by the objective of ensuring that these firms did not earn excess returns. In these circumstances, firms may actually gain in value by giving up their legal monopolies, if they get pricing freedom in

6

Companies like Coca Cola have taken advantage of the global perception that they represent American culture, and used it to grow strongly in other markets.

26 return. We could argue that this has already occurred, in great part, in the airline and longdistance telecommunications businesses and will occur in the future in other regulated businesses. In the aftermath of deregulation, the firms that retain competitive advantages will gain value at the expense of others in the business.

3.3: Switching Costs There are some businesses where neither brand name nor a patent provides adequate protection against competition. Products have short life cycles, competition is fierce and customers develop little loyalty to companies or products. This describes the computer software business in the 1980s and it still applies to a significant portion of that business today. How, then, did Microsoft succeed so well in establishing its presence in the market? Although many would attribute its success entirely to its ownership of the operating system needed to run the software, there is another reason. Microsoft recognized earlier than most other firms that the most significant barrier to entry in the software business is the cost to the end-user of switching from one product to a competitor. In fact, Microsoft Excel, early in its life, had to overcome the obstacle that most users were working with Lotus spreadsheets and did not want to bear the switching cost. Microsoft made it easy for end-users to switch to its products (by allowing Excel to open Lotus spreadsheets, for instance), and it made it more and more expensive for them to switch to a competitor by creating the Microsoft Office Suite. Thus, a user who has Microsoft Office installed on his or her system and who wants to try to switch from Microsoft Word to WordPerfect has to overcome multiple barriers - Will the conversion work well on the hundreds of Word files that exist already? Will the user still be able to cut and paste from Microsoft Excel and Power Point into WordPerfect documents? The end result, of course, is that it becomes very difficult for competitors who do not have Microsoft’s resources to compete with it in this arena. There are a number of other businesses where the switching cost concept can be used to augment an argument for value enhancement or debunk it. For instance, there are many who argue that the high valuations of Internet companies such as Amazon.com and eToys reflect their first-mover advantage, i.e, the fact that they are pioneers in the online business. However, the switching costs in online retailing seem to be minimal, if any, and

27 these companies have to come up with a way of increasing switching costs if they want to earn high returns in the future.

3.4: Cost Advantages There are several ways in which firms can establish a cost advantage over their competitors and use it as a barrier to entry. •

In businesses where scale can be used to reduce costs, economies of scale can give bigger firms advantages over smaller firms. This is the advantage, for instance, that the Home Depot has used to gain market share at the expense of its smaller and often local competitors.

•

Owning or having exclusive rights to a distribution system can provide firms with a cost advantage over its competitors. For instance, American Airlines’ ownership of the Sabre airline reservation system gave it an advantage over its competitors in attracting customers.

•

Having access to lower-cost labor or resources can also provide cost advantages. Thus Southwest Airlines, with its non-unionized labor force, has an advantage over its unionized competitors, as do natural resource companies with access to reserves that are less expensive to exploit.

These cost advantages will influence value in one of two ways: The firm with the cost advantage may charge the same price as its competitors but have a much higher operating margin. Or the firm may charge lower prices than its competitors and have a much higher capital turnover ratio. In fact, the net effect of increasing margins or turnover ratios (or both) will increase the return on capital and through it expected growth. The cost advantage of economies of scale can create high capital requirements that prevent new firms from entering the business. In businesses such as aerospace and automobiles, the competition is almost entirely among existing competitors. The absence of new competitors may allow these firms to maintain above-normal returns, though the competition between existing firms will constrain the magnitude of these returns.

28 Illustration 31.7: Potential for Increasing the Length of the High Growth Period We examine the potential for increasing barriers to entry and by extension the excess returns and the length of the high growth period at Cisco and Motorola. The competitive advantages are different for the two firms and the potential for building on these advantages is different as well. •

Cisco’s most significant differential advantage seems to be its capacity to generate much larger excess returns on its new investments than its competitors. Since most of these investments take the form of acquisitions of other firms, Cisco’s excess returns rest on whether it can continue to maintain its success in this area. The primary challenge, however, is that as Cisco continues to grow, it will need to do even more acquisitions each year to maintain the growth rate it had the previous year. It is possible that there might be both external and internal constraints on this process. The number of firms that are potential takeover targets is limited and the firm may not have the resources to replicate its current success if the number of acquisitions doubles or triples.

•

Motorola’s research capabilities and the patents that emerge from the research represent its most significant competitive advantage. However, it is not viewed as the technological leader in either of the two businesses that it operates in. Firms like Nokia are viewed as more innovative when it comes to mobile communications (cellular phones) and Intel is considered the leading innovator among large semiconductor manufacturers.

We begin by valuing each of these firms using their current returns on capital and estimated reinvestment rates as inputs for the high growth period. Table 31.6 summarizes the inputs used in the base case valuations and the value per share estimated with these assumptions. Table 31.6: Inputs for valuing Cisco and Motorola Cisco Motorola High Growth Stable Growth High Growth Stable Growth Beta

1.43

1.00

1.21

1.00

29 Cost of Equity

11.72%

10.00%

10.85%

10.00%

4.03%

4.03%

4.23%

4.23%

0.18%

10.00%

6.86%

6.86%

Cost of Capital

11.71%

9.40%

10.39%

9.58%

Return on Capital

34.07%

16.52%

12.12%

12.12%

Reinvestment Rate

106.8%

30.27%

52.99%

41.07%

Expected Growth

36.39%

5.00%

6.45%

5.00%

After-tax Cost of Debt Debt Ratio

Rate Value per share

$44.13

$20.99

In the base case, we assume 12 years of high growth for Cisco – six years of high growth and six years of transition – and 5 years of high growth for Motorola. We then consider how much the value per share changes as we change the growth period in Figure 31.12. Figure 31.12: Value per Share and Length of High Growth $70.00

$60.00

Value per share

$50.00

$40.00 Cisco Motorola $30.00

$20.00

$10.00

$0.00 0

2

4

6

8

Length of High Growth

10

12

14

30 The effect of changing the length of the growth period is very different for the two firms. For Cisco, the value per share changes significantly as the length of the growth period change, increasing as it gets longer. For Motorola, the effect is muted and the value per share is relatively insensitive to changes in the length of the growth period. The reason lies in the excess returns that we are assuming for the two firms over the length of the growth period. For Cisco, the excess returns are very large and thus the impact on value is also large. For Motorola, we assume that the excess returns are relatively small and the effect on value is also much lower. Lead Times from Competitive Advantages A key question that we often face when looking at the effects of a competitive advantage on value is how long a competitive advantage lasts. This is a difficult question to answer because there are a number of firm specific factors but there are few interesting studies in corporate strategy that try to address the issue. Levin, Klevorick, Nelson and Winter (1987) estimate, for instance, that it takes between 3-5 years to duplicate a patented product or process and 1-3 years to duplicate an unpatented product or process. In the same study, they find that patenting is often much less effective at preventing imitation that moving quickly down the learning curve (producing more advanced versions of the product at lower cost) and establishing efficient sales and service networks. For example, Intel was able to maintain its competitive advantages even as its computer chips were being cloned by AMD by using the lead time it had to move quickly to the next generation chips.

4. Reduce the cost of financing The cost of capital for a firm is a composite cost of debt and equity financing. The cash flows generated over time are discounted to the present at the cost of capital. Holding the cash flows constant, reducing the cost of capital will increase the value of the firm. In this section, we will explore the ways in which a firm may reduce its cost of capital, or more generally, increase its firm value by changing both financing mix and type.

31 4.1. Change Operating Risk The operating risk of a firm is a direct function of the kinds of products or services it provides and the degree to which these products or services are discretionary to the customer. The more discretionary they are, the greater the operating risk faced by the firm. Both the cost of equity and cost of debt of a firm are affected by the operating risk of the business or businesses in which it operates. In the case of equity, only that portion of the operating risk that is not diversifiable will affect value. Firms can reduce their operating risk by making their products and services less discretionary to their customers. Advertising clearly plays a role, but finding new uses for a product or service is another.

4.2: Reduce Operating Leverage The operating leverage of a firm measures the proportion of its costs that are fixed. Other things remaining equal, the greater the proportion of the costs of a firm that are fixed, the more volatile its earnings and the higher its cost of capital. Reducing the proportion of the costs that are fixed will make firms much less risky and reduce their cost of capital. Firms can reduce their fixed costs by using outside contractors for some services; if business does not measure up, the firm is not stuck with the costs of providing this service. They can also tie expenses to revenues; for instance, tying wages paid to revenues made will reduce the proportion of costs that are fixed. This basic idea of tying expenses to revenues is often described as making the cost structure more flexible. A more flexible cost structure influences three inputs in a valuation. It leads to a lower unlevered beta (due to the lower operating leverage), reduces the cost of debt (because of the reduction in default risk) and increases the optimal debt ratio. All three reduce the cost of capital and increase firm value.

4.3: Change the Financing Mix A third way to reduce the cost of capital is to change the mix of debt and equity used to finance the firm. As we argued in the chapters on capital structure, debt is always cheaper than equity, partly because lenders bear less risk and partly because of the tax advantage associated with debt. This benefit has to be weighed off against the additional

32 risk of bankruptcy created by the borrowing; this higher risk increases both the beta for equity and the cost of borrowing. The net effect will determine whether the cost of capital will increase or decrease as the firm takes on more debt. Note, however, that firm value will increase as the cost of capital decreases, if and only if the operating cash flows are unaffected by the higher debt ratio. If, as the debt ratio increases, the riskiness of the firm increases, and this, in turn, affects the firm's operations and cash flows; the firm value may decrease even as cost of capital declines. If this is the case, the objective function when designing the financing mix for a firm has to be restated in terms of firm value maximization rather than cost of capital minimization.

wacc.xls: There is a dataset on the web that summarizes debt ratios and costs of capital by industry group for the United States. Illustration 31.8: The Effect of Financing Mix on Value To analyze the effect of changing the financing mix on value, you would need to estimate the costs of equity and debt at each debt ratio. In Table 31.7, the costs of equity and debt are estimated for Motorola for debt ratios from 0% to 90%.

Debt

Table 31.7: Cost of Capital and Firm Value: Motorola Beta Cost of Bond Interest rate Tax Rate Cost of Debt

Ratio

Equity

Rating

on debt

WACC

(after-tax)

0%

1.16

10.63%

AAA

6.20%

35.00%

4.03%

10.63%

10%

1.24

10.96%

A-

7.25%

35.00%

4.71%

10.33%

20%

1.34

11.38%

B-

10.25%

35.00%

6.66%

10.43%

30%

1.48

11.91%

CC

12.00%

35.00%

7.80%

10.68%

40%

1.72

12.90%

C

13.50%

26.34%

9.94%

11.72%

50%

2.07

14.28%

C

13.50%

21.07%

10.66%

12.47%

60%

2.63

16.54%

D

16.00%

14.82%

13.63%

14.79%

70%

3.51

20.05%

D

16.00%

12.70%

13.97%

15.79%

80%

5.27

27.07%

D

16.00%

11.11%

14.22%

16.79%

90%

10.54

48.14%

D

16.00%

9.88%

14.42%

17.79%

33 Note that the cost of equity is estimated based upon the levered beta. As the debt ratio increases, the beta increases as well.7 The cost of debt is estimated based upon a synthetic rating that is determined by the interest coverage ratio at each debt ratio. As the debt ratio increases, the interest expense increases leading to a drop in the ratings and higher costs of debt. As Motorola moves from a 0% debt ratio to a 10% debt ratio, the cost of capital decreases (and firm value increases). At a 10% debt ratio, Motorola’s cost of capital is 10.33%, which is lower than the current cost of capital of 10.39%. Beyond 10%, though, the trade off operates against debt, the cost of capital increases as the debt ratio increases.

4.4: Change Financing Type A fundamental principle in corporate finance is that the financing of a firm should be designed to ensure, as far as possible, that the cash flows on debt match as closely as possible the cash flows on the asset. By matching cash flows on debt to cash flows on the asset, a firm reduces its risk of default and increases its capacity to carry debt, which, in turn, reduces its cost of capital and increases value. Firms that mismatch cash flows on debt and cash flows on assets (by using shortterm debt to finance long-term assets, debt in one currency to finance assets in a different currency or floating-rate debt to finance assets whose cash flows tend to be adversely impacted by higher inflation) will have higher default risk, higher costs of capital and lower firm value. Firms can use derivatives and swaps to reduce these mismatches and, in the process, increase firm value. Alternatively, they can replace their existing debt with debt that is more closely matched to their assets. Finally, they can use innovative securities that allow them to pattern cash flows on debt to cash flows on investments. The use of catastrophe bonds by insurance companies and commodity bonds by natural resource firms are good examples. What about Miller-Modigliani?

7 Levered Beta = Unlevered Beta (1 + (1- tax rate) (Debt/ Equity))

34 One of corporate finance’s best known and most enduring propositions – the Miller-Modigliani theorem – argues that the value of a firm is independent of its capital structure. In other words, changing your financing mix should have no effect on your firm value. How would we reconcile our arguments in this section with the Miller Modigliani theorem? Note that the original version of the theorem was derived for a world with no taxes and default. With these assumptions, debt creates no tax advantages and no bankruptcy costs and does not affect value. In a world with taxes and default risk, you are much more likely to have to make trade offs and debt can increase value, decrease value or leave it unaffected depending upon how the trade offs operate. The Value Enhancement Chain We can categorize the range of actions firms can take to increase value in several ways. One is in terms of whether they affect cash flows from assets in place, growth, the cost of capital or the length of the growth period. There are two other levels at which we can distinguish between actions that create value. a. Does an action create a value trade off or is it a pure value creator? Very few actions increase value without any qualifications. Among these are the divestitures of assets when the divestiture value exceeds the continuing value and the elimination of deadweight costs that contribute nothing to the firm’s earnings or future growth. Most actions have both positive and negative effects on value and it is the net effect that determines whether these actions are value enhancing. In some cases, the tradeoff is largely internal and the odds are much better for value creation. An example is a firm changing its mix of debt and equity to reduce the cost of capital. In other cases, however, the net effect on value will be a function of how competitors react to a firm’s actions. As an example, changing pricing strategy to increase margins may not work as a value enhancement measure, if competitors react and change prices as well. b. How quickly do actions pay off? Some actions generate an immediate increase in value. Among these are divestitures and cost cutting. Many actions, however, are designed to create value in the long term. Thus, building up a

35 respected brand name clearly creates value in the long term but is unlikely to affect value today. Table 31.8 summarizes a value enhancement chain, where actions that create value are categorized both on how quickly they create value and on how much control the firm has over the value creation. Under the first column, titled “Quick Fixes”, we have listed actions in which the firm has considerable control over the outcome and the benefit in terms of value creation is immediate. Under the second column, titled "Odds on", we have included actions that are likely to create value in the near or medium term and where the firm still continues to exercise significant control over the outcome. The third column, titled "Long Term", includes actions designed to create value in the long term. This is where the major strategic initiatives of the firm show up. Illustration 31.9: A Value Enhancement Plan In Illustration 31.7, we valued Motorola at $22.05 using its current return on capital of 12.18% and debt ratio of 6.86% in the valuation. Figure 31.13 summarizes this valuation. Note, though, that the current return on capital is well below what the firm has earned historically and lags the industry average (of 22.36%) by almost 10%. If Motorola could increase its return on capital to 17.22% on its new investments (leaving its existing investments earning 12.18%) and increase its debt ratio to its optimal of 10%, its value per share would increase to $23.86. The restructured valuation is summarized in Figure 31.14. valenh.xls: This spreadsheet allows you to estimate the approximate effect of changing the way a firm is run on its value.

Figure 31.13: Motorola: A Status Quo Valuation Current Cashflow to Firm EBIT(1-t) : 3,110 - Nt CpX 1,522 - Chg WC 126 = FCFF 1,462 Reinvestment Rate = 52.99%

Return on Capital 12.18%

Reinvestment Rate 52.99%

Expected Growth in EBIT (1-t) .5299*.1218 = .0645 6.45%

Stable Growth g = 5%; Beta = 1.00; D/(D+E) =6.86% ;ROC=12.18% Reinvestment Rate=41.07% Terminal Value10 = 2631/(.0958-.05) = 57418

Firm Value: 41587 + Cash: 9244 - Debt: 5426 =Equity 45,405 -Options 283 Value/Share $20.97

EBIT(1-t) - Reinvestment FCFF

$3,311 $1,754 $1,556

$3,524 $1,867 $1,657

$3,752 $1,988 $1,764

$3,994 $2,116 $1,878

$4,251 $2,253 $1,999

Discount at Cost of Capital (WACC) = 10.85% (0.93) + 4.23% (0.07) = 10.39%

Cost of Equity 10.85%

Cost of Debt (6%+ 0.50%)(1-.35) = 4.23%

Riskfree Rate: Government Bond Rate = 6%

+

Beta 1.21

Unlevered Beta for Sectors: 1.18

Weights E = 93.14% D = 6.86%

X

Risk Premium 4%

Firm’s D/E Ratio: 7.36%

Historical US Premium 4%

Country Risk Premium 0%

4464 1833 2631

Figure 31.14: Motorola: A Restructured Valuation Current Cashflow to Firm EBIT(1-t) : 3,110 - Nt CpX 1,522 - Chg WC 126 = FCFF 1,462 Reinvestment Rate = 52.99%

Return on Capital 17.22%

Reinvestment Rate 52.99%

Expected Growth in EBIT (1-t) .5299*.1722 = .0912 9.12%

Stable Growth g = 5%; Beta = 1.00; D/(D+E) =10% ;ROC=12.18% Reinvestment Rate=41.07%

Terminal Value5= 2978/(.0947-.05) = 66606 Firm Value: 47812 + Cash: 9244 - Debt: 5426 =Equity 51630 -Options 283 Value/Share $23.86

EBIT(1-t) - Reinvestment FCFF

$3,394 $1,798 $1,595

$3,703 $1,962 $1,741

$4,041 $2,142 $1,900

$4,410 $2,337 $2,073

$4,813 $2,550 $2,262

Discount at Cost of Capital (WACC) = 10.96% (0.9) + 4.71% (0.1) = 10.33%

Cost of Equity 10.96%

Cost of Debt (6%+ 1.25%)(1-.35) = 4.71%

Riskfree Rate: Government Bond Rate = 6%

+

Beta 1.24

Unlevered Beta for Sectors: 1.18

Weights E = 90% D = 10%

X

Risk Premium 4%

Firm’s D/E Ratio: 11.11%

Historical US Premium 4%

Country Risk Premium 0%

5053 2075 2978

Table 31.8: The Value Enhancement Chain More control

Less control

Payoff quickly

Existing Investments

Expected Growth

Length of High Growth Period

Cost of Financing

Quick Fixes a. Divest assets/projects with Divestiture Value > Continuing Value. b. Terminate projects with Liquidation Value > Continuing Value. c. Eliminate operating expenses that generate no revenues and no growth. d. Take advantage of tax law to increase cash flow. Eliminate new capital expenditures that are expected to earn less than the cost of capital. If any of the firm’s products or services can be patented and protected, do so. a. Use swaps and derivatives to match debt more closely to firm’s assets. b. Recapitalize to move the firm towards its optimal debt ratio.

Payoff in long term

Odds on.. Long Term 1. Reduce net working capital 1. Change pricing strategy to requirements, by reducing maximize the product of inventory and accounts profit margins and turnover receivable, or by increasing ratio. accounts payable. 2. Move to more efficient 2. Reduce capital maintenance technology for operations expenditures on assets in to reduce expenses and place. improve margins.. 3. Reduce marginal tax rate.

Increase reinvestment rate or marginal return on capital or both in firm’s existing businesses. Use economies of scale or cost advantages to create higher return on capital.

Increase reinvestment rate or marginal return on capital or both in new businesses.

a. Build up brand name. b. Increase the cost of switching from product and reduce cost of switching to it. a. Change financing type and Reduce the operating risk of the use innovative securities to firm, by making products less reflect the types of assets being discretionary to customers. financed. b. Use the optimal financing mix to finance new investments. c. Make cost structure more flexible to reduce operating leverage.

39 Closing Thoughts on Value Enhancement Almost all firms claim to be interested in value enhancement but very few are able to increase value consistently. If value enhancement is as simple as it is made out to be in this chapter, you might wonder why this is so. There are four basic propositions you need to consider in the context of value enhancement. 1. Value enhancement is hard work, takes time and may make life uncomfortable for existing managers: There are no magic bullets that increase value painlessly. Increasing cash flows requires hard decisions on layoffs and cost cutting and, in some cases, admitting past mistakes. Increasing the reinvestment rate will require that you analyze new investments with more care and that you invest in the infrastructure you need to manage these investments. Increasing your debt ratio may also create new pressures to make interest payments and to deal with ratings agencies and banks. 2. For a firm to enhance value, all of its component parts need to buy into the value enhancement plan: You cannot increase value by edict and you cannot do it from the executive offices (or the finance department). As you probably noted in the discussion, every part of the firm has a role to play in increasing value. Table 31.9 summarizes the role of each part of the firm in the value enhancement actions that we have described in this chapter. Departments have to cooperate for value enhancement to become a reality. Table 31.9: Value Enhancement Actions: Who is responsible? Value enhancing action Increasing operating efficiency

Primary responsibility Operating managers and personnel, from shop-floor stewards to factory managers.

Reducing working capital needs

Inventory personnel Credit personnel

Increasing revenue growth

Sales and marketing personnel

Increasing return on capital/ reinvestment

Strategic Teams, with help from financial

rate

analysts

40 Build brand name

Advertising personnel

Other competitive advantages

Strategic analysts

Reduce cost of financing

Finance department

3. Value enhancement has to be firm-specific: No two firms in trouble share the same problems and using a cook-book approach seldom works in value enhancement. You have to begin by diagnosing the specific problems faced by the firm you are analyzing and tailor a response to these problems. Thus, the value enhancement plan you would devise for a mature firm with cost overruns will be very different from the plan you would devise for a young firm that has a product that no longer meets market needs. 4. Price enhancement may not always follow value enhancement: This is perhaps the most disappointing aspect of value enhancement. A firm that takes all the right actions may not necessarily be rewarded immediately by financial markets. In some cases, markets may even punish such firms because of the effects of these actions on reported earnings. We remain convinced that in the long terms, markets will recognize value enhancing actions and reward them, but the manager who took these actions may not be around to share in the rewards. Summary Value enhancement is clearly on the minds of many managers today. Building on the discounted cash flow principles developed in the last chapter, the value of a firm can be increased by changing one of the four primary inputs into valuation: the cash flows from assets in place, the expected growth rate during the high growth period, the length of the high growth period and the cost of capital. Conversely, actions that do not change any of these variables cannot create value. Cash flows from assets in place can be increased by cost cutting and more efficient operations, as well as by lowering taxes paid on income and reducing investment needs (capital maintenance and non-cash working capital investments). Expected growth can be increased by increasing the reinvestment rate or the return on capital, but increases in the reinvestment rate will generate value only if the return on capital exceeds the cost of capital. High growth, at least the value creating kind,

41 can be made to last longer by generating new competitive advantages or augments existing ones. Finally, the cost of capital can be lowered by moving towards an optimal debt ratio, using debt that is more suited for the assets being financed and by reducing market risk.

42 Problems 1. Marion Manufacturing, a steel company, announces that it will be taking a major restructuring charge that will lower earnings this year by $500 million. Assume that the charge is not tax deductible and has no effects on operations. a. What will the effect of this charge be on the value of the firm? a. When the firm announces the charge, what effect would you expect it to have on the stock price? Is your answer consistent with your response to (a)? 2. Universal Health Care (UHC) is a company whose stock price has declined by 40% in the last year. In the current year, UHC earned $300 million in pre-tax operating income on revenues of $10 billion. The new CEO of the firm has proposed cost-cutting measures she anticipates will save the firm $100 million in expenses, without any effect on revenues. Assume the firm is growing at a stable rate of 5% a year and its cost of capital is 10%; neither number is expected to change as a consequence of the cost cutting. The firm’s tax rate is 40%. (You can assume that the firm reinvests $100 million each year and that this reinvestment will not change as the firm cuts costs.) •

What effect will the cost cutting have on value?

•

What effect will the cost cutting have on value, if the expected growth rate will drop to 4.5% as a consequence? (Some of the costs cut were designed to generate future growth)

3. Atlantic Cruise Lines operates cruise ships and is headquartered in Florida. The firm had $100 million in pre-tax operating income in the current year, of which it reinvested $25 million. The firm expects its operating income to grow 4% in perpetuity and maintain its existing reinvestment rate. Atlantic has a capital structure composed 60% of equity and 40% of debt. Its cost of equity is 12% and it has a pretax cost of borrowing of 8%. The firm currently faces a tax rate of 40%. a. Estimate the value of the firm. b. Assume now that Atlantic Cruise Lines will move its headquarters to the Cayman Islands. If its tax rate drops to 0% as a consequence, estimate the effect on value of the shift.

43 4. Furniture Depot is a retail chain selling furniture and appliances. The firm has after-tax operating income of $250 million in the current year on revenues of $5 billion. The firm also has non-cash working capital of $1 billion. The net capital expenditures this year is $100 million and expects revenues, operating income and net capital expenditures to grow 5% a year forever. The firm’s cost of capital is 9%. a. Assume that non-cash working capital remains at the existing percent of revenues, estimate the value of the firm. b. Assume now that the firm is able to reduce its non-cash working capital requirement by 50%. Estimate the effect on value of this change. c. If as a consequence of this non-cash working capital change, earnings growth declines to 4.75%, what would the effect on value be of the drop in non-cash working capital? 5. General Systems is a firm that manufactures personal computers. As a top manager in the firm, you are considering changes in the way the firm is run. Currently, the firm has after-tax operating income of $50 million on capital invested of $250 million (at the beginning of the year). The firm also reinvests $25 million in net capital expenditures and working capital. a. Estimate the expected growth rate in earnings, given the firm’s current return on capital and reinvestment rate. b. Holding the return on capital constant, what would happen to the expected growth rate if the firm increased its reinvestment rate to 80%? c. What would the effect on growth be, if as the reinvestment rate increases to 80%, the return on capital on investments drops by 5%? (For instance, if the return on capital is currently 18%, it will drop to 13%.) 6. Compaq Computers has seen its stock price decline from $45 to $24. The firm is expected to reinvest 50% of its expected after-tax operating income of $2 billion in new investments and to earn a return on capital of 10.69%. The firm is all equity financed and has a cost of equity of 11.5%. a. What is the firm’s expected growth rate, assuming that it maintains its existing reinvestment rate and return on capital?

44 b. Assuming that this growth is perpetual, what is the value of the firm? c. How much value is being created or destroyed by the firm’s new investments? 7. (Refer to problem 6) Now assume that Compaq’s optimal debt ratio is 20%. Its cost of equity will increase to 12.5% and its after-tax cost of debt will be 4.5% at the optimal debt ratio. a. What is the firm’s expected growth rate, assuming it maintains its existing reinvestment rate and return on capital? b. Assuming this growth is perpetual, what is the value of the firm? c. How much value is being created or destroyed by the firm’s new investments? 8. Coca Cola is considered to have one of the most valuable brand names in the world. The firm has an after-tax operating margin of 20% on revenues of $25 billion. The capital invested in the firm is $10 billion. In addition, Coca Cola reinvests 50% of its after-tax operating earnings. a. Estimate the expected growth in operating earnings, assuming Coca Cola can sustain these values for the foreseeable future. b. Assume generic soft drink manufacturers have after-tax operating margins of only 7.5%. If Coca Cola maintains its existing reinvestment rate but loses its brand name value, estimate the expected growth rate in operating earning. (You can assume that, with the loss in brand name value, Coca Cola’s operating margins would drop to 7.5%, as well.) 9. BioMask Genetics is a biotechnology firm with only one patent to its name. The aftertax operating earnings in the current year is $100 million and the firm has no reinvestment needs. The patent will expire in 3 years and the firm will have a 15% growth rate in earnings during that period. After year 3, operating earnings are expected to remain constant forever. The firm’s management is considering an advertising plan designed to build up the brand name of its patented product. The advertising campaign will cost $50 million (pre-tax) a year over the next 3 years; the firm’s tax rate is 40%. The firm believes this campaign will allow it to maintain a 15% growth rate for 10 years, as the brand name

45 compensates for the loss of the patent protection. After year 10, the operating earnings are expected to remain constant forever. The firm has a cost of capital of 10%. a. Estimate the value of the firm, assuming it does not embark on the advertising campaign. b. Estimate the value of the firm, with the advertising campaign. c. Assume there is no guarantee the growth rate will last 10 years as a result of the campaign. What would the probability of success need to be for the campaign to be financially viable? 10. Sunmask is a cosmetics firm that has seen its stock price fall and its earnings decline in the last year. You have been hired as the new CEO of the company and a careful analysis of Sunmask’s current financials reveals the following. -

The firm currently has after-tax operating earnings of $300 million on revenues of $10 billion and a capital turnover ratio (sales/book value of capital) of 2.5.

-

The firm is expected to reinvest 60% of its after-tax operating income.

-

The firm is all equity financed and has a cost of capital of 10%. a. Estimate the value of the firm, assuming existing policies continue forever. (Returns on capital and reinvestment rates remain constant forever, as well.) b. Assume that you can increase operating margins from 3% to 5% without affecting the capital turnover ratio, that you can lower the reinvestment rate to 40%, and that the cost of capital will become 9%, if you shift to your optimal debt ratio. How much would your firm value increase if you were able to make these changes?

1 CHAPTER 32 VALUE ENHANCEMENT: EVA, CFROI AND OTHER TOOLS The traditional discounted cash flow model provides for a rich and thorough analysis of all the different ways in which a firm can increase value; but it can become complex, as the number of inputs increases. It is also very difficult to tie management compensation systems to a discounted cash flow model, since many of the inputs need to be estimated and can be manipulated to yield the results management wants. If we assume that markets are efficient, we can replace the unobservable value from the discounted cash flow model with the observed market price and reward or punish managers based upon the performance of the stock. Thus, a firm whose stock price has gone up is viewed as having created value, whereas one whose stock price has fallen has destroyed value. Compensation systems based upon the stock price, including stock grants and warrants, have become a standard component of most management compensation package. While market prices have the advantage of being up to date and observable, they are also noisy. Even if markets are efficient, stock prices tend to fluctuate around the true value and markets sometimes do make mistakes. Thus, a firm may see its stock price go up and its top management rewarded, even as it destroys value. Conversely, the managers of a firm may be penalized as its stock price drops, even though the managers may have taken actions that increase firm value. The other problem with stock prices as the basis for compensation is that they are available only for the entire firm. Thus, stock prices cannot be used to analyze the managers of individual divisions of a firm or for their relative performance. In the last decade, while firms have become more focused on value creation, they have remained suspicious of financial markets. While they might understand the notion of discounted cash flow value, they are unwilling to tie compensation to a value that is based upon dozens of estimates. In this environment, new mechanisms for measuring value that are simple to estimate and use, do not depend too heavily on market movements and do not require a lot of estimation, find a ready market. The two mechanisms that seem to have made the most impact are:

2 1.

Economic Value Added, which measures the dollar surplus value created by a firm on its existing investment, and

2.

Cash Flow Return on Investment, which measured the percentage return made by a firm on its existing investments

In this chapter, we look at how each is related to discounted cash flow valuation. We also look at the conditions under which firms using these approaches to judge performance and evaluate managers may end up making decisions that destroy value rather than create it. Economic Value Added The economic value added (EVA) is a measure of the dollar surplus value created by an investment or a portfolio of investments. It is computed as the product of the "excess return" made on an investment or investments and the capital invested in that investment or investments. Economic Value Added = (Return on Capital Invested – Cost of Capital) (Capital Invested) = After tax operating income – (Cost of Capital) (Capital Invested) In this section, we will begin by looking at the measurement of economic value added, then consider its links to discounted cash flow valuation and close with a discussion of its limitations as a value enhancement tool. Calculating EVA The definition of EVA outlines three basic inputs we need for its computation the return on capital earned on investments, the cost of capital for those investments and the capital invested in them. In measuring each of these, we will make many of the same adjustments we discussed in the context of discounted cash flow valuation. How much capital is invested in existing assets? One obvious answer is to use the market value of the firm, but market value includes capital invested not just in assets in place but in expected future growth1. Since we want to evaluate the quality of assets in place, we need a measure of the market value of just these assets. Given the difficulty of estimating market value of assets in place, it is not surprising that we turn to the book

3 value of capital as a proxy for the market value of capital invested in assets in place. The book value, however, is a number that reflects not just the accounting choices made in the current period, but also accounting decisions made over time on how to depreciate assets, value inventory and deal with acquisitions. At the minimum, the three adjustments we made to capital invested in the discounted cashflow valuation – converting operating leases into debt, capitalizing R&D expenses and eliminating the effect of one-time or cosmetic charges – have to be made when computing EVA as well. The older the firm, the more extensive the adjustments that have to be made to book value of capital to get to a reasonable estimate of the market value of capital invested in assets in place. Since this requires that we know and take into account every accounting decision over time, there are cases where the book value of capital is too flawed to be fixable. Here, it is best to estimate the capital invested from the ground up, starting with the assets owned by the firm, estimating the market value of these assets and cumulating this market value. To evaluate the return on this invested capital, we need an estimate of the after-tax operating income earned by a firm on these investments. Again, the accounting measure of operating income has to be adjusted for operating leases, R&D expenses and one-time charges to compute the return on capital. The third and final component needed to estimate the economic value added is the cost of capital. In keeping with our arguments both in the investment analysis and the discounted cash flow valuation sections, the cost of capital should be estimated based upon the market values of debt and equity in the firm, rather than book values. There is no contradiction between using book value for purposes of estimating capital invested and using market value for estimating cost of capital, since a firm has to earn more than its market value cost of capital to generate value. From a practical standpoint, using the book value cost of capital will tend to understate cost of capital for most firms and will understate it more for more highly levered firms than for lightly levered firms. Understating the cost of capital will lead to overstating the economic value added.

1

As an illustration, computing the return on capital at Microsoft using the market value of the firm, instead of book value, results in a return on capital of about 3%. It would be a mistake to view this as a sign of poor investments on the part of the firm's managers.

4 EVA Computation in Practice During the 1990s, EVA was promoted most heavily by Stern Stewart, a New York based consulting firm. The firm’s founders Joel Stern and Bennett Stewart became the foremost evangelists for the measure. Their success spawned a whole host of imitators from other consulting firms, all of which were variants on the excess return measure. Stern Stewart, in the process of applying this measure to real firms found that it had to modify accounting measures of earnings and capital to get more realistic estimates of surplus value. Bennett Stewart, in his book titled “The Quest for Value” mentions some of the adjustments that should be made to capital invested including adjusting for goodwill (recorded and unrecorded). He also suggests adjustments that need to be made to operating income including the conversion of operating leases into financial expenses. Many firms that adopted EVA during this period also based management compensation upon measured EVA. Consequently, how it was defined and measured became a matter of significant concern to managers at every level. Economic Value Added, Net Present Value and Discounted Cashflow Valuation One of the foundations of investment analysis in traditional corporate finance is the net present value rule. The net present value (NPV) of a project, which reflects the present value of expected cash flows on a project, netted against any investment needs, is a measure of dollar surplus value on the project. Thus, investing in projects with positive net present value will increase the value of the firm, while investing in projects with negative net present value will reduce value. Economic value added is a simple extension of the net present value rule. The net present value of the project is the present value of the economic value added by that project over its life2. t =n

NPV = ∑ t =1

2

EVA t (1 + k c )t

This is true, though, only if the expected present value of the cash flows from depreciation is assumed to be equal to the present value of the return of the capital invested in the project. A proof of this equality can be found in my paper on value enhancement in the Contemporary Finance Digest in 1999.

5 where EVAt is the economic value added by the project in year t and the project has a life of n years. This connection between economic value added and NPV allows us to link the value of a firm to the economic value added by that firm. To see this, let us begin with a simple formulation of firm value in terms of the value of assets in place and expected future growth. Firm Value = Value of Assets in Place + Value of Expected Future Growth Note that in a discounted cash flow model, the values of both assets in place and expected future growth can be written in terms of the net present value created by each component. t =∞

Firm Value = Capital Invested Assets in Place + NPVAssets in Place + ∑ NPVFuture Projects, t t =1

Substituting the economic value added version of net present value into this equation, we get: t =∞

Firm Value = Capital Invested Assets in Place + ∑ t =1

EVA t, Assets in Place

(1 + k c ) t

t =∞

+∑ t =1

EVA t, Future Projects

(1 + k c )t

Thus, the value of a firm can be written as the sum of three components, the capital invested in assets in place, the present value of the economic value added by these assets and the expected present value of the economic value that will be added by future investments. Illustration 32.1: Discounted Cashflow Value and Economic Value Added Consider a firm that has existing assets in which it has capital invested of $100 million. Assume these additional facts about the firm. 1. The after-tax operating income on assets in place is $15 million. This return on capital of 15% is expected to be sustained in the future and the company has a cost of capital of 10%. 2. At the beginning of each of the next 5 years, the firm is expected to make investments of $10 million each. These investments are also expected to earn 15% as a return on capital and the cost of capital is expected to remain 10%.

6 3. After year 5, the company will continue to make investments and earnings will grow 5% a year, but the new investments will have a return on capital of only 10%, which is also the cost of capital. 4. All assets and investments are expected to have infinite lives3. Thus, the assets in place and the investments made in the first five years will make 15% a year in perpetuity, with no growth. This firm can be valued using an economic value added approach, as shown in Table 32.1. Table 32.1: Economic Value Added Valuation of Firm Capital Invested in Assets in Place + EVA from Assets in Place =

$100

(0.15 - 0.10 )(100 )

$ 50

0.10

+ PV of EVA from New Investments in Year 1 =

(0.15 - 0.10 )(10) (0.10)

$5

+ PV of EVA from New Investments in Year 2 =

(0.15 - 0.10 )(10) (0.10)(1.10)1

$ 4.55

+ PV of EVA from New Investments in Year 3 =

(0.15 - 0.10 )(10) (0.10)(1.10)2

$ 4.13

+ PV of EVA from New Investments in Year =

(0.15 - 0.10 )(10) (0.10)(1.10)3

+ PV of EVA from New Investments in Year 5 = Value of Firm

(0.15 - 0.10 )(10) (0.10)(1.10)4

$ 3.76

$ 3.42

$ 170.85

Note that the present values are computed assuming that the cash flows on investments are perpetuities. In addition, the present value of the economic value added by the investments made in future years are discounted to the present, using the cost of capital. To illustrate, the present value of the economic value added by investments made at the

3

Note that this assumption is purely for convenience, since it makes the net present value easier to compute.

7 beginning of year 2 is discounted back two years. The value of the firm, which is $170.85 million, can be written using the firm value equation. t= ∞

Firm Value = Capital Invested

Assets in Place

+

∑ t=1

$170.85 mil=

$100 mil

EVA t, Assets in Place t =∞ EVA t, Future Projects +∑ (1+k c )t (1+k c )t t=1

+ $50 mil

+ $20.85 mil

The value of existing assets is therefore $150 million and the value of future growth opportunities is $ 20.85 million. Another way of presenting these results is in terms of Market Value Added (MVA). The market value added, in this case, is the difference between the firm value of $170.85 million and the capital invested of $100 million, which yields $70.85 million. This value will be positive only if the return on capital is greater than the cost of capital and will be an increasing function of the spread between the two numbers. Conversely, the number will be negative if the return on capital is less than the cost of capital. Note that although the firm continues to grow operating income and makes new investments after the fifth year, these marginal investments create no additional value because they earn the cost of capital. A direct implication is that it is not growth that creates value, but growth in conjunction with excess returns. This provides a new perspective on the quality of growth. A firm can be increasing its operating income at a healthy rate, but if it is doing so by investing large amounts at or below the cost of capital, it will not be creating value and may actually be destroying it. This firm could also have been valued using a discounted cash flow valuation, with free cashflows to the firm discounted at the cost of capital. Table 32.2 shows expected free cash flows and the firm value, using the cost of capital of 10% as the discount rate. In looking at this valuation, note the following. •

The capital expenditures occur at the beginning of each year and thus are shown in the previous year. The investment of $10 million in year 1 is shown in year 0, the year 2 investment in year 1 and so on.

•

In year 5, the net investment needed to sustain growth is computed by using two assumptions – that growth in operating income would be 5% a year beyond year 5, and that the return on capital on new investments starting in year 6 (which is shown in year 5) would be 10%.

8 Net Investment5 =

EBIT6 (1 − t )− EBIT5 (1 − t ) $23.625 − $22.50 = = $11.25 million ROC 6 0.10

The value of the firm obtained by discounting free cash flows to the firm at the cost of capital is $170.85, which is identical to the value obtained using the economic value added approach.

9

Table 32.2: Firm Value using DCF Valuation 0 EBIT (1-t) from Assets in Place

$0.00

EBIT(1-t) from Investments - Yr 1

1 $

2 15.00

$

$

3 15.00

$

4 15.00

$

5 15.00

$

15.00

1.50 $

1.50 $

1.50 $

1.50 $

1.50

$

1.50 $

1.50 $

1.50 $

1.50

$

1.50 $

1.50 $

1.50

$

1.50 $

1.50

$

1.50

EBIT(1-t) from Investments - Yr 2 EBIT(1-t) from Investments - Yr 3 EBIT(1-t) from Investments - Yr 4 EBIT(1-t) from Investments - Yr 5 Total EBIT(1-t)

Term. Year

$

16.50

$

18.00

$

19.50

$

21.00

$

22.50

$

23.63

$10.00

$

10.00

$

10.00

$

10.00

$

10.00

$

11.25

$

11.81

FCFF

($10)

$

6.50 $

8.00 $

9.50 $

11.00

$

11.25

$

11.81

PV of FCFF

($10)

$

5.91 $

6.61 $

7.14 $

7.51 $

6.99

Terminal Value

$

236.25

PV of Terminal Value

$

146.69

- Net Capital Expenditures

Value of Firm

$170.85

Return on Capital

15%

15%

15%

15%

15%

15%

10%

Cost of Capital

10%

10%

10%

10%

10%

10%

10%

10 Illustration 32.2: An EVA Valuation of Boeing - 1998 The equivalence of traditional DCF valuation and EVA valuation can be illustrated for Boeing. We begin with a discounted cash flow valuation of Boeing and summarize the inputs we used in Table 32.3. Table 32.3: Summary of Inputs: Boeing

Length Growth Inputs - Reinvestment Rate - Return on Capital - Expected Growth rate Cost of Capital Inputs - Beta - Cost of Debt - Debt Ratio - Cost of Capital General Information - Tax Rate

High Growth Phase 10 years

Stable Growth Phase Forever after year 10

65.98% 6.59% 4.35%

59.36% 8.42% 5.00%

1.01 5.50% 19.92% 9.18%

1.00 5.50% 30.00% 8.42%

35%

35%

With these inputs, we can estimate the free cashflows to the firm in Table 32.4. Table 32.4: Expected Free Cashflows to the Firm: Boeing

Year

EBIT(1-t)

FCFF

Present Value at 9.18%

Current

$1,651

1

$1,723

$1,137

$586

$537

2

$1,798

$1,186

$612

$513

3

$1,876

$1,238

$638

$490

4

$1,958

$1,292

$666

$469

5

$2,043

$1,348

$695

$448

6

$2,132

$1,407

$725

$428

7

$2,225

$1,468

$757

$409

8

$2,321

$1,532

$790

$391

9

$2,422

$1,598

$824

$374

Reinvestment

11 10

$2,528

$1,668

$860

Terminal year

$2,654

$1,575

$1,078

$357

The sum of the present value of the cash flows over the growth period is $4,416 million. The terminal value can be estimated based upon the cash flow in the terminal year and the cost of capital of 8.42%. Terminal value =

1,078 = $31,529 million 0.0842 − 0.05

The discounted cash flow estimate of the value is shown below: Value of Boeing’s operating assets = 4,416 +

31,529 = $17,516 10 1.0918

In Table 32.5, we estimate the EVA for Boeing each year for the next 10 years, and the present value of the EVA. To make these estimates, we begin with the current capital invested in the firm of $26,149 million and add the reinvestment each year from Table 32.4 to obtain the capital invested in the following year. Table 32.5: Present Value of EVA at Boeing Year Capital Invested at beginning

Return on

Cost of

EVA

PV of EVA

of year

Capital

Capital

1

$26,149

6.59%

9.18%

($678)

($621)

2

$27,286

6.59%

9.18%

($707)

($593)

3

$28,472

6.59%

9.18%

($738)

($567)

4

$29,710

6.59%

9.18%

($770)

($542)

5

$31,002

6.59%

9.18%

($804)

($518)

6

$32,350

6.59%

9.18%

($839)

($495)

7

$33,757

6.59%

9.18%

($875)

($473)

8

$35,225

6.59%

9.18%

($913)

($452)

9

$36,756

6.59%

9.18%

($953)

($432)

10

$38,354

6.59%

9.18%

($994)

($413)

PV of EVA over 10 years =

($5,107)

The sum of the present values of the EVA is -$5,107 million. To get to the value of the operating assets of the firm, we add two more components.

12 •

The capital invested in assets in place at the beginning of year 1 (current), which is $26,149 million.

•

The present value of the EVA in perpetuity on assets in place in year 10, which is computed as follows:

[(EBIT11(1-t) – Capital Invested11*Cost of Capital11)/Cost of Capital11]/(1+Current Cost EBIT11 (1 − t )− (Capital Invested11 )(Cost of Capital11 ) (Cost of Capital11 )(1 + Cost of Capital )10 2,653.93 − (40,022 )(0.0842 ) 10 = of Capital) (0.0842 )(1.0918)10 = −$3,536 million Note that while the marginal return on capital on new investments is equal to the cost of capital after year 10, the existing investments continue to make 6.59%, which is lower than the cost of capital of 8.42%, in perpetuity. The total value of the firm can then be computed as follows: Capital Invested in Assets in Place =

$ 26,149 million

PV of EVA from Assets in Place =

-$ 8,643 million

Value of Operating Assets =

$17,506 million

fcffeva.xls: This spreadsheet allows you to convert a discounted cash flow valuation into an EVA valuation and vice versa. EVA Valuation versus DCF valuation: Whey will they disagree? To get the same value from discounted cashflow and EVA valuations, you have to ensure that the following conditions hold. •

The after-tax operating income that you use to estimate free cash flows to the firm should be equal to the after-tax operating income that you use to compute economic value added. Thus, if you decide to adjust the operating income for operating leases and research and development expenses, when doing discounted cashflow valuation, you have to adjust it for computing EVA as well.

•

The growth rate you use to estimate after-tax operating income in future periods should be estimated from fundamentals when doing discounted cash flow valuation. In other words, it should be set to

13 Growth rate = Reinvestment rate * Return on capital If growth is an exogenous input into a DCF model and the relationship between growth rates, reinvestments and return on capital outlined above does not hold, you will get different values from DCF and EVA valuations. •

The capital invested, which is used to compute EVA in future periods, should be estimated by adding the reinvestment in each period to the capital invested at the beginning of the period. The EVA in each period should be computed as follows: EVAt = After-tax Operating Incomet – Cost of capital* Capital Investedt-1

•

You have to make consistent assumptions about terminal value in your discounted cash flow and EVA valuations. In the special case, where the return on capital on all investments – existing and new - is equal to the cost of capital after your terminal year, this is simple to do. The terminal value will be equal to your capital invested at the beginning of your terminal year. In the more general case, you will have to ensure that the capital invested at the beginning of your terminal year is consistent with your assumption about return on capital in perpetuity. In other words, if your after-tax operating income in your terminal year is $1.2 billion and you are assuming a return on capital of 10% in perpetuity, you will have to set your capital invested at the beginning of your terminal year to be $12 billion.

EVA and Firm Value: Potential Conflicts Assume that a firm adopts economic value added as its measure of value and decides to judge managers on their capacity to generate greater-than-expected economic value added. What is the potential for abuse? Is it possible for a manager to deliver greater than expected economic value added, while destroying firm value at the same time? If so, how can we protect stockholders against these practices? To answer these questions, let us go back to the earlier equation where we decomposed firm value into capital invested, the present value of economic value added by assets in place and the present value of economic value added by future growth. t =∞

Firm Value = Capital Invested Assets in Place + ∑ t =1

EVA t, Assets in Place (1 + k c )

t

t =∞

EVA t, Future Projects

t =1

(1 + k c )

+∑

t

14 The Capital Invested Game The first two terms in the equation above, the capital invested and the present value of economic value added by these investments, are both sensitive to the measurement of capital invested. If capital invested is reduced, keeping the operating income constant, the first term in the equation will drop but the present value of economic value added will increase proportionately. To illustrate, consider the firm we valued in Illustration 32.1. Assume that the capital invested is estimated to be $50 million rather than $100 million and that the operating income on these investments stays at $15 million. The assumptions about future investments remain unchanged. The firm value can then be written as shown in Table 32.6. Table 32.6: EVA Valuation of Firm: EVA and Assets in Place Capital Invested in Assets in Place + EVA from Assets in Place =

(0.30 - 0.10 )(50)

$ 50 $ 100

0.10

+ PV of EVA from New Investments in Year 1 =

(0.15 − 0.10)(10)

$5

0.10

+ PV of EVA from New Investments in Year 2 =

(0.15 − 0.10)(10) (0.10)(1.10)1

$ 4.55

+ PV of EVA from New Investments in Year 3 =

(0.15 − 0.10)(10) (0.10)(1.10)2

$ 4.13

+ PV of EVA from New Investments in Year 4 =

(0.15 − 0.10)(10) (0.10)(1.10)3

$ 3.76

+ PV of EVA from New Investments in Year 5 =

(0.15 − 0.10)(10) (0.10)(1.10)4

$ 3.42

Value of Firm

$ 170.85

The value of the firm is unchanged, but it is redistributed to the economic value added component. When managers are judged on the economic value added, there will be strong incentives to reduce the capital invested, at least as measured for EVA computations. There are some actions managers can take to reduce capital invested that truly create value. Thus, in the above example, if the reduction in capital invested came from closing down a plant that does not (and is not expected to) generate any operating income,

15 the cash flow generated by liquidating the plant’s assets will increase value. Some actions, however, are purely cosmetic in terms of their effects on capital invested and thus do not create and may even destroy value. For instance, firms can take one-time restructuring charges, reducing capital or lease assets rather than buy them, because the capital impact of leasing may be smaller. To illustrate the potential destructiveness of these actions, assume that the managers of the firm in Illustration 32.1 are able to replace half their assets with leased assets. Assume further that the estimated capital invested in these leased assets is only $40 million, which is lower than the capital invested in the replaced assets of $50 million. In addition, assume that the action actually reduces the adjusted annual operating income from these assets from $15 million to $14.8 million. The value of the firm can now be written in Table 32.7. Table 32.7: Value Reduction with Higher EVA Capital Invested in Assets in Place + EVA from Assets in Place =

$ 90

(0.1644 - 0.10 )(90)

$ 58

0.10

+ PV of EVA from New Investments in Year 1 =

(0.15 − 0.10)(10)

$5

0.10

+ PV of EVA from New Investments in Year 2 =

(0.15 − 0.10)(10) (0.10)(1.10)1

$ 4.55

+ PV of EVA from New Investments in Year 3 =

(0.15 − 0.10)(10) (0.10)(1.10)2

$ 4.13

+ PV of EVA from New Investments in Year 4 =

(0.15 − 0.10)(10) (0.10)(1.10)3

$ 3.76

+ PV of EVA from New Investments in Year 5 =

(0.15 − 0.10)(10) (0.10)(1.10)4

$ 3.42

Value of Firm

$ 168.85

Note that the firm value declines by $ 2 million, but the economic value added increases by $ 8 million. When economic value added is estimated for divisions, the capital invested at the divisional level is a function of a number of allocation decisions made by the firm, with

16 the allocation based upon pre-specified criteria (such as revenues or number of employees). While we would like these rules to be objective and unbiased, they are often subjective and over allocate capital to some divisions and under-allocate it to others. If this misallocation were purely random, we could accept it as error and use changes in economic value added to measure success. Given the natural competition that exists among divisions in a firm for the marginal investment dollar, however, these allocations are also likely to reflect the power of individual divisions to influence the process. Thus, the economic value added will be over-estimated for those divisions that are under allocated capital and under-estimated for divisions that are over-allocated capital. The Future Growth Game The value of a firm is the value of its existing assets and the value of its future growth prospects. When managers are judged on the basis of economic value added in the current year, or on year-to-year changes, the economic value added that is being measured is just from assets in place. Thus, managers may trade off the economic value added from future growth for higher economic value added from assets in place. Again, this point can be illustrated simply using the firm in Illustration 32.1. The firm earned a return on capital of 15% on both assets in place and future investments. Assume that there are actions the firm can take to increase the return on capital on assets in place to 16%, but that this action reduces the return on capital on future investments to 12%. The value of this firm can then be estimated in Table 32.8: Table 32.8: Trading Off Future Growth for Higher EVA Capital Invested in Assets in Place + EVA from Assets in Place =

(0.16 - 0.10 )(100 )

$ 100 $ 60

0.10

+ PV of EVA from New Investments in Year 1 =

(0.12 − 0.10)(10)

$2

0.10

+ PV of EVA from New Investments in Year 2 =

(0.12 − 0.10)(10) (0.10)(1.1)

$ 1.82

+ PV of EVA from New Investments in Year 3 =

(0.12 − 0.10)(10) (0.10)(1.1)2

$ 1.65

17 + PV of EVA from New Investments in Year 4 =

(0.12 − 0.10)(10) (0.10)(1.1)3

$ 1.50

+ PV of EVA from New Investments in Year 5 =

(0.12 − 0.10)(10) (0.10)(1.1)4

$ 1.37

Value of Firm

$ 168.34

Note that the value of the firm has decreased, but the economic value added in year 1 is higher now than it was before. In fact, the economic value added at this firm for each of the next five years is graphed in Figure 32.1 for both the original firm and this one. Figure 32.1: Annual EVA: With and Without Growth Trade-Off $8.00

$7.00

$6.00

EVA

$5.00 EVA (Original) EVA (Growth Trade-Off)

$4.00

$3.00

$2.00

$1.00

$1

2

3

4

5

Year

The growth trade off, while leading to a lower firm value, results in economic value added in each of the first three years that is larger than it would have been without the trade off. Compensation mechanisms based upon EVA are sometimes designed to punish managers who give up future growth for current EVA. Managers are partly compensated based upon the economic value added this year, but another part is held back in a compensation bank and is available to the manager only after a period (say three or four years). There are significant limitations with these approaches. First, the limited tenure that managers have with firms implies that this measure can at best look at economic

18 value added only over the next 3 or 4 years. The real costs of the growth trade off are unlikely to show up until much later. Second, these approaches are really designed to punish managers who increase economic value added in the current period while reducing economic value added in future periods. In the more subtle case, where the economic value added continues to increase but at a rate lower than it otherwise would have, it is difficult to devise a punishment for managers who trade off future growth. In the example above, for instance, the economic value added with the growth trade off increases over time. The increases are smaller than they would have been without the trade off, but that number would not have been observed anyway. The Risk Shifting Game The value of a firm is the sum of the capital invested and the present value of the economic value added. The latter term is therefore a function not just of the dollar economic value added but also of the cost of capital. A firm can invest in projects to increase its economic value added but still end up with a lower value, if these investments increase its operating risk and cost of capital. Again, using the firm in Illustration 32.1, assume that the firm is able to increase its return on capital on both assets in place and future investments from 15% to 16.25%. Simultaneously, assume that the cost of capital increases to 11%. The economic value added in each year for the next five years is contrasted with the original economic value added in each year in Figure 32.2.

19 Figure 32.2: EVA: Higher Risk and Return $9.00 $8.00 $7.00 $6.00 $5.00 Year

EVA (Original) EVA (Risk Trade-Off) $4.00 $3.00 $2.00 $1.00 $1

2

3

4

5

EVA

While the economic value added in each year is higher with the high-risk strategy, the value of the firm is shown in Table 32.9. Table 32.9: EVA with High Risk Strategy Capital Invested in Assets in Place + EVA from Assets in Place =

(0.1625 - 0.11)(100 )

$ 100 $ 47.73

0.11

+ PV of EVA from Investments in Year 1 =

(0.1625 - 0.11)(10)

$ 4.77

0.11

+ PV of EVA from Investments in Year 2 =

(0.1625 - 0.11)(10) (0.11)(1.11)

$ 4.30

+ PV of EVA from Investments in Year 3 =

(0.1625 - 0.11)(10) (0.11)(1.11)2

$ 3.87

+ PV of EVA from Investments in Year 4 =

(0.1625 - 0.11)(10) (0.11)(1.11)3

$ 3.49

+ PV of EVA from Investments in Year 5 =

(0.1625 - 0.11)(10) (0.11)(1.11)4

$ 3.14

20 Value of Firm

$ 167.31

Note that the risk effect dominates the higher excess dollar returns and the value of the firm decreases. This risk shifting can be dangerous for firms that adopt economic value added based on objective functions. When managers are judged based upon year-to-year economic value added changes, there will be a tendency to shift into riskier investments. This tendency will be exaggerated if the measured cost of capital does not reflect the changes in risk or lags4 it. In closing, economic value added is an approach skewed toward assets in place and away from future growth. It should not be surprising, therefore, that when economic value added is computed at the divisional level of a firm, the higher growth divisions end up with the lowest economic value added and in some cases with negative economic value added. Again, while these divisional managers may still be judged based upon changes in economic value added from year to year, the temptation at the firm level to reduce or eliminate capital invested in these divisions will be strong, since it will make the firm’s overall economic value added look much better. EVA and Market Value Will increasing economic value added cause market value to increase? While an increase in economic value added will generally lead to an increase in firm value, barring the growth and risk games described earlier, it may or may not increase the stock price. This is because the market has built into its expectations of future economic value added. Thus, a firm like Microsoft is priced on the assumption that it will earn large and increasing economic value added over time. Whether a firm’s market value increases or decreases on the announcement of higher economic value added will depend in large part on what the expected change in economic value added was. For mature firms, where the market might have expected no increase or even a decrease in economic value added, the announcement of an increase will be good news and cause the market value to increase.

4

In fact, beta estimates that are based upon historical returns will lag changes in risk. With a five-year return estimation period, for instance, the lag might be as long as three years and the full effect will not show up for five years after the change.

21 For firms that are perceived to have good growth opportunities and are expected to report an increase in economic value added, the market value will decline if the announced increase in economic value added does not measure up to expectations. This should be no surprise to investors, who have recognized this phenomenon with earnings per share for decades; the earnings announcements of firms are judged against expectations and the earnings surprise is what drives prices. We would therefore not expect any correlation between the magnitude of the economic value added and stock returns or even between the change in economic value added and stock returns. Stocks that report the biggest increases in economic value added should not necessarily earn high returns for their stockholders5. These priors are confirmed by a study done by Richard Bernstein at Merrill Lynch, who examined the relationship between EVA and stock returns. •

A portfolio of the 50 firms which had the highest absolute levels6 of economic value added earned an annual return on 12.9% between February 1987 and February 1997, while the S&P index returned 13.1% a year over the same period.

•

A portfolio of the 50 firms that had the highest growth rates7 in economic value added over the previous year earned an annual return of 12.8% over the same time period.

eva.xls: There is a dataset on the web that summarizes economic value added by industry group for the United States. Equity Economic Value Added While EVA is usually calculated using total capital, it can easily be modified to be an equity measure. Equity EVA = (Return on Equity - Cost of Equity) (Equity Invested in Project or Firm) = Net Income – (Cost of Equity)(Equity Invested in Project or Firm)

5

A study by Kramer and Pushner found that differences in operating income (NOPAT) explained differences in market value better than differences in EVA. O'Byrne (1996), however, finds that changes in EVA explain more than 55% of changes in market value over 5-year periods. 6 See Quantitative Viewpoint, Merrill Lynch, December 19, 1997.

22 Again, a firm that earns a positive equity EVA is creating value for its stockholders while a firm with a negative equity EVA is destroying value for its stockholders. Why might a firm use this measure rather than the traditional measure? In Chapter 21, when we looked at financial service firms, we noted that defining debt (and therefore capital) may create measurement problems, since so much of the firm could potentially be categorized as debt. Consequently, we argued that financial service firms should be valued using equity valuation models and multiples. Extending that argument to economic value added, we believe that equity EVA is a much better measure of performance for financial service firms than the traditional EVA measure. We would hasten to add that all of the issues that we raised in the context of the traditional EVA measure affect the equity EVA measure as well. Banks and insurance companies can play the capital invested, growth and risk games to increase equity EVA just as other firms can with traditional EVA. EVA for High Growth firms The fact that the value of a firm is a function of the capital invested in assets in place, the present value of economic value added by those assets and the economic value added by future investments, points to some of the dangers of using it as a measure of success or failure for high growth and especially high-growth technology firms.

In

particular, there are three problems. •

We have already noted many of the problems associated with how accountants measure capital invested at technology firms. Given the centrality of capital invested to economic value added, these problems have a much bigger effect when firms use EVA than when discounted cash flow valuation.

•

When 80% to 90% of value comes from future growth potential, the risks of managers trading off future growth for current EVA are magnified. It is also very difficult to monitor these trade offs at young firms.

7

See Quantitative Viewpoint, Merrill Lynch, February 3, 1998.

23 •

The constant change that these firms go through also makes them much better candidates for risk shifting. In this case, the negative effect (of a higher discount rate) can more than offset the positive effect of a higher economic value added. Finally, it is unlikely that there will be much correlation between actual changes in

economic value added at technology firms and changes in market value. The market value is based upon expectations of economic value added in future periods and investors expect an economic value added that grows substantially each year. Thus, if the economic value added increases, but by less than expected, you could see its market value drop on the report. Cash Flow Return on Investment The cash flow return on investment (CFROI) for a firm is the internal rate of return on existing investments, based upon real cash flows. Generally, it should be compared to the real cost of capital to make judgments about the quality of these investments. Calculating CFROI The cash flow return on investment for a firm is calculated using four inputs. The first is the gross investment (GI) the firm has in its existing assets, obtained by adding back cumulated depreciation and inflation adjustments to the book value. The second input is the gross cash flow (GCF) earned in the current year on gross investment, which is usually defined as the sum of the after-tax operating income of a firm and the non-cash charges against earnings, such as depreciation and amortization. The third input is the expected life of the assets (n) in place at the time of the original investment, which varies from sector to sector but reflects the earning life of the investments in question. The expected value of the assets (SV) at the end of this life, in current dollars, is the final input. This is usually assumed to be the portion of the initial investment, such as land and building, that is not depreciable, adjusted to current dollar terms. The CFROI is the internal rate of return of these cash flows, i.e, the discount rate that makes the net present value of the gross cash flows and salvage value equal to the gross investment and it can thus be viewed as a composite internal rate of return, in current dollar terms.

24 An alternative formulation of the CFROI allows for setting aside an annuity to cover the expected replacement cost of the asset at the end of the project life. This annuity is called the economic depreciation. Economic Depreciation =

Replacement Cost in Current dollars (k c ) (1 + k c )n − 1

where n is the expected life of the asset. The expected replacement cost of the asset is defined in current dollar terms to be the difference between the gross investment and the salvage value. The CFROI for a firm or a division can then be written as follows: CFROI =

Gross Cash Flow - Economic Depreciation Gross Investment

For instance, assume that you have existing assets with a book value of $2,431 million, a gross cash flow of $390 million, an expected salvage value (in today’s dollar terms) of $607.8 million and a life of 10 years. The conventional measure of CFROI is 11.71% and the real cost of capital is 8%. The estimate using the alternative approach is computed. Economic Depreciation = CFROI =

($2,431 - $607.8)(0.08) = $125.86 million 1.08 − 1 10

390 - 125.86 = 10.87% 2,431

The differences in the reinvestment rate assumption accounts for the difference in CFROI estimated using the two methods. In the first approach, intermediate cash flows get reinvested at the internal rate of return, while in the second, at least the portion of the cash flows that are set aside for replacement get reinvested at the cost of capital. In fact, if we estimated that the economic depreciation using the internal rate of return of 11.71%, the two approaches would yield identical results8.

8

With an 11.71% rate, the economic depreciation works out to $105.37 million and the CFROI to 11.71%.

25 Cashflow Return on Investment, Internal Rate of Return and Discounted Cashflow Value If net present value provides the genesis for the economic value added approach to value enhancement, the internal rate of return is the basis for the CFROI approach. In investment analysis, the internal rate of return on a project is computed using the initial investment on the project and all cash flows over the project’s life. ATCF

Initial Investment

1

ATCF

ATCF

ATCF

SV ATCF

2

3

4

n

Where the ATCF is the after-tax cash flow on the project and SV is the expected salvage value of the project assets. This analysis can be done entirely in nominal terms, in which case the internal rate of return is a nominal IRR and is compared to the nominal cost of capital, or in real terms, in which case it is a real IRR and is compared to the real cost of capital. At first sight, the CFROI seems to do the same thing as IRR. It uses the gross investment in the project (in current dollars) as the equivalent of the initial investment, assumes that the gross current-dollar cash flow is maintained over the project life and computes a real internal rate of return. There are, however, some significant differences. The internal rate of return does not require the after-tax cash flows to be constant over a project’s life, even in real terms. The CFROI approach assumes that real cash flows on assets do not increase over time. This may be a reasonable assumption for investments in mature markets, but will understate project returns if there is real growth. Note, however, that the CFROI approach can be modified to allow for real growth. The second difference is that the internal rate of return on a project or asset is based upon incremental future cash flows. It does not consider cash flows that have occurred already, since these are viewed as “sunk.” The CFROI, on the other hand, tries to reconstruct a project or asset, using both cash flows that have occurred already and cashflows that are yet to occur. To illustrate, consider the project described in the previous section. At the time of the original investment, assuming that the inputs for initial investment, after-tax cash flows and salvage value are unchanged, both the internal

26 rate of return and the CFROI of this project would have been 11.71%. The CFROI is, however, being computed three years into the project life and remains at 11.71%, since none of the original inputs have changed. The IRR of this project will change, though. It will now be based upon the current market value of the asset, the expected cash flows over the remaining life of the asset and a life of seven years. Thus, if the market value of the asset has increased to $2.5 billion, the internal rate of return on this project would be computed to be only 6.80%. $607.8 mil $390 mil

$ 3,000 mil

1

$390 mil

2

$390 mil

3

$390 mil

4

$ 390 mil

7

Given the real cost of capital of 8%, this would mean that the CFROI is greater than the cost of capital, while the internal rate of return is lower. Why is there a difference between the two measures and what are the implications? The reason for the difference is that IRR is based entirely on expected future cash flows, whereas the CFROI is not. A CFROI that exceeds the cost of capital is viewed as a sign that a firm is deploying its assets well. If the IRR is less than the cost of capital, that interpretation is false, because the owners of the firm would be better off selling the asset and getting the market value for it rather than continuing its operation. To link the cash flow return on investment with firm value, let us begin with a simple discounted cash flow model for a firm in stable growth. Firm Value =

FCFF1 kc − gn

where FCFF is the expected free cash flow to the firm, kc is the cost of capital and gn is the stable growth rate. Note that this can be rewritten, approximately, in terms of the CFROI. Firm Value =

((CFROI )(GI )- DA )(1 - t )− (CX - DA )- ∆WC kc − gn

where CFROI is the cash flow return on investment, GI is the gross investment, DA is the depreciation and amortization, CX is the capital expenditure and ∆WC is the change in

27 working capital. To illustrate, consider a firm with a CFROI of 30%, a gross investment of $100 million, capital expenditures of $15 million, depreciation of $10 million and no working capital requirements. If we assume a 10% cost of capital, a 40% tax rate and a 5% stable growth rate, it would be valued as follows: Firm Value =

((0.30 )(100 )- 10)(1 - 0.4 )- (15 - 10)- 0) = $140 million 0.10 − 0.05

More important than the mechanics, however, is the fact that the firm value, while a function of the CFROI is also a function of the other variables in the equation – the gross investment, the tax rate, the growth rate, the cost of capital and the firm’s reinvestment needs. Again, sophisticated users of CFROI do recognize the fact that value comes from the CFROI not just on assets in place but also on future investments. In fact, Holt Associates, one of CFROI’s leading proponents, allows for a fade factor in CFROI, where the current CFROI fades towards the real cost of capital over time. The "fade factor" is estimated empirically by looking at firms in different CFROI classes and tracking them over time. Thus, a firm that has a current CFROI of 20% and real cost of capital of 8% will be projected to have lower CFROI over time. The value of the firm, in this more complex format, can then be written as a sum of the following. •

The present value of the cash flows from assets in place over their remaining life, t =n

which can be written as

∑ t =1

(CFROI )(GI ), aip

aip

(1 + kc ) t

where CFROI aip is the CFROI on

assets in place, GI aip is the gross investment in assets in place and kc is the real cost of capital. •

The present value of the excess cash flows from future investments, which can be t =∞

written in real terms as

∑ t =1

(CFROI )(∆GI ) − ∆GI t , NI

(1 + kc ) t

t

t

, where CFROIt,NI is the CFROI

on new investments made in year t and ∆GIt is the new investment made in year t. Note that if CFROIt,NI = kc , this present value is equal to zero.

28 Thus, a firm's value will depend upon the CFROI it earns on assets in place and both the abruptness and the speed with which this CFROI fades towards the cost of capital. Thus, a firm can therefore potentially increase its value by doing any of the following. •

Increase the CFROI from assets in place, for a given gross investment.

•

Reduce the speed at which the CFROI fades towards the real cost of capital.

•

Reduce the abruptness with which CFROI fades towards the cost of capital. Note that this is no different from our earlier analysis of firm value in the

discounted cash flow approach, in terms of cash flows from existing investments (increase current CFROI), the length of the high growth period (reduce fade speed) and the growth rate during the growth period (keep excess returns from falling as steeply). cfroi.xls: This spreadsheet allows you to estimate the cash flow return on investment for a firm or project. CFROI Innovations: The Fade Factor and Implied Cost of Capital The biggest contribution made by practitioners who use CFROI has been the work that they have done on how returns on capital fade over time towards the cost of capital. Madden (1999) makes the argument that not only is this phenomenon wide spread but that it is at least partially predictable. He presents evidence done by Holt Associates, a leading proponent of CFROI, who sorted the largest 1000 firms by CFROI, from highest to lowest and tracked them over time, to find a convergence towards an average. We should note that we have used fade factors, without referring to them as such, in the chapters on discounted cash flow valuation. The fade to a lower return on capital occurred either precipitously in the terminal year or over a transition period. We noted that the return on capital could converge to the cost of capital or to the industry average. To compute the cost of capital, CFROI practitioners look to the market instead of the risk and return models that we have used to compute DCF value. Using the current market values of stocks and their estimates of expected aggregate cash flows, they compute internal rates of return that they use as the cost of capital in analysis. In Chapter 7, we used a very similar approach to estimate an implied risk premium, though we use this premium as an input into traditional risk and return models.

29 CFROI and Firm Value: Potential Conflicts The relationship between CFROI and firm value is less intuitive than the relationship between EVA and firm value, partly because it is a percentage return. Notwithstanding this fundamental weakness, managers can take actions that increase CFROI while reducing firm value. a. Reduce Gross Investment: If the gross investment in existing assets is reduced, the CFROI may be increased. Since it is the product of CFROI and Gross Investment that determines value, it is possible for a firm to increase CFROI and end up with a lower value. b. Sacrifice Future Growth: CFROI, even more than EVA, is focused on existing assets and does not look at future growth. To the extent that managers increase CFROI at the expense of future growth, the value can decrease while CFROI goes up. c. The Risk Trade Off: While the CFROI is compared to the real cost of capital to pass judgment on whether a firm is creating or destroying value, it represents only a partial correction for risk. The value of a firm is still the present value of expected future cash flows. Thus, a firm can increase its spread between the CFROI and cost of capital but still end up losing value if the present value effect of having a higher cost of capital dominates the higher CFROI. In general, then, an increase in CFROI does not, by itself, indicate that the firm value has increased, since it might have come at the expense of lower growth and/or higher risk. CFROI and Market Value There is a relationship between CFROI and market value. Firms with high CFROI generally have high market value. This is not surprising, since it mirrors what we noted about economic value added earlier. However, it is changes in market value that create returns, not market value per se. When it comes to market value changes, the relationship between EVA changes and value changes tends to be much weaker. Since market values reflect expectations, there is no reason to believe that firms that have high CFROI will earn excess returns.

30 The relationship between changes in CFROI and excess returns is more intriguing. To the extent that any increase in CFROI is viewed as a positive surprise, firms with the biggest increases in CFROI should earn excess returns. In reality, however, the actual change in CFROI has to be measured against expectations; if CFROI increases, but less than expected, the market value should drop; if CFROI drops but by less than expected, the market value should increase. A Postscript on Value Enhancement The value of a firm has three components. The first is its capacity to generate cash flows from existing assets, with higher cash flows translating into higher value. The second is its willingness to reinvest to create future growth and the quality of these reinvestments. Other things remaining equal, firms that reinvest well and earn significant excess returns on these investments will have higher value. The final component of value is the cost of capital, with higher costs of capital resulting in lower firm values. To create value then a firm has to: •

Generate higher cash flows from existing assets, without affecting its growth prospects or its risk profile.

•

Reinvest more and with higher excess returns, without increasing the riskiness of its assets.

•

Reduce the cost of financing its assets in place or future growth, without lowering the returns made on these investments.

All value enhancement measures are variants on these simple themes. Whether these approaches measure dollar excess returns, as does economic value added, or percentage excess returns, like CFROI, they have acquired followers because they seem simpler and less subjective than discounted cash flow valuation. This simplicity comes at a cost, since these approaches make subtle assumptions about other components of value that are often not visible or not recognized by many users. Approaches that emphasize economic value added and reward managers for increasing the same, often assume that increases in economic value added are not being accomplished at the expense of future growth or by increasing risk. Practitioners who judge performance based upon the cash flow return on investment make similar assumptions.

31 Is there something of value in the new value enhancement measures? Absolutely, but only in the larger context of valuation. One of the inputs we need for traditional valuation models is the return on capital (to get expected growth). Making the adjustments to operating income suggested by those who use economic value added and augmenting it with a cash flow return, with CFROI, may help us come up with a better estimate of this number. The terminal value computation in traditional valuation models, where small changes in assumptions can lead to large changes in value, becomes much more tractable if we think in terms of excess returns on investments rather than just growth and discount rates. Finally, the empirical evidence that has been collected by practitioners who use CFROI on fade factors can be invaluable in traditional valuation models, where practitioners sometimes make the mistake of assuming that current project returns will continue forever. Summary In this chapter, we consider two widely used value enhancement measures. Economic value added measures the dollar excess return on existing assets. The cash flow return on investment is the internal rate of return on existing assets, based upon the original investment in these assets and the expected future cash flows. While both approaches can lead to conclusions consistent with traditional discounted cash flow valuation, their simplicity comes at a cost. Managers can take advantage of measurement limitations in both approaches to make their firms look better with either approach, while reducing firm value. In particular, they can trade off less growth in the future for higher economic value added today and shift to riskier investments. As we look at various approaches to value enhancement, we should consider a few facts. The first is that no value enhancement mechanism will work at generating value unless there is a commitment on the part of managers to making value maximization their primary objective. If managers put other goals first, then no value enhancement mechanism will work. Conversely, if managers truly care about value maximization, they can make almost any mechanism work in their favor. The second is that while it is sensible to connect whatever value enhancement measure we have chosen to management compensation, there is a down side. Managers, over time, will tend to focus their

32 attention on making themselves look better on that measure even if it leads to reducing firm value. Finally, there are no magic bullets that create value. Value creation is hard work in competitive markets and almost involves a trade off between costs and benefits. Everyone has a role in value creation and it certainly is not the sole domain of financial analysts. In fact, the value created by financial engineers is smaller and less significant than the value created by good strategic, marketing, production or personnel divisions.

33 Problems 1. Everlast Batteries Inc. has hired you as a consultant. The firm had after-tax operating earnings in 1998 of $180 million, net income of $100 million and it paid a dividend of $50 million. The book value of equity at the end of 1998 was $1.25 billion and the book value of debt was $350 million. The firm raised $50 million of new debt during 1998. The market value of equity at the end of 1998 was twice the book value of equity and the market value of debt was the same as the book value of debt. The firm has a cost of equity of 12% and an after-tax cost of debt of 5%. a. Estimate the return on capital earned by Everlast Batteries b. Estimate the cost of capital earned by Everlast Batteries c. Estimate the economic value added by Everlast Batteries 2. Assume, in the last problem, that Everlast Batteries is in stable growth and that it expects its economic value added to grow at 5% a year forever. a. Estimate the value of the firm. b. How much of this value comes from excess returns? c. What is the market value added (MVA) of this firm? c. How would your answers to (a), (b) and (c) change if you were told that there would be no economic value added after year 5? 3. Stereo City is a retailer of stereos and televisions. The firm has operating income of $150 million, after operating lease expenses of $50 million. The firm has operating lease commitments for the next 5 years and beyond. Year

yr 6-15

Operating lease commitment 1

55

2

60

3

60

4

55

5

50 40Each year

34 The book value of equity is $1 billion and the firm has no debt outstanding. The firm has a cost of equity of 11% and a pre-tax cost of borrowing of 6%. The tax rate is 40%. a. Estimate the capital invested in the firm, before and after adjusting for operating leases. b. Estimate the return on capital, before and after adjusting for operating leases. c. Estimate the economic value added, before and after adjusting for operating leases. (The market value of equity is $2 billion.) 4. Sevilla Chemicals earned $1 billion in after-tax operating income on capital invested of $5 billion last year. The firm’s cost of equity is 12%, its debt to capital ratio is 25% and the after-tax cost of debt is 4.5%. a. Estimate the economic value added by Sevilla Chemicals last year. b. Assume now that the entire chemical industry earned $40 billion after taxes on capital invested of $180 billion and that the cost of capital for the industry is 10%. Estimate the economic value added by the entire industry. c. Based on economic value added, how did Sevilla do, relative to the industry? 5. Jeeves Software is a small software firm in high growth. The firm is all equity financed. In the current year, the firm earned $20 million in after-tax operating income on capital invested of $60 million. The firm’s cost of equity is 15%. a. Assume that the firm will be able to grow its economic value added 15% a year for the next 5 years and that there will be no excess returns after year 5. Estimate the value of the firm. How much of this value comes from the EVA and how much from capital invested? b. Now, assume the firm is able to reduce its capital invested this year by $20 million by selling its assets and leasing them back. Assuming operating income and cost of capital do not change as a result of the sale-lease back, estimate the value of the firm now. How much of the value of the firm now comes from EVA and how much from capital invested? 6. Healthy Soups is a company that manufactures canned soups made without preservatives. The firm has assets that have a book value of $100 million. The assets are 5 years old and have been depreciated $50 million over that period. In addition, the inflation rate over those 5 years has averaged 2% a year. The assets are currently earning $15

35 million in after-tax operating income. They have a remaining life of 10 years and the depreciation each year is expected to be $5 million. At the end of these 10 years, the assets will have an expected salvage value, in current dollars, of $50 million. a. Estimate the CFROI of Healthy Foods, using the conventional CFROI approach. b. Estimate the CFROI of Healthy Foods, using the economic depreciation approach. c. If Healthy Foods has a cost of capital in nominal terms of 10% and the expected inflation rate is 2%, evaluate whether Healthy Foods’ existing investments are value creating or destroying.

1

CHAPTER 33 VALUING BONDS The value of a bond is the present value of the expected cash flows on the bond, discounted at an interest rate that is appropriate to the riskiness of that bond. Since the cash flows on a straight bond are fixed at issue, the value of a bond is inversely related to the interest rate that investors demand for that bond. The interest rate charged on a bond is determined by both the general level of interest rates, which applies to all bonds and financial investments, and the default premium specific to the entity issuing the bond. This chapter examines the determinants of both the general level of interest rates and the magnitude of the default premia on specific bonds. The general level of interest rates incorporates expected inflation and a measure of real return and reflects the term structure, with bonds of different maturities carrying different interest rates. The default premia varies across time, depending in large part on the health of the economy and investors' risk preferences. Bonds often have special features embedded in them that have to be factored into the value. Some of these features are options - to convert into stock (convertible bonds), to call the bond back if interest rates go down (callable bonds) and to put the bond back to the issuer at a fixed price under specific circumstances (putable bonds). Other bond characteristics, such as interest rate caps and floors, have option features. Some of these options reside with the issuer of the bond, some with the buyer of the bond, but they all have to be priced. Option pricing models can be used to value these special features and price complex fixed income securities. Some special features in bonds such as sinking funds, subordination of further debt and the type of collateral may affect the prices of bonds, as well. Bond Prices and Interest Rates The value of a straight bond is determined by the level of and changes in interest rates. As interest rates rise, the price of a bond will decrease and vice versa. This inverse relationship between bond prices and interest rates arises directly from the present value relationship that governs bond prices.

2 a. The Present Value Relationship The value of a bond, like all financial investments, is derived from the present value of the expected cash flows on that bond, discounted at an interest rate that reflects the default risk associated with the cash flows. There are two features that set bonds apart from equity investments. First, the cash flows on a bond, i.e., the coupon payments and the face value of the bond, are usually set at issue and do not change during the life of the bond. Even when they do change, as in floating rate bonds, the changes are generally linked to changes in interest rates. Second, bonds usually have fixed lifetimes, unlike stocks, since most bonds1 specify a maturity date. As a consequence, the present value of a 'straight bond' with fixed coupons and specified maturity is determined entirely by changes in the discount rate, which incorporates both the general level of interest rates and the specific default risk of the bond being valued. The present value of a bond, expected to mature in N time periods, with coupons every period can be calculated. t=N

PV of Bond =

∑ t=1

Coupon t Face Value + (1+r) t (1+r) N

where, Coupon t = Coupon expected in period t Face Value = Face value of the bond r = Discount rate for the cash flows The discount rate used to calculate the present value of the bond will vary from bond to bond depending upon default risk, with higher rates used for riskier bonds and lower rates for safer ones. If the bond is traded, and a market price is therefore available for it, the internal rate of return can be computed for the bond, i.e., the discount rate at which the present value of the coupons and the face value is equal to the market price. This internal rate of return is called the yield to maturity on the bond.

1

Console bonds are the exception to this rule, since they are perpetuities.

3 There are several details, relating to both the magnitude and timing of cash flows, that can affect the value of a bond and its yield to maturity. First, the coupon payment on a bond may be semi-annual, in which case the discounting has to allow for the semi-annual cash flows. (The first coupon will be discounted back half a year, the second one year, the third a year and a half and so on.) Second, once a bond has been issued, it accrues coupon interest between coupon payments and this accrued interest has to be added on to the price of the bond, when valuing the bond. Illustration 33.1: Valuing a straight bond at issue The following is a valuation of a thirty-year U.S. Government Bond at the time of issue. The coupon rate on the bond is 7.50%, and the market interest rate is 7.75%. The price of the bond can be calculated. t=30

PV of Bond =

75.00

∑ (1.0775)

t

+

t=1

1,000 = $971.18 (1.0775)30

This is based upon annual coupons. If the calculation is based upon semi-annual coupons, the value of the bond is: t=30

PV of Bond =

37.50 ∑ (1.0775)

t=0.5

t

+

1,000 = $987.62 (1.0775)30

Illustration 33.2: Valuing a seasoned straight bond The following is a valuation of a seasoned Government bond, with twenty years left to expiration and a coupon rate of 11.75%. The next coupon is due in two months. The current twenty-year bond rate is 7.5%. The value of the bond can be calculated. t=19.5

PV of Bond =

58.75 ∑ (1.075)

t=0.5

t

+

58.75 1,000 = $1505.31 2/12 + (1.075) (1.075)19.67

This bond trades at well above face value, because of its high coupon rate. Note that the second term of the equation is the present value of the next coupon. b. A Measure of Interest Rate Risk in Bonds When the fact that the cash flows on a bond are fixed at issue is combined with the present value relationship governing bond prices, there is a clear rationale for why interest

4 changes affect bond prices so directly. Any increase in interest rates, either at the economy wide level or because of an increase in the default risk of the company issuing the bond, will lower the present value of the stream of expected cash flows and hence the value of the bond. Any decrease in interest rates will have the opposite impact. The effect of interest rate changes on bond prices will vary from bond to bond and will depend upon a number of characteristics of the bond. (a) the maturity of the bond - Holding coupon rates and default risk constant, increasing the maturity of a straight bond will increase its sensitivity to interest rate changes. The present value of cash flows changes much more for cash flows further in the future, as interest rates change, than for cash flows which are nearer in time. Figure 33.1 illustrates the present values of six bonds - a 5-year, a 10-year, a 15-year, a 20-year, a 30-year and a 50-year bonds, all with 8% coupons for a range of interest rates. Figure 33.1: Bond Values and Interest Rates $1,400.00

$1,200.00

$1,000.00

$800.00 r=6% r=7% r=8% r=9% r=10% $600.00

$400.00

$200.00

$0.00 5 year

10 year

15 years

20 years

30 years

50 years

Bond Maturities

The longer-term bonds are much more sensitive to interest rate changes than the shorter term bonds. For instance, an increase in interest rates from 8% to 10% results in a decline in value of 7.61% for the five-year bond and of 19.83% for the fifty-year bonds. (b) the coupon rate of the bond - Holding maturity and default risk constant, increasing the coupon rate of a straight bond will decrease its sensitivity to interest rate changes. Since higher coupons result in more cash flows earlier in the bond's life, the present value will

5 change less as interest rates change. At the extreme, if the bond is a 'zero-coupon' bond, the only cash flow is the face value at maturity, and the present value is likely to vary much more as a function of interest rates. Figure 33.2 illustrates the percentage changes in bond prices for six thirty-year bonds with coupon rates ranging from 0% to 10% for a range of interest rates. Figure 33.2: Percent Change in Bond Price - Interest rate changes from 8% 100.00%

80.00%

Percent Change in Bond Price

60.00%

40.00%

20.00%

0.00% 0%

2%

4%

6%

8%

10%

-20.00%

-40.00%

-60.00% Coupon Rate Interest rate drops 2%

Interest rate drops 1%

Interest rate rises 1%

Interest rate rises 2%

The bonds with the lower coupons are much more sensitive, in percentage terms, to interest rate changes than those with higher coupons. While the maturity and the coupon rate are the key determinants of how sensitive the price of a bond is to interest rate changes, a number of other factors impinge on this sensitivity. Any special features that the bond has, including convertibility and callability, make the maturity of the bond less definite and can therefore affect the bond price's sensitivity to interest rate changes. If there is any relationship between the level of interest rates and the default premia on bonds, the default risk of a bond can affect its price sensitivity. c. A More Formal Measure of Interest Rate Risk - Duration

6 Since the interest rate risk of a bond is a significant component of its total risk, a more formal measure of interest risk is needed, which consolidates the effects of maturity, coupon rates and the bond's special features. To arrive at this measure, consider the present value relationship developed earlier in this chapter.– t=N

PV of Bond =

∑ t=1

Coupon t Face Value + (1+r) t (1+r) N

Differentiating the bond price with respect to interest rate should provide a formal measure of bond price sensitivity to interest rate changes.  t = N t * Coupon t N * Face Value  + ∑ t N  dP/P (1 + r) (1 + r)  t =1  Duration of Bond = = t=N dr/r  Coupon t Face Value  ∑ t + N  (1 + r)   t =1 (1 + r)

The bond price differential,

dP / P , is called the duration of the bond and measures the dr / r

interest rate sensitivity of the bond. The duration of a bond is a weighted maturity of all the cash flows on the bond including the coupons, where the weights are based upon both the timing and the magnitude of the cash flows. Larger and earlier cash flows are weighted more than smaller and later cash flows. By incorporating the magnitude and timing of all the cash flows on the bond, duration encompassed all the variables that affect bond price sensitivity in one measure. The higher the duration of a bond, the more sensitive it is to changes in interest rates. The duration of a bond will always be less than the maturity for a coupon bond and equal to the maturity for a zero-coupon bond, with no special features. In general, the duration of a bond will decrease as the coupon rate on the bond increases. The measure of duration described here is called 'Macaulay duration' and it is the simplest version, based upon yields to maturity. It is based upon the assumption of a flat term structure and modified versions of duration, which are more flexible in their assumptions about the term structure and its shifts over time Illustration 33.3: Estimating durations for coupon bonds

7 In this example, we estimate the duration of a seasoned Government bond, with twenty years left to expiration and a coupon rate of 11.75%. The interest rate is 7.5%. The duration of the bond, assuming annual coupon payments, can be calculated as follows. t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Cashflow $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $117.50 $1,117.50

PV of Cashflow t * PV of Cashflow $109.30 $109.30 $101.68 $203.35 $94.58 $283.75 $87.98 $351.94 $81.85 $409.23 $76.14 $456.81 $70.82 $495.77 $65.88 $527.06 $61.29 $551.57 $57.01 $570.10 $53.03 $583.36 $49.33 $591.99 $45.89 $596.58 $42.69 $597.65 $39.71 $595.67 $36.94 $591.05 $34.36 $584.17 $31.97 $575.38 $29.74 $564.98 $263.07 $5,261.48 $1,433.27 $14,501.21 $14,501 = 10.12 Duration of the Bond = $1,433

Determinants of Interest Rates The discount rate used to discount cash flows on a bond is determined by a number of variables - the general level of interest rates in the economy, the term structure of interest rates and the default risk of the bond. Figure 33.3 provides the building blocks for arriving at the interest rate on a straight corporate bond.

8 Figure 33.3: Building Blocks for Interest Rates

Default Premium

Maturity Premium

Instantaneous (Short-Term Default-free Rate)

The first block is the level of short-term default free interest rates and it captures the overall level of rates in the economy. The second block is a maturity premium, which reflects the difference between longer-term default free rates and short-term default free rates, and is generally positive. The third block is a default premium, which is related to the default risk of the bond is question. This section takes a closer look at these blocks. a. Level of Interest Rates The short-term default free rate can be decomposed into two components - an expected inflation rate during the period and an expected real rate of return. Short-term default free rate = Expected Inflation + Expected Real Rate of Return This identity is known as the Fisher equation and essentially implies that changes in short-term rates can be traced to changes in either expected inflation or the expected real rate of return. The more precise version of the Fisher equation allows for the compounding effect. (1+r) = (1+I) (1+R) where, r = Nominal interest rate I = Expected Inflation

9 R = Expected real rate of return It should be emphasized that the Fisher equation is an identity and there is no question of it being proved or disproved. The real questions that arise from the equation are the specific assumptions about the real rate and expected inflation. I. Expected Inflation Expected inflation is clearly the dominant variable determining interest rates. Generally speaking, a forecaster who can predict changes in inflation well should also post a good track record in predicting interest rate changes. The first step in forecasting inflation is the understanding of its determinants. The Determinants of Inflation There is consensus on the determinants of inflation, though there is little agreement about the consequences of specific actions on inflation. To understand both the determinants of inflation and the sources of disagreement between the different schools of thought on inflation, consider another identity. P=

MV Y

Where P = Price level M = Money supply in the economy V = Velocity of money circulation in the economy Y = Real Output in the economy The velocity of money measures how often the currency, used to define the money supply 'M', circulates in the economy and how much is created in terms of transactions for every unit of currency created. Thus, if a $1 in additional currency created $3 in transactions, the velocity of money is 3. While the money supply used in the equation can be defined in a number of different ways, ranging from just currency to broader aggregates, the velocity has to be defined consistently. This identity can be stated in terms of changes as follows dP =

dM dV dY

10 The left hand side of this identity is the inflation rate and the right hand side provides the three determinants of the inflation rate. (a) the change in the money supply (dM): If the money supply increases, with no concurrent change in real output and money velocity, the inflation rate will increase. This is the basis for the argument by many monetarists, who believe that there is no linkage between real output and money supply and that money velocity is stable over long periods, that loose monetary policy (increasing money supply) is the reason for high inflation. While some monetarists will concede that monetary policy can have short term effects on real output, most argue that it cannot impact real output in the long term. They also argue that while money velocity may change over time, that these changes occur over the very long term and are unlikely to have a major impact on inflation. (b) the change in money velocity (dV): If the money velocity increases, with no concurrent change in money supply and real output, the inflation rate will increase. Economists have long debated why money velocity changes over time. One determinant is technology, since changes in the way people save (from checking accounts to money market accounts) and in the way they spend (from cash transactions to credit card transactions) affect the money velocity. Another is the faith the public has in the currency. In hyper-inflationary environments, individuals are much less willing to hold currency (because it depreciates in value so quickly) and therefore attempt to convert the currency into real goods. This unwillingness to hold currency translates into higher money velocity. Thus, if the central bank is viewed as having eased the reins on money supply, there is often a concurrent increase in money velocity, leading to a surge in inflation. (c) the change in real output: If the real output increases, with no concurrent change in money supply and money velocity, the inflation rate will decrease. This is often the basis of the argument used by Keynesians for easing monetary policy during economic downturns. Increasing the money supply, they argue, results in a concomitant increase in real output, since there is excess capacity, and the effects on inflation are therefore muted or non-existent. Measuring Inflation

11 A true measure of inflation would consider changes in the prices of all goods and services used in an economy, weighted by their usage values. The reported measures of inflation, either at the consumer or the producer level, attempt to do so, but often lag changes in true inflation because of a number of reasons. The first is that not all goods and services are traded in a market place, where prices are easily available and goods are fairly standardized. Thus, it is easy to gauge the inflation in medical prescription prices, but much more difficult to gauge the inflation in the prices of medical services. The second is that all inflation indices are based upon samplings of prices of goods, rather than the universe of all goods traded. Even if the sample is not biased, there is the possibility of sampling error that enters into the numbers. The third is the issue of weighting on the basis of usage value. Due to practical considerations of time and resources, the weights are not adjusted every time the inflation index is computed to allow for changes in usage. Instead index weights are adjusted infrequently, leading to biased in the measured inflation. Thus, the inflation indices which kept the usage of gasoline by households constant in the late seventies while oil prices were climbing (and people were cutting back on the use of gasoline) tended to overstate the inflation rate during that period. The final consideration is about the level at which inflation is to be measured, since counting goods at every level of the process (from commodity to manufactured good to retailed good) would result in double or even triple counting the same good. Different inflation indices examine inflation at different stages in the process and can lead to different conclusions about whether inflation is increasing, decreasing or staying unchanged. Forecasting Inflation Since changes in inflation signal changes in interest rates, economists and analysts have expended considerable time and resources forecasting inflation, with mixed results. The forecasting models used range from the naive to the sophisticated and are based upon everything from gut feeling to elaborate mathematics. The output from these models can be contrasted with predictions based purely upon past inflation - either the inflation in the last time period or time-series models that examine trends and shifts in past inflation and the results for the most part are mixed. Elaborate forecasting models do no better than time series models in the short term, but may better capture changes in inflation in the

12 long term because they consider information beyond what’s available in past inflation rates. The introduction of inflation-adjusted treasury bonds a few years ago has provided an interesting alternative for those who would rather rely on markets for their inflation estimates than economists. In particular, if we view the market interest rate on an inflation indexed treasury bond as a riskless real rate and the market interest rate on a nominal treasury bond of equal maturity as a nominal rate, the expected inflation rate can be estimated as follows: Expected Inflation Rate =

(1+ Nominal Rate) - 1 = Expected Inflation Rate (1+ Real Rate)

For instance, if the nominal rate is 5.1% and the real rate is 2.7%, you can estimate the expected inflation rate as follows: Expected Inflation Rate = 1.051/1.027 = .0233 or 2.33% Testing the Fisher Equation As mentioned earlier, the Fisher equation is an identity that cannot be proved or disproved. There have, however, been numerous attempts to impose additional constraints on the model, to test the usefulness of the model in explaining changes in interest rates over time. These studies go back to Fisher's own work on interest rates and inflation, where he found that the correlation between the rate of inflation and the commercial paper rate was low in both his sample periods – 1890 to 1914 and 1915 to 1927. The correlation between inflation and the commercial paper rate did not improve as various leads and lags on inflation were tried. Fama (1976) made the assumption that real rates do not change much over time and that changes in interest rates should therefore almost entirely be caused by changes in inflation. He tested this proposition by regressing interest rates against expected inflation. It = a + b R t where, Rt = Nominal interest rate during period t It = Expected inflation during period t

13 He argued that if his initial assumption about constant real rates was true, this regression would yield the following: (a) The intercept would be equal to the constant real rate over the period. (b) The slope of the regression would be one, since all changes in interest rates would be a consequence of changes in inflation. Lacking an adequate measure of expected inflation, he used the one-month treasury bill rate at the start of each month as a measure of expected inflation during the month and the one and three-month treasury bill rates as measures of nominal rates. His results, for the period 1953 to 1971, were as follows CPI regressed against one-month T.Bills It =

0.0007 -

0.98 Rt

(0.0003)

(0.10)

R2 = 0.29

CPI regressed against three-month T.Bills It =

0.0023 -

0.92 Rt

(0.0011)

(0.11)

R2 = 0.48

Based upon this regression, he concluded that the hypothesis of constant real rates was supported and that the slope was statistically indistinguishable from one, suggesting that there was a one-to-one relationship between changes in interest rates and expected inflation. The studies that followed up have generally not been as encouraging. Wood, for instance, updates Fama's regression, after adding a lagged measure of inflation

and

contrasts the results for two periods – 1953 to 1971 and 1974 to 1981. It = a + b Rt + c It-1 Period 1953-71

1974-81

R2

Regression It = 0.0006

- 0.84 Rt

+ 0.09 It-1

(0.0003)

(0.111)

(0.064)

It = - 0.0023

- 0.25 Rt

+ 0.47 It-1

(0.0008)

(0.12)

0.309

0.371

(0.11)

The coefficient on nominal interest rates (Rt ) which was close to one for the 1953-71 time period, used by Fama in his study, drops to 0.25 for the 1974-81 time period.

14 The reason for the surprisingly good results from 1953 to 1971 may be traceable to the fact that inflation was very stable during this period and that changes in inflation tended to be small. Thus, it seems likely that the hypothesis of stable real rates and a oneto-one relationship between interest rates and inflation will be rejected in any period or any economy where there is volatility in interest rates and inflation. Since the importance of forecasting increases with the volatility of interest rates and inflation, the cautionary notes on forecasting short-term interest rates based only upon expected inflation should be taken to heart. II. Expected Real Rate of Return The other component of the Fisher equation is the expected real rate of return. On an intuitive level, the expected real rate of return is the rate at which individuals are willing to trade off current consumption for future consumption. Given the human preference for present consumption, the expected real rate of return should be positive, but can vary widely across time and across economies. If individuals in a society have a strong desire for current consumption, the expected real rate of return will have to be high to induce them to defer consumption. a. Realized Real Rates of Return Since the expected real rate of return is based upon the preference functions of individuals, which are difficult to observe, we are reduced to observing realized real rates of return, which can be defined to be – Realized Real Rate of Return = Nominal Interest Ratet - Actual Inflationt where, Nominal Interest Ratet = Nominal interest rate at the beginning of period t Actual Inflationt = Actual Inflation during period t While the expected real rate of return should be positive, the realized real rate of return can be positive or negative, depending upon the period under observation. During the 1970s, for instance, bond investors in the United States earned negative real rates of return as actual inflation outstripped expected inflation. b. Expected Real Return and Expected Real Growth

15 Ultimately, real returns to investors in an economy comes from real growth in the economy. One way to approach the estimation of expected real return is to estimate the expected real growth rate in the economy. Thus, the expected real return in an economy growing in the long term at 2.5% a year, should be approximately 2.5%. If the expected real return increases above the long term growth rate in the economy, the imbalance will lead to a depletion of savings and a shortfall in investments. Alternatively, if the real return decreases below the long term growth rate, the imbalance will lead to an accumulation of savings and over-investment. The Role of the Central Bank Central banks do not set interest rates, but they certainly can influence them in two ways. On a short term basis, central banks can tighten or loosen its reins on the money supply and try to slow an overheated economy or regenerate a sluggish economy. In either case, though, we should not attribute more power to central banks than they actually have. The only interest rate that the Federal Reserve in the United States, for instance, directly controls is the Federal funds rate. By raising or lowering this rate, it can hope to affect other rates but the market does not always cooperate. It is generally true that market interest rates tend to move with the Federal funds rate, but there are two caveats. The first is that markets tend to lead the Federal reserve as bond investors build in expectations of changes in Fed policy. And the second is that the correlation tends to be strongest for short term rates (treasury bills and commercial paper) and weaker for long maturity bonds. On a long-term basis, central banks can have a much bigger impact on interest rates through their conduct of monetary policy and the resolution that they show about fighting inflation. It is no coincidence that high inflation occurs most often when central banks are undisciplined when it comes to monetary policy and show no resolve when it comes to taking tough measures to fight inflation. b. Maturity Premium The maturity premium refers to the difference in interest rates between a shortterm (or instantaneous) default-free bond and a longer-maturity default-free bond. In the

16 following section, the maturity premium is clarified further and a number of different theories designed to explain the magnitude of the maturity premium are examined. a. The Yield Curve The relationship between maturity and interest rates is usually captured by a yield curve, which graphs yields on bonds against bond maturities. Figure 33.4 summarizes the treasury yield curve in January and June 2001.

Figure 33.4: Yield Curves - January 2001 and June 2001

6.00%

5.00%

4.00%

3.00%

2.00%

1.00%

0.00% 3 month

6 month

Jun-01 1 year Maturity

2 year

5 year

Jan-01 10 year

30 year

In January 2001, the yield curve was slightly downward sloping. But by June 2001, the yield curve had reverted – short term rates dropped while long term rates increased slightly. While the yield curve has generally been upward sloping over much of this century, there have been periods where the yield curve has been downward sloping. Figure 33.5 shows the yield curves from 1980 to 2001.

17 Figure 33.5: Yield Curves : 1980-2001

16.00%

14.00%

12.00%

10.00%

8.00%

6.00%

4.00%

2.00%

Interest Rate

2001

1999

6 month

2000

1997

1998

1995

1996

1994

1992

2 year

1993

1991

1989 Year

1990

10 year

1988

1986

1987

1984

1985

1982

1983

1980

1981

0.00%

In the early 1980s, short term rates were higher than long term rates for a period. Over the last two decades, rates have dropped at both ends of the spectrum. While the yield curves are generally constructed using the yields to maturity of government bonds, the presence of coupons on these bonds affects the calculated yield to maturity. This limitation can be overcome in one of two ways. The first is to construct a yield curve using only zero coupon government coupon bonds of different maturity. The second is to extract spot interest rates from the yields to maturity of coupon bonds and to plot the spot rates against maturities. The following example illustrates the process of extracting spot rates. Illustration 33.4: Yields to Maturity and Spot Rates The following table provides prices and yields to maturity on one to five year bonds and extracts spot rates from the yields to maturity. Maturity

Yields to Maturity

Spot Rate

1 year

4.00%

4.00%

2 year

4.25%

4.26%

18 3 year

4.40%

4.41%

4 year

4.50%

4.514%

5 year

4.58%

4.60%

The spot rate is estimated from the two year rate as follows – Price of two year bond =

Coupon1 Face Value + Coupon 2 + 1+ 0 r1 (1+ 0 r2 )2

Assuming the bond is priced at par, 1000 =

42.50 1042.50 + 1.04 (1+ 0 r2 )2

Solve for0r2.    1042.50    0 r2 =  1000 − 42.50     1.04 

0 .5

− 1 = 4.26%

The other rates are extracted using a similar process, 1000 =

44.00 44.00 1044.00 + + 2 1.04 1.0426 (1+ 0 r3 )3

1000 =

45.00 45.00 45.00 1045.00 + + + 2 3 1.04 1.0426 1.0441 (1+ 0 r4 )4

1000 =

45.80 45.80 45.80 45.80 1045.80 + + + + 2 3 4 1.04 1.0426 1.0441 1.0451 (1+ 0 r5 )5

The difference between yields to maturity and spot rates increases as the bond maturity increases. b. Spot and Forward Rates The spot rate on a multi-period bond is an average rate that applies over the periods. The forward rate is a one-period rate for a future period and can be extracted from the spot rates. For instance, if 0S2 is the two-period spot rate and 0S1 is the oneperiod spot rate, the forward rate for the second period, 1F2, can be obtained. 1 F2 =

(1+ 0 S2 )2 1+ 0 S1

19 The forward rate for period three can be extracted using the spot rates for periods 2 and 3. In general, the forward rate for period n can be written as: n −1 Fn =

(1+ 0 Sn )n (1+ 0 Sn -1 )n −1

If the yield curve for spot rates is upward sloping, the yield curve using forward rates will be even more so. Alternatively, if the spot rate yield curve is downward sloping, the forward rate yield curve will be even more so. The following illustration builds on the previous one and extracts forward rates from spot rates. Illustration 33.5: Spot Rates and Forward Rates The forward rates are extracted from the spot rates for one to five year bonds. This is illustrated in the following table. YTM

Spot Rate

Forward Rate

1

4.00%

4.00%

4.00%

2

4.25%

4.26%

4.52%

3

4.40%

4.41%

4.71%

4

4.50%

4.51%

4.81%

5

4.58%

4.60%

4.96%

Forward rate for year 2 =

1.0426 2 − 1 = 4.52% 1.04

Forward rate for year 3 =

1.04413 − 1 = 4.71% 2 1.0426

Forward rate for year 4 =

1.04514 − 1 = 4.81% 3 1.0441

Forward rate for year 5 =

1.04605 − 1 = 4.96% 4 1.0451

c. Determinants of the Maturity Premium The magnitude of the maturity premium is determined by a number of factors including expectations about inflation, investor preferences for liquidity and demands from specific market segments. Each of these factors is examined in more detail in the following section.

20 1. Expected Inflation Expectations about future inflation are a key determinant of longer term rates. In general, if inflation is expected to go up in future periods, longer term rates will be higher than shorter term rates. Alternatively, if inflation is expected to go down in future period, longer term rates will be lower than short term rates. An extreme version of this story is the 'pure expectations hypothesis', where the term structure is driven entirely by the expectations on inflation. Under this hypothesis, the yield curve will be upward sloping if investors expect inflation to rise in future periods, flat if investors expect inflation to remain unchanged in future periods, and downward sloping if investors expect inflation to decline in future periods. This is illustrated in Figure 33.6. Figure 33.6: Pure Expectations Hypothesis Spot Rate

No change in inflation

Increasing Inflation

Spot Rate

Maturity

Decreasing Inflation Spot Rate

Maturity

Maturity

The pure expectations hypothesis can also be stated in terms of forward rates and expected spot rates. If the hypothesis is correct, the forward rate for period n should be the best predictor of the expected spot rate in that period. n-1Fn = Exp(n-1Sn) where, n-1Fn = Forward rate for period n Exp(n-1Sn) = Expected one-period spot rate in period n While the pure expectations hypothesis may be extreme in assuming that forward rates are determined entirely by expected spot rates, it does highlight the importance of expected inflation in determining the maturity premium.

21 2. Liquidity Preference The liquidity preference theory is not an alternative to the expectations theory. It builds on expectations by taking into account uncertainty and risk aversion. In the form in which it was originally developed by Hicks (1946), the uncertainty was seen as accruing to the lender who concurrently charged a liquidity premium for lending for longer time periods. This uncertainty can also be stated in terms of bond prices, with long term bonds being viewed as more volatile than short term bonds, as interest rates change. Under this theory, holding expectations of inflation constant, longer term rates will be higher than shorter term rates. Stated in terms of forward rates and expected spot rates, F = Exp(n -1Sn )+ L t

n −1 n

where, Lt = Liquidity premium corresponding to a bond maturity of t periods Figure 33.7 illustrates how the liquidity premium builds on top of the pure expectations hypothesis. Figure 33.7: Term Structure with Liquidity Premium Spot Rate

No change in inflation

Increasing Inflation

Spot Rate

Maturity

Decreasing Inflation Spot Rate

Maturity

Maturity

: Pure Expectations Hypothes : Pure Expectations + Liquidity Premium

While the traditional theory assumes a positive liquidity premium (Lt ), the assumption that all lenders prefer to lend short term over long term may not be always appropriate. For instance, a lender with fixed liabilities twenty years from now may view a twentyyear zero-coupon bond as less risky than a treasury bill of six months, because it matches

22 cash inflows to cash outflows. The question therefore becomes an empirical one – Does the average lender prefer to lend short or long term? McCulloch (1975) attempted to estimate term premia for different time periods, and arrived at the following estimates. Maturity

6 month

1 year

5 year

10-year

20-year

30-year

Estimate

0.41%

0.43%

0.43%

0.43%

0.43%

0.43%

Standard Error

0.06%

0.07%

0.07%

0.07%

0.07%

0.07%

There are two key findings that emerge from this study. The positive term premia suggest that, on average at least, lenders prefer lending short to long term. The term premia also do not seem sensitive to bond maturity. The second result has been challenged in a number of studies. Van Horne (1965) finds term premia increasing, albeit at a decreasing rate, with bond maturity. 3. Demands from Specific Market Segments The price of bonds, like any other security, is determined by demand and supply. If the market is segmented, and there are sizable groups of investors whose demand is for a specific maturity, the term structure will be affected by these groups. Again, considering the extreme case, where investors will lend and borrow only for specific maturities, the interest rate at each maturity will be determined by demand and supply at that maturity. This is illustrated in Figure 33.8.

23 Figure 33.8: Market Segmentation and Term Structure Spot Rate

Maturity Under this scenario, the term structure can take any shape, depending upon the demand and supply at each maturity. The assumption that investors will lend or borrow only for specific maturities and not substitute other maturities even when it is extremely favorable for them to do so is an extreme one. In reality, market segments do exist and do affect the term structure but only at the margin and for one or two maturities. For instance, the demand from Japanese investors in the late eighties for the just-issued thirty year bonds resulted in a slight kink in the term structure, where the thirty-year bond rates were slightly lower than twentynine year bond rates, even though the rest of the yield curve was upward sloping. The Empirical Evidence on Maturity Premia Empirical studies of the term structure have examined several questions including the relative frequency of upward and downward sloping term structures, the magnitude of liquidity premia and the presence of market segments. The evidence can be summarized as follows. •

The yield curve, at least in this century, has been more likely to be upward sloping than downward sloping. Examining yield curves at the beginning of each year from 1900 to 2000, the yield curve has been downward sloping in only 29 of the 100 years.

24 This is inconsistent2 with a pure expectations hypothesis, where downward sloping yield curves should be just as likely as flat or upward sloping yield curves. It is, however, consistent with a combination of the expectation and liquidity preference hypotheses, where positive liquidity premia are demanded over and above expected inflation. •

The term structure is much more likely to be downward sloping when the level of interest rates is high, relative to historical rates. The table below3 summarizes the frequency of downward-sloping yield curves as a function of the level of interest rates. 1-year Corporate Bond Rate

1900-70

1971-00

Slope of Yield Curve Positive

Flat

Negative

Above 4.40%

0

0

20

3.25% - 4.40%

10

10

5

Below 3.25%

26

0

0

Above 8.00%

4

2

3

Below 8.00%

13

6

0

This evidence is consistent with the expectations and liquidity preference hypotheses, but it is also consistent with a hypothesis that interest rates move within a normal range. When they approach the upper end (lower end) of the normal range, the yield curve is more likely to be downward sloping (upward sloping). •

Studies have generally found that expectations about future interest rates are important in shaping the term structure. Meiselman computed high positive correlations between forecasting errors and changes in various forward rates, and stable term premiums. In contrast, there are many researchers who argue that the volatility in interest rates is much too great to be explained by just expectations about future rates and constant term premia. Shiller (1979) concludes that the greater the volatility in interest rates, the larger the term premium.

2

Prior to the abandonment of the Gold Standard in the 1930s, negatively sloped yield curves were just as likely to occur as positively sloped yield curves. 3 Some of the data table is extracted from Wood (1984).

25 •

Attempts by the government to alter the shape of the yield curve by adjusting the maturity of issues have largely been unsuccessful in the long term. For instance, "Operation Twist" in 1962 was designed to make the yield curve flatter4 by lowering long term rates and raising short term rates, by issuing short term debt to finance deficits. Though the yield curve did flatten, long term yields did not decline. This can be viewed as evidence of the weakness of the market segmentation hypothesis.

•

There is evidence that the shape of the term structure has strong predictive power for future changes in the real economy. Harvey (1991) examined the G-7 countries (Canada, France, Germany, Italy, Japan, U.K., U.S.A.) and concluded that 54% of world economic growth could be explained the term structure.

c. Default Premium While there is no possibility of default for bond issues made by the United States Treasury, corporate bonds or state/local bonds can default on interest or principal payments. If there is any possibility of default on a bond, there will be a default premium in addition to the maturity premium on the bond. The default premium will increase with the perceived default risk of the bond and is generally also a function of the maturity and terms of the specific bond. We examined this issue in detail in Chapter 7, as part of the discussion of how best to estimate the cost of debt for a firm. Reviewing that discussion, we concluded that: •

The most direct measure of default risk is the default rate which measures defaulted issues as a percentage of the par value of debt outstanding. Hickman investigated the default experience of fixed-income corporate bonds between 1900 and 1943, as a function of the bond rating. Ratings

Size of Issue

4

I

II

III

IV

V-IX

No Rating

> $ 5 millions 5.9%

6.0%

13.4%

19.1%

42.4%

28.6%

≤ $ 5 millions 10.2%

15.5%

9.9%

25.2%

32.6%

27.0%

A similar, though less formal, attempt was made in 1993 by the Treasury Department to raise short term rates and lower long term rates by issuing more short term bonds and less long term bonds. It was successful at raising short term rates, but long term rates increased concomitantly.

26 Hickman's study have been extended by several researchers and data availability has made this easier to do. Altman computes default rates for high yield bonds from 1970 to the present, on an annual basis and relates them to bond ratings. •

Default spreads on bonds tend to increase during economic downturns and decrease during economic booms.

•

Default spreads are generally larger for longer term bonds than they are for shorter term bonds, for any given level of default risk. There may be specific circumstances, though, where the reverse is true. Johnson defines a "crisis-atmaturity" scenario, usually in the midst of a recession or a depression, where a firm is perceived to have insufficient funds to meet its immediate debt servicing needs, though it is expected to revert to health in the long term. In this scenario, the default premia will be lower for longer maturity bonds than for shorter maturity bonds. Johnson found evidence of inverted default premia term structures during 1934, in the midst of the depression. Corporate Bonds in Emerging Markets In the framework that we have developed, you build up to the rate on a corporate

bond by adding a default spread to the government bond rate. This process works only when the government is viewed as having no default risk. When governments have default risk, as is often the case in emerging markets, the process becomes more complicated. To estimate the appropriate interest rate on a corporate bond in an emerging market, you have to begin by estimating a riskless rate. The best way to do it is to build it up from the Fisher equation – add an expected inflation rate to the real rate of return in that market. The latter can be set equal to the expected real growth rate in the economy, but the former can be a volatile number in high inflation markets. An alternative approach is to begin with the government bond rate and subtract out the estimated default spread for the government – this default spread can be obtained using the rating for the government. You could alternatively estimate the corporate bond rate for a company in an emerging market in a different currency – U.S. dollars or Euros. In this case, the riskless rate will be defined in that currency – the treasury bond rate in the U.S. for dollars and the

27 German Euro-denominated government bond rate. The default spread for the company can then be added on to this riskless rate to estimate the corporate bond rate. There is one final point that needs to be confronted with corporate bonds in emerging markets and it relates to whether you should incorporate the country default risk spread into the corporate bond rate. For instance, should the interest rate on a bond issued by Embraer, the Brazilian aerospace firm, incorporate the default spread on Brazilian government bonds? For smaller firms, the answer should generally be yes. For larger firms with substantial operations outside the country, we have a little more leeway. These firms may be able to borrow at rates lower than the sovereign rate. Special Feature in Bonds and Pricing Effects In the last section, we examined the question of how to price a government or a corporate bond based upon the expected coupons and the appropriate interest rate for the bond. Most bonds though have other features added on, some of which make the bonds more valuable and some less valuable. In this section, we consider how best to value these special features. I. Convertibility A convertible bond is a bond that can be converted into a pre-determined number of shares, at the option of the bondholder. While it generally does not pay to convert at the time of the bond issue, conversion becomes a more attractive option as stock prices increase. Firms generally add conversions options to bonds to lower the interest rate paid on the bonds. The Conversion Option In a typical convertible bond, the bondholder is given the option to convert the bond into a specified number of shares of stock. The conversion ratio measures the number of shares of stock for which each bond may be exchanged. Stated differently, the market conversion value is the current value of the shares for which the bonds can be exchanged. The conversion premium is the excess of the bond value over the conversion value of the bond.

28 Thus a convertible bond with a par value of $1,000, which is convertible into 50 shares of stock, has a conversion ratio of 50. The conversion ratio can also be used to compute a conversion price - the par value divided by the conversion ratio, yielding a conversion price of $20. If the current stock price is $25, the market conversion value is $1,250 (50 * $25). If the convertible bond is trading at $1,300, the conversion premium is $50. The effect of including a conversion option in a bond is illustrated in Figure 33.9. Figure 33.9: Bond Value and Conversion Option

Determinants of Value The conversion option is a call option on the underlying stock and its value is therefore determined by the variables that affect call option values – the underlying stock price, the conversion ratio (which determines the strike price), the life of the convertible bond, the variance in the stock price and the level of interest rates. The payoff diagrams on a call option and on the conversion option in a convertible bond are illustrated in Figure 33.10.

29 Figure 33.10: Call Option and Conversion Option: Comparing Payoffs Payoffs on Conversion Option

Payoffs on Call Option

Payoffs on Call

Payoffs on Conversion Option

Conversion Price

Strike Price Value of Underlying Asset

Price of the Stock

Like a call option, the value of the conversion option will increase with the price of the underlying stock, the variance of the stock and the life of the conversion option and decrease with the exercise price (determined by the conversion option). The effects of increased risk in the firm can cut both ways in a convertible bond it will decrease the value of the straight bond portion while increasing the value of the conversion option. These offsetting effects will generally mean that convertible bonds will be less exposed to changes in the firm’s risk than are other types of securities. Option pricing models can be used to value the conversion option with three caveats – conversion options are long term, making the assumptions about constant variance and constant dividend yields much shakier, conversion options result in stock dilution, and conversion options are often exercised before expiration, making it dangerous to use European option pricing models. These problems can be partially alleviated by using a binomial option pricing model, allowing for shifts in variance and early exercise and factoring in the dilution effect. These changes are described in more detail in Chapter 15. The following illustration provides an example of the use of option pricing models in valuing a conversion option in a convertible bond. The value of a convertible bond is also affected by a feature shared by most convertible bonds that allow for the adjustment of the conversion ratio (and price) if the firm issues new stock below the conversion price or has a stock split or dividend. In some cases, the conversion price has to be lowered to the price at which new stock is issued. This is designed to protect the convertible bondholder from misappropriation by the firm.

30 Illustration 33.6: Valuing a conversion option / convertible bond In December 1994, General Signal had convertible bonds outstanding with the following features. •

The bonds matured in June 2002. There were 100,000 shares of convertible bonds outstanding.

•

They had a face value of $1000, and were convertible into 25.32 shares per bond until June 2002.

•

The coupon rate on the bond was set at 5.75%.

•

The company was rated A-. Straight bonds of similar rating and similar maturity were yielding 9.00%.

•

The stock price in December 1994 was $32.50. The volatility (standard deviation in ln stock prices) based upon historical data was 50.00%.

•

There were 47.35 million shares of equity outstanding. Exercising the convertible bonds will create 2.532 million additional shares (100,000 * 25.32 shares).

The two components of the convertible bond can be valued as follows. A. Straight Bond Component If this bond had been a straight bond, with a coupon rate of 5.75% and a yield to maturity of 9.00% (based upon the bond rating), the value of this straight bond can be calculated. t=7.5

PV of Bond =

28.75 ∑ (1.09)

t

t=1

+

1,000 = $834.79 (1.09)7.5

This is based upon semi-annual coupon payments (of $28.75 for semi-annual periods). B. Valuing the Conversion Option The value of the conversion option is estimated using the Black-Scholes model, with the following parameters for the conversion option. Type of Option = Call

Number of Calls/Bond = 25.32

Stock Price = $32.50

Strike Price = $1000/25.32 = $39.49

Time to Expiration = 7.5 years

Standard Deviation in Stock Prices (ln) = 0.5

Riskless rate = 7.75% (Rate on 7.5 year Treasury Bond) Dividend yield on Stock = 3.00%

31 Allow for the dilution inherent in the exercise (See chapter 5 on warrant pricing for details on the valuation correction). Value of one Call = $ 12.85 Value of the Conversion Option = $ 12.85 * 25.32 = $325.43 C. Value of Convertible Bond The value of the convertible bond is the sum of the straight bond and conversion option components. Value of Convertible Bond

= Value of Straight Bond + Value of Conversion Option = $ 832.73 + $325.43 = $1158.16

This valuation is based upon the assumption that the conversion option is unconstrained and that the bonds are not callable. The effects of introducing these changes into the analysis will be examined in the following sections. The Effect of Forced Conversion Companies that issue convertible bonds sometimes have the right to force conversion if the stock price rises to a specified level. This right to force conversion caps the profit that can be made on the conversion option, and hence affects its value. Figure 33.11 illustrates the effect of forced conversion on the expected payoffs. Figure 33.11: Value of a Capped Call

K1

K2 Value of Underlying Asset

The value of a capped call, with an exercise price of K1 and a cap of K2 can be calculated as follows. Value of capped call (K1, K2) = Value of Call (K1) - Value of Call (K2)

32 This is because the cash flows on a capped call can be replicated by buying the call with a strike price of K 1 and selling the call with a strike price of K2. II. Callability The issuer of a callable bond preserves the right to call back the bond and pay a fixed price (generally at a premium over the par value) for it. Thus, if interest rates decline (bond prices rise) after the initial issue, the firm can refund the bonds at the fixed price instead of the market value. Adding the call option to a bond should make it less attractive to buyers, since it reduces the potential upside on the bond. As interest rates go down, and the bond price increases, the bonds are more likely to be called back. The distinction between a straight bond and a callable bond are illustrated in the Figure 33.12. Figure 33.12: Callable versus Straight Bonds

The difference on the upside between straight and callable bonds is quite clearly illustrated in Figure 33.12. As interest rates decline, the values of the two bonds diverge, whereas they converge as interest rates increase. There are several common features shared by most callable bonds. Most callable bonds come with an initial period of call protection, during which the bonds cannot be called back. Such bonds are called deferred callable bonds. The call price on most callable

33 bonds is set at an initial level above par value plus one annual coupon payment, but declines as time passes and approaches the par value. Valuing the Callability Option The issuer's right to call back a bond if interest rates drop (or bond prices rise) to an attractive level is a call option on the bond and can be valued as such. The payoffs on a callable bond are shown in Figure 33.13. Figure 33.13: Payoffs on Call Feature on Bond to Seller of Bond Payoffs on Call Feature on Bond

Payoffs on Call Option

Payoffs on Call

Payoffs on Call Feature

Call Price

Strike Price Value of Underlying Asset

Value of Bond

The value of the callable feature on a callable bond will increase as interest rates decline, and as the volatility of interest rates increases. Since the callable feature is held by the issuer of the bond, the value of a callable bond can be written as follows: Value of Callable Bond = Value of Straight Bond - Value of Call Feature in Bond A callable bond should therefore sell for less than an otherwise similar straight bond. Traditional Analysis The traditional approach to analyzing callable bonds is to estimate yields to call as well as yields to maturity. The former is based upon the assumption that the bond will be called at the first call date while the latter assumes holding the bond until maturity. The two yields are compared and the investor chooses the lower of the two as a measure of his expected return on the bond. This approach can also be extended to calculate the yield to all possible call dates and picking the lowest of these yields as the expected yield on the callable bond. This yield is called the yield to worst. While this approach may give the investor some sense of the potential downside from the callability of the bond, it suffers from all the standard problems of the ‘yield to

34 maturity’ calculation. First, it assumes that the investor can reinvest all coupons until the bond is called at the yield to call, which is not a realistic assumption since calls are much more likely if interest rates go down. Second, it does not examine the rate at which the proceeds from the called bond can be reinvested by the investor. Third, it assumes that the bond will be called on the call date, which takes away the option characteristics of the call feature. Illustration 33.7: Estimating yields to maturity and call on a callable bond Consider a corporate bond, with 20 years to maturity and a 12% coupon rate that is callable in two years at 105% of the face value. The bond is trading at 98 currently. The yields to maturity and the yields to call on the corporate bond are as follows: Price =

t=20

60.00 1,000 + ∑ (1+r) (1+r) t

= $980

20

t=0.5

The yield to maturity, r, is approximately 12.26%. The yield to call can be similarly calculated. Price =

t=2

60.00 1,000 + ∑ (1+r) (1+r) t

2

= $1050

t=0.5

The yield to call is approximately 13.25%. Price/Yield Relationship for a Callable Bond The price/yield relationship on a callable bond is different because the potential that the bond will be called back puts an upper limit on the price. This makes the relationship between price and yield convex, for some range of the yields. The difference is illustrated in Figure 33.14.

35 Figure 33.14: Callable Bond Prices and Interest Rates

The section of the price/yield relationship on the callable bond when the yield falls below y* has negative convexity - i.e., the price appreciation on this bond will be less than the price depreciation for a given change (down or up) in interest rates. Determinants of Value - Option Pricing Approach The call feature in a callable bond can be valued using option pricing models. It is a series of call options on the underlying bond and its value is determined by the level and volatility of interest rates. There are some modifications that need to be made to the standard option pricing models before they can be applied in this context. Once the call feature is valued as a series of option, the yield on a callable bond can be adjusted for the option features and the difference between this adjusted yield and treasuries of equivalent maturity is called the option adjusted spread. This approach is a more realistic way of considering the effects of the call feature on expected yields than the traditional yield to call approach. The following illustration values the call feature on a callable bond. Illustration 33.8: Valuing a callable bond

36 The following analysis values a 17-year callable bond with a coupon rate of 12% by valuing the straight bond, the call feature on the straight bond and the value of the callable bond as a function of the yield on the bond. The actual option valuation was done using a binomial option pricing model, using an interest rate volatility of 12% and a short term interest rate of 6%. Yield

Value of Straight Bond

Value of Call Feature Value of Callable Bond

20.51%

$ 60.00

$ 0.00

$ 60.00

19.55%

$ 63.00

$ 0.00

$ 63.00

18.66%

$ 66.00

$ 0.00

$ 66.00

17.59%

$ 70.00

$ 0.00

$ 70.00

16.63%

$ 74.00

$ 0.00

$ 74.00

15.54%

$ 79.00

$ 0.02

$ 78.98

14.56%

$ 84.00

$ 0.06

$ 83.94

13.51%

$ 90.00

$ 0.22

$ 89.78

12.57%

$ 96.00

$ 0.67

$ 95.33

11.46%

$104.00

$ 2.11

$101.89

10.59%

$111.00

$ 4.60

$106.40

9.59%

$120.00

$ 9.80

$110.20

8.60%

$130.00

$17.81

$112.19

7.73%

$140.00

$27.21

$112.79

While the value of the straight bond increases as the yield drops, the callable bond’s value stops increasing because the call feature becomes more and more valuable as the yield becomes lower. In fact the value of the callable bond is maximized at $112.94. Effective Duration and Effective Convexity In the previous section we defined duration to be a measure of a bond’s sensitivity to interest rate changes. While doing so, it was assumed that cash flows did not change as interest rates changed. This assumption is clearly violated for callable bonds, where the cash flows on the bond are influenced by the level of rates - if interest rates drop enough, the bond will be called. For bonds such as these, there is a different measure of duration

37 that is more appropriate called the effective duration. The duration of any bond can be approximated as follows, for a small change in interest rates. Duration =

P- − P+ P0 (y + − y - )

where P- = Price of the bond if yield drop by x basis points P+ = Price of the bond if yield increases by x basis points P0 = Price of the bond initially y + = Initial yield + x basis points y - = Initial yield - x basis points This approach can be used to estimate the effective duration of callable bonds for any segment of the yield curve. It can also be used for any other bonds with embedded options, such as putable bonds, or mortgage backed securities, which have the prepayment option embedded in them. A similar adjustment can be made to the standard convexity measure to arrive at the effective convexity of any bond with embedded options. [NOTE: There was no equation for convexity.] Effective Convexity =

P+ + P- − 2P0 2 P0 (0.5(y + − y - ))

Valuing a Callable-Convertible Bond Many convertible bonds have embedded call features. The presence of two options in the bond, one possessed by the buyer of the bond and the other possessed by the seller of the bond, and the interaction between the two options, implies that the two options have to be valued together. Brennan and Schwartz (1977, 1980) provide an analysis of convertible bonds with call features, default risk and stock price dilution. The simplest approach for illustrating the interaction between the various options is a binomial option pricing model. Empirical Evidence on Call Feature When a convertible bond is callable, holders of the convertible bond lose the opportunity to make further returns on the bond as stock prices increase. Companies can establish a variety of call policies such as calling the instant the market value of the

38 convertible rises above the call price or waiting until the market value is well in excess of the call price. Ingersoll (1977) argues that a bond should be called when its conversion value equals its call price. Given that a thirty-day notice has to be given to bondholders of a call, firms may prefer to build a cushion to protect against risk during this period. The empirical evidence however suggests that firms do not usually follow the optimal policy. Ingersoll, for instance, finds that between 1968 and 1975, the average conversion value was 43.9% above the call price for bonds and 38.5% for preferred stocks. The call policy chosen by a firm and communicated to financial markets implicitly through its actions, has an effect on the value of the convertible bond. III. Pre-payment Option Mortgage backed securities, which came of age in the eighties, securitized residential mortgages, by packaging them and issuing marketable securities of various types on them – either as flow through investments where holders receive a share of the total cash flows on the pool of mortgages or as derivative products, where holders receive customized packages of cash flows depending upon their preferences. The latter, called collateralized mortgage obligations, in its simplest form, divide cash flows on the mortgage pool into four tranches, with cash flows on each tranche starting as the cash flows on the prior tranche are completed. Figure 33.15 illustrates this type of security. Figure 33.15: Cash flows on a Mortgage Pool

39

In recent years, CMOs have been refined further and even more specialized products have been created including stripped mortgage-backed securities (where cash flows are divided on the basis of principal and interest), floating rate classes and inverse floaters (where the interest rate on the security increases as the index rate decreases). Mortgages can be pre-paid by borrowers, if interest rates decline. This prepayment option that resides with borrowers affects the cash flows, and therefore the value, of all mortgage-backed securities. The Prepayment Option The homeowner may prepay a loan for any number of reasons, but the level of interest rates is a critical variable. If interest rates declines sufficiently, the potential gain from pre-payment may exceed the cost of pre-payment. The following graph illustrates the percentage of homeowners who prepay as a function of the difference between interest rate and the coupon rate, based upon historical data.

40

If the level of interest rates were the only determinant of prepayment and homeowners were rational about prepayment decisions, the prepayment option could be valued very similarly to the call option in a callable bond (as a function of the level and volatility of interest rates). There are, however, other variables besides the level of interest rates that determine whether homeowners prepay. For instance, there is a correlation between prepayment and the age of a mortgage, irrespective of interest rates. Furthermore, some homeowners may never prepay their mortgages no matter how much interest rates drop. There are also seasonal factors that affect prepayment. Consequently, option pricing models alone fall short in pricing prepayment options in mortgage backed securities. A number of researchers have attempted to develop models that explain prepayment, as a basis for pricing the prepayment option, with characteristics such as age and coupon rate as inputs, in addition to specific characteristics of the borrowers in the pool. In cases where a specific rather than a generic pool of mortgages is being priced, the historical payment record of the specific5 pool is useful and is often the basis for estimating prepayments.

5

A number of variables have been found to be useful in explaining prepayments - the market price relative to the original purchase price and geographical differences, for instance.

41 Valuing the prepayment option The effect of the prepayment option on value will vary with the type of mortgage backed security. Consider, for instance, the price behavior of interest-only and principalonly securities, as interest rates changes. As interest rates increase, the interest payments on the interest-only securities goes up, leading to a higher value for the security, at least initially, though the present value effects (which are negative) start to dominate beyond a certain point. As interest rates decrease, the prepayments lead to lower interest payments and a lower value for the security. The principal-only securities behave more like conventional bonds, increasing in value as interest rates decline and decreasing in value as they increase. Figure 33.16 illustrates this relationship. Figure 33.16: Mortgage Rates and Security Values

IO: Interest Only Security

PO: Principal Only Security

IV. Interest Rate Caps and Floors A floating rate bond is a bond which has an interest rate linked up to an index either a government bond rate (treasury bond or bill) or to the LIBOR. The rationale for issuing such bonds is to reduce the interest rate risk for both the issuer and the buyer of the bond. Most floating rate bond issuers, however, cap their floating rate obligations to ensure that interest rates do not rise above a pre-specified rate (the cap). Some floating rate bonds offer buyers some compensation by providing a floor, below which interest rates will not decline. If a floating rate bond has a cap and a floor, a collar is created.

42 Caps, Floors and Collars The presence of a cap on a floating rate bond can be illustrated best by contrasting a bond with a cap against a floating rate bond without one, as shown in Figure 33.17. Figure 33.17: Effects of Caps on Floating Rate Loans Effecti ve In teres t Rat e (%)

Flo at in g Rate Bo nd

Cap

Fl oat in g Rat e + Cap

K(c) Index Rat e (for Cap)

The cap on a floating rate bond has the same effect as a call option on interest rates with a strike price of K c, with the issuer of the bond holding the option. A call option on interest rates translates6 into a put option on the underlying bond. The price of a floating rate bond with a cap can then be written as: Price of floating rate bond with cap = Price of floating rate bond without cap - Value of put on bond The presence of a floor on interest rates can also be illustrated using a similar comparison of a bond with a floor against a bond without one in Figure 33.18.

The translation is not one to one. A call option on interest rates is the equivalent of α options on the underlying bill or bond, where α = 1/ Exercise price of equivalent bill. 6

43 Figure 33.18: Effects of Caps on Floating Rate Loans Floating Rate Bond Effective Interest Rate (%) Floating Rate + Floor

Cap

K(f)

Floor

The floor on a floating rate bond has the same effect as adding a put option on interest rates with a strike price of Kf, with the buyer of the bond holding the put. A put option on interest rates can be translated into a call option on the underlying bond. The price of a floating rate bond with a floor can then be written as: Price of floating rate bond with floor = Price of floating rate bond without cap + Value of call on bond Finally, the presence of both a cap and a floor can be illustrated in Figure 33.19. Figure 33.19: Effects of Caps on Floating Rate Loans

44 Floating Rate Bond Effective Interest Rate (%)

Collared Bond

Cap

K(f)

K(c) Index Rate (for Cap) Floor

The presence of a collar on a floating rate bond creates two options - a call option with a strike price of K c for the issuer of the bond and a put option with a strike price of Kf for the buyer of the bond. These options on interest rates can be stated again in terms on options on the underlying bond. Price of floating rate bond with collar = Price of floating rate bond without collar + Value of call on bond - Value of put on bond Valuing caps and floors Option pricing models can be used to value caps, floors and collars with some caveats. The key assumption in the Black Scholes model of constant volatility over the life of the option is likely to be violated for interest rate options, both because of the long term nature of these options and because the variance in the bond price is likely to change as the bond approaches maturity. There have been attempts to use yield instead of price and assume that it conforms to a lognormal distribution.

45 Subrahmanyam (1990) notes that the value of a cap on interest rates can be written as a series of put options on the price of an equivalent bill or bond. Briys, Crouhy and Schobel (1991) provide a framework for pricing caps, floors and collars. They argue that caps and floors can be modeled as a series of independent options on zero coupon bonds. They allow for the fact that bond prices do not follow the geometric Brownian motion used by Black and Scholes (1973), but adopt a different stochastic process to price caps, floors and collars. Illustration 33.9: Valuing a 2-year Cap/Floor on 6 Month LIBOR Assume that the current 6-month LIBOR rate is 8%, and that the cap/floor has an exercisable price of 8%. The cap consists of three options which are exercisable at the end of 6 months (183 days), 12 months (365 days) and 18 months (548 days). Each of these options is on the $LIBOR rate (of 183 days for the first, 182 days for the second and 183 days for the third). The options can be valued using the bill prices (rather than interest rates) and the inputs used in the Black-Scholes Model are as follows. Option Maturity Bill price

Exercise Price

Forward Price

Volatility

183

0.9609

0.9611

0.9626

0.0100

365

0.9250

0.9609

0.9609

0.0100

548

0.8890

0.9611

0.9615

0.0100

The first column provides the maturity period for each of the three options. The second column is the value of a zero-coupon bond with a maturity equal to the maturity of the zero-coupon bond - $1 discounted back 183 days at 8% is $0.9609, $1 discounted back 365 days at 8% is $0.9250 and so on. The third column is the strike price, based upon the cap rate, for each option. The fourth column is the forward price of the bill at the option expiration date. The final column is the assumed annualized volatility in bill prices of 1%. The values of the call and puts options with these maturities on bills is provided in the following table in basis points. These can be converted into option values for options on interest rates by multiplying by the number of put options on bills that is equivalent to one call option on the interest rate. Adjustment Factor = α = 1/Exercise price of equivalent bill option

46 T. Bill Option

Interest Rate Options

Put

Call

Call

Put

183

19.6133

33.6639

20.4065

35.0254

365

34.6903

36.4439

36.1010

37.9259

548

39.8620

43.5135

41.4742

45.2734

Value of the Cap =

97.9817

Value of the Floor =

120.2237

To illustrate the calculation, the values of the interest rate options for the 183 day option can be estimated as follows. Adjustment factor for 183 day option =

1 = 1.0405 0.9611

Value of 183-day put on T.Bill = 19.6133 Value of 183-day call on interest rate = 19.6133 * 1.0405 = 20.4065 Valuing Options Embedded in Bonds A corporate bond can often have three or four options embedded in it and to value the bonds, you have to value the options. While conventional option pricing models can be used to value fixed income options, you should note the following. •

The assumption of constant volatility that we often use to value options on stocks cannot be used to value options on bonds such as callability. Bonds are finite life instruments and their volatility will decrease as they approach maturity. You will have to model the change in volatility over time to price the option.

•

When multiple options exist in a bond, you will have to examine the relationship between the options to price them. For instance, consider a callable, convertible bond. While both callability and convertibility are options – one is held by the bond issuer and the other by the bond buyer – the exercise of one of these options voids the other. This will become a factor when the options will be exercised and how much they are worth.

•

The key underlying variable for some bond options – such as interest rate caps and floors – is the interest rate process and how it is modeled can have a significant impact on the value of the options.

47 V. Other Features There are a number of other bond features which affect the value of the bond - a sinking fund provision, where the firm plans to retire a specified face value of the bonds outstanding each year, provisions relating to the subordination of future debt issues and bond covenants on investment and dividend policy. Sinking Funds Most industrial bond issues come with sinking fund provisions, requiring the issuer to retire a specified portion of the bond issue each year, starting a period of time (five or ten years) after the initial issue. The sinking fund provision can take one of two forms. (a) A trustee collects a cash payment from the bond issuer and calls bonds for redemption at the sinking-fund call price, usually based upon a lottery. (b) The bond issuer can buy back bonds in the open market and deliver the specified number of bonds to the trustee in the periods specified. If the bond issuer has the option to do the latter, bonds will be bought back and delivered if the market price is less than the call price and cash will be delivered to the trustee to make the call if the market price is greater than the call price. Sinking funds usually relate to a single issue, but they can sometimes cover multiple issues ("funnel sinking fund"). Most sinking funds also allow the bond issuer to accelerate call backs if it is in the issuer's favor to do so (i.e., interest rates have gone down since the issue). A sinking fund has two effects, one of which benefits the issuer of the bond and the other which benefits the buyer of the bond. The issuer of the bond gets a delivery option, because he has an option to either deliver the cash for the call price or to buy the bonds at the market price. The value of this call option (similar to the option in a callable bond) will increase with the volatility of interest rates and decrease with the level of interest rates. The buyer of the bond has less default risk because of the requirement that some of the debt be retired each period. The net effect will determine whether a sinking fund provision adds or detracts from the value of a bond.

48 The empirical evidence on the sinking fund provision is mixed. While some of the earlier studies concluded that a sinking fund provision added to bond value, Ho and Lee (1985) find that its net value is insignificant overall, but that it adds more value as default risk increases than it does as interest rate volatility increases. Subordination of Further Debt and Collateral Existing debt holders are negatively affected by the issue of new debt, especially if the new debt has superior claims on the assets of the issuer. Therefore, some bond issues have subordination clauses, which put restrictions on the issue of additional debt. Additional debt might have to be subordinated to existing debt; i.e., in the event of bankruptcy, subordinated debt will be paid off after existing debt is fully paid. The presence of subordination clauses in a bond agreement should make it less risky and therefore more valuable. Some bonds are issued with specific collateral issued behind them, with a specific asset of the firm backing up the promised payments on the bond. If the collateral is property, the bond is called a mortgage bond, whereas, if it is securities, it is a collateral trust bond. Other bonds are issued without specific collateral and are called unsecured bonds. Other things remaining equal, secured bonds should be viewed as less risky and more valuable than equivalent unsecured bonds. The Effect of Bond Covenants Most bond issues are accompanied by a set of covenants that restrict the investment and dividend policies of the firm. These covenants are designed to protect bondholders from stockholders, who might try to expropriate wealth from them by: (a) investing in much riskier projects, especially if the firm is highly levered, or (b) paying significantly higher dividends than expected. Bond covenants should reduce the risk of expropriation on a bond and increase the value of the bond. Conclusion The price of a bond is the present value of the cashflows on the bond – coupons and face value – discounted back at an appropriate interest rate. To estimate that interest

49 rate, we began with the instantaneous riskless interest rate and added a maturity premium and a default premium to it. Bonds become increasingly complex as special features are added to them, since these special features affect the cash flows, risk and value of these bonds. Many of these special features have option characteristics - the chance to convert the bond into other securities or assets, the option to call the bond back if interest rates go down and the option to put the bond back to the issuer if contractual obligations are not met. Traditional option pricing models can be used to value these options, some of which reside with the buyer (thus increasing the value of the bond) and some of which reside with the seller (which would reduce value). The presence of more than one of these options in the same bond (for example, a callable convertible bond) does add to the complexity of the process, but it can be overcome.

50 Problems 1. Estimate the value of a just-issued 20-year government bond with an 8% coupon rate if interest rates are at 9%. How much will this value change if interest rates go up by 2%? if they go down by 2%? (Coupons are paid semi-annually.) 2. Estimate the value of seasoned government bond with a 7.5% coupon rate and twelve years to maturity, if interest rates are at 8.0%. (Coupons are paid semi-annually, and the next coupon is due in three months.) 3. Estimate the duration of a government bond with a coupon rate of 10% and a 5-year maturity, if the yield to maturity on the bond is 8%. (You can assume, for purposes of simplicity, that the coupons are paid annually.) 4. Why are longer-term bonds more sensitive to a given change in interest rates than shorter term bonds? Why are zero-coupon bonds more sensitive than coupon bonds of equal maturity? 5. If the nominal interest rate is 8% and the expected inflation is 5%, estimate the expected real rate of return. Why might the actual real rate of return deviate from this expectation? 6. You are provided with the following information on government bonds of different maturities. Maturity

Yield to Maturity

1 year

5.0%

2 years

5.5%

3 years

6.0%

4 years

6.5%

5 years

7.0%

You can assume that the bonds are trading at par and, therefore, the coupon rates are equal to the yields to maturity. a. Plot the yield curve using the yields to maturity. b. Estimate the spot rates for the different maturities. c. Estimate the forward rates for each of the four one-year periods.

51 7. If lenders demand a liquidity premium for lending long term, yield curves will always be upward sloping. Is this statement true? Why or why not? 8. Some studies that looked at low-rated bonds in the 1980s found that the default premiums received on these bonds were much larger than the default rate on them. (In other words, investors in these bonds made more over the period, even after adjusting for actual defaults, than investors in higher-rated or default free bonds.) They then concluded that the default premiums were too high. Would you agree? Why or why not? 9. You are analyzing a convertible bond with a face value of $1000 and an annual coupon of 4%, which is convertible into 30 shares of stock anytime over the next 20 years. The current stock price is $27 and the convertible is trading at $1177. Estimate the following: a. the conversion ratio and conversion price. b. the conversion premium. c. if the interest rate on straight bonds issued by the same company is 8%, estimate the value of the conversion option. 10. ITC Corporation has convertible bonds outstanding with the following features: •

The bonds mature in fifteen years; there are 100,000 bonds outstanding.

•

Each bond can be converted into 50 shares of stock any time until expiration.

•

The coupon rate on the bond is 5%; straight bonds issued by the company are yielding 10%.

•

The current stock price is $15 per share and the standard deviation in ln(stock prices return) is 40%.

•

There are 20 million shares outstanding. a. Value the conversion option. b. Estimate the value of the straight bond portion. c. If these bonds were issued at par, who would be gaining? Who would be losing? d. What impact would forced conversion have on the value of this convertible bond?

52 11. A company has two issues of bonds outstanding - they both have the same maturities and coupon rates, but differ in one respect. The first issue (Issue A) is callable, while the second is not. Respond true or false to the following statements. a. The callable bonds will trade for a higher price than the non-callable bonds. b. The callable bonds have a shorter duration than the non-callable bonds. c. The callable bonds will have a higher yield than the non-callable bonds. d. The callable bonds will be more sensitive to interest rate changes than the noncallable bonds. 12. You are evaluating the yield on a callable bond, with a 10-year maturity and a 9% coupon rate. The bonds can be called back at 110% of par in 3 years. The bond is trading at $950. a. Estimate the yield to maturity. b. Estimate the yield to call. c. Which of the two would you use in analyzing the bond? 13. Collateralized Mortgage Obligations (CMOs) provide investors with the opportunity to invest in cash flows from mortgage obligations. These cash flows are affected by mortgage prepayments. Assume that you have valued (and bought) CMOs on the assumption that homeowners will prepay as soon as it is rational for them to do so. What would be the effect on your returns if: i. homeowners consistently waited too long before prepaying mortgages. ii. homeowners consistently prepaid mortgages at the right time. 14. Answer true or false to the following statements and explain. a. A floating rate loan with no cap or floor has very low or no duration. b. A floating rate loan with a cap will have a higher interest rate than a similar floating rate loan with no cap. c. A floating rate loan with a floor will have a higher interest rate than a similar floating rate loan with no floor. d. A loan with a sinking fund provision will have a lower interest rate than a similar loan with no sinking fund provision.

1 CHAPTER 34 VALUING FUTURES AND FORWARD CONTRACTS A futures contract is a contract between two parties to exchange assets or services at a specified time in the future at a price agreed upon at the time of the contract. In most conventionally traded futures contracts, one party agrees to deliver a commodity or security at some time in the future, in return for an agreement from the other party to pay an agreed upon price on delivery. The former is the seller of the futures contract, while the latter is the buyer. This chapter explores the pricing of futures contracts on a number of different assets - perishable commodities, storable commodities and financial assets - by setting up the basic arbitrage relationship between the futures contract and the underlying asset. It also examines the effects of transactions costs and trading restrictions on this relationship and on futures prices. Finally, the chapter reviews some of the evidence on the pricing of futures contracts. Futures, Forward and Option Contracts Futures, forward and option contracts are all viewed as derivative contracts because they derive their value from an underlying asset. There are however some key differences in the workings of these contracts. How a Futures Contract works There are two parties to every futures contract - the seller of the contract, who agrees to deliver the asset at the specified time in the future, and the buyer of the contract, who agrees to pay a fixed price and take delivery of the asset.

2 Figure 34.1: Cash Flows on Futures Contracts

Buyer's Payoffs

Futures Price Spot Price on Underlying Asset

Seller's Payoffs

While a futures contract may be used by a buyer or seller to hedge other positions in the same asset, price changes in the asset after the futures contract agreement is made provide gains to one party at the expense of the other. If the price of the underlying asset increases after the agreement is made, the buyer gains at the expense of the seller. If the price of the asset drops, the seller gains at the expense of the buyer. Futures versus Forward Contracts While futures and forward contracts are similar in terms of their final results, a forward contract does not require that the parties to the contract settle up until the expiration of the contract. Settling up usually involves the loser (i.e., the party that guessed wrong on the direction of the price) paying the winner the difference between the contract price and the actual price. In a futures contract, the differences is settled every period, with the winner's account being credited with the difference, while the loser's account is reduced. This process is called marking to the market. While the net settlement is the same under the two approaches, the timing of the settlements is different and can

3 lead to different prices for the two types of contracts. The difference is illustrated in the following example, using a futures contract in gold. Illustration 34.1: Futures versus Forward Contracts - Gold Futures Contract Assume that the spot price of gold is $400, and that a three-period futures contract on gold has a price of $415. The following table summarizes the cash flow to the buyer and seller of this contract on a futures and forward contract over the next 3 time periods, as the price of the gold futures contract changes. Time Period

Gold Futures Buyer's CF:

Seller's CF:

Buyer's CF: Seller's

Contract

Forward

Forward

1

$420

$0

$0

$5

-$5

2

$430

$0

$0

$10

-$10

3

$425

$10

-$10

-$5

$5

$10

-$10

$10

-$10

Net

Futures

CF:

Futures

The net cash flow from the seller to the buyer is $10 in both cases, but the timing of the cash flows is different. On the forward contract, the settlement occurs at maturity. On the futures contract, the profits or losses are recorded each period. Futures and Forward Contracts versus Option Contracts While the difference between a futures and a forward contract may be subtle, the difference between these contracts and option contracts is much greater. In an options contract, the buyer is not obligated to fulfill his side of the bargain, which is to buy the asset at the agreed upon strike price in the case of a call option and to sell the asset at the strike price in the case of a put option. Consequently the buyer of an option will exercise the option only if it is in his or her best interests to do so, i.e., if the asset price exceeds the strike price in a call option and vice versa in a put option. The buyer of the option, of course, pays for this privilege up front. In a futures contract, both the buyer and the seller are obligated to fulfill their sides of the agreement. Consequently, the buyer does not gain an advantage over the seller and should not have to pay an up front price for the futures contract itself. Figure 34.2 summarizes the differences in payoffs on the two types of contracts in a payoff diagram. Figure 34.2: Buying a Futures Contract versus Buying a Call Option

4 Futures Contract

Call Option

Futures Price Spot Price on Underlying Asset

Traded Futures Contracts - Institutional Details A futures contract is an agreement between two parties. In a traded futures contract, an exchange acts as an intermediary and guarantor, and also standardizes and regulates how the contract is created and traded. Buyer of Contract ----------->Futures Exchange

Growth rate of economy

Stable growth model No

Replace current Is the firm earnings with likely to normalized survive? earnings

Yes

Are the firm’s competitive advantges time limited?

Yes

2-stage model No

Adjust margins over time to nurse firm to financial health

Does the firm have a lot of debt?

Yes Value Equity as an option to liquidate

No Estimate liquidation value

No 3-stage or n-stage model

16 Choosing the Right Relative Valuation Model Many analysts choose to value assets using relative valuation models. In making this choice, two basic questions have to be answered -- Which multiple will be used in the valuation? Will this multiple be arrived at using the sector or the entire market? Which multiple should I use? In the chapters on multiples, we presented a variety of multiples. Some were based upon earnings, some on book value and some on revenues. For some multiples, we used current values and for others, we used forward or forecast values. Since the values you obtain are likely to be different using different multiples, deciding which multiple to use can make a big difference to your estimate of value. There are three ways you can answer this question –the first is to adopt the cynical view that you should use the multiple that reflects your biases, the second is to value your firm with different multiples and try to use all of the values that you obtain and the third is to pick the best multiple and base your valuation on it. The Cynical View You can always use the multiple that best fits your story. Thus, if you are trying to sell a company, you will use the multiple which gives you the highest value for your company. If you are buying the same company, you will choose the multiple that yields the lowest value. While this clearly crosses the line from analysis into manipulation, it is a more common practice than you might realize. Even if you never plan to employ this practice, you should consider ways in which how you can protect yourself from being victimized by it. First, you have to recognize that conceding the choice of multiple and comparables to an analyst is the equivalent of letting him or her write the rules of the game. You should play an active role in deciding which multiple should be used to value a company and what firms will be viewed as comparable firms. Second, when presented with a value based upon one multiple, you should always ask what the value would have been if an alternative multiple had been used. The Bludgeon View

17 You can always value a company using a dozen or more multiples and then use all of the values, different thought they might be, in your final recommendation. There are three ways in which can present the final estimate of value. The first is in terms of a range of values, with the lowest value that you obtained from a multiple being the lower end of the range and the highest value being the upper limit. The problem with this approach is that the range is usually so large that it becomes useless for any kind of decision-making. The second approach is a simple average of the values obtained from the different multiples. While this approach has the virtue of simplicity, it gives equal weight to the values from each multiple, even though some multiples may yield more precise answers than others. The third approach is a weighted average, with the weight on each value reflecting the precision of the estimate. This weight can either be a subjective one or a statistical measure – you can, for instance, use the standard error on a prediction from a regression. The Best Multiple While we realize that you might be reluctant to throw away any information, the best estimates of value are usually obtained by using the one multiple that is best suited for your firm. There are three ways in which you can find this multiple. •

The Fundamentals approach: You should consider using the variable that is most highly correlated with your firm’s value. For instance, current earnings and value are much more highly correlated in consumer product companies than in technology companies. Using price earnings ratios makes more sense for the former than for the latter.

•

The Statistical approach: You could run regressions of each multiple against the fundamentals that we determined affected the value of the multiple in earlier chapters and use the R-squared of the regression as a measure of how well that multiple works in the sector. The multiple with the highest R-squared is the multiple that you can best explain using fundamentals and should be the multiple you use to value companies in that sector.

•

The Conventional Multiple approach: Over time, we usually see a specific multiple become the most widely used one for a specific sector. For instance,

18 price to sales ratios are most commonly used multiple to analyze retail companies. Table 35.1 summarizes the most widely used multiples by sector. Table 35.1: Most widely used Multiples by Sector Sector

Multiple Used

Rationale/ Comments

Cyclical Manufacturing

PE, Relative PE

Often with normalized earnings.

High Tech, High Growth

PEG

Big differences in growth across firms make it difficult to compare PE ratios.

High Growth/Negative

PS, VS

Earnings Infrastructure

Assume future margins will be positive.

V/EBITDA

Firms in sector have losses in early years and reported earnings can

vary

depending

on

depreciation method. REIT

P/CF

Restrictions on investment policy and large depreciation charges make cashflows better measure than equity earnings.

Financial Services

PBV

Book value often

marked to

market. Retailing

PS

If leverage is similar across firms.

VS

If leverage is different.

In an ideal world, you should see all three approaches converge – the fundamental that best explains value should also have the highest R-squared and be the conventional multiple used in the sector. In fact, when the multiple in use conventionally does not reflect fundamentals, which can happen if the sector is in transition or evolving, you will get misleading estimates of value.

19 Market or Sector Valuation In most relative valuations, you value a firm relative to other firms in the industry that the firm operates and attempt to answer a simple question: Given how other firms in the business (sector) are priced by the market, is this firm under or over valued? Within this approach, you can define comparable firms narrowly as being firms that not only operate in the business in which your firm operates but also look like your firm in terms of size or market served, or broadly in which case you will have far more comparable firms. If you are attempting to control for differences across firms subjectively, you should stick with the narrower group. If, on the other hand, you plan to control for differences statistically – with a regression, for instance – you should go with the broader definition. In the chapters on relative valuation, we presented an alternative approach to relative valuation, where we valued firms relative to the entire market. When we do this, we are not only using a much larger universe of questions, but asking a different question: Given how other firms in the market are priced, is this firm under or over valued? A firm can be under valued relative to its sector but overvalued relative to the market (or vice versa), if the entire sector is mispriced. The approach you use for relative valuation will depend again upon what your task is defined to be. If you want to stay narrowly focused on your sector and make judgments on which stocks are under or over valued, you should stick with sector based relative valuation. If you have more leeway and are trying to find under or overvalued stocks across the market, you should look at the second approach – perhaps in addition to the first one. Can a firm be under and over valued at the same time? If you value a firm using both discounted cash flow and relative valuation models, you may very well get different answers using the two – the firm may be under valued using relative valuation models but over valued using discounted cash flow models. What do we make of these differences and why do they occur? If a firm is overvalued using a discounted cash flow model and undervalued using relative valuation, it is usually an indication that the sector is over valued, relative to its fundamentals. For instance, in

20 March 2000, we valued Amazon at $30 a share using a discounted cash flow model, when it was trading at $70 a share – it was clearly overvalued. At the same time, a comparison of Amazon to other dot com firms suggested that it was undervalued relative to these firms. If a firm is undervalued using a discounted cashflow model and overvalued using relative valuation, it usually indicates that the sector is under valued. By March 2001, Amazon’s stock price had dropped to $15 but the values of other internet stocks dropped by almost 90%. In March 2001, a discounted cash flow valuation suggested that Amazon was under valued but a relative valuation indicated that it was now over valued relative to the sector. As an investor, you can use both discounted cash flow and relative valuation to value a company. Optimally, you would like to buy companies that are under valued using both approaches. That way, you benefit from market corrections both across time (which is the way you make money in discounted cash flow valuation) and across companies. When should you use the option pricing models? In the chapters on applying option pricing models to valuation, we presented a number of scenarios where option pricing may yield a premium on traditional discounted cash flow valuation. We do not intend to revisit those scenarios, but offer the following general propositions that you should keep in mind when using option pricing models. •

Use Options sparingly: Restrict your use of options to where they make the biggest difference in valuation. In general, options will affect value the most at smaller firms that derive the bulk of their value form assets that resemble options. Therefore, valuing patents as options to estimate firm value makes more sense for a small biotechnology firm than it does for a drug giant like Merck. While Merck may have dozens of patents, it derives much of its value from a portfolio of developed drugs and the cash flows they generate.

•

Opportunities are not always options: You should be careful not to mistake opportunities for options. Analysts often see a firm with growth potential and assume that there must be valuable options embedded in the firm. For

21 opportunities to become valuable options, you need some degree of exclusivity for the firm in question – this can come from legal restrictions on competition or a significant competitive edge. •

Do not double count options: All too often, analysts incorporate the effect of options on fundamentals in the company value and then proceed to add on premiums to reflect the same options. Consider, for instance, the undeveloped oil reserves owned by an oil company. While it is legitimate to value these reserves as options, you should not add this value to a discounted cashflow valuation of the company, if your expected growth rate in the valuation is set higher because of the firm’s undeveloped reserves.

Conclusion The analyst faced with the task of valuing a firm/asset or its equity has to choose among three different approaches -- discounted cashflow valuation, relative valuation and option pricing models; and within each approach, they must also choose among different models. These choices will be driven largely by the characteristics of the firm/asset being valued - the level of its earnings, its growth potential, the sources of earnings growth, the stability of its leverage and its dividend policy. Matching the valuation model to the asset or firm being valued is as important a part of valuation as understanding the models and having the right inputs. Once you decide to go with one or another of these approaches, you have further choices to make – whether to use equity or firm valuation in the context of discounted cashflow valuation, which multiple you should use to value firms or equity and what type of option is embedded in a firm.