The Dark Side of Valuation: Valuing Young, Distressed, and Complex Businesses (2nd Edition)

From the Library of Melissa Wong The Dark Side of Valuation Second Edition Valuing Young, Distressed, and Complex Busi...

Author: Aswath Damodaran

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From the Library of Melissa Wong

The Dark Side of Valuation Second Edition Valuing Young, Distressed, and Complex Businesses Aswath Damodaran


Vice President, Publisher: Tim Moore Associate Publisher and Director of Marketing: Amy Neidlinger Executive Editor: Jim Boyd Editorial Assistants: Myesha Graham, Pamela Boland Development Editor: Russ Hall Operations Manager: Gina Kanouse Senior Marketing Manager: Julie Phifer Publicity Manager: Laura Czaja Assistant Marketing Manager: Megan Colvin Cover Designer: Alan Clements Managing Editor: Kristy Hart Project Editor: Betsy Harris Copy Editor: Gayle Johnson Proofreader: Water Crest Publishing Indexer: Lisa Stumpf Senior Compositor: Gloria Schurick Manufacturing Buyer: Dan Uhrig © 2010 by Pearson Education, Inc. Publishing as FT Press Upper Saddle River, New Jersey 07458 This book is sold with the understanding that neither the author nor the publisher is engaged in rendering legal, accounting, or other professional services or advice by publishing this book. Each individual situation is unique. Thus, if legal or financial advice or other expert assistance is required in a specific situation, the services of a competent professional should be sought to ensure that the situation has been evaluated carefully and appropriately. The author and the publisher disclaim any liability, loss, or risk resulting directly or indirectly, from the use or application of any of the contents of this book. FT Press offers excellent discounts on this book when ordered in quantity for bulk purchases or special sales. For more information, please contact U.S. Corporate and Government Sales, 1-800-382-3419, [email protected]. For sales outside the U.S., please contact International Sales at [email protected]. Company and product names mentioned herein are the trademarks or registered trademarks of their respective owners. All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Printed in the United States of America First Printing July 2009 ISBN-10: 0-13-712689-1 ISBN-13: 978-0-13-712689-7 Pearson Education LTD. Pearson Education Australia PTY, Limited. Pearson Education Singapore, Pte. Ltd. Pearson Education North Asia, Ltd. Pearson Education Canada, Ltd. Pearson Educación de Mexico, S.A. de C.V. Pearson Education—Japan Pearson Education Malaysia, Pte. Ltd. Library of Congress Cataloging-in-Publication Data Damodaran, Aswath. The dark side of valuation : valuing young, distressed and complex businesses / Aswath Damodaran. p. cm. ISBN 978-0-13-712689-7 (hardback : alk. paper) 1. Valuation. I. Title. HG4028.V3D352 2010 658.15’5--dc22 2009009418


To my family, who remind me daily of the things that truly matter in life (and valuation is not in the top-ten list)


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CONTENTS Preface Chapter 1

The Dark Side of Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 2

Intrinsic Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chapter 3

Probabilistic Valuation: Scenario Analysis, Decision Trees, and Simulations . . . . . . . . . . . . . . . . . . . . 64

Chapter 4

Relative Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Chapter 5

Real Options Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Chapter 6

A Shaky Base: A “Risky” Risk-Free Rate . . . . . . . . . . . . . 144

Chapter 7

Risky Ventures: Assessing the Price of Risk . . . . . . . . . . 168

Chapter 8

Macro Matters: The Real Economy . . . . . . . . . . . . . . . . . 194

Chapter 9

Baby Steps: Young and Start-Up Companies . . . . . . . . . 213

Chapter 10

Shooting Stars? Growth Companies . . . . . . . . . . . . . . . . 263

Chapter 11

The Grown-Ups: Mature Companies . . . . . . . . . . . . . . . 312

Chapter 12

Winding Down: Declining Companies . . . . . . . . . . . . . . 361

Chapter 13

Ups and Downs: Cyclical and Commodity Companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Chapter 14

Mark to Market: Financial Services Companies. . . . . . . 449

Chapter 15

Invisible Investments: Firms with Intangible Assets . . . 476

Chapter 16

Volatility Rules: Emerging-Market Companies . . . . . . . 505

Chapter 17

The Octopus: Multibusiness Global Companies . . . . . . 535

Chapter 18

Going Over to the Light: Vanquishing the Dark Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

v From the Library of Melissa Wong

PREFACE The Dark Side of Valuation, Second Edition The first edition of this book is showing its age and origins. The idea for the first edition of The Dark Side of Valuation was born at the end of 1999, toward the end of the dotcom boom. It was triggered by two phenomena: Q

Q

The seeming inability of traditional valuation models to explain stratospheric stock prices for technology (especially new technology) companies The willingness of analysts to abandon traditional valuation metrics and go over to the “dark side” of valuation, where prices were justified using a mix of new metrics and storytelling

The publication of the first edition coincided with the bursting of that bubble. As markets have evolved and changed, the focus has shifted. The bubble and the concurrent rationalization using new paradigms and models have shifted to new groups of stocks (Chinese and Indian equities) and new classes of assets (subprime mortgages). I have come to the realization that the dark side of valuation beckons any time analysts have trouble fitting companies into traditional models and metrics. This second edition reflects that broader perspective. Rather than focusing on just young, high-tech (Internet) companies, as I did in the first edition, I want to look at companies that are difficult to value across the spectrum. Chapters 2 through 5 review the basic tools available in valuation. In particular, they summarize conventional discounted cash flow models, probabilistic models (simulations, decision trees), relative valuation models, and real options. Much of what is included in this part has already been said in my other books on valuation. Chapters 6 through 8 examine some of the estimation questions and issues surrounding macro variables that affect all valuation. Chapter 6 looks at the risk-free rate, the building block for all other inputs, and challenges the notion that government bond rates are always good estimates of risk-free rates. Chapter 7 expands the discussion to look at equity risk premiums. This is another number that is often taken as a given in valuation, primarily because risk premiums in mature markets have been stable for long periods. In shifting and volatile markets, risk premiums can change significantly over short periods. Failing to recognize this reality will create skewed valuations. Chapter 8 examines vi From the Library of Melissa Wong

other macroeconomic assumptions that are often implicit in valuations about growth in the real economy. It also looks at exchange rates and inflation and how inconsistencies in these valuations affect the conclusions we draw. Chapters 9 through 12 look at valuation challenges across a firm’s life cycle. Figure P.1 shows the challenges. A Life Cycle of Valuation Idea Companies

Young Growth

Mature Growth

Mature

Decline

Revenues $ Revenues/ Earnings Earnings

Time Valuation Players/Setting

Owners Angel Finance

Venture Capitalists IPO

Growth Investors Equity Analysts

Value Investors Private Equity Funds

Revenue/Earnings

1. What is the potential market? 2. Will this product sell and at what price? 3. What are the expected margins?

1. Can the company scale up? (How will revenue growth change as firm gets larger?) 2. How will competition affect margins?

1. As growth declines, 1. Is there the possibility how will the firm's of the firm being reinvestment policy restructured? change? 2. Will financing policy change as firm matures?

Survival Issues

Will the firm make it?

Will the firm be acquired?

Key Valuation Inputs

Potential Market Margins Capital Investment Key Person Value?

Revenue Growth Target Margins

Data Issues

No History No Financials

Low Revenues Negative Earnings Changing Margins

Vulture Investors Break-Up Valuations

Low, as projects dry up.

Will the firm be taken private?

Will the firm be liquidated/go bankrupt?

Return on Capital Reinvestment Rate Length of Growth

Current Earnings Efficiency Growth Changing Cost of Capital

Asset Divestiture Liquidation Values

Past data reflects smaller company.

Numbers can change if management changes.

Declining Revenues Negative Earnings?

Figure P.1: A Life Cycle View of Valuation

Chapter 9 reviews the challenges faced in valuing young and “idea” businesses, which have an interesting idea for a product or service but no tangible commercial product yet. It also considers the baby steps involved as the idea evolves into a commercial product, albeit with very limited revenues and evidence of market success. Thus, it looks at the challenges faced in the first stages of entrepreneurial valuation. These are the challenges that venture capitalists have faced for decades when providing “angel financing” to small companies. Chapter 10 climbs the life cycle ladder to look at young growth companies, whose products and services have found a market and where revenues are growing fast. This chapter also examines the valuation implications of going public as opposed to staying private and the sustainability of growth. In addition, this chapter looks at growth companies that have survived the venture capital cycle and have gone

Preface

vii


public. These companies have a well-established track record of growth, but their size is working against them. Chapter 11 looks at “mature companies,” where growth is in the past, and the efforts made by these firms to increase value, including acquisitions, operating restructuring, and financial restructuring. In the process, we also consider how a private equity investor may view value in a “mature” company in the context of a leveraged buyout and the value of control in this company. Chapter 12 considers firms in decline, where growth can be negative, and the potential for distress and bankruptcy may be substantial. Chapters 13 through 17 look at specific types of firms that have proven difficult to value for a variety of reasons. Chapter 13 looks at two broad classes of firms—commodity companies (oil, gold) and cyclical companies, where volatile earnings driven by external factors (commodity prices, state of the economy) make projections difficult. The special challenges associated with financial services firms—banks, insurance companies, and investment banks—are examined in Chapter 14, with an emphasis on how regulatory changes can affect value. Chapter 15 looks at companies that are heavily dependent on intangible assets: patents, technological prowess, and human capital. The nature of the assets in these firms, combined with flaws in the accounting standards that cover them, make them challenging from a valuation perspective. Chapter 16 looks at companies that operate in volatile and young economies (emerging markets) and how best to estimate their value. Chapter 17 looks at companies in multiple businesses that operate in many countries and how best to deal with the interactions between the different pieces within these companies. In summary, this second edition is a broader book directed at dark practices and flawed methods in valuation across the spectrum—not just in young technology companies.

viii

Preface


ABOUT THE AUTHOR Aswath Damodaran is Professor of Finance at the Stern School of Business at New York University. He teaches the corporate finance and equity valuation courses in the MBA program. He received his MBA and Ph.D from the University of California at Los Angeles. He has written several books on corporate finance, valuation, and portfolio management. He has been at NYU since 1986 and has received the Stern School of Business Excellence in Teaching Award (awarded by the graduating class) eight times. He was profiled in BusinessWeek as one of the top twelve business school professors in the United States in 1994.

ix From the Library of Melissa Wong

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1 The Dark Side of Valuation have always believed that valuation is simple and that practitioners choose to make it complex. The intrinsic value of a cash flow-generation asset is a function of how long you expect it to generate cash flows, as well as how large and predictable these cash flows are. This is the principle that we use in valuing businesses, private as well as public, and in valuing securities issued by these businesses. Although the fundamentals of valuation are straightforward, the challenges we face in valuing companies shift as firms move through the life cycle. We go from idea businesses, often privately owned, to young growth companies, either public or on the verge of going public, to mature companies, with diverse product lines and serving different markets, to companies in decline, marking time until they are liquidated. At each stage, we are called on to estimate the same inputs—cash flows, growth rates, and discount rates—but with varying amounts of information and different degrees of precision. All too often, when confronted with significant uncertainty or limited information, we are tempted by the dark side of valuation, in which first principles are abandoned, new paradigms are created, and common sense is the casualty. This chapter begins by describing the determinants of value for any company. Then it considers the estimation issues we face at each stage in the life cycle and for different types of companies. We close the chapter by looking at manifestations of the dark side of valuation.

I

Foundations of Value We will explore the details of valuation approaches in the next four chapters. But we can establish the determinants of value for any business without delving into the models themselves. In this section, we will first consider a very simple version of an intrinsic value model. Then we will use this version to list the classes of inputs that determine value in any model.

Intrinsic Valuation Every asset has an intrinsic value. In spite of our best efforts to observe that value, all we can do, in most cases, is arrive at an estimate of value. In discounted cash flow (DCF) valuation, the intrinsic value of an asset can be written as the present value of expected cash flows over its life, discounted to reflect both the time value of money and the riskiness of the cash flows. t= N

Value of Asset =

E (CF t )

∑ (1 + r)

t

t =1

1 From the Library of Melissa Wong

In this equation, E(CFt) is the expected cash flow in period t, r is the risk-adjusted discount rate for the cash flow, and N is the life of the asset. Now consider the challenges of valuing an ongoing business or company, which, in addition to owning multiple assets, also has the potential to invest in new assets in the future. Consequently, not only do we have to value a portfolio of existing assets, but we also have to consider the value that may be added by new investments in the future. We can encapsulate the challenges by framing a financial balance sheet for an ongoing firm, as shown in Figure 1.1. Assets

Liabilities

Existing Investments Generate Cash Flows Today Includes Long-Lived (Fixed) and Short-Lived (Working Capital) Assets

Assets in Place

Debt

Expected Value That Will Be Created by Future Investments

Growth Assets

Equity

Fixed Claim on Cash Flows Little or No Role in Management Fixed Maturity Tax Deductible

Residual Claim on Cash Flows Significant Role in Management Perpetual Lives

Figure 1.1: A Financial Balance Sheet

Thus, to value the company, we have to value both the investments already made (assets in place) and growth assets (investments that are expected in the future) while factoring in the mix of debt and equity used to fund the investments. A final complication must be considered. At least in theory, a business, especially if it is publicly traded, can keep generating cash flows forever, thus requiring us to expand our consideration of cash flows to cover this perpetual life: t= ∞

Value of Business =

E (CF t )

∑ (1+ r)

t

t =1

Because estimating cash flows forever is not feasible, we simplify the process by estimating cash flows for a finite period (N) and then a “terminal value” that captures the value of all cash flows beyond that period. In effect, the equation for firm value becomes the following: t= N

Value of Business =

E (CF t )

∑ (1+ r)

t

+

t =1

Terminal Value (1+r)N

N

Although different approaches can be used to estimate terminal value, the one most consistent with intrinsic value for a going concern is to assume that cash flows beyond year N grow at a constant rate forever, yielding the following variation on valuation: t= N

Value of Business =

t

t =1

2

E (CF t )

∑ (1 + r)

+

E(CFN+1 ) (r – g n )(1+r)N

THE DARK SIDE OF VALUATION


Because no firm can grow at a rate faster than the overall economy forever, this approach to estimating terminal value can be used only when the firm becomes a mature business. We will examine the details of estimating the inputs—cash flows, discount rates, and growth rates—in Chapter 2, “Intrinsic Valuation.”

Determinants of Value Without delving into the details of estimation, we can use the equation for the intrinsic value of the business to list the four broad questions that we need to answer in order to value any business: Q

Q Q

Q

What are the cash flows that will be generated by the existing investments of the company? How much value, if any, will be added by future growth? How risky are the expected cash flows from both existing and growth investments, and what is the cost of funding them? When will the firm become a stable growth firm, allowing us to estimate a terminal value?

What Are the Cash Flows Generated by Existing Assets? If a firm has already made significant investments, the first inputs into valuation are the cash flows from these existing assets. In practical terms, this requires estimating the following: Q

Q Q

How much the firm generated in earnings and cash flows from these assets in the most recent period How much growth (if any) is expected in these earnings/cash flows over time How long the assets will continue to generate cash flows

Although data that allows us to answer all these questions may be available in current financial statements, it might be inconclusive. In particular, cash flows can be difficult to obtain if the existing assets are still not fully operational (infrastructure investments that have been made but are not in full production mode) or if they are not being efficiently utilized. There can also be estimation issues when the firm in question is in a volatile business, where earnings on existing assets can rise and fall as a result of macroeconomic forces.

How Much Value Will Be Added by Future Investments (Growth)? For some companies, the bulk of value is derived from investments you expect them to make in the future. To estimate the value added by these investments, you have to make judgments on two variables. The first is the magnitude of these new investments relative to the size of the firm. In other words, the value added can be very different if you assume that a firm reinvests 80% of its earnings into new investments than if you assume that it reinvests 20%. The second variable is the quality of the new investments measured in terms of excess returns. These are the returns the firm makes on the investments over and above the cost of funding those investments. Investing in new assets that generate returns of 15%, when the cost of capital is 10%, will add value, but investing in new assets that generate returns of 10%, with the same cost of capital, will not. In other words, it is growth with excess returns that creates value, not growth per se. Chapter 1 The Dark Side of Valuation

3


Because growth assets rest entirely on expectations and perception, we can make two statements about them. One is that valuing growth assets generally poses more challenges than valuing existing assets; historical or financial statement information is less likely to provide conclusive results. The other is that there will be far more volatility in the value of growth assets than in the value of existing assets, both over time and across different people valuing the same firm. Not only will analysts be likely to differ more on the inputs into growth asset value—the magnitude and quality of new investments—but they will also change their own estimates more over time as new information about the firm comes out. A poor earnings announcement by a growth company may alter the value of its existing assets just a little, but it can dramatically shift expectations about the value of growth assets.

How Risky Are the Cash Flows, and What Are the Consequences for Discount Rates? Neither the cash flows from existing assets nor the cash flows from growth investments are guaranteed. When valuing these cash flows, we have to consider risk somewhere, and the discount rate is usually the vehicle that we use to convey the concerns that we may have about uncertainty in the future. In practical terms, we use higher discount rates to discount riskier cash flows and thus give them a lower value than more predictable cash flows. While this is a commonsense notion, we run into issues when putting this into practice when valuing firms: Q

Q

Q

Dependence on the past: The risk that we are concerned about is entirely in the future, but our estimates of risk are usually based on data from the past—historical prices, earnings, and cash flows. While this dependence on historical data is understandable, it can give rise to problems when that data is unavailable, unreliable, or shifting. Diverse risk investments: When valuing firms, we generally estimate one discount rate for its aggregate cash flows, partly because of how we estimate risk parameters and partly for convenience. Firms generate cash flows from multiple assets, in different locations, with varying amounts of risk, so the discount rates we use should be different for each set of cash flows. Changes in risk over time: In most valuations, we estimate one discount rate and leave it unchanged over time, again partly for ease and partly because we feel uncomfortable changing discount rates over time. When valuing a firm, though, it is entirely possible, and indeed likely, that its risk will change over time as its asset mix changes and it matures. In fact, if we accept the earlier proposition that the cash flows from growth assets are more difficult to predict than cash flows from existing assets, we should expect the discount rate used on the cumulative expected cash flows of a growth firm to decrease as its growth rate declines over time.

When Will the Firm Become Mature? The question of when a firm will become mature is relevant because it determines the length of the high-growth period and the value we attach to the firm at the end of the period (the terminal value). This question may be easy to answer for a few firms. This includes larger and more stable

4



firms that are either already mature businesses or close to maturity, or firms that derive their growth from a single competitive advantage with an expiration date (for instance, a patent). For most firms, however, the conclusion will be murky for two reasons: Q

Q

Making a judgment about when a firm will become mature requires us to look at the sector in which the firm operates, the state of its competitors, and what they will do in the future. For firms in sectors that are evolving, with new entrants and existing competitors exiting, this is difficult to do. We are sanguine about mapping pathways to the terminal value in discounted cash flow models. We generally assume that every firm makes it to stable growth and goes on. However, the real world delivers surprises along the way that may impede these paths. After all, most firms do not make it to the steady state that we aspire to and instead get acquired, are restructured, or go bankrupt well before the terminal year.

In summary, not only is estimating when a firm will become mature difficult to do, but considering whether a firm will make it as a going concern for a valuation is just as important. Pulling together all four questions, we get a framework for valuing any business, as shown in Figure 1.2. What is the value added by growth assets? When will the firm become a mature firm, and what are the potential roadblocks?

What are the cash flows from existing assets? How risky are the cash flows from both existing assets and growth assets?

Figure 1.2: The Fundamental Questions in Valuation

Although these questions may not change as we value individual firms, the ease with which we can answer them can change. This happens not only as we look across firms at a point in time, but also across time, even for the same firm. Getting from the value of the business to the value of the equity in the business may seem like a simple exercise: subtracting the outstanding debt. But the process can be complicated if the debt is not clearly defined or is contingent on an external event (a claim in a lawsuit). Once we have the value of equity, getting the value of a unit claim in equity (per share value) can be difficult if different equity claims have different voting rights, cash flow claims, or liquidity.

Valuation Across Time Valuing all companies becomes more complicated in an unsettled macroeconomic environment. In fact, three basic inputs into every valuation—the risk-free rate, risk premiums, and overall economic growth (real and nominal)—can be volatile in some cases, making it difficult to value any company. In this section, we will look at the reasons for volatility in these fundamental inputs and how they can affect valuations.

Chapter 1 The Dark Side of Valuation

5


Interest Rates To value a risky asset, we have to answer a fundamental question: What can you expect to earn as a rate of return on a riskless investment? The answer to this question is the risk-free rate. Although we take it as a given in most valuations, it can sometimes be difficult to identify. When the risk-free rate is unknown, everything else in the valuation is open to question as well. To understand why estimating the risk-free rate can be problematic, let us define a risk-free rate. It is the rate of return you can expect to make on an investment with a guaranteed return. For an investment to deliver such a return, it must have no default risk, which is why we use government bond rates as risk-free rates. In addition, the notion of a risk-free rate must be tied to your time horizon as an investor. The guaranteed return for a six-month investment can be very different from the guaranteed return over the next five years. So, what are the potential issues? The first is that, with some currencies, the governments involved either do not issue bonds in those currencies, or the bonds are not traded. This makes it impossible to get a long-term bond rate in the first place. The second issue is that not all governments are default-free, and the potential for default can inflate the rates on bonds issues by these entities, thus making the observed interest rates not risk-free. The third issue is that the riskless rate today may be (or may seem to be) abnormally high or low, relative to fundamentals or history. This leaves open the question of whether we should be locking in these rates for the long term in a valuation.

Market Risk Premiums When valuing individual companies, we draw on market prices for risk for at least two inputs and make them part of every valuation. The first is the equity risk premium. This is the additional return that we assume investors demand for investing in risky assets (equities) as a class, relative to the risk-free rate. In practice, this number is usually obtained by looking at long periods of historical data, with the implicit assumption that future premiums will converge to this number sooner rather than later. The second input is the default spread for risky debt, an input into the cost of debt in valuation. This number is usually obtained by either looking at the spreads on corporate bonds in different ratings classes or looking at the interest rates a company is paying on the debt it has on its books right now. In most valuations, the equity risk premium and default spread are assumed to be either known or a given. Therefore, analysts focus on company-specific inputs—cash flows, growth, and risk— to arrive at an estimate of value. Furthermore, we usually assume that the market prices for risk in both equity and debt markets remain stable over time. In emerging markets, these assumptions are difficult to sustain. Even in mature markets, we face two dangers. The first is that economic shocks can change equity risk premiums and default spreads significantly. If the risk premiums that we use to value companies do not reflect these changes, we risk undervaluing or overvaluing all companies (depending on whether risk premiums have increased or decreased). The second danger is that there are conditions, especially in volatile markets, where the equity risk premium that we estimate for the near term (the next year or two) will be different from the equity risk premium that we believe will hold in the long term (after year 5, for instance). To get realistic valuations of companies, we have to incorporate these expected changes into the estimates we use for future years.

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The Macro Environment It is impossible to value a company without making assumptions about the overall economy in which it operates. Since instability in the economy feeds into volatility in company earnings and cash flows, it is easier to value companies in mature economies, where inflation and real growth are stable. Most of the changes in company value over time, then, come from changes in company-specific inputs. We face a very different challenge when we value companies in economies that are in flux, because changes in the macroeconomic environment can dramatically change values for all companies. In practice, three general macro economic inputs influence value. The first is the growth in the real economy. Changes in that growth rate will affect the growth rates (and values) of all companies, but the effect will be largest for cyclical companies. The second is expected inflation; as inflation becomes volatile, company values can be affected in both positive and negative ways. Companies that can pass through the higher inflation to their customers will be less affected than companies without pricing power. All companies can be affected by how accounting and tax laws deal with inflation. The third and related variable is exchange rates. When converting cash flows from one currency into another, we have to make assumptions about expected exchange rates in the future. We face several dangers when valuing companies in volatile economies. The first is that we fail to consider expected changes in macroeconomic variables when making forecasts. Using today’s exchange rate to convert cash flows in the future, from one currency to another, is an example. The second danger is that we make assumptions about changes in macroeconomic variables that are internally inconsistent. Assuming that inflation in the local currency will increase while also assuming that the currency will become stronger over time is an example. The third danger is that the assumptions we make about macroeconomic changes are inconsistent with other inputs we use in the valuation. For instance, assuming that inflation will increase over time, pushing up expected cash flows, while the risk-free rate remains unchanged, will result in an overvaluation of the company.

Valuation Across the Life Cycle Although the inputs into valuation are the same for all businesses, the challenges we face in making the estimates can vary significantly across firms. In this section, we first break firms into four groups based on where they are in the life cycle. Then we explore the estimation issues we run into with firms in each stage.

The Business Life Cycle Firms pass through a life cycle, starting as young idea companies, and working their way to high growth, maturity, and eventual decline. Because the difficulties associated with estimating valuation inputs vary as firms go through the life cycle, it is useful to start with the five phases that we divide the life cycle into and consider the challenges in each phase, as shown in Figure 1.3. Note that the time spent in each phase can vary widely across firms. Some, like Google and Amazon, speed through the early phases and quickly become growth companies. Others make the adjustment much more gradually. Many growth companies have only a few years of growth before they become mature businesses. Others, such as Coca-Cola, IBM, and Wal-Mart, can


7


stretch their growth periods to last decades. At each phase in the cycle, some companies never make it through, either because they run out of cash and access to capital or because they have trouble making debt payments. Start-Up or Idea Companies

Young Growth

Mature Growth

Mature

Decline

Revenues $ Revenues/ Earnings Earnings

Time Revenues/Current Operations

Nonexistent or Low Revenues/Negative Operating Income

Revenues Increasing/Income Still Low or Negative

Revenues in High Growth/Operating Income Also Growing

Revenue Growth Slows/Operating Income Still Growing

Revenues and Operating Income Growth Drops Off

Operating History

None

Very Limited

Some Operating History

Operating History Can Be Used in Valuation

Substantial Operating History

Comparable Firms

None

Some, but in Same Stage of Growth

More Comparable, at Different Stages

Large Number of Comparables, at Different Stages

Declining Number of Comparables, Mostly Mature

Source of Value

Entirely Future Growth

Mostly Future Growth

Portion from Existing Assets/Growth Still Dominates

More from Existing Assets Than Growth

Entirely from Existing Assets

Figure 1.3: Valuation Issues Across the Life Cycle

Early in the Life Cycle: Young Companies Every business starts with an idea. The idea germinates in a market need that an entrepreneur sees (or thinks he sees) and a way of filling that need. Most ideas go nowhere, but some individuals take the next step of investing in the idea. The capital to finance the investment usually comes from personal funds (from savings, friends, and family), and in the best-case scenario, it yields a commercial product or service. Assuming that the product or service finds a ready market, the business usually needs to access more capital. Usually it is supplied by venture capitalists, who provide funds in return for a share of the equity in the business. Building on the most optimistic assumptions again, success for the investors in the business ultimately is manifested as a public offering to the market or sale to a larger entity. At each stage in the process, we need estimates of value. At the idea stage, the value may never be put down on paper, but it is the potential for this value that induces the entrepreneur to invest both time and money in developing the idea. At subsequent stages of the capital-raising process, the valuations become more explicit, because they determine what the entrepreneur must give up as a share of ownership in return for external funding. At the time of the public offering, the valuation is key to determining the offering price. Using the template for valuation that we developed in the preceding section, it is easy to see why young companies also create the most daunting challenges for valuation. There are few or no existing assets; almost all the value comes from expectations of future growth. The firm’s current

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financial statements provide no clues about the potential margins and returns that will be generated in the future, and little historical data can be used to develop risk measures. To cap the estimation problem, many young firms will not make it to stable growth, and estimating when that will happen for firms that survive is difficult to do. In addition, these firms are often dependent on one or a few key people for their success, so losing them can have significant effects on value. A final valuation challenge we face with valuing equity in young companies is that different equity investors have different claims on the cash flows. The investors with the first claims on the cash flows should have the more valuable claims. Figure 1.4 summarizes these valuation challenges. Making judgments on revenues/profits is difficult because you cannot draw on history. If you have no product/service, it is difficult to gauge market potential or profitability. The company's entire value lies in future growth, but you have little to base your estimate on. Cash flows from existing assets, nonexistent, or negative

What is the value added by growth assets?

What are the cash flows from existing assets? Different claims on cash flows can affect value of equity at each stage. What is the value of equity in the firm?

How risky are the cash flows from both existing assets and growth assets? Limited historical data on earnings and no market prices for securities makes it difficult to assess risk.

When will the firm become a mature firm, and what are the potential roadblocks? Will the firm make it through the gauntlet of market demand and competition? Even if it does, assessing when it will become mature is difficult because there is so little to go on.

Figure 1.4: Valuation Challenges

Given these problems, it is not surprising that analysts often fall back on simplistic measures of value, “guesstimates,” or rules of thumb to value young companies.

The Growth Phase: Growth Companies Some idea companies make it through the test of competition to become young growth companies. Their products or services have found a market niche, and many of these companies make the transition to the public market, although a few remain private. Revenue growth is usually high, but the costs associated with building market share can result in losses and negative cash flows, at least early in the growth cycle. As revenue growth persists, earnings turn positive and often grow exponentially in the first few years. Valuing young growth companies is a little easier than valuing start-up or idea companies. The markets for products and services are more clearly established, and the current financial statements provide some clues to future profitability. Five key estimation issues can still create valuation uncertainty. The first is how well the revenue growth that the company is reporting will scale up. In other words, how quickly will revenue growth decline as the firm gets bigger? The answer will differ across companies and will be a function of both the company’s competitive advantages and the market it serves. The second issue is determining how profit margins will evolve over


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time as revenues grow. The third issue is making reasonable assumptions about reinvestment to sustain revenue growth, with concurrent judgments about the returns on investment in the business. The fourth issue is that as revenue growth and profit margins change over time, the firm’s risk will also shift, with the requirement that we estimate how risk will evolve in the future. The final issue we face when valuing equity in growth companies is valuing options that the firm may grant to employees over time and the effect that these grants have on value per share. Figure 1.5 captures the estimation issues we face in valuing growth companies.

Historical data exists, but growth rates in revenues, operating margins, and other measures of operations are all changing over time.

Although the firm may be growing fast, the key question is whether the firm can scale up growth. In other words, as the firm becomes bigger, how will growth change? New competition will affect margins/returns on new investments. What is the value added by growth assets?

What are the cash flows from existing assets? Options granted to employees and managers can affect value of equity per share.

How risky are the cash flows from both existing assets and growth assets? Risk measures will change as the firm's growth changes.

What is the value of equity in the firm?

When will the firm become a mature firm, and what are the potential roadblocks? Many growth companies do not make it to stable growth. Closely linked to the scaling question is how quickly the firm will hit the wall of stable growth.

Figure 1.5: Estimation Issues in Growth Companies

As firms move through the growth cycle, from young growth to more established growth, some of these questions become easier to answer. The proportion of firm value that comes from growth assets declines as existing assets become more profitable and also accounts for a larger chunk of overall value.

Maturity—a Mixed Blessing: Mature Firms Even the best of growth companies reach a point where size works against them. Their growth rates in revenues and earnings converge on the growth rate of the economy. In this phase, the bulk of a firm’s value comes from existing investments, and financial statements become more informative. Revenue growth is steady, and profit margins have settled into a pattern, making it easier to forecast earnings and cash flows. Although estimation does become simpler with these companies, analysts must consider potential problems. The first is that the results from operations (including revenues and earnings) reflect how well the firm is utilizing its existing assets. Changes in operating efficiency can have a large impact on earnings and cash flows, even in the near term. The second problem is that mature firms sometimes turn to acquisitions to re-create growth potential. Predicting the magnitude and consequences of acquisitions is much more difficult to do than estimating growth

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from organic or internal investments. The third problem is that mature firms are more likely to look to financial restructuring to increase their value. The mix of debt and equity used to fund the business may change overnight, and assets (such as accounts receivable) may be securitized. The final issue is that mature companies sometimes have equity claims with differences in voting right and control claims, and hence different values. Figure 1.6 frames the estimation challenges at mature companies.

Lots of historical data on earnings and cash flows. Key questions remain if these numbers are volatile over time or if the existing assets are not being efficiently utilized.

Growth is usually not very high, but firms may still be generating healthy returns on investments, relative to the cost of funding. Questions include how long they can generate these excess returns and with what growth rate in operations. Restructuring can change both inputs dramatically, and some firms maintain high growth through acquisitions. What is the value added by growth assets?

What are the cash flows from existing assets? Equity claims can vary in voting rights and dividends. What is the value of equity in the firm?

How risky are the cash flows from both existing assets and growth assets?

When will the firm become a mature firm, and what are the potential roadblocks?

Maintaining excess returns or high growth Operating risk should be stable, but the firm for any length of time is can change its financial leverage. This can difficult to do for a affect both the cost of equity and capital. mature firm.

Figure 1.6: Estimation Challenges in Mature Companies

Not surprisingly, mature firms usually are targeted in hostile acquisitions and leveraged buyouts, where the buyer believes that changing how the firm is run can result in significant increases in value.

Winding Down: Dealing with Decline Most firms reach a point in their life cycle where their existing markets are shrinking and becoming less profitable, and the forecast for the future is more of the same. Under these circumstances, these firms react by selling assets and returning cash to investors. Put another way, these firms derive their value entirely from existing assets, and that value is expected to shrink over time. Valuing declining companies requires making judgments about the assets that will be divested over time and the profitability of the assets that will be left in the firm. Judgments about how much cash will be received in these divestitures and how that cash will be utilized (pay dividends, buy back shares, retire debt) can influence the value attached to the firm. Another concern overhangs this valuation. Some firms in decline that have significant debt obligations can become distressed. This problem is not specific to declining firms but is more common with them. Finally, the equity values in declining firms can be affected significantly by the presence of underfunded pension obligations and the overhead of litigation costs—more so than with other firms. Figure 1.7 shows these questions.


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Growth can be negative, as the firm sheds assets and shrinks. As less profitable assets are shed, the firm's remaining assets may improve in quality.

Historical data often reflects flat or declining revenues and falling margins. Investments often earn less than the cost of capital.

What is the value added by growth assets?

What are the cash flows from existing assets? Underfunded pension obligations and litigation claims can lower value of equity. Liquidation preferences can affect value of equity.

How risky are the cash flows from both existing assets and growth assets? Depending upon the risk of the assets being divested and the use of the proceeds from the divestiture (to pay dividends or retire debt), the risk in both the firm and its equity can change.

What is the value of equity in the firm?

When will the firm become a mature firm, and what are the potential roadblocks? There is a real chance, especially with high financial leverage, that the firm will not make it. If it is expected to survive as a going concern, it will be as a much smaller entity.

Figure 1.7: Questions About Decline

Valuing firms in decline poses a special challenge for analysts who are used to conventional valuation models that adopt a growth-oriented view of the future. In other words, assuming that current earnings will grow at a healthy rate in the future or forever will result in estimates of value for these firms that are way too high.

Valuation Across the Business Spectrum The preceding section considered the different issues we face in estimating cash flows, growth rates, risk, and maturity across the business life cycle. In this section, we consider how firms in some businesses are more difficult to value than others. We consider five groups of companies: Q Q Q Q Q

Financial services firms, such as banks, investment banks, and insurance companies Cyclical and commodity businesses Businesses with intangible assets (human capital, patents, technology) Emerging-market companies that face significant political risk Multibusiness global companies

With each group, we examine what it is about the firms within that group that generates valuation problems.

Financial Services Firms While financial services firms have historically been viewed as stable investments that are relatively simple to value, financial crises bring out the dangers of this assumption. In 2008, for instance, the equity values at most banks swung wildly, and the equity at many others, including Lehman Brothers, Bear Stearns, and Fortis, lost all value. It was a wake-up call to analysts who had used fairly simplistic models to value these banks and had missed the brewing problems.

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So what are the potential problems with valuing financial services firms? We can frame them in terms of the four basic inputs into the valuation process: Q

Q

Q

Q

The existing assets of banks are primarily financial, with a good portion being traded in markets. While accounting rules require that these assets be marked to market, these rules are not always consistently applied across different classes of assets. Since the risk in these assets can vary widely across firms, and information about this risk is not always forthcoming, accounting errors feed into valuation errors. The risk is magnified by the high financial leverage at banks and investment banks. It is not uncommon to see banks have debt-to-equity ratios of 30 to 1 or higher, allowing them to leverage up the profitability of their operations. Financial services firms are, for the most part, regulated, and regulatory rules can affect growth potential. The regulatory restrictions on book equity capital as a ratio of loans at a bank influence how quickly the bank can expand over time and how profitable that expansion will be. Changes in regulatory rules therefore have big effects on growth and value, with more lenient (or stricter) rules resulting in more (or less) value from growth assets. Finally, since the damage created by a troubled bank or investment bank can be extensive, it is also likely that problems at these entities will evoke much swifter reactions from authorities than at other firms. A troubled bank will be quickly taken over to protect depositors, lenders, and customers, but the equity in the banks will be wiped out in the process. As a final point, getting to the value of equity per share for a financial services firm can be complicated by the presence of preferred stock, which shares characteristics with both debt and equity. Figure 1.8 summarizes the valuation issues at financial services firms.

Existing assets are usually financial assets or loans, often marked to market. Earnings do not provide much information on underlying risk.

Growth can be strongly influenced by regulatory limits and constraints. Both the amount of new investments and the returns on these investments can change with regulatory changes. What is the value added by growth assets?

What are the cash flows from existing assets? Preferred stock is a significant source of capital. What is the value of equity in the firm?

How risky are the cash flows from both existing assets and growth assets? Most financial service firms have high financial leverage, magnifying their exposure to operating risk. If operating risk changes significantly, the effects will be magnified on equity.

When will the firm become a mature firm, and what are the potential roadblocks? In addition to all the normal constraints, financial service firms also have to worry about maintaining capital ratios that are acceptable to regulators. If they do not, they can be taken over and shut down.

Figure 1.8: Valuation Issues at Financial Services Firms

Analysts who value banks go through cycles. In good times, they tend to underestimate the risk of financial crises and extrapolate from current profitability to arrive at higher values for financial


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services firms. In crises, they lose perspective and mark down the values of both healthy and unhealthy banks, without much discrimination.

Cyclical and Commodity Companies If we define a mature company as one that delivers predictable earnings and revenues, period after period, cyclical and commodity companies will never be mature. Even the largest, most established of them have volatile earnings. The earnings volatility has little to do with the company. It is more reflective of variability in the underlying economy (for cyclical firms) or the base commodity (for a commodity company). The biggest issue with valuing cyclical and commodity companies lies in the base year numbers that are used in valuation. If we do what we do with most other companies and use the current year as the base year, we risk building into our valuations the vagaries of the economy or commodity prices in that year. As an illustration, valuing oil companies using earnings from 2007 as a base year will inevitably result in too high a value. The spike in oil prices that year contributed to the profitability of almost all oil companies, small and large, efficient and inefficient. Similarly, valuing housing companies using earnings and other numbers from 2008, when the economy was drastically slowing down, will result in values that are too low. The uncertainty we feel about base year earnings also percolates into other parts of the valuation. Estimates of growth at cyclical and commodity companies depend more on our views of overall economic growth and the future of commodity prices than they do on the investments made at individual companies. Similarly, risk that lies dormant when the economy is doing well and commodity prices are rising can manifest itself suddenly when the cycle turns. Finally, for highly levered cyclical and commodity companies, especially when the debt was accumulated during earnings upswings, a reversal of fortune can very quickly put the firm at risk. In addition, for companies like oil companies, the fact that natural resources are finite—only so much oil is under the ground—can put a crimp in what we assume about what happens to the firm during stable growth. Figure 1.9 shows the estimation questions. Company growth often comes from movements in the economic cycle for cyclical firms, or commodity prices for commodity companies. What is the value added by growth assets? What are the cash flows from existing assets? Historical revenue and earnings data are volatile, as the economic cycle and commodity prices change.

How risky are the cash flows from both existing assets and growth assets? Primary risk is from the economy for cyclical firms and from commodity price movements for commodity companies. These risks can stay dormant for long periods of apparent prosperity.

When will the firm become a mature firm, and what are the potential roadblocks? For commodity companies, the fact that there are only finite amounts of the commodity may put a limit on growth forever. For cyclical firms, there is the peril that the next recession may put an end to the firm.

Figure 1.9: Estimation Questions for Cyclical and Commodity Companies

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When valuing cyclical and commodity companies, analysts often make implicit assumptions about the economy and commodity prices by extrapolating past earnings and growth rates. Many of these implicit assumptions turn out to be unrealistic, and the valuations that lead from them are equally flawed.

Businesses with Intangible Assets In the last two decades, we have seen mature economies, such as the U.S. and Western Europe, shift from manufacturing to services and technology businesses. In the process, we have come to recognize how little of the value at many of our largest companies today comes from physical assets (like land, machinery, and factories) and how much of the value comes from intangible assets. Intangible assets range from brand name at Coca-Cola to technological know-how at Google and human capital at firms like McKinsey. As accountants grapple with how best to deal with these intangible assets, we face similar challenges when valuing them. Let us state at the outset that there should be no reason why the tools that we have developed over time for physical assets cannot be applied to intangible assets. The value of a brand name or patent should be the present value of the cash flows from that asset, discounted at an appropriate risk-adjusted rate. The problem that we face is that the accounting standards for firms with intangible assets are not entirely consistent with the standards for firms with physical assets. An automobile company that invests in a new plant or factory is allowed to treat that expenditure as a capital expenditure, record the item as an asset, and depreciate it over its life. A technology firm that invests in research and development, with the hope of generating new patents, is required to expense the entire expenditure and record no assets, and it cannot amortize or depreciate the item. The same can be said of a consumer products company that spends millions on advertising with the intent of building a brand name. The consequences for estimating the basic inputs for valuation are profound. For existing assets, the accounting treatment of intangible assets makes both current earnings and book value unreliable. The former is net of R&D, and the latter does not include investments in the firm’s biggest assets. Since reinvestment and accounting return numbers are flawed for the same reasons, assessing expected growth becomes more difficult. Since lenders tend to be wary about lending to firms with intangible assets, they tend to be funded predominantly with equity, and the risk of equity can change quickly over a firm’s life cycle. Finally, estimating when a firm with intangible assets gets to steady state can be complex. On the one hand, easy entry into and exit from the business and rapid changes in technology can cause growth rates to drop quickly at some firms. On the other hand, the long life of some competitive advantages like brand name and the ease with which firms can scale up (they do not need heavy infrastructure or physical investments) can allow other firms to maintain high growth, with excess returns, for decades. The problems that we face in valuing companies with intangible assets are shown in Figure 1.10. When faced with valuing firms with intangible assets, analysts tend to use the accounting earnings and book values at these firms, without correcting for the miscategorization of capital expenditures. Any analyst who compares the price earnings (PE) ratio for Microsoft to the PE ratio for GE is guilty of this error. In addition, there is also the temptation, when doing valuations, to add arbitrary premiums to estimated value to reflect the value of intangibles. Thus, adding a 30% premium to the value estimate of Coca-Cola is not a sensible way of capturing the value of a brand name.


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If capital expenditures are miscategorized as operating expenses, it becomes very difficult to assess how much a firm is reinvesting for future growth and how well its investments are doing. What is the value added by growth assets? What are the cash flows from existing assets? The capital expenditures associated with acquiring intangible assets (technology, human capital) are miscategorized as operating expenses, leading to incorrect accounting earnings and measures of capital invested.



Intangible assets such as brand name and customer It can be more difficult to borrow against loyalty can last for very long intangible assets than it is against tangible periods or dissipate assets. The risk in operations can change overnight. depending upon how stable the intangible asset is.

Figure 1.10: Questions About Valuing Companies with Intangible Assets

Emerging-Market Companies In the last decade, the economies that have grown the fastest have been in Asia and Latin America. With that growth, we have also seen an explosion of listings in financial markets in these emerging economies and increased interest in valuing companies in these markets. In valuing emerging-market companies, the overriding concern that analysts have is that the risk of the countries that these companies operate in often overwhelms the risk in the companies themselves. Investing in a stable company in Argentina will still expose you to considerable risk, because country risk swings back and forth. While the inputs to valuing emerging-market companies are familiar—cash flows from existing and growth assets, risk and getting to stable growth— country risk creates estimation issues with each input. Variations in accounting standards and corporate governance rules across emerging markets often result in a lack of transparency when it comes to current earnings and investments, making it difficult to assess the value of existing assets. Expectations of future growth rest almost as much on how the emerging market that the company is located in will evolve as they do on the company’s own prospects. Put another way, it is difficult for even the best-run emerging-market company to grow if the market it operates in is in crisis. In a similar vein, the overlay of country risk on company risk indicates that we have to confront and measure both if we want to value emerging-market companies. Finally, in addition to economic crises that visit emerging markets at regular intervals, putting all companies at risk, there is the added risk that companies can be nationalized or appropriated by the government. The challenges associated with valuing emerging-market companies are shown in Figure 1.11. Analysts who value emerging-market companies develop their own coping mechanisms for dealing with the overhang of country risk, with some mechanisms being healthier than others. In its most unhealthy form, analysts avoid even dealing with the risk. They switch to more stable

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currencies for their valuations and adopt very simple measures of country risk, such as adding a fixed premium to the cost of capital to every company in a market. In other cases, their preoccupation with country risk leads them to double-count and triple-count the risk and pay insufficient attention to the company being valued. Big shifts in economic environment (inflation, interest rates) can affect operating earnings history. Poor corporate governance and weak accounting standards can lead to lack of transparency on earnings.

Growth rates for a company will be affected heavily by growth rate and political developments in the country in which it operates. What is the value added by growth assets?

What are the cash flows from existing assets? Cross holdings can affect value of equity. What is the value of equity in the firm?

How risky are the cash flows from both existing assets and growth assets? Even if the company's risk is stable, there can be significant changes in country risk over time.

When will the firm become a mature firm, and what are the potential roadblocks? Economic crises can put many companies at risk. Government actions (nationalization) can affect long-term value.

Figure 1.11: Challenges Associated with Valuing Emerging-Market Companies

Multibusiness and Global Companies As investors globalize their portfolios, companies are also becoming increasingly globalized, with many of the largest ones operating in multiple businesses. Give that these businesses have very different risk and operating characteristics, valuing the multibusiness global company can be a challenge to even the best-prepared analyst. The conventional approach to valuing a company has generally been to work with the consolidated earnings and cash flows of the business and to discount those cash flows using an aggregated risk measure for the company that reflects its mix of businesses. Although this approach works well for firms in one or a few lines of business, it becomes increasingly difficult as companies spread their operations across multiple businesses in multiple markets. Consider a firm like General Electric, a conglomerate that operates in dozens of businesses and in almost every country around the globe. The company’s financial statements reflect its aggregated operations, across its different businesses and geographic locations. Attaching a value to existing assets becomes difficult, since these assets vary widely in terms of risk and return-generating capacity. While GE may break down earnings for its different business lines, those numbers are contaminated by the accounting allocation of centralized costs and intrabusiness transactions. The expected growth rates can be very different for different parts of the business, in terms of not only magnitude but also quality. Furthermore, as the firm grows at different rates in different businesses, its overall risk changes to reflect the new business weights, adding another problem to valuation. Finally, different pieces of the company may approach stable growth at different points in time, making it difficult to stop and assess the terminal value. Figure 1.12 summarizes the estimation questions that we have to answer for complex companies.


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Growth rates can vary widely across businesses and across countries. Trying to estimate "one" growth rate for a firm can be difficult to do. What is the value added by growth assets? What are the cash flows from existing assets? The firm reports aggregate earnings from its investments in many businesses and many countries as well as in many currencies. Breakdown of earnings and operating variables can be either incomplete or misleading.



Different parts of the company will reach stable Because risk can vary widely depending growth at different points upon the cash flow stream, estimating one in time. cost of equity and capital for a multibusiness, global company that can be maintained over time is an exercise in futility.

Figure 1.12: Estimation Questions for Complex Companies

Analysts who value multibusiness and global companies often draw on the averaging argument to justify not knowing as much as they should about individual businesses. Higher growth (or risk) in some businesses will be offset by lower growth (or risk) in other businesses, they argue, thus justifying their overall estimates of growth and risk. They underestimate the dangers of the unknown. All too often, with companies like these, what you do not know is more likely to contain bad news than good news.

Seeing the Dark Side of Valuation When confronted with estimation challenges, analysts have one of two choices. The healthy response is to confront the challenge and adapt existing models to reflect the differences in the company being valued. The more common response is to bend the rules of valuation and use shortcuts to justify whatever price they are predisposed to pay for the company. The latter approach is “the dark side of valuation.” This section looks at its many manifestations.

Input Phase In the input phase, we look for the standard starting points for valuing individual companies— earnings and operating details from the most recent financial statements; forecasts for the future, provided by analysts and management; and data for macroeconomic inputs such as risk-free rates, risk premiums, and exchange rates. We see some standard patterns in valuations: Q

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Base year fixation: Analysts often treat the current year as the base year in valuation and build these numbers in making forecasts. While this is understandable, it can also lead to serious errors in valuation when either of the following occurs: Q Current numbers do not reflect the firm’s long-term earnings capability. As we noted earlier, this is especially true of commodity and cyclical companies, but it is also the case for young and start-up companies.



Inconsistencies in the accounting treatment of operating and capital expenditures are skewing current values for earnings and book value. With technology and human capital companies, this will be an issue. Outsourcing key inputs: When it comes to macroeconomic inputs, analysts usually go to outside sources. This is especially true with equity risk premiums and betas, where services offer estimates of the numbers, backed up by volumes of data. While this may give analysts someone else to blame if things go wrong, it also means that little independent thought goes into whether the numbers being used actually make sense. Q

Q

Q

Trusting management forecasts: The most difficult task in valuing a company is forecasting future revenues, earnings, and reinvestment. This is especially true with younger companies that have significant growth prospects. When managers offer to provide forecasts of these numbers, analysts, not surprisingly, jump at the opportunity and rationalize their use of these forecasts by arguing that managers know more about the company than they do. What they fail to consider is that these forecasts are likely to be biased.

Valuation Phase The inputs feed into valuation models and metrics to provide the final judgments on value. At this stage in the process, it is natural for analysts to feel uncertain about the reliability of these numbers—more so for some companies than others. In the process of dealing with this uncertainty, some common errors show up in valuations: Q

Q

Q

Q

Ignoring the scaling effect: As firms get larger, it becomes more and more difficult to maintain high growth rates. In making forecasts, analysts often fail to consider this reality and continue to use growth rates derived from history long into their forecast periods. Inconsistencies in valuation: Good valuations should be internally consistent, but it is easy for inconsistencies to enter valuations. As you will see in the coming chapters, assumptions about growth, reinvestment, and risk not only have to make sense individually but also have to tie together. Estimating high growth rates with little or no reinvestment into the business to generate this growth may be possible, but it is unlikely. The assumptions that we make about inflation in our cash flow estimates have to be consistent with the assumptions (often implicit) about expected inflation in interest rates and exchange rates. Valuing for the exception: Analysts often draw on anecdotal evidence to justify their assumptions. The fact that Wal-Mart was able to continue growing, even as it became larger, is used to justify maintaining high revenue growth rates for firms for long periods. Analysts point to companies like Coca-Cola and Microsoft to justify assumptions about maintaining high margins and returns on investment for small-growth companies. It is worth nothing that Wal-Mart, Coca-Cola, and Microsoft are the exceptions, rather than the rule. Paradigm shifts: When analysts abandon age-old principles of economics and valuation, talking about how the rules have changed, it is time to be skeptical. It is true that economies and markets change, and we have to change with them. But we cannot repeal


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Q

Q

the laws of demand and supply or the notion that businesses eventually have to make money to be valuable. Black-box models: As data becomes more easily accessible and building bigger models becomes more feasible, one response to uncertainty is to build bigger and more complex models. Two problems come out of more detailed models. One is the fact that they require far more inputs to arrive at a number. Uncertainty often multiplies as we add more detail, and it is “garbage in, garbage out.” The other problem is that the model becomes a black box, with analysts having little sense of what happens inside the box. Rules of thumb: If one response to complexity is to build bigger and better models, the other response is to look for a simple solution. In many valuations, this takes the form of using a rule of thumb to arrive at the value of an asset. An analyst faced with a particularly troublesome set of inputs may decide to value a company at three times revenues because that is what investors have traditionally paid for companies in this sector. While using these shortcuts may provide the illusion of precision, it is far better to confront uncertainty than to ignore it.

Post-Valuation Phase In many cases, the real damage to valuation principles occurs after the valuation has been done— at least in terms of mechanics. At least two common practices wreak havoc on valuations: Q

Q

Valuation garnishing: This is the all-too-common practice of adding premiums and discounts to estimated value to reflect what the analyst believes are missed components. It is not uncommon in acquisition valuations, for instance, to add a 20% premium for control, just as it is standard practice in private company valuation to reduce value by 20 to 25% to reflect illiquidity. Similar premiums/discounts are added/subtracted to reflect the effects of brand names and other intangibles and emerging-market risk. The net result of these adjustments is that the value reflects whatever preconceptions the analyst might have had about the company. Market feedback: With publicly traded companies, the first number that we look at after we have done a valuation is the market price. When analysts are uncertain about the numbers that go into their valuations, big differences between the value and the market price lead to their revisiting the valuation. As inputs change, the value drifts inexorably toward the market price, rendering the entire process pointless. If we believe that markets are right, why bother doing valuation in the first place?

In summary, the dark side of valuation can take many different forms, but the end result is always the same. The valuations we arrive at for individual businesses reflect the errors and biases we have built into the process. All too often, we find what we want to find rather than the truth.

Conclusion Some companies are easier to value than others. When we have to leave the comfort zone of companies with solid earnings and predictable futures, we invariably stray into the dark side of valuation. Here we invent new principles, violate established ones, and come up with unsustainable values for businesses.

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This chapter described the four inputs that we have to estimate to value any company: Q Q Q Q

The expected cash from investments that the business has already made (existing assets) The value that will be added by new investments (growth assets) The risk in these cash flows The point in time where we expect the firm to become a mature firm

The estimation challenges we face will vary widely across companies, so we must consider how estimation issues vary across a firm’s life cycle. For young and start-up firms, the absence of historical data and the dependence on growth assets make estimating future cash flows and risk particularly difficult. With growth firms, the question shifts to whether growth rates can be maintained and, if so, for how long, as firms scale up. With mature firms, the big issue in valuation shifts to whether existing assets are being efficiently utilized and whether the financial mix used by the firm makes sense. Restructuring the firm to make it run better may dramatically alter value. For declining firms, estimating revenues and margins as assets get divested is messy, and considering the possibility of default can be tricky. The estimation challenges we face can also be different for different subsets of companies. Cyclical and commodity companies have volatile operating results. Companies with intangible assets have earnings that are skewed by how accountants treat investments in these assets. The risk in emerging-market and global companies can be difficult to assess. Finally, valuing any company can become more difficult in economies where the fundamentals—risk-free rates, risk premiums, and economic growth—are volatile. In the last part of the chapter, we turned our attention to how analysts respond to uncertainty, with an emphasis on some of the more unhealthy responses. The dark side of valuation manifests itself at each phase of a valuation; our task for the rest of the book is clear. Accepting the fact that uncertainty will always be with us and that we have to sometimes value “difficult” businesses, we will look at healthy ways of responding to uncertainty.


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2 Intrinsic Valuation very asset that generates cash flows has an intrinsic value that reflects both its cash flow potential and its risk. Many analysts claim that when significant uncertainty about the future exists, estimating intrinsic value becomes not just difficult but pointless. But we disagree. Notwithstanding this uncertainty, we believe that it is important to look past market perceptions and gauge, as best we can, the intrinsic value of a business or asset. This chapter considers how discounted cash flow valuation models attempt to estimate intrinsic value and describes estimation details and possible limitations.

E

Discounted Cash Flow Valuation In discounted cash flow (DCF) valuation, an asset’s value is the present value of the expected cash flows on the asset, discounted back at a rate that reflects the riskiness of these cash flows. This section looks at the foundations of the approach and some of the preliminary details of how we estimate its inputs.

The Essence of DCF Valuation We buy most assets because we expect them to generate cash flows for us in the future. In discounted cash flow valuation, we begin with a simple proposition. The value of an asset is not what someone perceives it to be worth; it is a function of the expected cash flows on that asset. Put simply, assets with high and predictable cash flows should have higher values than assets with low and volatile cash flows. The notion that the value of an asset is the present value of the cash flows that you expect to generate by holding it is neither new nor revolutionary. The earliest interest rate tables date back to 1340, and the intellectual basis for discounted cash flow valuation was laid by Alfred Marshall and Bohm-Bawerk in the early part of the twentieth century.1 The principles of modern valuation were developed by Irving Fisher in two books—The Rate of Interest in 1907 and The Theory of Interest in 1930.2 In these books, he presented the notion of the internal rate of return. In the last 50 years, we have seen discounted cash flow models extend their reach into security and business valuation, and the growth has been aided and abetted by developments in portfolio theory.

1

Marshall, A., 1907, Principles of Economics, Macmillan, London; Bohm-Bawerk, A. V., 1903, Recent Literature on Interest, Macmillan.

2

Fisher, I., 1907, The Rate of Interest, Macmillan, New York; Fisher, I., 1930, The Theory of Interest, Macmillan, New York.

22 From the Library of Melissa Wong

Using discounted cash flow models is in some sense an act of faith. We believe that every asset has an intrinsic value, and we try to estimate that intrinsic value by looking at an asset’s fundamentals. What is intrinsic value? Consider it the value that would be attached to an asset by an all-knowing analyst with access to all information available right now and a perfect valuation model. No such analyst exists, of course, but we all aspire to be as close as we can to this perfect analyst. The problem lies in the fact that none of us ever gets to see the true intrinsic value of an asset. Therefore, we have no way of knowing whether our discounted cash flow valuations are close to the mark.

Equity Versus Firm Valuation Of the approaches for adjusting for risk in discounted cash flow valuation, the most common one is the risk-adjusted discount rate approach. Here we use higher discount rates to discount expected cash flows when valuing riskier assets and lower discount rates when valuing safer assets. We can approach discounted cash flow valuation in two ways, and they can be framed in terms of the financial balance sheet introduced in Chapter 1, “The Dark Side of Valuation.” The first is to value the entire business, with both existing assets (assets-in-place) and growth assets; this is often called firm or enterprise valuation. Figure 2.1 shows an example. Firm Valuation Assets Cash flows considered are cash flows from assets, prior to any debt payments but after the firm has reinvested to create growth assets.

Liabilities

Assets in Place

Debt

Growth Assets

Equity

Discount rate reflects the cost of raising both debt and equity financing, in proportion to their use.

Present value is the value of the entire firm and reflects the value of all claims on the firm.

Figure 2.1: Valuing a Firm (Business)

The cash flows before debt payments and after reinvestment needs are called free cash flows to the firm, and the discount rate that reflects the composite cost of financing from all sources of capital is the cost of capital. The second way is to value just the equity stake in the business; this is called equity valuation. Figure 2.2 shows an example. The cash flows after debt payments and reinvestment needs are called free cash flows to equity, and the discount rate that reflects just the cost of equity financing is the cost of equity. With publicly traded firms, it can be argued that the only cash flow equity investors get from the firm is dividends, and that discounting expected dividends back at the cost of equity should yield the value of equity in the firm. Note also that we can always get from the former (firm value) to the latter (equity value) by netting out the value of all nonequity claims from firm value. Done right, the value of equity should

Chapter 2 Intrinsic Valuation

23


be the same whether it is valued directly (by discounting cash flows to equity at the cost of equity) or indirectly (by valuing the firm and subtracting the value of all nonequity claims). Equity Valuation Assets

Liabilities

Assets in Place Cash flows considered are cash flows from assets, after debt payments and after making reinvestments needed for future growth.

Debt Discount rate reflects only the cost of raising equity financing.

Growth Assets

Equity

Present value is the value of just the equity claims on the firm.

Figure 2.2: Valuing Equity

Inputs to a DCF Valuation While we can choose to value just the equity or the entire business, we need four basic inputs for a value estimate. How we define the inputs will differ depending on whether we do firm or equity valuation. Figure 2.3 summarizes the determinants of value. Growth from New Investments Growth created by making new investments; function of amount and quality of investments

Efficiency Growth Growth generated by using existing assets better

Expected Growth During High-Growth Period

Current Cash Flows Cash flows from existing investments, net of any reinvestments needed to sustain future growth; can be computed before debt cash flows (to the firm) or after debt cash flows (to equity investors)

Terminal Value of the Firm (Equity) Stable growth firm, with no or very limited excess returns

Length of the High-Growth Period Since value-creating growth requires excess returns, this is a function of -Magnitude of competitive advantages -Sustainability of competitive advantages

Cost of Financing (Debt or Capital) to Apply to Discounting Cash Flows Determined by -Operating risk of the company -Default risk of the company -Mix of debt and equity used in financing

Figure 2.3: Determinants of Value

The first input is the cash flow from existing assets. This is defined as either pre-debt (and to the firm) or post-debt (and to equity) earnings, net of reinvestment to generate future growth. With equity cash flows, we can use an even stricter definition of cash flow and consider only dividends paid. The second input is growth. Growth in operating income is the key input when valuing the entire business. Growth in equity income (net income or earnings per share) is the focus when

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valuing equity. The third input is the discount rate. This is defined as the cost of the firm’s overall capital when valuing the business and as cost of equity when valuing equity. The final input, allowing for closure, is the terminal value, defined as the firm’s (equity’s) estimated value at the end of the forecast period in firm (equity) valuation. The rest of this section will focus on estimating the inputs into discounted cash flow models. We will start with cash flows and then move on to risk (and discount rates). We will close with a discussion of how best to estimate the growth rate for the high-growth period and the value at the end of that period.

Cash Flows Leading up to this section, we noted that cash flows can be estimated either to just equity investors (cash flows to equity) or to all suppliers of capital (cash flows to the firm). This section begins with the strictest measure of cash flow to equity—the dividends received by investors. Then it will move to more expansive measures of cash flows, which generally require more information.

Dividends When an investor buys stock in a publicly traded company, he generally expects to get two types of cash flows—dividends during the holding period, and an expected price at the end of the holding period. Since this expected price is itself determined by future dividends, the value of a stock is the present value of just expected dividends. If we accept this premise, the only cash flow to equity that we should be considering in valuation is the dividend paid. Estimating that dividend for the last period should be a simple exercise. Since many firms do not pay dividends, this number can be zero, at least for the near term, but it should never be negative.

Augmented Dividends One of the limitations of focusing on dividends is that many companies, especially in the U.S. but increasingly around the world, have shifted from dividends to stock buybacks as their mechanism for returning cash to stockholders. While only stockholders who sell back their stock receive cash, it still represents cash returned to equity investors. In 2007, for instance, firms in the U.S. returned twice as much cash in the form of stock buybacks as they did in dividends. Focusing only on dividends will result in the undervaluation of equity. One simple way of adjusting for this is to augment the dividend with stock buybacks and look at the cumulative cash returned to stockholders: Augmented Dividends = Dividends + Stock Buybacks One problem, though, is that unlike dividends that are smoothed out over time, stock buybacks can spike in some years and be followed by years of inaction. Therefore, we must normalize buybacks by using average buybacks over a period of time (say, five years) to arrive at more reasonable annualized numbers.

Potential Dividends (Free Cash Flow to Equity) With both dividends and augmented dividends, we trust managers at publicly traded firms to return to pay out to stockholders any excess cash left over after meeting operating and reinvestment needs. However, we do know that managers do not always follow this practice, as evidenced


25


by the large cash balances that you see at most publicly traded firms. To estimate what managers could have returned to equity investors, we develop a measure of potential dividends that we call the free cash flow to equity. Intuitively, this measures the cash left over after taxes, reinvestment needs, and that debt cash flows have been met. It is measured as follows: FCFE = Net Income – Reinvestment Needs – Debt Cash Flows = Net Income – (Capital Expenditures – Depreciation + Change in Noncash Working Capital) – (Principal Repayments – New Debt Issues) Consider the equation in pieces. We begin with net income, since that is the earnings generated for equity investors; it is after interest expenses and taxes. We compute what the firm has to reinvest in two parts: Q

Q

Reinvestment in long-lived assets is measured as the difference between capital expenditures (the amount invested in long-lived assets during the period) and depreciation (the accounting expense generated by capital expenditures in prior periods). We net the latter because it is not a cash expense and hence can be added back to net income. Reinvestment in short-lived assets is measured by the change in noncash working capital (Δ working capital). In effect, increases in inventory and accounts receivable represent cash tied up in assets that do not generate returns—wasting assets. The reason we don’t consider cash in the computation is because we assume that companies with large cash balances generally invest them in low-risk, marketable securities like commercial paper and Treasury bills. These investments earn a low but fair rate of return and therefore are not wasting assets.3 To the extent that they are offset by the use of supplier credit and accounts payable, the effect on cash flows can be muted. The overall change in noncash working capital therefore is investment in short-term assets.

Reinvestment reduces cash flow to equity investors, but it provides a payoff in terms of future growth. We will reconsider whether the net effect is positive or negative after we consider how best to estimate growth. The final input into the process are the negative cash flows associated with the repayment of old debt and the positive cash flows to equity investors from raising new debt. If old debt is replaced with new debt of exactly the same magnitude, this term will be zero, but it will generate positive (or negative) cash flows when debt issues exceed (or are less than) debt repayments. Focusing on just debt cash flows allows us to zero in on a way to simplify this computation. In the special case where the capital expenditures and working capital are expected to be financed at a fixed debt ratio δ, and principal repayments are made from new debt issues, the FCFE is measured as follows: FCFE = Net Income + (1 – δ) (Capital Expenditures – Depreciation) + (1 – δ) Δ Working Capital

3

26

Note that we do not make the distinction between operating and nonoperating cash that some analysts do (they proceed to include operating cash in working capital). Our distinction is between wasting cash (which would include currency or cash earning below-market rate returns) and nonwasting cash. We are assuming that the former will be a small or negligible number at a publicly traded company.



In effect, we are assuming that a firm with a 30% debt ratio that is growing through reinvestment will choose to fund 30% of its reinvestment needs with new debt and replace old debt that comes due with new debt. There is one more way in which we can present the free cash flow to equity. If we define the portion of the net income that equity investors reinvest into the firm as the equity reinvestment rate, we can state the FCFE as a function of this rate: Equity Reinvestment Rate (Capital Expenditures – Depreciation + Δ Working Capital) (1 – δ) = Net Income FCFE = Net Income (1 – Equity Reinvestment Rate)

A final note is needed on the contrast between the first two measures of cash flows to equity (dividends and augmented dividends) and this measure. Unlike those measures, which can never be less than zero, the free cash flow to equity can be negative for a number of reasons. The first is that the net income could be negative, a not-uncommon phenomenon even for mature firms. The second reason is that reinvestment needs can overwhelm net income, which is often the case for growth companies, especially early in the life cycle. The third reason is that large debt repayments coming due that have to be funded with equity cash flows can cause negative FCFE. Highly levered firms that are trying to bring down their debt ratios can go through years of negative FCFE. The fourth reason is that the quirks of the reinvestment process, where firms invest large amounts in long-lived and short-lived assets in some years and nothing in others, can cause the FCFE to be negative in the big reinvestment years and positive in others. As with buybacks, we have to consider normalizing reinvestment numbers across time when estimating cash flows to equity. If the FCFE is negative, the firm needs to raise fresh equity.

Cash Flow to the Firm The cash flow to the firm should be both after taxes and after all reinvestment needs have been met. Since a firm raises capital from debt and equity investors, the cash flow to the firm should be before debt cash flows—interest expenses, debt repayments, and new debt issues. The cash flow to the firm can be measured in two ways. One is to add up the cash flows to all the different claim holders in the firm. Thus, the cash flows to equity investors (estimated using one of the three measures described in this section) are added to the cash flows to debt holders (interest and net debt payments) to arrive at the cash flow. The other approach is to start with operating earnings and to estimate the cash flows to the firm prior to debt payments but after reinvestment needs have been met: Free Cash Flow to Firm (FCFF) = After-Tax Operating Income – Reinvestment = After-Tax Operating Income – (Capital Expenditures – Depreciation + Δ Working Capital) It is easiest to understand FCFF by contrasting it with FCFE. First, we begin with after-tax operating income instead of net income. The former is before interest expenses, whereas the latter is after interest expenses. Second, we adjust the operating income for taxes, computed as if we were


27


taxed on the entire income, whereas net income is already an after-tax number.4 Third, while we subtract reinvestment, just as we did to arrive at free cash flows to equity, we do not net out the effect of debt cash flows, since we are now looking at cash flows to all capital, not just to equity. Another way of presenting the same equation is to cumulate the net capital expenditures and working capital change into one number and state it as a percentage of the after-tax operating income. This ratio of reinvestment to after-tax operating income is called the reinvestment rate, and the free cash flow to the firm can be written as follows: Reinvestment Rate =

(Capital Expenditures – Depreciation + Δ Working Capital) After-Tax Operating Income

Free Cash Flow to the Firm = EBIT (1 – t) (1 – Reinvestment Rate)

Note that the reinvestment rate can exceed 100%5 if the firm has substantial reinvestment needs. The reinvestment rate can also be less than zero for firms that are divesting assets and shrinking capital. A few final thoughts about free cash flow to the firm are worth noting before we move on to discount rates. First, the free cash flow to the firm can be negative, just as the FCFE can, but debt cash flows can no longer be the culprit. Even highly levered firms that are paying down debt will report positive FCFF while also registering negative FCFE. If the FCFF is negative, the firm will raise fresh capital, with the mix of debt and equity being determined by the mix used to compute the cost of capital. Second, the cash flow to the firm is the basis for all cash distributions made by the firm to its investors. Dividends, stock buybacks, interest payments, and debt repayments all have to be made out of these cash flows.

Estimating Cash Flows for a Firm: 3M in 2007 Minnesota Mining and Manufacturing (3M) is a large market capitalization company with operations in transportation, health care, office supplies, and electronics. • In 2007, the firm reported operating income, before taxes, of $5,344 million and net income of $4,096 million. Interest expenses for the year amounted to $210 million, and interest income on cash and marketable securities was $132 million. The firm also paid dividends of $1,380 million during the year and bought back $3,239 million of stock. The effective tax rate during the year was 32.1%, but the marginal tax rate is 35%.

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4

In effect, when computing taxes on operating income, we act like we have no interest expenses or tax benefits from those expenses while computing the cash flow. This is because we will be counting the tax benefits from debt in the cost of capital (through the use of an after-tax cost of debt). If we use actual taxes paid or reflect the tax benefits from interest expenses in the cash flows, we are double-counting its effect.

5

In practical terms, this firm will have to raise external financing, either from debt or equity or both, to cover the excess reinvestment.



• During 2007, 3M reported $1,422 million in capital expenditures and cash acquisitions of $539 million. The depreciation and amortization charges for the year amounted to $1,072 million. The noncash working capital increased by $243 million during 2007. • Finally, 3M repaid $2,802 million of debt during the year but raised $4,024 million in new debt. With this data, we can first estimate the free cash flows to equity, as shown in Figure 2.4. Net capital expenditures includes acquisitions.

Net Income = – (Capital Expenditures – Depreciation) = – Change in Noncash Working Capital = + Net Debt Issued (Paid) = FCFE

$4,010 – $889 – $243 + $1,222 = $4,100

Working capital increases drained cash flows.

Total Equity Reinvestment = 889 + 243 –1222 = - 90 Equity Reinvestment Rate = -90/4010 = -2.27%

Figure 2.4: Free Cash Flows to Equity

Note that the net debt issued reflects the new debt issues, netted out against debt repaid. The free cash flow to the firm for 2007 can also be computed, as shown in Figure 2.5. Net capital expenditures includes acquisitions.

EBIT (1–t) – (Capital Expenditures – Depreciation) – Change in Noncash Working Capital Free Cash Flow to the Firm (FCFF)

$3,474 – $889 – $243 = $2,342

Working capital increases drained cash flows.

Total Reinvestment = 889 + 243 = 1132 Equity Reinvestment Rate = 1132/3474= 36.37%

Figure 2.5: Free Cash Flow to 3M

Figure 2.6 summarizes all four estimates of cash flows for 3M for 2007—dividends, augmented dividends, free cash flows to equity, and free cash flows to the firm.


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$5,000 $4,500 $4,000 $3,500 $3,000 $2,500 $2,000 $1,500 $1,000 $500 $0

Dividends

Dividends + Buybacks

FCFE

FCFF

Figure 2.6: Comparison of Cash Flow Estimates: 3M in 2007

How can we reconcile these very different numbers? During 2007, 3M increased its borrowing and used the funds from the additional debt and cash accumulated in prior years to buy back stock.

Risk Cash flows that are riskier should be assessed a lower value than more stable cash flows, but how do we measure risk and reflect it in value? In conventional discounted cash flow valuation models, the discount rate becomes the vehicle for conveying our concerns about risk. We use higher discount rates on riskier cash flows and lower discount rates on safer cash flows. This section begins by contrasting how the risk in equity can vary from the risk in a business. Then it considers the mechanics of estimating the cost of equity and capital.

Business Risk Versus Equity Risk Before we delve into the details of risk measurement and discount rates, we should draw a contrast between two different ways of thinking about risk that relate to the financial balance sheet presented in Chapter 1. In the first, we think about the risk in a firm’s operations or assets—the risk in the business. In the second, we look at the risk in the equity investment in this business. Figure 2.7 captures the differences between the two measures. As with any other aspect of the balance sheet, this one has to balance as well, with the weighted risk in the assets being equal to the weighted risk in the ingredients to capital—debt and equity. Note that the risk in the equity investment in a business is determined partly by the risk of the business the firm is in and partly by its choice of how much debt to use to fund that business. The equity in a safe business can be rendered risky if the firm uses substantial debt to fund that business.

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Assets

Risk in a Firm's Business and Asset Mix

Risk in the Cash Flows from Existing Investments

Liabilities Existing Assets

Growth Assets Risk in Cash Flows from New Investments

Debt

Equity

Risk in Debt and Cost of Debt

Risk in Equity and Cost of Equity

Risk in a Firm's Capital Mix Must Equate to the Risk in its Business and Asset Mix

Figure 2.7: Risk in Business Versus Risk in Equity

In discount rate terms, the risk in the equity in a business is measured with the cost of equity, whereas the risk in the business is captured in the cost of capital. The latter is a weighted average of the cost of equity and the cost of debt, with the weights reflecting the proportional use of each source of funding.

Measuring Equity Risk and the Cost of Equity Measuring the risk in equity investments and converting that risk measure into a cost of equity is rendered difficult by two factors. The first is that equity has an implicit cost, which is unobservable, unlike debt, which comes with an explicit cost in the form of an interest rate. The second factor is that risk in the eyes of the beholder and different equity investors in the same business can be very different. Therefore, they might demand different expected returns as a consequence. The Diversified Marginal Investor If a company had only one equity investor, estimating equity risk and the cost of equity would be far simpler. We would measure the risk to the investor of investing in equity in that company. Then we would assess a reasonable rate of return, given that risk. In a publicly traded company, we run into the practical problem that the equity investors number in the hundreds, if not the thousands. They vary not only in size, from small to large investors, but also in risk aversion. So, whose perspective should we take when measuring risk and cost of equity? In corporate finance and valuation, we develop the notion of the marginal investor—the investor most likely to influence the market price of publicly traded equity. The marginal investor in a publicly traded stock has to own enough stock in the company to make a difference and must be willing to trade on that stock. The common theme shared by risk-and-return models in finance is that the marginal investor is diversified, and we measure the risk in an investment as the risk added to a diversified portfolio. Put another way, only that portion of the risk in an investment that can be attributed to the broader market or economy, and hence is not diversifiable, should be built into expected returns. Models for Expected Return (Cost of Equity) It is on the issue of how best to measure this nondiversifiable risk that the different risk-andreturn models in finance part ways. Let us consider the alternatives: Q

In the capital asset pricing model (CAPM), this risk is captured in the beta that we assign an asset/business. That number has the burden of measuring exposure to all the components of market risk. The expected return on an investment can then be specified as a


31


function of three variables: the risk-free rate, the beta of the investment, and the equity risk premium (the premium demanded for investing in the average risk investment): Expected Return = Risk-Free Rate + Betainvestment (Equity Risk Premium) The risk-free rate and equity risk premium are the same for all investments in a market, but the beta captures the investment’s market risk exposure. A beta of 1 represents an average risk investment. Betas above (or below) 1 indicate investments that are riskier (or safer) than the average risk investment in the market. Q

The arbitrage pricing and multifactor models allow for multiple sources of nondiversifiable (or market) risk and estimate betas against each one. The expected return on an investment can be written as a function of the multiple betas (relative to each market risk factor) and the risk premium for that factor. If the model has k factors, with βji and risk premiumj representing the beta and risk premium of factor j, the expected return on the investment can be written as follows: j=k

Expected Return = Risk-Free Rate +

∑β

j

(Risk Premium j )

j=1

Q

Note that the capital asset pricing model can be written as a special case of these multifactor models, with a single factor (the market) replacing the multiple factors. The final class of models can be categorized as proxy models. With these models, we essentially give up on measuring risk directly. Instead, we look at historical data for clues on what types of investments (stocks) have earned high returns in the past. Then we use the common characteristic(s) they share as a measure of risk. For instance, researchers have found that market capitalization and price-to-book ratios are correlated with returns. Stocks with small market capitalization and low price-to-book ratios have historically earned higher returns than large market stocks with higher price-to-book ratios. Using the historical data, we can then estimate the expected return for a company based on its market capitalization and price-to-book ratio: Expected Return = a + b(Market Capitalization) + c(Price-to-Book Ratio) Since we are no longer working within the confines of an economic model, it is not surprising that researchers keep finding new variables (trading volume, price momentum) that improve the predictive power of these models. The open question, though, is whether these variables are truly proxies for risk or indicators of market inefficiency. In effect, we may be explaining away the market’s misvaluation of classes of stock by using proxy models for risk.

Estimation Issues With the CAPM and multifactor models, the inputs that we need for the expected return are straightforward. We need to come up with a risk-free rate and an equity risk premium (or premiums in the multifactor models) to use across all investments. Once we have these market-wide estimates, we measure the risk (beta or betas) in individual investments. This section lays out the broad principles that govern these estimates. Future chapters will return to the details of how best to make these estimates for different types of businesses.

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Q

The risk-free rate is the expected return on an investment with guaranteed returns; in effect, your expected return is also your actual return. Since the return is guaranteed, an investment must meet two conditions to be risk-free. The first is that the entity making the guarantee can have no default risk; this is why we use government securities to derive risk-free rates, a necessary though not always sufficient condition. As you will see in Chapter 6, default risk in many government securities is priced into the expected return. The second condition is that the time horizon matters. A six-month Treasury bill is not risk-free if you are looking at a five-year time horizon, since we are exposed to reinvestment risk. In fact, even a five-year Treasury bond may not be riskless, since the coupons received every six months have to be reinvested. Clearly, getting a risk-free rate is not as simple as it looks at the outset.

Q

The equity risk premium is the premium that investors demand for investing in risky assets (or equities) as a class, relative to the risk-free rate. It is a function not only of how much risk investors perceive in equities as a class, but also the risk aversion that they bring to the market. It also follows that the equity risk premium can change over time, as market risk and risk aversion both change. The conventional practice for estimating equity risk premiums is to use the historical risk premium—the premium investors have earned over long periods (say, 75 years) investing in equities instead of risk-free (or close to risk-free) investments. Chapter 7, “Risky Ventures: Assessing the Price of Risk,” questions the efficacy of this process and offers alternatives. To estimate the beta in the CAPM and betas in multifactor models, we draw on statistical techniques and historical data. The standard approach for estimating the CAPM beta is to run a regression of returns on a stock against returns on a broad equity market index. The slope captures how much the stock moves for any given market move. To estimate betas in the arbitrage pricing model, we use historical return data on stocks and factor analysis to extract both the number of factors in the models and factor betas for individual companies. As a consequence, the beta estimates that we obtain always look backward (since they are derived from past data) and are noisy (they are statistical estimates, with standard errors). In addition, these approaches clearly will not work for investments that do not have a trading history (young companies, divisions of publicly traded companies). One solution is to replace the regression beta with a bottom-up beta—one that is based on industry averages for the businesses that the firm is in, adjusted for differences in financial leverage.6 Since industry averages are more precise than individual regression betas, and the weights on the businesses can reflect a firm’s current mix, bottom-up betas generally offer better estimates for the future.

Q

6

The simplest and most widely used equation relating betas to debt-to-equity ratios is based on the assumption that debt provides a tax advantage and that the beta of debt is 0: Beta for Equity = Beta of Business * (1 + (1 – Tax Rate) (Debt / Equity)) The beta for equity is a levered beta, whereas the beta of the business is called an unlevered beta. Regression betas are equity betas and thus are levered. The debt-to-equity ratio over the regression period is embedded in the beta.


33


Estimating the Cost of Equity for 3M Because 3M is a publicly traded stock with a long history, we can use its price history to run a regression against the market index to derive a regression beta. Figure 2.8 provides a regression beta for 3M against the S&P 500 using two years of weekly returns against the S&P 500. The regression (raw) beta is 0.79; the adjusted beta, which is the raw beta moved toward the market average beta of 1, is 0.86.

Figure 2.8: Regression Beta for 3M

Although we do have a regression beta, all the normal caveats we listed in the preceding section apply. It is backward-looking (for the last two years) and has a standard error (albeit a small one of 0.07). The regression results would have been very different if we had run the regression using a different time period (say, five years) and different return intervals (daily or monthly) and if we had used a different market index. To yield a contrasting value, we estimated a beta for 3M by breaking it into individual businesses and taking a weighted average of the business betas (see Table 2.1).

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Table 2.1 Bottom-Up Beta Estimate for 3M Business

Revenues

EV/Sales

Estimated Value

Weight in Firm

Unlevered Beta

Industrial and transportation

$7,724

1.07

$8,265

27.42%

0.82

Health care

$3,968

1.83

$7,261

24.09%

1.40

Display and graphics

$3,892

1.63

$6,344

21.04%

1.97

Consumer and office

$3,403

0.78

$2,654

8.80%

0.99

Safety, security, and protection

$3,070

1.09

$3,346

11.10%

1.16

Electronics and communications

$2,775

0.82

$2,276

7.55%

1.32

$30,146

100.00%

1.29

3M as a firm

The unlevered betas of the businesses are obtained by averaging the regression betas of publicly traded firms in each business and adjusting the average regression beta for the average financial leverage (D/E ratio) in each business. The EV/sales ratio measures the typical multiple of revenues that firms in each business trade for. Applying 3M’s debt-to-equity ratio of 8.80% in 2007 (based on market values for debt and equity) to the unlevered beta of 1.29 yields an equity beta of 1.36 for 3M: Levered (Equity) Beta = 1.29 (1 + (1 – .35) (8.80%)) = 1.36 Using the ten-year Treasury bond rate of 3.72% in September 2007 as the riskfree rate and a 4% equity risk premium yields a cost of equity of 9.16%: Cost of Equity = Risk-Free Rate + Beta * Equity Risk Premium = 3.72% + 1.36 * 4% = 9.16% Obviously, using a higher equity risk premium would have led to a higher cost of equity.

The Cost of Debt While equity investors receive residual cash flows and bear the bulk of the operating risk in most firms, lenders to the firm also face the risk that they will not receive their promised payments—interest expenses and principal repayments. To cover this default risk, lenders add a “default spread” to the riskless rate when they lend money to firms; the greater the perceived risk of default, the greater the default spread and the cost of debt. The other dimension on which debt and equity can vary is in their treatment for tax purposes, with cash flows to equity investors (dividends and stock buybacks) coming from after-tax cash flows, whereas interest payments are Chapter 2 Intrinsic Valuation

35


tax-deductible. In effect, the tax law provides a benefit to debt and lowers the cost of borrowing to businesses. To estimate the cost of debt for a firm, we need three components. The first is the risk-free rate, an input to the cost of equity as well. As a general rule, the risk-free rate used to estimate the cost of equity should be used to compute the cost of debt as well. If the cost of equity is based on a long-term risk-free rate, as it often is, the cost of debt should be based on the same rate. The second component is the default spread. Three approaches are used, depending on the firm being analyzed: Q

Q

Q

If the firm has traded bonds outstanding, the current market interest rate on the bond (yield to maturity) can be used as the cost of debt. This is appropriate only if the bond is liquid and is representative of the firm’s overall debt; even risky firms can issue safe bonds, backed up by the firms’ most secure assets. If the firm has a bond rating from an established ratings agency such as S&P or Moody’s, we can estimate a default spread based on the rating. In September 2008, for instance, the default spread for BBB-rated bonds was 2% and would have been used as the spread for any BBB-rated company. If the firm is unrated and has debt outstanding (bank loans), we can estimate a “synthetic” rating for the firm based on its financial ratios. A simple, albeit effective, approach for estimating the synthetic rating is to base it entirely on a firm’s interest coverage ratio (EBIT/interest expense); higher interest coverage ratios yield higher ratings and lower interest coverage ratios.

The final input needed to estimate the cost of debt is the tax rate. Since interest expenses save you taxes at the margin, the tax rate that is relevant for this calculation is not the effective tax rate but the marginal tax rate. In the U.S., where the federal corporate tax rate is 35% and state and local taxes add to this, the marginal tax rate for corporations in 2008 was close to 40%, much higher than the average effective tax rate, across companies, of 28%. The after-tax cost of debt for a firm therefore is as follows: After-Tax Cost of Debt = (Risk-Free Rate + Default Spread) (1 – Marginal Tax Rate) The after-tax cost of debt for most firms will be significantly lower than the cost of equity for two reasons. First, debt in a firm generally is less risky than its equity, leading to lower expected returns. Second, a tax saving is associated with debt that does not exist with equity.

Estimating the Cost of Debt for 3M To estimate the synthetic rating for 3M, we begin with an estimate of the interest coverage ratio in 2007: Interest Coverage Ratio =

After-Tax Operating Income $5,361 = = 23.63 Interest Expenses $227

Given its large market capitalization (more than $50 billion), we use Table 2.2 to extract the synthetic rating and the default spread on 3M debt.

36



Table 2.2

Interest Coverage Ratios, Ratings, and Default Spreads—October 2008

Interest Coverage Ratio

Rating

Typical Default Spread

> 12.5

AAA

0.75%

9.50 to 12.50

AA

1.25%

7.50 to 9.50

A+

1.40%

6.00 to 7.50

A

1.50%

4.50 to 6.00

A–

1.70%

4.00 to 4.50

BBB

2.50%

3.50 to 4.00

BB+

3.20%

3.00 to 3.50

BB

3.65%

2.50 to 3.00

B+

4.50%

2.00 to 2.50

B

5.65%

1.50 to 2.00

B–

6.50%

1.25 to 1.50

CCC

7.50%

0.80 to 1.25

CC

10.00%

0.50 to 0.80

C

12.00%

< 0.50

D

20.00%

The rating that we assign to 3M is AAA, with a default spread of 0.75%. Adding this spread to the ten-year Treasury bond rate of 3.72% results in a pre-tax cost of debt of 4.49%. Just as a contrast, we compute the book interest rate by dividing the interest expenses in 2007 by the book value of debt: Book Interest Rate =

$210 Interest Expenses = = 4.27% Book Value of Debt $4920

Given how sensitive the book interest rate is to different definitions of book value of debt, we remain skeptical about its usefulness. Using the marginal tax rate of 35% on the pre-tax cost of debt of 4.49%, we derive an after-tax cost of debt of 2.91% for the company: After-Tax Cost of Debt = (Risk-Free Rate + Default Spread for Debt) (1 – Marginal Tax Rate) = (3.72% + 0.75%) (1 – .35) = 2.91%

Debt Ratios and the Cost of Capital After we have estimated the costs of debt and equity, we still have to assign weights to the two ingredients. To come up with this value, we could start with the mix of debt and equity that the firm uses right now. In making this estimate, the values that we should use are market values,


37


rather than book values. For publicly traded firms, estimating the market value of equity is usually a trivial exercise, where we multiply the share price by the number of shares outstanding. Estimating the market value of debt usually is a more difficult exercise, since most firms have some debt that is not traded. Though many practitioners fall back on book value of debt as a proxy of market value, estimating the market value of debt is still a better practice. Once we have the current market value weights for debt and equity for use in the cost of capital, we have a follow-up judgment to make in terms of whether these weights will change or remain stable. If we assume that they will change, we have to specify both what the right or target mix for the firm will be and how soon the change will occur. In an acquisition, for instance, we can assume that the acquirer can replace the existing mix with the target mix instantaneously. As passive investors in publicly traded firms, we have to be more cautious, since we do not control how a firm funds its operations. In this case, we may adjust the debt ratio from the current mix to the target over time, with concurrent changes in the costs of debt, equity, and capital. In fact, the last point about debt ratios and costs of capital changing over time is worth reemphasizing. As companies change over time, we should expect the cost of capital to change as well.

Estimating the Cost of Capital for 3M In the second sidebar, we estimated a cost of equity of 9.16% for 3M, based on a bottom-up beta estimate of 1.36. In the third sidebar, we concluded that the after-tax cost of debt for 3M is 2.91%, based on the synthetic AAA rating we assigned the firm. We estimated the market values of equity and debt for the firm in September 2008 (with the resulting weights and overall costs of capital) and derived the cost of capital for the firm. Table 2.3 shows the results. Table 2.3 3M’s Cost of Capital Market Value

Proportion of Capital

Cost

Equity

$57,041

91.50%

9.16%

Debt

$5,297

8.50%

2.91%

Capital

$62,338

100.00%

8.63%

At its current debt ratio of 8.50%, the cost of capital for 3M is 8.63%.

Growth Rates No other ingredient in discounted cash flow valuation evokes as much angst as estimating future growth. Unlike cash flows and discount rates, where we often have the security of historical data, growth rates require us to grapple with the future. This section looks at why growth rates can be different for equity and operating earnings. It examines two of the standard approaches for estimating growth (looking at the past, and using analyst estimates). This section closes with a discussion of the fundamentals that determine growth.

38



Equity Versus Operating Earnings As with cash flows and discount rates, a contrast has to be drawn between growth in equity earnings and growth in operating earnings. To make the distinction, consider the simplified version of an income statement shown in Table 2.4. Table 2.4 An Income Statement: Revenues to Earnings per Share Item

Factors That Explain Differences in Growth

Revenues – Operating expenses

Changes in operating efficiency/performance Operating leverage

EBITDA – Depreciation and amortization

Changes in depreciation schedules/rules Amortization of intangibles

EBIT – Interest expenses + Income from cash holdings – Taxes

Changes in financial leverage (debt) Changes in cash holdings/interest rates Changes in tax rates/rules

Net Income / Number of shares

Stock buybacks and issues Exercise of past option grants

Earnings per Share We are assuming that the firm has no minority holdings in other companies, which would result in an additional line item, just above the net income line, for income from these holdings. The growth rates in different measures of earnings (operating income, net income, and earnings per share) generally will be different for most firms. This is especially true of growth firms and firms in transition. Q

Q

Share issues and buybacks: If the number of shares remains fixed, the growth rate in earnings per share should be the same as the growth rate in net income. Firms that generate excess cash flows and use these cash flows to buy back stock register higher growth rates in earnings per share than in net income. Conversely, firms that make a practice of raising new equity (issuing new shares) to fund investments or acquisitions can have higher growth rates in net income than in earnings per share. Financial leverage: The growth rates in operating and net income can diverge if the net interest expense (interest expense minus interest income) grows at a rate different from operating income. Firms that use increasing amounts of debt to fund their operations generally report higher growth rates in operating income than net income. However, if that debt is used to buy back shares, the earnings per share growth reflect the fewer shares outstanding. Chapter 2 Intrinsic Valuation

39


Q

Operating leverage: The growth in operating income can also be very different from the growth in revenues, primarily because some operating expenses are fixed and others are variable. The higher the proportion of the costs that are fixed (higher operating leverage), the greater the growth rate in operating income relative to the growth in revenues.

In effect, when asked to estimate growth rates, the first question an analyst has to ask is, “In what item?” If our task is to estimate growth in operating income, we cannot use growth rates in earnings per share as substitutes.

Historical and Forecasted Growth Rates When confronted with the task of estimating growth, it is not surprising that analysts turn to the past. In effect, they use growth in revenues or earnings in the recent past as a predictor of growth in the future. Before we put this practice under the microscope, we should add that the historical growth rates for the same company can yield different estimates for the following reasons: Q

Earnings measure: As we noted, the growth rates in earnings per share, net income, operating income, and revenues can be very different for the same firm over a specified time period.

Q

Period of analysis: For firms that have been in existence for a long time, the growth rates can be very different if we look at ten years of history as opposed to five years. Averaging approach: Even if we agree on an earnings measure and time period for the analysis, the growth rates we derive can be different, depending on how we compute the values. We could, for instance, compute the growth rate in each period and average the growth rates over time, yielding an arithmetic average. Alternatively, we could use just the starting and ending values for the measure and compute a geometric average. For firms with volatile earnings, the latter can generate a very different (and lower) value for growth than the former.

Q

A debate on how best to estimate historical growth makes sense only if it is a good predictor of future growth. Unfortunately, studies that have looked at the relationship have generally concluded that Q Q Q

The relationship between past and future growth is a very weak one. Scaling matters, with growth dropping off significantly as companies grow. Firms and sectors grow through growth cycles, with high growth in one period followed by low growth in the next.

If historical growth is not a useful predictor of future growth, we can use another source for future growth. We can draw on those who know the firm better than we do—equity research analysts who have tracked the firm for years, or the managers in the firm—and use their estimates of growth. On the plus side, these forecasts should be based on better information than we have available. After all, managers should have a clearer sense of how much they will reinvest in their own businesses and what the potential returns on investments are when they do. And equity research analysts have sector experience and informed sources they can draw on for better information. On the minus side, neither managers nor equity research analysts are objective about the future; managers are likely to overestimate their capacity to generate growth, and analysts have their own biases. In addition, both analysts and managers can get caught up in the mood

40



of the moment, overestimating growth in buoyant times and underestimating growth in down times. As with historical growth, studies indicate that neither analyst estimates nor management forecasts are good predictors of future growth.

Fundamental Growth Rates If we cannot draw on history or trust managers and analysts, how, then, do we estimate growth? The answer lies in the fundamentals within a firm that ultimately determine its growth rate. This section considers the two sources of growth—new investments that expand the business, and improved efficiency on existing investments. Decomposing Growth The best way to consider earnings growth is to break it down algebraically into its constituent parts. Define Et to be the earnings in period t, It to be the investment at the start of period t, and ROIt as the return on that investment. Thus, we can rewrite Et as follows: Et = ROIt * It The change in earnings from period t–1 to t, ΔE, can then be written as follows: ΔE = Et – Et–1 = ROIt * It – ROIt–1 * It–1 The growth rate is written in terms of ΔE and Et–1: g = ΔE / Et–1 = (ROIt * It – ROIt–1 * It–1) / Et–1 Consider the simplest scenario, in which the ROI is stable and does not change from period to period (ROI = ROIt = ROIt–1). The expected growth rate in earnings for this firm is as follows: g = ΔE / Et–1 = ROI (It – It–1) / Et–1 = ROI * (ΔΙ/Ετ–1) In other words, the firm’s growth rate is a function of only two variables—the return it makes on new investments (ROI), and the proportion of its earnings that are put into new investments (ΔΙ/Ετ–1). The more general scenario is one in which the return on investment does change from period to period. In this case, the expected growth rate can be written as: g = ΔE / Et–1 = ROIt * (ΔΙ/Ετ–1) + (ROIt – ROIt–1) / ROIt–1 This equation is based on the assumption that the return on new investments in period t is identical to the return earned on existing investments in that period. In fact, this can be generalized even further. If we allow the return on new investments, ROINew,t, to be different from the return on existing assets, ROIExisting,t, the expected growth rate can be written as: g = ΔE / Et–1 = ROINew,t * (ΔΙ/Ετ–1) + (ROIExisting,t – ROIExisting,t–1)/ ROIExisting,t–1 The first term in this equation captures the growth from new investments, determined by the marginal return on those investments and the proportion invested in these investments. The second term captures the effect of changes in the return on investment on existing assets, a


41


component that we will call efficiency growth. Increasing the return on investment (improving efficiency) will create additional earnings growth, whereas declining efficiency (with drops in the return on investment) will reduce earnings growth. Growth from New Investments While investment and return on investment are generic terms, how we define them depends on whether we are looking at equity earnings or operating income. When looking at equity earnings, our focus is on the investment in equity, and the return is the return on equity. When looking at operating earnings, the focus is on the investment in capital, and the return is the return on capital. In the cash flow definitions introduced at the start of this chapter, the change in investment is computed as the reinvestment, and the measurement of the reinvestment again varies, depending on the cash flow being discounted. In dividend discount models, reinvestment is defined as retained earnings (any income not paid out as dividends). In free cash flow to equity (firm) models, reinvestment is defined in terms of the equity reinvestment rate (reinvestment rate). Central to any estimate of fundamental growth is the estimate of return on capital or equity. Table 2.5 summarizes the inputs for each measure, depending on the measure of cash flow that we are focused on. Table 2.5 Measuring Investment and Return on Investment

Operating income

Change in Investment

Return on Investment

Reinvestment Rate =

Return on invested capital (ROC or ROIC)

(Cap Ex – Deprec'n + ΔWC) EBIT(1 – t)

Net income (noncash)

Equity Reinvestment Rate =

(Cap Ex – Deprec'n + ΔWC – ΔDebt) Net Income

Earnings per share

Retention Ratio =

Noncash return on equity (NCROE) Return on equity (ROE)

Dividends 1− Net Income

It is conventional practice to use accounting measures of investment and return on investment. Thus, the book values of equity and invested capital and accounting earnings are used to compute returns on equity and capital: Return on Capital (ROIC) =

Operating Incomet (1 – Tax Rate) Book Value of Invested Capital t -1

Noncash Return on Equity (NCROE) = Return on Equity (ROE) =

42

Net Income t – Interest Income from Casht (1 – Tax Rate) Book Value of Equityt -1 − Cash t -1

Net Income t Book Value of Equityt -1



The problem with accounting measures on both dimensions is well documented. Accounting choices on restructuring charges, amortization, and capitalization all make a difference in the final number.7 The final issue that we have to consider is the difference between marginal and average returns. Note that the return on investment that we use to compute the growth from new investments should be the return earned on those investments alone—a marginal return. The return on existing assets is an average return on a portfolio of investments already made. While we often use the same value for both numbers in valuation, they can be different in practice. Efficiency Growth For many mature firms with limited investment opportunities, the potential for growth from new investments is limited. These firms cannot maintain a high reinvestment rate and deliver a high return on capital with that reinvestment. However, they can still grow at healthy rates if they can improve the returns that they earn on existing assets. Conversely, declines in returns on existing assets can translate into drops in earnings growth rates. Stated again in terms of different measures of earnings, efficiency growth can be written as shown in Table 2.6. Table 2.6 Determinants of Efficiency Growth in Earnings Measure of Return on Existing Assets

Efficiency Growth

Operating income

Return on capital

(ROC t − ROC t−1 ) ROC t−1

Net income (noncash)

Noncash return on equity

(NCROE t – NCROEt−1 ) NCROEt−1

Earnings per share

Return on equity

(ROE t − ROE t−1 ) ROE t−1

When valuing companies, efficiency growth is pure gravy in terms of value created, since the growth comes with no concurrent cost. Unlike growth from new investments, where the positive effects of growth have to be offset against the negative effect of more investment, improving the return on capital on existing assets increases the growth rate without adversely affecting the cash flows. It should as come as no surprise, then, that analysts who want to increase a company’s value draw on the efficiency argument to justify much higher growth rates than those estimated using fundamentals. While the potential for efficiency growth is always there, we should put some commonsense constraints on how much we can draw on this growth: Q

7

Mature firms have more potential for efficiency growth, with poor returns on capital (equity), than firms that are performing well. This is true for two reasons. First, improving the return on capital is a much more feasible option for a firm that generates a

To get a sense of the problems with using accounting numbers, and how best to correct for them, see Damodaran, A., 2007, “Return on Capital, Return on Invested Capital and Return on Equity: Measurement and Implications,” working paper, SSRN.


43


Q

return on capital that is well below the sector average than at a firm that already outperforms the sector. Second, the effect of an improvement in returns on growth is much greater when the return on capital is low than when it is high. A firm that improves its return on capital from 5% to 6% will report a 20% growth rate from efficiency in that period. On the other hand, a firm that improves its return on capital from 25% to 26% will generate a 4% growth rate from efficiency in that period. You can draw on increased efficiency to justify growth only for finite periods. After all, a firm cannot be infinitely inefficient. Once the inefficiencies, no matter how significant, are fixed, the firm must revert to its sustainable growth rate, based on new investments. In discounted cash flow valuation, this has a practical consequence: You can draw on both efficiency and new investments to justify growth during the high-growth period, but only on new investments to justify growth forever (in the terminal value computation).

In closing, growth in a specific firm can come from new investments or improved efficiency, but it has to be earned either way. None of us has the power to endow companies with higher growth rates just because we like the managers or want to make the firms’ value increase.

Estimating Growth for 3M It makes sense to start with an estimate of historical growth in earnings at 3M. Figure 2.9 presents different estimates of past earnings growth for 3M, given different definitions of earnings and different time periods. 20.00% 18.00% 16.00% 14.00% 12.00% Operating Income Net Income EPS

10.00% 8.00% 6.00% 4.00% 2.00% 0.00%

Last 5 years

Last 10 years

Figure 2.9: Historical Growth Rates in Earnings for 3M

44



Note the wildly divergent numbers that we get for past growth. In September 2008, analysts were estimating growth in earnings per share at 3M of between 8 and 9% a year for the next five years. Looking at the fundamentals, it seems unlikely that 3M, given its high existing return on capital and equity, can generate much in terms of efficiency growth. It is, however, reinvesting in new assets. This reinvestment, in conjunction with high returns on capital on new investments, will generate growth. Table 2.7 summarizes growth in dividends, noncash net income, and after-tax operating income using the reinvestment and return characteristics we have estimated for 3M. Table 2.7 Dividends, Net Income, and After-Tax Operating Income: Fundamentals In the Last Financial Year, 2007

Expected for the Next Five Years

Return

Expected Growth

Reinvestment Return

Dividends 66.31%

33.93%

22.50%

Not forecast

Noncash –2.27% net income

47.65%

–1.08%

25.00%

30.00%

7.50%

After-tax operating income

25.31%

9.21%

30.00%

25.00%

7.50%

Reinvestment

36.37%

Expected Growth

Note that we have stayed fairly close to last year’s estimates of the reinvestment rate and return on capital for 3M. However, we changed the equity reinvestment rate substantially for the next few years to reflect the historical average for this number from 2003 to 2007.

Terminal Value Publicly traded firms do not have finite lives. We cannot estimate cash flows forever. Therefore, we generally impose closure in valuation models by stopping our estimation of cash flows sometime in the future and then computing a terminal value that reflects all cash flows beyond that point. Three approaches generally are used to estimate the terminal value. The most common approach, which is to apply a multiple to earnings in the terminal year to arrive at the terminal value, is inconsistent with intrinsic valuation. Since these multiples are usually obtained by looking at what comparable firms are trading at in the market today, this is a relative valuation, rather than a discounted cash flow valuation. Two more legitimate ways of estimating terminal value exist. The first is to estimate a liquidation value for the firm’s assets, assuming that the assets are sold in the terminal year. The other is to estimate a going concern or a terminal value.

Liquidation Value If we assume that the business will be ended in the terminal year and that its assets will be liquidated at that time, we can estimate the proceeds from the liquidation. This liquidation value


45


still has to be estimated, using a combination of market-based numbers (for assets that have ready markets) and cash flow-based estimates. For firms that have finite lives and marketable assets (like real estate), this represents a fairly conservative way of estimating terminal value. For other firms, estimating liquidation value becomes more difficult, either because the assets are not separable (brand-name value in a consumer product company) or because there is no market for the individual assets. One approach is to use the estimated book value of the assets as a starting point and to estimate the liquidation value based on the book value.

Going Concern or Terminal Value If we treat the firm as a going concern at the end of the estimation period, we can estimate the value of that concern by assuming that cash flows will grow at a constant rate forever afterwards. This perpetual growth model draws on a simple present-value equation to arrive at terminal value:

Terminal Value

n

=

Cash Flow in Year n +1 (Discount Rate − Perpetual Growth Rate)

Our definitions of cash flow and growth rate have to be consistent with whether we are valuing dividends, cash flows to equity, or cash flows to the firm. The discount rate is the cost of equity for the first two and the cost of capital for the last. The perpetual growth model is a powerful one, but it can be easily misused. In fact, analysts often use it as a piggy bank that they go to whenever they feel that the value they have derived for an asset is too low or high. Small changes in the inputs can alter the terminal value dramatically. Consequently, three key constraints should be imposed on its estimation: Q

Cap the growth rate: Small changes in the stable-growth rate can change the terminal value significantly, and the effect gets larger as the growth rate approaches the discount rate used in the estimation. The fact that a stable-growth rate is constant forever, however, puts strong constraints on how high it can be. Since no firm can grow forever at a rate higher than the growth rate of the economy in which it operates, the constant growth rate cannot be greater than the overall growth rate of the economy. So, what is the maximum stable-growth rate that you can use in a valuation? The answer depends on whether the valuation is being done in real or nominal terms. If it’s the latter, the currency used to estimate cash flows will determine what the contraint on the growth rate will be. With the former, you would use the real-growth rate in the economy as your constraint. With the latter, you would add expected inflation in the currency to the real growth. Setting the stable-growth rate to be less than or equal to the economy’s growth rate is not only the consistent thing to do, but it also ensures that the growth rate will be less than the discount rate. This is because of the relationship between the riskless rate that goes into the discount rate and the economy’s growth rate. Note that the riskless rate can be written as follows: Nominal Riskless Rate = Real Riskless Rate + Expected Inflation Rate In the long term, the real riskless rate converges on the economy’s real-growth rate, and the nominal riskless rate approaches the economy’s nominal growth rate. In fact, a simple rule of thumb about the stable-growth rate is that it should not exceed the riskless rate used in the valuation.

46



Q

Q

Use mature company risk characteristics: As firms move from high growth to stable growth, we need to give them the characteristics of stable-growth firms. A firm in stable growth is different from that same firm in high growth on a number of dimensions. In general, you would expect stable-growth firms to be less risky and use more debt. In practice, we should move betas toward one for even high-risk firms toward stable growth and give them debt ratios more consistent with larger, more stable cash flows. Reinvestment and excess-return assumptions: Stable-growth firms tend to reinvest less than high-growth firms. It is critical that we both capture the effects of lower growth on reinvestment and ensure that the firm reinvests enough to sustain its stable-growth rate in the terminal phase. Given the relationship between growth, reinvestment rate, and returns that we established in the section “Decomposing Growth,” we can estimate the reinvestment rate that is consistent with expected growth in Table 2.8.

Table 2.8 Reinvestment in Stable Growth Model

Reinvestment Rate in Stable Growth

Dividend

Stable Growth Rate Return on Equity in Stable Growth

FCFE

Stable Growth Rate Noncash Return on Equity in Stable Growth

FCFF

Stable Growth Rate Return on Capital in Stable Phase

Linking the reinvestment rate and retention ratio to the stable-growth rate also makes the valuation less sensitive to assumptions about stable growth. Although increasing the stable-growth rate while holding all else constant can dramatically increase value, changing the reinvestment rate as the growth rate changes creates an offsetting effect: Terminal Value =

EBIT n +1 (1 − t)(1− Reinvestment Rate) Cost of Capital n − Stable Growth Rate

The gains from increasing the growth rate are partially or completely offset by the loss in cash flows because of the higher reinvestment rate. Whether value increases or decreases as the stable growth increases depends entirely on what you assume about excess returns. If the return on capital is higher than the cost of capital in the stable-growth period, increasing the stable-growth rate increases value. If the return on capital is equal to the cost of capital in stable growth, increasing the stable-growth rate has no effect on value. Substituting the stable-growth rate as a function of the reinvestment rate from before, you get this:

Terminal Value =

EBIT n +1 (1 − t)(1 − Reinvestment Rate) Cost of Capital n − (Reinvestm ent Rate * Return on Capital)


47


Setting the return on capital equal to the cost of capital, you arrive at the following: Terminal Value ROC = Cost of Capital =

EBITn +1 (1 − t) Cost of Capital n

You could establish the same propositions with equity income and cash flows and show that the terminal value of equity is a function of the difference between the return on equity and cost of equity: ⎛ gn ⎞ Net Income n +1 ⎜1 ⎟ ⎝ ROE n ⎠ Terminal Value of Equity = (Cost of Equity n − g n )

Terminal Value ROE =Cost of Equity =

Net Income n +1 Cost of Equity n

In closing, the key assumption in the terminal value computation is not what growth rate you use in the valuation, but what excess returns accompany that growth rate. If you assume no excess returns, the growth rate becomes irrelevant. Some valuation experts believe that this is the only sustainable assumption, since no firm can maintain competitive advantages forever. In practice, though, there may be some wiggle room, insofar as the firm may become a stable-growth firm before its excess returns go to zero. If that is the case and the firm’s competitive advantages are strong and sustainable (even if they do not last forever), we may be able to give the firm some excess returns in perpetuity. As a simple rule of thumb, these excess returns forever should be modest ( X, take the project: The project has positive net present value. If V < X, do not take the project: The project has negative net present value. If the firm does not invest in the project, it incurs no additional cash flows, though it will lose what it originally invested in the project. This relationship can be presented in a payoff diagram of cash flows on this project, as shown in Figure 5.3. This assumes that the firm holds out until the end of the period for which it has exclusive rights to the project.2 PV of Cash Flows

Initial Investment in Project

Present Value of Expected Cash Flows

Project has negative NPV in this range.

Project’s NPV turns positive in this range.

Figure 5.3: Payoff Diagram on Option to Delay

Note that this payoff diagram is that of a call option. The underlying asset is the investment. The option’s strike price is the initial outlay needed to initiate the investment. The option’s life is how long the firm has rights to the investment. 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.

Valuing an Option to Delay On the surface, the inputs needed to apply option pricing theory to valuing the option to delay are the same as those needed for any option. 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 (cost of delay). Actually estimating these inputs for product patent valuation can be difficult, however: Q Value of the underlying asset: In this case, the underlying asset is the investment itself. 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, which can be obtained by doing a standard capital budgeting analysis. There is likely to be a substantial amount of error 2

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McDonald, R. and D. Siegel, 2002, “The Value of Waiting to Invest,” Quarterly Journal of Economics, v101, 707–728.



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 why the project delay option has value. If the expected cash flows on the project were known with certainty and were not expected to change, there would be no need to adopt an option pricing framework, because the option would have no value. Q Variance in the value of the asset: The present value of the expected cash flows that measures the value of the asset will change over time. This is partly because the product’s potential market size may be unknown and partly because technological shifts can change the product’s cost structure and profitability. The variance in the present value of cash flows from the project can be estimated in one of three ways:

•

•

If similar projects have been introduced in the past, the variance in the cash flows from those projects can be used as an estimate. This may be how a consumer products company like Gillette might estimate the variance associated with introducing a new blade for its razors. Probabilities can be assigned to various market scenarios, cash flows estimated under each scenario, and the variance estimated 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.

•

The variance in the market value of publicly traded firms involved in the same business (as the project being considered) can be used as an estimate of the variance. Thus, the average variance in firm 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 delay a project in a stable business will be less than the value of a similar option in an environment where technology, competition, and markets are all changing rapidly. Q Exercise price on option: A project delay option is exercised when the firm owning the rights to the project decides to invest in it. The cost of making this investment is the option’s exercise price. The underlying assumption is that this cost remains constant (in present-value dollars) and that any uncertainty associated with the product is reflected in the present value of cash flows on the product. Q 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 0 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 option’s expiration. While this input can be estimated easily when firms have explicit rights to a project (through a license or patent, for instance), it becomes far more difficult to obtain when firms have only a competitive advantage to take a project. Q Cost of delay (dividend yield): There is a cost to delaying taking a project once the net present value turns positive. Since the project rights expire after a fixed period, and

Chapter 5 Real Options Valuation

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excess profits (which are the source of positive present value) are assumed to disappear after that time as new competitors emerge, each year of delay translates into one less year of value-creating cash flows.3 If the cash flows are evenly distributed over time, and the patent’s life is n years, the cost of delay can be written as follows: Thus, if the project rights are for 20 years, the annual cost of delay works out to 5% a 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-delay exercise larger over time. Annual Cost of Delay =

1 n

Practical Considerations While it is quite clear that the option to delay is embedded in many investments, 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 would argue 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 to 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 prices move in small increments continuously (an assumption of the Black-Scholes model), and that the variance in value remains unchanged over time, may be difficult to justify in the context of a real investment. For instance, a sudden technological change may dramatically change a project’s value, either positively or negatively. Third, there may be no specific period for which the firm has rights to the project. For instance, a firm may have significant advantages over its competitors. This may, in turn, provide it with virtually exclusive rights to a project for a period of time. The rights are not legal restrictions, however, and they could erode faster than expected. In such cases, the expected life of the project itself is uncertain and is only an estimate. Ironically, uncertainty about the option’s expected life can increase the variance in present value, and through it, the expected value of the rights to the project.

Applications of the Option to Delay The option to delay provides interesting perspectives on three common investment problems. The first is in the valuation of patents, especially those that are not viable today but could be viable in the future. By extension, this also allows us to look at whether R&D expenses deliver value. The second is in the analysis of natural resource assets such as vacant land and undeveloped oil reserves.

Patents A product patent gives a firm the right to develop and market a product. But the firm will do so only if the present value of the expected cash flows from the product sales exceed the cost of

3

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



development, as shown in Figure 5.4. 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 developing the product, and V is the present value of the expected cash flows from development, the payoffs from owning a product patent can be written as follows: 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 itself is the underlying asset.4 Net Payoff to Introducing Product

Cost of Product Introduction Present Value of Expected Cash Flows on Product

Figure 5.4: Payoff to Introducing Product

The implications of viewing patents as options can be significant. First, it implies that nonviable patents will continue to have value, especially in businesses that have substantial volatility. Second, it indicates that firms may hold off on developing viable patents if they feel that they gain more from waiting than they lose in terms of cash flows. This behavior is more common if no significant competition is on the horizon. Third, the value of patents will be higher in risky businesses than in safe businesses, since option value increases with volatility. If we consider R&D to be the expense associated with acquiring these patents, this would imply that research should have its biggest payoff when directed to areas where less is known and more uncertainty exists. Consequently, we should expect pharmaceutical firms to spend more of their R&D budgets on gene therapy than on flu vaccines.5 We return to examine this issue in more depth in Chapter 15, “Invisible Investments: Firms with Intangible Assets.”

4

Schwartz, E., 2002, “Patents and R&D as Real Options,” working paper, Anderson School at UCLA.

5

Pakes, A., 1986, “Patents as Options: Some Estimates of the Value of Holding European Patent Stocks,” Econometrica, v54, 755–784. While this paper does not explicitly value patents as options, it examines the returns investors would have earned investing in companies that derive their value from patents. The return distribution resembles that of a portfolio of options, with most investments losing money but the winners providing disproportionate gains.


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Natural Resource Options In a natural resource investment, the underlying asset is the natural resource, and the asset’s value is based on two variables: the estimated quantity and the price of the resource. Thus, in a gold mine, for example, the value of the underlying asset is the value of the estimated gold reserves in the mine, based on the current price of gold. In most such investments, an initial cost is associated with developing the resource. The difference between the value of the asset extracted and the cost of the development is the profit to the owner of the resource (see Figure 5.5). Defining the cost of development as X, and the estimated value of the developed resource as V, the potential payoffs on a natural resource option can be written as follows: Payoff on Natural Resource Investment = V – X =0

if V > X if V≤ X

Thus, the investment in a natural resource option has a payoff function similar to a call option.6 Net Payoff to Extracting Reserve

Cost of Developing Reserve Value of Estimated Reserve of Natural Resource

Figure 5.5: Payoff from Developing Natural Resource Reserves

What are the implications of viewing natural resource reserves as options? The first is that the value of a natural resource company can be written as a sum of two values: the conventional riskadjusted value of expected cash flows from developed reserves, and the option value of undeveloped reserves. While both will increase in value as the price of the natural resource increases, the latter will respond positively to increases in price volatility. Thus, the values of oil companies should increase if oil price volatility increases, even if oil prices themselves do not go up. The second implication is that conventional discounted cash flow valuation will understate the value of natural resource companies, even if the expected cash flows are unbiased and reasonable, because it will miss the option premium inherent in their undeveloped reserves. The third implication is that development of natural resource reserves will slow down as the volatility in prices increases. The time premium on the options will increase, making exercise of the options (development of the reserves) less likely. The same type of analysis can be extended to any other commodity company (gold and copper reserves, for instance) and even to vacant land or real estate properties.

6

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Brennan, M. and E. Schwartz, 1985, “Evaluating Natural Resource Investments,” The Journal of Business, v58, 135–157.



The owner of vacant land in Manhattan can choose whether and when to develop the land and will make that decision based on real estate values.7 Mining and commodity companies have been at the forefront of using real options in decision making. Their usage of the technology predates the current boom in real options. One reason is that natural resource options come closest to meeting the prerequisites for the use of option pricing models. Firms can learn a great deal by observing commodity prices and can adjust their behavior (in terms of development and exploration) quickly. In addition, if we consider exclusivity to be a prerequisite for real options to have value, that exclusivity for natural resource options derives from their natural scarcity. After all, only a finite amount of oil and gold is under the ground, and there’s only so much vacant land in Manhattan. Finally, natural resource reserves come closest to meeting the arbitrage/replication requirements that option pricing models are built on; both the underlying asset (the natural resource) and the option can often be bought and sold. We will examine the use of real options models in commodity company valuations in more depth in Chapter 13, “Ups and Downs: Cyclical and Commodity Companies.”

The Option to Expand an Investment In some cases, a firm takes an investment because doing so allows it either to make other investments or to enter other markets in the future. In such cases, it can be argued that the initial investment provides the firm with an option to expand, and the firm should therefore be willing to pay a price for such an option. Consequently, a firm may be willing to lose money on the first investment because it perceives the option to expand as having a large-enough value to compensate for the initial loss. To examine this option, assume that the present value of the expected cash flows from entering the new market or taking the new project is V, and the total investment needed to enter this market or take this project is X. Furthermore, assume that the firm has a fixed time horizon, at the end of which it must decide whether to take advantage of this opportunity. Finally, assume that the firm cannot move forward on this opportunity if it does not take the initial investment. This scenario implies the option payoffs shown in Figure 5.6. PV of Cash Flows

Initial Investment Cost of Expansion in Project

Expansion has negative NPV in this range.

Expansion NPV turns positive in this range.

Present Value of Expected Cash Flows

Figure 5.6: Cash Flows on Expansion 7

Quigg, L., 1993, “Empirical Testing of Real Option-Pricing Models,” Journal of Finance, vol. 48, 621–640. The author examined transaction data on 2,700 undeveloped and 3,200 developed real estate properties between 1976 and 1979 and found evidence of a premium arising from the option to wait in the former.


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As you can see, at the expiration of the fixed time horizon, the firm enters the new market or takes the new investment if the present value of the expected cash flows at that point in time exceeds the cost of entering the market. Consider a simple example of an option to expand. Disney is considering starting a Spanish version of the Disney Channel in Mexico. It estimates the investment will lose money and have a negative net present value. The negative net present value normally would suggest that rejecting the investment is the best course. However, assume that if the Mexican venture does better than expected, Disney plans to expand the network into the rest of Latin America at a significant cost. Based on its current assessment of this market, Disney believes that the present value of the expected cash flows on this investment will be less than the cost, yielding a negative net present value for that investment as well. The saving grace is that the latter present value is an estimate and Disney does not have a firm grasp of the market, and there is significant uncertainty about that value. Finally, assume that Disney will have to make this expansion decision within a fixed period (say, five years) of the Mexican investment. We can value the Latin American expansion as an option, with the uncertainty about its value generating the value for the option. If the value of the expansion option is greater the value lost on the initial investment in Mexico, Disney could justify the investment. 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 cases where a life can be estimated for the option, neither the size nor the product’s potential market may be known, and estimating either can be problematic. To illustrate, consider again the Disney example. While we adopted a period of five years, at the end of which Disney must decide on its future expansion into Latin America, it is entirely possible that this time frame is not specified when the Mexican channel goes on the air. Furthermore, we have assumed that both the cost and present value of expansion are known initially. In reality, the firm may not have good estimates for either before making the first investment, since it does not have much information on the underlying market.

Implications The option to expand is implicitly used by firms to rationalize making investments that have negative net present value but that provide significant opportunities to tap into new markets or sell new products. While the option pricing approach adds rigor to this argument by estimating the value of this option, it also provides insight into 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 for stable businesses with lower returns (such as housing, utilities, or automobile production). Specifically, the option to expand is at the basis of arguments that an investment should be made because of strategic considerations or that large investments should be broken into smaller phases. It can also be considered a rationale for why firms may accumulate cash or hold back on borrowing, thus preserving financial flexibility.

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Strategic Considerations In many acquisitions or investments, the acquiring firm believes that the transaction will give it competitive advantages in the future. These competitive advantages run the gamut: Q Entry into a growing or large 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. A good example of this is the acquisition of a Mexican retail firm by a U.S. firm, with the intent of expanding into the Mexican market. Q 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 expand into a new market. Q 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 to expand into new markets in the future. While all these potential advantages may be used to justify initial investments that do not meet financial benchmarks, not all of them create valuable options. The value of the option is derived from the degree to which these competitive advantages, assuming that they do exist, translate into sustainable excess returns. As a consequence, these advantages can be used to justify premiums only in cases where the acquiring firm believes that it has some degree of exclusivity in the targeted market or technology. Two examples can help illustrate this point. A telecommunications firm should be willing to pay a premium for a Chinese telecomm firm if the latter has exclusive rights to service a large segment of the Chinese market. The option to expand into the Chinese market could be worth a significant amount.8 On the other hand, a developed market retailer should be wary about paying a real options premium for an Indian retail firm, even though it may believe that the Indian market could grow to be a lucrative one. The option to expand into this lucrative market is open to all entrants, not just existing retailers, so it might not translate into sustainable excess returns.

Multistage Projects and Investments When entering new businesses or making new investments, firms sometimes can enter the business in stages. While doing so may reduce potential upside, it also protects the firm from 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. Two propositions follow: Q Some projects that do not look good on a full investment basis may be value-creating if the firm can invest in stages. Q 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 multistage investments must be weighed against the cost. Taking investments in stages may allow competitors who decide to enter the market on a 8

A note of caution needs to be added here. If the exclusive rights to a market come with no pricing power—in other words, the government sets the price you charge your customers—it may very well translate into zero excess returns (and no option value).


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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 multistage and one-time investments in an option framework. Here are some cases where the gains will be largest from making the investment in multiple stages: Q Projects that have significant barriers to entry from competitors entering the market and that take 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 product. Q Projects that have significant uncertainty about the size of the market and the project’s eventual success: Here, starting small and expanding 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 then be useful in subsequent stages in both product design and marketing. Hsu argues that venture capitalists invest in young companies in stages. This is partly to capture the value option of waiting/learning at each stage and partly to reduce the likelihood that the entrepreneur will be too conservative in pursuing risky (but good) opportunities.9 Q Projects that need a substantial investment in infrastructure (large fixed costs) and high operating leverage: Since the savings from doing a project in multiple stages can be traced to investments needed at each stage, they are 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) will gain more from the options created by taking the project in multiple stages.

Growth Companies In the stock market boom of the 1990s, we witnessed the phenomenon of young start-up Internet companies with large market capitalizations but little to show in terms of earnings, cash flows, or even revenues. Conventional valuation models suggested that it would be difficult, if not impossible, to justify these market valuations with expected cash flows. In an interesting twist on the option-to-expand argument, some people argued that investors in these companies were buying options to expand to be part of a potentially huge e-commerce market, rather than conventional stock.10 While the argument is alluring and serves to pacify investors in growth companies who may feel that they are paying too much, clear dangers exist in making this stretch. The biggest one is that the “exclusivity” component that is necessary for real options to have value is being given short shrift. Suppose that you invested in an Internet stock in 1999, and assume that you are paying a premium to be part of a potentially large online market today. Assume further that this market comes to fruition. Could you partake in this market without paying that upfront premium for a

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9

Hsu, Y., 2002, “Staging of Venture Capital Investment: A Real Options Analysis,” working paper, University of Cambridge.

10

Schwartz, E. S. and M. Moon, 2001, “Rational Pricing of Internet Companies Revisited,” The Financial Review, 36, pp. 7–26. A simpler version of the same argument was made in Mauboussin, M., 1998, “Get Real: Using Real Options in Security Analysis,” CSFB Publication, June 23, 1999.



dot-com company? We don’t see why not. After all, GE and Nokia were just as capable of being part of this online market, as were any number of new entrants into the market.

Financial Flexibility When making decisions about how much to borrow and how much cash to return to stockholders (in dividends and stock buybacks), managers should consider the effects that such decisions will have on their capacity to make new investments or meet unanticipated contingencies in the future. 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 for firms, it also has costs. The large cash balances might earn below-market returns, and excess debt capacity implies that the firm is giving up some value by maintaining a higher cost of capital. Using an option framework, it can be argued that a firm that maintains a large cash balance and preserves excess debt capacity does so to have the option to invest in unexpected projects with high returns that may arise in the future. To value financial flexibility as an option, consider the following framework: A firm has expectations about how much it will need to reinvest in future periods, based on its own history and current conditions in the industry. On the other side of the ledger, a firm also has expectations about how much it can raise from internal funds and its normal access to capital markets in the future. Assume that actual reinvestment needs can be very different from the expected reinvestment needs. For simplicity, we will assume that the firm knows its capacity to generate funds. 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 excess debt capacity and surplus cash. The payoff from these projects, however, comes from the excess returns that the firm expects to make on them. Looking at financial flexibility as an option yields valuable insights into when financial flexibility is most valuable. Using the framework we just developed, for instance, we would argue the following: Q 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 that earn large excess returns on their projects can use the need for financial flexibility as the justification for holding large cash balances and excess debt capacity. Q 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. Young and growing firms that have small or negative earnings, and therefore much lower capacity to generate internal funds, will value flexibility more. As supporting evidence, note that technology firms usually borrow very little and accumulate large cash balances. Q 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 a firm’s capacity (and willingness) 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, value financial flexibility more than larger firms. The existence of corporate bond markets can also


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make a difference in how much flexibility is valued. In markets where firms cannot issue bonds and have to depend entirely on banks for financing, there is less access to capital and a greater need to maintain financial flexibility. Q The need for and 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 sectors where reinvestment needs are volatile on a period-to-period basis. In conventional corporate finance, the optimal debt ratio is the one that minimizes the cost of capital. There is little incentive for firms to accumulate cash balances. This view of the world, though, flows directly from the implicit assumption we make that capital markets are open and can be accessed with little or no cost. Introducing external capital constraints, internal or external, into the model leads to a more nuanced analysis where rational firms may borrow less than optimal and hold back on returning cash to stockholders.

The Option to Abandon an Investment The final option to consider is the option to abandon a project when its cash flows do not measure up to expectations. One way to reflect this value is through decision trees, as discussed in Chapter 3. The decision tree has limited applicability in most real-world investment analyses; it typically works only for multistage projects, and it requires inputs on probabilities at each stage of the project. The option pricing approach provides a more general way of estimating and building the value of abandonment into investment analysis. 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 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: Payoff from Owning an Abandonment Option = 0 =L–V

if V > L if V ≤ L

These payoffs are graphed in Figure 5.7 as a function of the expected value from continuing the investment. PV of Cash Flows from Project

Salvage Value from Abandonment

Figure 5.7: Payoff Diagram on the Abandonment Option

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Unlike the prior two cases, the option to abandon takes on the characteristics of a put option. Consider a simple example. Assume that a firm is considering taking a ten-year project that requires an initial investment of $100 million in a real estate partnership, where the present value of expected cash flows is $90 million. While the net present value of –$10 million is negative, assume that the firm has the option to abandon this project anytime in the next ten years by selling its share of the ownership to the other partners in the venture for $50 million. If the value of this abandonment option is greater than $10 million (which is the negative net present value of the investment), the investment makes sense. Note, though, that abandonment becomes a more and more attractive option as the remaining project life decreases, since the present value of the remaining cash flows decreases. In the preceding analysis, we assumed, rather unrealistically, that the abandonment value was clearly specified up front and that it 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 doing so has to be estimated (with error) up front. 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 present value of the expected cash flows from continuing with the investment are even more negative.

Implications The fact that the option to abandon has value provides a rationale for firms to build in operating flexibility to scale back or terminate projects if they do not measure up to expectations. It also indicates that firms that focus on generating more revenues by offering their customers the option to walk away from commitments may be giving up more than they gain.

Escape Clauses When a firm enters into a long-term risky investment that requires a large up-front investment, it should do so with the clear understanding that it may regret making this investment fairly early in its life. Being able to get out of such long-term commitments that threaten to drain more resources in the future is at the heart of the option to abandon. It is true that some of this flexibility is determined by the business you are in; getting out of bad investments is easier to do in service businesses than in heavy infrastructure businesses. However, it is also true that firms can take actions at the time of making these investments that give them more choices if things do not go according to plan. The first and most direct way is to build operating flexibility contractually with the parties that are involved in the investment. First, contracts with suppliers may be written on an annual basis rather than 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. Second, the initial capital investment can be shared with another investor, presumably with deeper pockets and a greater willingness to stay with the investment, even if it


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turns sour. This provides a rationale for joint venture investing, especially for small firms that have limited resources; finding a cash-rich, larger company to share the risk may well be worth the cost. None of these actions is costless. Entering into short-term agreements with suppliers and leasing the physical plant may be more expensive than committing for the life of the investment, but that additional cost has to be weighed against the benefit of maintaining the abandonment option.

Customer Incentives Firms that are intent on increasing revenues sometimes offer customers abandonment options to induce them to buy their products and services. Consider a firm that sells its products on multiyear contracts and that offers customers the option to cancel their contracts at any time, with no cost. While this may sweeten the deal and increase sales, a substantial cost is likely. In the event of a recession, customers who are unable to meet their obligations are likely to cancel their contracts. In effect, the firm has made its good times better and its bad times worse. The cost of this increased volatility in earnings and revenues has to be measured against the potential gain in revenue growth to see if the net effect is positive. This discussion should also be a cautionary note for firms that are run with marketing objectives such as maximizing market share or posting high-revenue growth. Those objectives can often be accomplished by giving customers valuable options. Salespeople will want to meet their sales targets and are not particularly concerned about the long-term costs they may create with their commitments to customers—and the firm may be worse off as a consequence.

Switching Options While the abandonment option considers the value of shutting down an investment, an intermediate alternative is worth examining. Firms can sometimes alter production levels in response to demand. Being able to do so can make an investment more valuable. Consider, for instance, a power company that is considering a new plant to generate electricity. Assume that the company can run the plant at full capacity and produce 1 million kilowatt-hours of power or run it at half capacity (and substantially less cost) and produce 500,000 kilowatt-hours of power. In this case, the company can observe both the demand for power and the revenues per kilowatt-hour and decide if it makes sense to run at full or half capacity. The value of this switching option can then be compared to the cost of building in this flexibility in the first place. The airline business provides an interesting case study in how different companies manage their cost structure and the payoffs to their strategies. One reason that Southwest Airlines has been able to maintain its profitability in a deeply troubled airline sector is that the company has made cost flexibility a central component of its decision process. From its choice of using only one type of aircraft for its entire fleet11 to its refusal, for the most part, to fly into large urban airports (with high gate costs), the company’s operations have created the most flexible cost structure in the business. Thus, when revenues dip (as they inevitably do when the economy weakens), Southwest can trim its costs and stay profitable while other airlines teeter on the brink of bankruptcy.

11

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From its inception until recently, Southwest used the Boeing 737 as its workhorse, thus reducing the need to keep different maintenance crews at each airport it flies into.



Caveats for Real Options The discussion of the potential applications of real options should provide a window into why they are so alluring to practitioners and businesses. In essence, we are ignoring the time-honored rules of capital budgeting, which include rejecting investments that have negative net present value, when real options are present. Not only does the real options approach encourage you to make investments that do not meet conventional financial criteria, it also makes it more likely that you will do so the less you know about the investment. Ignorance, rather than being a weakness, becomes a virtue, because it increases the uncertainty in the estimated value and the resulting option value. To prevent the real options process from being hijacked by managers who want to rationalize bad (and risky) decisions, we have to impose some reasonable constraints on when it can be used. And when it is used, we have to specify how to estimate its value. First, 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, three key questions need to be answered affirmatively: Q Is the first investment a prerequisite 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 option. Now consider the Disney expansion into Mexico. The initial investment in a Spanish channel provides Disney with information about market potential, without which presumably it is unwilling to expand into the larger Latin American market. Unlike the examples of patents and undeveloped reserves, the initial investment is not a prerequisite for the second, although management might view it as such. The connection gets even weaker 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 Brazilian brewery to preserve the option to enter the Brazilian beer market are examples of such transactions. Q 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 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 that case, it is questionable whether these investments can generate any excess returns. In reality, most investments


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fall in between these two extremes, with greater competitive advantages being associated with higher excess returns and larger option values. Q How sustainable are the competitive advantages? In a competitive marketplace, excess returns attract competitors, and competition drives out excess returns. The more sustainable the competitive advantages possessed by a firm, the greater 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 that have 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 advantage is likely to be sustainable for longer periods. Alternatively, if the competitive advantage comes from being the first mover in a market or technological expertise, it will come under assault far sooner. The most direct way of reflecting this in the value of the option is in its life. The option’s life can be set to the period of competitive advantage. Only the excess returns earned over this period count toward the value of the option. Second, 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 taking a project with poor returns or for paying a premium on an acquisition on the basis of real options should be required to value these real options. They also should be required to show that the economic benefits exceed the costs. Two arguments can be 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 with error is better than no estimate at all. The process of quantitatively trying to estimate the value of a real option is, in fact, the first step to understanding what drives its value. We should mention a final note of caution about the use of option pricing models to assess the value of real options. Option pricing models, whether they are of the binomial or BlackScholes variety, are based on two fundamental precepts—replication and arbitrage. For either to be feasible, you have to be able to trade on the underlying asset and on the option. This is easy to accomplish with a listed option on a traded stock; you can trade on both the stock and the listed option. It is much more difficult to pull off when valuing a patent or an investment expansion opportunity. Neither the underlying asset (the product that emerges from the patent) nor the option itself is traded. This does not mean that you cannot estimate the value of a patent as an option, but it does indicate that monetizing this value will be much more difficult. In the Avonex example from earlier in the chapter, the option value for the patent was $907 million, whereas the conventional risk-adjusted value was only $547 million. Much as you may believe in the former as the right estimate of value, it is unlikely that any potential buyer of the patent will come close to paying that amount.

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Conclusion In contrast to the approaches that focus on downside risk—risk-adjusted value, simulations, and decision trees—the real options approach brings an optimistic view to uncertainty. While conceding that uncertainty can create losses, it argues that uncertainty can also be exploited for potential gains and that updated information can be used to augment the upside and reduce the downside risks inherent in investments. In essence, you are arguing that the conventional riskadjustment approaches fail to capture this flexibility and that you should add an option premium to the risk-adjusted value. This chapter considered three potential real options and applications of each. The first is the option to delay. This is where a firm with exclusive rights to an investment has the option of deciding when to take that investment and to delay taking it, if necessary. The second is the option to expand. This is where a firm may be willing to lose money on an initial investment in the hopes of expanding into other investments or markets further down the road. The third is the option to abandon an investment if it looks like a money loser, early in the process. While it is clearly appropriate to attach value to real options in some cases—patents, reserves of natural resources, or exclusive licenses—the argument for an option premium gets progressively weaker as we move away from the exclusivity inherent in each of these cases. In particular, a firm that invests in an emerging market in a money-losing enterprise, using the argument that the market is a large and potentially profitable one, could be making a serious mistake. After all, the firm could be right in its assessment of the market, but absent barriers to entry, it may not be able to earn excess returns in that market or keep out the competition. Not all opportunities are options, and not all options have significant economic value.

Appendix 5.1: Basics of Options and 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. Because 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.

Option Payoffs A call option gives the option buyer 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 option buyer buys the stock at the exercise price and the difference between the asset value and the exercise price comprises the gross profit on the 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 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 the Figure 5A.1.


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Net Payoff

Strike Price Price of Underlying Asset

Figure 5A.1: Payoff on Call Option

A put option gives the option buyer the right to sell the underlying asset at a fixed price, again called the strike or exercise price, 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 at 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 5A.2. Net Payoff

Strike Price Price of Underlying

Figure 5A.2: Payoff on Put Option

There is one final distinction that needs to be made. Options are usually categorized as American or European options. A primary distinction between the two is that American options can be exercised at any time prior to their expiration, whereas 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

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most cases, the time premium associated with the remaining life of an option and transactions costs makes early exercise suboptimal. 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.1

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. Because 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 increases. 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 the value of the option. This is true for both calls and puts. Although it might seem counterintuitive that an increase in a risk measure (variance) should increase value, options are different from other securities because 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: We can expect the value of the underlying asset to decrease if dividend payments are made on the asset during the life of the 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. A more intuitive way of thinking about dividend payments, for call options, is as 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, that is, 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 means 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 declines as the strike price increases. In the case of puts, where the holder has the right to sell at a fixed price, the value increases 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 1

Although early exercise is not optimal generally, there are at least two exceptions to this rule. One is a case in which 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.


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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: Because the buyer of an option pays the price of the option up front, an opportunity cost is involved. This cost depends on 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 because the exercise price does not have to be paid (received) until expiration on calls (puts). Increases in the interest rate increase the value of calls and reduce the value of puts. Table 5A.1 summarizes the variables and their predicted effects on call and put prices. Table 5A.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

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 derive their final formulation. Although 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 on a simple formulation for the asset price process, in which the asset can move to one of two possible prices in any time period. The general formulation of a stock price process that follows the binomial is shown in Figure 5A.3.

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Su

2

Su

S

Sud

Sd

Sd

2

Figure 5A.3: General Formulation for Binomial Price Path

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. The objective in creating a replicating portfolio is to use a combination of risk-free borrowing/ lending and the underlying asset to create 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 preceding general formulation, 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 involves borrowing $B and acquiring Δ of the underlying asset, where: Δ = Number of Units of the Underlying Asset Bought = (Cu – 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 multiperiod binomial process, the valuation has to proceed iteratively; that is, starting with the last time period and moving backward 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 Δ 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 Consider a simple example. 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:


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t=2

Call Price

100

50

50

0

25

0

t=1 Call Strike Price = 50 Expires at t = 2

70

t=0 50

35

Now assume that the interest rate is 11%. In addition, define the following: Δ = Number of Shares in the Replicating Portfolio B = Dollars of Borrowing in the Replicating Portfolio The objective is to combine Δ 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: t=2

Call Value

Replicating Portfolio

100

50

(100 ) – (1.11 B) = 50

50

0

(50 ) – (1.11 B) = 0 | Solving for and B = 1 ; B = 45 Buy 1 Share; Borrow $45

t=1 70

Thus, if the stock price is $70 at t = 1, borrowing $45 and buying 1 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 therefore: Value of Call = Value of Replicating Position = 70 Δ – B = 70 – 45 = 25 Considering the other leg of the binomial tree at t = 1,

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t=2

Call Value


50

0

(50 ) – (1.11 B) = 0

25

0

(25 ) – (1.11 B) = 0 | Solving for and B =0;B=0

t=1 35

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. t=1


70

(70 ) – (B 1.11) = 25 (from step 1)

35

(35 ) – (1.11 B) = 0 (from step 1) | Solving for and B = 5/7; B = 22.5; Buy 5/7 Shares; Borrow 22.5

t=0 50

In other words, borrowing $22.50 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: Value of Call = Value of Replicating Position = 5/7 * Current Stock Price – $22.50 = $13.20 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—that is, 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 be guaranteed the difference as a profit. The cash flows on the two positions 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.


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The Black-Scholes Model The binomial model is a discrete-time model for asset price movements, including a time interval (t) between price movements. As the time interval is shortened, the limiting distribution, as t approaches 0, can take one of two forms. If, as t approaches 0, price changes become smaller, the limiting distribution is the normal distribution and the price process is a continuous one. If, as t approaches 0, price changes remain large, the limiting distribution is the Poisson distribution— that is, a distribution that allows for price jumps. The Black-Scholes model applies when the limiting distribution is the normal distribution,2 and it explicitly assumes that the price process is continuous.

The Model The original Black-Scholes model was designed to value European options, which were dividendprotected. Thus, neither the possibility of early exercise nor the payment of dividends affects the value of options in this model. The value of a call option in the Black-Scholes model can be written as a function of the following 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 model itself can be written as: Value of Call = S N (d1) – K e-rt N(d2) where ln d1 =

σ2 S + (r + )t K 2 σ t

d2 = d1 - σ √t

The process of valuation of options using the Black-Scholes model involves the following steps: Step 1: The inputs to the Black-Scholes model are used to estimate d1 and d2. Step 2: The cumulative normal distribution functions, N(d1) and N(d2), corresponding to these standardized normal variables are estimated. Step 3: The present value of the exercise price is estimated, using the continuous time version of the present value formulation: 2

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Stock prices cannot drop below zero because of the limited liability of stockholders in publicly listed firms. Hence, stock prices by themselves cannot be normally distributed because a normal distribution requires some probability of infinitely negative values. The distribution of the natural logs of stock prices is assumed to be log-normal in the Black-Scholes model. This is why the variance used in this model is the variance in the log of stock prices.



Present Value of Exercise Price = K e-rt Step 4: The value of the call is estimated from the Black-Scholes model. The determinants of value in the Black-Scholes model are the same as those in the binomial—the current value of the stock price, the variability in stock prices, the time to expiration on the option, the strike price, and the riskless interest rate. The principle of replicating portfolios that is used in binomial valuation also underlies the Black-Scholes model. In fact, embedded in the Black-Scholes model is the replicating portfolio: Value of Call = S N (d1)

–

Buy N(d1) Shares

K e-rt N(d2) Borrow This Amount

N(d1), which is the number of shares that are needed to create the replicating portfolio, is called the option delta. This replicating portfolio is self-financing and has the same value as the call at every stage of the option’s life.

Model Limitations and Fixes The version of the Black-Scholes model presented previously does not take into account the possibility of early exercise or the payment of dividends, both of which impact the value of options. Adjustments exist, which although not perfect, provide partial corrections to value. Dividends The payment of dividends reduces the stock price. Consequently, call options become less valuable and put options more valuable as dividend payments increase. One approach to dealing with dividends is to estimate the present value of expected dividends 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. Because this becomes impractical as the option life becomes longer, we would suggest an alternate approach. If the dividend yield (y = Dividends/Current Value of the Asset) of 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 ln d1 =

σ2 S )t + (r – y + 2 K σ t

d2 = d1 - σ √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 value from dividend payments. Second, the interest rate is offset by the dividend yield to reflect the lower carrying cost from holding the stock (in the replicating portfolio). The net effect is a reduction in the value of calls, with the adjustment, and an increase in the value of puts.


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Early Exercise The Black-Scholes model is designed to value European options, whereas most options that we consider are American options, which can be exercised anytime before expiration. Without working through the mechanics of valuation models, an American option should always be worth at least as much and generally more than a European option because of the early exercise option. There are three basic approaches for dealing with the possibility of early exercise. The first is to continue to use the unadjusted Black-Scholes model and regard the resulting value as a floor or conservative estimate of the true value. The second approach is 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 third approach is to use a modified version of the binomial model to consider the possibility of early exercise. Although it is difficult to estimate the prices for each node of a binomial, variances estimated from historical data can be used to compute the expected up and down movements in the binomial. 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 = Exp [(r – s2/2)(T/m) + √(s2T/m)] d = Exp [(r – σ2/2)(T/m) – √(σ2T/m)] 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. Multiplying the stock price at each stage by u and d yields the up and the down prices. These can then be used to value the asset. The Impact of Exercise on the Value of the Underlying Asset The derivation of the Black-Scholes model is based on 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 affect the stock price.3 The expected negative impact (dilution) of exercise decreases 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 = (S ns + W nw)/(ns + nw) where S = Current Value of the Stock nw = Number of Warrants Outstanding W = Market Value of Warrants Outstanding ns = Number of Shares Outstanding When the warrants are exercised, the number of shares outstanding increases, reducing the stock price. The numerator reflects the market value of equity, including both stocks and warrants outstanding. The reduction in S reduces the value of the call option.

3 Warrants are call options issued by firms, either as part of management compensation contracts or to raise equity.

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There is an element of circularity in this analysis because 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 off the process with an estimated value of the warrant (say, the exercise value) and then iterating with the new estimated value for the warrant until there is convergence.

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 through an arbitrage relationship that specifies that: C – P = S – K e-rt where C is the value of the call and P is the value of the put (with the same life and exercise price). This arbitrage relationship can be derived fairly easily and is called put-call parity. To see why put-call parity holds, consider creating the following portfolio: (a) Sell a call and buy a put with exercise price K and the same expiration date “t” (b) Buy the stock at current stock 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*: Position Sell call

Payoffs at t if S*>K -(S* – K)

Payoffs at t if S*

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