Debt Financing Citibank

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Debt Financing July 1994

Debt Financing

Warning This workbook is the product of, and copyrighted by, Citibank N.A. It is solely for the internal use of Citibank, N.A., and may not be used for any other purpose. It is unlawful to reproduce the contents of these materials, in whole or in part, by any method, printed, electronic, or otherwise; or to disseminate or sell the same without the prior written consent of the Professional Development Center of Latin America Global Finance and the Citibank Asia Pacific Banking Institute. Please sign your name in the space below.

Table of Contents

TABLE OF CONTENTS

Introduction: Course Overview............................................................................. v Course Objectives.......................................................................... vii The Workbook ............................................................................... vii Unit 1: Fundamentals of Debt Financing Introduction ................................................................................... 1-1 Unit Objectives .............................................................................. 1-1 Key Terms..................................................................................... 1-1 What Is Debt Financing?............................................................... 1-2 Sources of Debt Capital ................................................................ 1-3 Debt Markets ...................................................................... 1-3 Participants.............................................................. 1-3 Types of Markets ..................................................... 1-5 Trading Debt Securities ........................................... 1-7 Bank Financing................................................................... 1-8 Provisions for Paying Off Debt ...................................................... 1-9 Interest Payments .............................................................. 1-9 Determining the Rate of Interest............................ 1-10 Determining Interest Payments ............................. 1-12 Principal Payments........................................................... 1-14 Classifying Debt Securities ......................................................... 1-15 Claims on Assets.............................................................. 1-16 Mortgage Bonds .................................................... 1-16 Collateral Trust Bonds ........................................... 1-17 Guaranteed Bonds ................................................ 1-17 Debentures ............................................................ 1-17 Asset-backed Securities ........................................ 1-18 Relative Priority of the Claim ............................................ 1-19

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Unit 1: Fundamentals of Debt Financing (Continued) Unit Summary ............................................................................. 1-20 Progress Check 1........................................................................ 1-23 Unit 2: Raising Debt Capital Introduction ................................................................................... 2-1 Unit Objectives .............................................................................. 2-1 Issuing Debt Securities ................................................................. 2-2 Public Offering.................................................................... 2-2 Private Placement .............................................................. 2-5 Bank Financing ............................................................................. 2-7 Unit Summary ............................................................................... 2-9 Progress Check 2........................................................................ 2-11 Unit 3: Valuing Debt Introduction ................................................................................... 3-1 Unit Objectives .............................................................................. 3-1 Calculating Yield ........................................................................... 3-2 Current Yield ...................................................................... 3-3 Yield-to-maturity ................................................................. 3-4 Yield-to-call......................................................................... 3-6 Realized Compound Yield.................................................. 3-6 Summary............................................................................ 3-8 Practice Exercise 3.1 .................................................................. 3-11 Calculating Price ......................................................................... 3-13 Zero-coupon Securities .................................................... 3-13 Discount Yield........................................................ 3-14 Fixed-income Securities ................................................... 3-17 Accumulated Interest............................................. 3-18 Summary.......................................................................... 3-19 Practice Exercise 3.2 .................................................................. 3-21 ver. 1.0 v.07/06/94 p.01/10/00

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Unit 3: Valuing Debt (Continued) Duration ...................................................................................... 3-23 Macauley Duration ........................................................... 3-23 Duration of a Perpetuity.................................................... 3-26 Modified Duration ............................................................. 3-27 Duration of a Portfolio ...................................................... 3-28 Duration Relationships ..................................................... 3-28 Convexity.......................................................................... 3-30 Summary.......................................................................... 3-32 Practice Exercise 3.3 .................................................................. 3-33 Unit Summary ............................................................................. 3-37 Progress Check 3........................................................................ 3-39 Unit 4: Debt Instruments Introduction ................................................................................... 4-1 Unit Objectives .............................................................................. 4-1 Short-term Markets ....................................................................... 4-1 Treasury Bills...................................................................... 4-2 Banker's Acceptance.......................................................... 4-2 Commercial Paper.............................................................. 4-4 Certificate of Deposit .......................................................... 4-5 Repurchase Agreements.................................................... 4-6 Medium-term Markets ................................................................... 4-7 U.S. Treasury Notes........................................................... 4-8 Medium-term Notes............................................................ 4-8 Long-term Markets ........................................................................ 4-9 U.S. Treasury Bonds ........................................................ 4-10 Corporate Bonds .............................................................. 4-10 Municipal Bonds ............................................................... 4-11 Eurobonds ........................................................................ 4-12 Brady Bonds..................................................................... 4-13 v.07/06/94 p.01/10/00

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Unit 4: Debt Instruments (Continued) Complex Debt Securities............................................................. 4-14 Equity-linked Debt ............................................................ 4-14 Convertible Debt .................................................... 4-15 Warrants................................................................ 4-15 Dual Currency Debt..................................................................... 4-16 Unit Summary ............................................................................. 4-17 Progress Check 4........................................................................ 4-19 Unit 5: Derivative Securities Introduction ................................................................................... 5-1 Unit Objectives .............................................................................. 5-1 Options.......................................................................................... 5-2 Background and Markets ................................................... 5-3 Payoff Profile for Calls and Puts......................................... 5-4 Call Options ............................................................. 5-5 Put Options.............................................................. 5-7 Swaps ........................................................................................... 5-9 Interest Rate Swaps ........................................................... 5-9 Currency Swaps ............................................................... 5-14 Forward Agreements................................................................... 5-15 Value for Buyer / Seller .................................................... 5-15 Price Discovery ................................................................ 5-16 Unit Summary ............................................................................. 5-20 Progress Check 5........................................................................ 5-23

Appendix Glossary........................................................................................ G-1

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Introduction

INTRODUCTION: DEBT FINANCING COURSE OVERVIEW This workbook provides a broad introduction to the debt markets, the participants in the markets, and some of the more common securities being issued and traded. The student completing this course will gain a basic working vocabulary of the key terms currently being used in the debt markets. Because this is an introductory course, we will cover a wide range of topics without going into great detail. Additional study will be necessary to gain a more complete knowledge of debt securities and the markets in which they are traded. UNIT 1: Fundamentals of Debt Financing Types of markets in which debt securities are traded are presented in the first unit. Some of the more common features found in debt securities are also introduced, including the provisions for making interest payments and repaying the principal. The unit also discusses different types of securities, based on the backing that the issuer provides for the bonds. The main focus is to introduce key terms and ideas that will be helpful in evaluating securities. UNIT 2: Raising Debt Capital Unit Two provides a discussion of the processes necessary to issue debt securities. Relative advantages and disadvantages of several methods for raising debt capital are discussed. These methods include a public offering of debt, a private offering, and securing a bank loan. Costs associated with each method are also presented. Once again, the unit focuses on introducing key terms and processes. UNIT 3: Valuing Debt The third unit focuses on the mathematics associated with debt instruments. The student learns how to calculate the appropriate yield of an instrument and how to compare the yields of different instruments. Formulas are provided for estimating an instrument's market price and the accumulated interest of an interest-bearing security. The unit concludes with an introduction to the concepts of duration and convexity and describes their applications. The student will find a financial calculator useful in making the required calculations.

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UNIT 4: Debt Instruments Some common debt securities are described in Unit Four. The securities are grouped according to their relative maturity. Some more complex securities are also discussed, including equity-linked debt instruments. The discussion of each security includes typical issuers of the security, common investors buying the instruments, and methods for pricing the securities. This unit focuses on building a useful vocabulary and developing an understanding of the securities.

UNIT 5: Derivative Securities The last unit provides an introduction to some common derivative securities, including options, swaps, and forward agreements. Brief descriptions of each security and the types of market participants who might use each type of security are presented along with reasons for their use. This unit is included so that students not only can begin to understand how debt, equity, and derivative securities are linked together, but also how investors can hedge the risk created by investing in one security by investing in another security. This unit briefly touches on some of the characteristics of derivative securities. For a more thorough discussion of these instruments, you should refer to the appropriate Citibank self-study course. As mentioned earlier, this course is designed to introduce a wide range of topics with a brief discussion of each. Additional study will be necessary to gain a more complete understanding of debt securities, how they are issued, and how they are evaluated by investors. Students should focus on learning the basic terms and understanding the concepts behind the calculations and relationships discussed in the workbook.

COURSE OBJECTIVES When you complete this workbook, you will be able to: Understand the fundamentals of debt markets, the participants, and the securities being issued and traded Understand some of the more common features found in debt instruments ver. 1.0 v.07/06/94 p.01/10/00

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Understand the basic mathematical calculations necessary for pricing debt securities, finding the appropriate measure of yield, and finding the accumulated interest on a coupon-paying instrument Describe the features of some of the more common debt instruments, grouped according to their relative maturity Identify some complex securities that combine debt and equity features Identify some common derivative securities, and describe their characteristics and uses

THE WORKBOOK This self-instruction workbook has been designed to give you complete control over your own learning. The material is broken into workable sections, each containing everything you need to master the content. You can move through the workbook at your own pace, and go back to review ideas that you didn't completely understand the first time. Each unit contains:

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Unit Objectives –

which point out important elements in the unit that you are expected to learn.

Text –

which is the "heart" of the workbook where the content is presented in detail.

Key Terms –

which also appear in the Glossary. They appear in bold face the first time they appear in the text.

Instructional Mapping –

terms or phrases in the left margin which highlight significant points in the lesson.

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✔ Practice Exercises and Progress Checks –

help you practice what you have learned and check your progress. Appropriate questions or problems are presented at strategic places within Unit Three and at the end of all units. You will not be graded on these by anyone else; they are to help you evaluate your progress. Each set of questions is followed by an Answer Key. If you have an incorrect answer, we encourage you to review the corresponding text and then try the question again.

In addition to these unit elements, the workbook includes the: Glossary –

which contains all of the key terms used in the workbook.

Index –

which helps you locate the glossary item in the workbook.

This is a self-instructional course; your progress will not be supervised. We expect you to complete the course to the best of your ability and at your own speed. Now that you know what to expect, you are ready to begin. Please turn to Unit One. Good Luck!

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Unit 1

UNIT 1: FUNDAMENTALS OF DEBT FINANCING

INTRODUCTION

In this unit, you are introduced to basic concepts that will help you understand the use of debt as a source of capital and as an investment vehicle. We discuss the sources of debt capital — bank financing and debt markets — and describe how debt financing is arranged from each source. We introduce two key considerations for any debt agreement: how debt is paid off and how security is provided for a loan.

UNIT OBJECTIVES

When you complete Unit One, you will be able to: n

n

Identify two sources of debt capital for a company Recognize the major types of debt markets and the types of transactions that occur

n

Identify the factors that affect the interest rate borrowers pay for debt capital

n

Recognize the conventions for paying interest and repaying principal

n

Recognize two methods for classifying debt

KEY TERMS

Let's begin by defining some key terms that we will use throughout the course. You will find it helpful to familiarize yourself with them now. Basis Point

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One one-hundredth of one percent (0.01%). Fifty basis points equal 1/2 of one percent. A basis point is sometimes referred to as a "tick."

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FUNDAMENTALS OF DEBT FINANCING

Loan

A debt agreement between two parties: a borrower and a lender

Principal

The amount of money the lender provides for the borrower to use; also known as the face value, or par value, of the security

Maturity

Length of time in days, weeks, months, or years before a loan or a debt security becomes due for repayment. The total length of time that the agreement is in force is sometimes called the security's "term" or "tenor."

Bond

A debt agreement in the form of a security issued by a company or a unit of government. The issuer promises to pay interest on the principal over the maturity of the bond and repay the principal when the bond becomes due.

Note

A debt agreement in the form of a security issued by a company or unit of government with a maturity of one to five years Because notes are similar to bonds in every aspect except maturity, analysts often group notes and bonds together when referring to debt securities.

WHAT IS DEBT FINANCING? Definition of debt financing

Debt financing is a major source of capital for most firms. Debt financing occurs when: n

n

Investors provide capital in the form of loans for the managers of a company to use to operate the business The company, in return, promises to repay the capital to the investors plus a rate of interest for the use of the capital

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SOURCES OF DEBT CAPITAL Debt markets and bank financing

Debt markets and bank financing are the two primary sources of debt capital. In bank financing, the company and the lending institution negotiate a debt agreement directly. In debt markets, the company issues securities representing the loan for investors to purchase. There are many types of debt securities with different structures and maturities. Most debt financing transactions take place through the sale of marketable securities (such as notes or bonds) or the sale of a securitized instrument (discussed later in this unit).

Debt Markets To give you an overview of debt markets, we will introduce the participants and the types of debt markets, and discuss how securities are traded. Participants

The major participants in debt markets are the same as those in equity markets: issuers (borrowers) and investors (lenders). These two parties may contact each other directly (i.e., when a company borrows money from a bank) or the two parties may use a financial intermediary (broker or dealer) when the issuer wishes to raise capital by selling securities to investors. Issuers sell marketable securities

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Technically, an issuer of debt is any entity that borrows capital in the debt markets. However, general practice reserves the term "issuer" for companies that sell marketable securities in debt markets. You would not call an individual who borrows money to build a home an issuer, but you would call a corporation selling bonds to fund the expansion of its business an issuer.

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The largest issuers in the debt markets are companies, corporations, governments, and government agencies. Together, these groups account for nearly all of the debt securities sold to investors, either directly or through intermediaries. We will discuss the process for issuing securities in Unit Two.

Investors lend capital to the debt markets

An investor is any entity that loans capital in debt markets. Investors may loan money directly on specific terms negotiated with the borrower, as a bank may do for an individual buying an automobile, or investors may provide capital by purchasing the securities issued by a company or a government. The largest investors in the debt markets are institutional investors — including insurance companies, mutual funds, pension funds, and banks. Institutional investors provide the majority of the capital raised in debt markets. Individual investors are also important sources of capital, but they have less influence than institutional investors over market activity.

Wholesale / retail markets

The wholesale (institutional) market refers to the purchase of securities by institutional investors. The retail market focuses on individual investors.

Targeting a market

Sometimes, issuers will target a specific market to sell their securities. If a company wishes to generate name recognition, it may target the retail market so that its securities are placed with many investors. A company issuing a complicated security may target the wholesale market to take advantage of the high degree of sophistication of institutional investors.

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Types of Markets

While there is no classification system for global debt markets, there are some commonly used conventions. From the perspective of a given country, analysts usually divide the global debt market into two groups: national markets and international markets. This classification is based on the location of the debt issuer relative to the country where the investor resides. Internal debt market

1. National Markets The national debt market is often called the internal debt market — the market where debt instruments are being traded within a country. The national market has two parts: domestic market and foreign market. n

Domestic market In the domestic market, securities are issued by companies based in the country where the securities trade. For example, a Mexican company issues peso-denominated bonds. If these bonds are traded in Mexico City, they are part of the Mexican domestic market.

n

Foreign market In the foreign market of a country, a company based outside that country issues securities in that country. For example, yen-denominated bonds issued by a Mexican company and traded in the Tokyo markets are considered foreign bonds.

Foreign bond nicknames

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Foreign bonds may have specific nicknames, i.e., analysts call the bonds in our example Samurai bonds. Dollardenominated bonds issued by non-U.S. companies trading in the U.S. are called Yankee bonds. Foreign bonds in the United Kingdom are known as Bulldog bonds; in Spain they are called Matador bonds; in the Netherlands, Rembrandt bonds.

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Foreign bond regulation

Most national governments regulate the issue of securities by companies outside the country. Usually their rules specify the: n

Types of securities that may be issued

n

Size of the issue

n

Waiting period for the issue

n

Credit standard for the issuer

n

Standard for information disclosure

n

Possible restrictions on the types of institutions that may underwrite the issue. (For more information about underwriting, see Unit Two in the Equity Financing workbook.)

As markets become more global and efficient, and investors become more sophisticated, governments are gradually eliminating these regulations. 2. International Markets Euromarket

The international debt markets may be referred to as the external debt markets or offshore markets. However, the most common name for the international markets is Euromarket. International market issues can take place in any location, although London is the most important issuing market. Most Euromarket issues are listed on the London or Luxembourg exchanges. These markets are not subject to the direct control of any government.

Classified by currency of issue

The Euromarket is divided into groups based on the currency in which the issue is denominated. For example, a Eurobond denominated in Japanese yen is referred to as a Euroyen bond issue; dollar-denominated bonds are called Eurodollar bonds. Eurodollar bonds represent the largest share of this market, but other important currencies include the Deutschemark, British pound sterling, Dutch guilder, Swiss franc, Japanese yen, Canadian dollar, and European Currency Unit (ECU).

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Key features of Eurobonds

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Several features distinguish Euromarket bonds. n

n

n

An international syndicate of investment banks usually underwrites the issue and offers securities to investors in several countries at the same time. Euromarket issues generally do not fall under the jurisdiction of any single country and have relatively few regulations for investors or issuers. This is a great advantage to issuers because the Euromarket enables companies to avoid many of the foreign market regulations mentioned earlier. International bonds are issued in an unregistered, or bearer, form. This is an advantage to investors seeking tax avoidance, since the investor's identity is not listed anywhere.

Consult Unit One in the Equity Financing workbook for more information about bearer shares and listing an issue on a particular exchange. Trading Debt Securities Types of transactions

There are two types of transactions in debt markets: 1. Primary market transactions take place when an investor provides capital to a borrower in return for an agreement outlining the payment of interest and the repayment of the principal . Primary market transactions directly affect the capital structure of the borrower. 2. Secondary market transactions take place when investors buy and sell debt securities in the open market with other investors. Secondary market transactions have no direct effect on the original issuer of the security.

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Location of markets


There is no single clearinghouse that processes debt security trades. Most open economy countries have at least one market where debt securities may be bought and sold (provided the specific security is listed on that exchange). The major debt markets have a large number of sophisticated investors that participate in the buying and selling of the securities. There are relatively few regulations for investors and issuers. The largest debt security markets are found in New York, Tokyo, Frankfurt, London, Zurich, and Amsterdam. As mentioned earlier, most Eurobond issues are listed in London, but some trade in Luxembourg.

Multiple market issues and listings

With the growth of the Eurobond market, many companies issue debt in several markets simultaneously. Investors sometimes are able to trade a single security around the clock because that security may be listed in Tokyo, New York, and London. U.S. Treasury instruments are examples of securities traded in more than one market. The investor simply buys or sells in the market that is open at the time the trade is desired. In this section, we presented an overview of the primary and secondary, national and international debt markets. The other source of debt capital is bank financing. Bank Financing

Direct agreement

Bank financing is a loan arrangement between a company and a lending institution. The two entities negotiate the maturity of the loan, the interest rate, and the payment schedule. Sometimes the agreement involves a syndicate, or group of banks, in order to spread the risk.

Easier to renegotiate

Banks require the company to have collateral (an asset that is used to secure the loan), but this requirement often is negotiable. If a company is having trouble meeting its obligations, it usually is easier to negotiate new terms for bank financing than for issued securities. This flexibility results from the ongoing relationship between the bank and the company.

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More costly to borrower

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Generally, bank financing is more costly to the borrower than a public issue in the national or Eurobond markets because the bank requires a higher interest rate to compensate for the perceived illiquidity (lack of a secondary market where the bank could sell the loan to another investor) and default risk. Small, lesser-known companies rely on bank financing to provide debt capital until they are able to access the debt securities markets.

PROVISIONS FOR PAYING OFF DEBT

Let's shift our focus from how companies access debt capital to how they repay the debt. The terms of a debt agreement specify the manner in which the borrower will repay the investor for the use of the capital. Debt agreements require the borrower to: n

Make interest payments in return for the use of the funds

n

Repay the borrowed principal

First, let's look at the factors that determine interest rates and the types of interest payments that may be made.

Interest Payments An issuer must pay the investor for the use of borrowed funds. An interest rate is used to calculate the amount of interest the borrower must pay.

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Determining the Rate of Interest Factors affecting the interest rate

The rate of interest a firm pays depends on several factors, including the real risk-free rate, expected inflation, credit standing of the issuer, and length of time the funds are borrowed. n

Real, risk-free rate The base component of interest rates, the real, risk-free rate, is determined by the conditions of the economy and the time preference of consumers for current-versus-future consumption. The real, risk-free rate is difficult to isolate from other factors, but most researchers believe that it has fluctuated between 2% and 4% in recent years. Analysts often use the interest rate paid on short-term U.S. Treasury securities as an approximation for the real, risk-free rate.

n

Expected inflation Expected inflation is an important factor affecting the general level of interest rates. Investors' expectations concerning the future level of inflation in an economy often influence current interest rates.

n

Credit standing Another influential factor in determining the rate of interest an issuer will pay is the credit standing of the issuer. Companies and units of government that are rated as good credit risks pay a lower rate of interest on borrowed funds, all other factors being equal. Several services rate the creditworthiness of companies. In U.S. markets, the two major companies providing credit rating services are Standard & Poor's and Moody's.

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Length of time the funds are borrowed The length of time funds are borrowed also affects the interest rate. Companies that borrow for 30 years pay a different rate than companies borrowing for 30 days, all other factors being equal. The relationship between short-term and long-term rates is called the yield curve. For a more thorough discussion on the relationship between interest rates and their determination, consult the self-study course on corporate finance or any finance textbook.

Benchmark interest rates

Many issuers and investors use key interest rates as benchmarks to set interest rates on their agreements. These include Treasury yield, U.S. prime lending rate, federal funds rate, and international benchmark rates. n

Treasury yield The rate of interest earned on U.S. Treasury securities is one important benchmark rate. Often referred to as the Treasury yield, it is usually quoted with the maturity (e.g., the six-month Treasury yield). Investors consider this rate a good proxy for a risk-free rate because they consider the U.S. Government to have no default risk.

n

U.S. prime lending rate This common benchmark rate is the short-term rate of interest U.S. banks charge their best, or "prime," customers.

n

Federal funds rate Most governments require banks to maintain a minimum percentage of deposits on reserve. Banks that find themselves temporarily short on reserves can borrow reserves from banks that have excess reserves. The interest rate charged on these short-term loans is called the federal funds rate. This rate is also used as a benchmark for other types of loans.

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n

International benchmark rates There are other important interest rates outside the U.S. market. The London Interbank Offer(ed) Rate (LIBOR) is the rate at which Eurobanks lend money to each other in the Eurodeposit market. LIBOR is the most common benchmark used in the Euromarkets. The London Interbank Bid Rate (LIBID) is the rate of interest paid on interbank deposits in London in the Eurocurrency market. LIBID is a few basis points lower than LIBOR and is used less frequently as a benchmark. Other benchmarks include HIBOR (Hong Kong Interbank Offer Rate) and SIBOR (Singapore Interbank Offer Rate), although they are much less common than LIBOR.

Determining Interest Payments Calculations

Having set the interest rate, the interest payment is calculated by multiplying the rate of interest by the principal of the loan. For example, a loan with a principal of $100,000 and annual interest rate of 7% requires a $7,000 interest payment each year the loan agreement is in force. For debt securities, such as bonds, this interest payment is called a coupon and the interest rate is referred to as the coupon rate.

Payment conventions

There are three standard ways for the borrower to pay interest to the lender: fixed rate payment, floating rate payment, and no interest payment (discounted securities). 1. Fixed Rate Payment In some loan agreements, the borrower and investor agree on the rate of interest at the time the agreement is entered. If the rate of interest remains the same for the entire maturity of the loan, it is a fixed-rate loan. The borrower makes a periodic interest payment at a fixed rate during the time the agreement is in effect.

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2. Floating Rate Payment Some loan agreements charge a rate of interest that changes over the period of the agreement. Such loans are called floating rate loans. The interest rate is based on a benchmark, such as the Treasury yield or LIBOR, plus a premium based on the creditworthiness of the borrower. The premium is usually quoted as a number of basis points or additional percentage (3month LIBOR plus 60 basis points or 6-month Treasury plus 2%). The agreement may set the interest rate at the beginning of the interest-paying period or at the time the interest payment is due, depending on the type of security. 3. No Interest Payment Zero-coupon securities

Zero-coupon securities require no interest payments during the time of the agreement. The borrower receives less than the face value of the loan at the time of the agreement (i.e., the bonds are sold at a discount). A zero-coupon security charges an implied interest rate that is represented by the rate of return earned by the investor.

Example

For example, an issuer sells a $1,000 bond at a discount and receives an amount that is less than $1,000 from the investor at the time of the transaction. During the time the loan agreement is in force, the borrower makes no interest payments. When the loan is due at maturity, the borrower repays the investor $1,000.

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Principal Payments Payment conventions

There are several ways to repay the principal (face value) of a loan, including the bullet payment, sinking fund, and callable debt methods. n

Face value at maturity

Bullet Payment The most common method is the bullet payment. During the course of the loan, the borrower pays only interest and makes no payment on principal until the loan matures. At maturity, the borrower repays the investor the entire face value of the loan. Most government securities and many corporate bonds use a bullet payment.

n

Sinking Fund

Gradual repayment

Because the issuer is likely to need a large amount of cash to repay the principal at the end of a loan agreement, many debt agreements set up a sinking fund that gradually repays the principal. A trustee is appointed to ensure the appropriate amount is deposited into the account, and the issuer makes periodic payments into the fund. The payment into the sinking fund is usually based on the depreciation schedule of the assets that were purchased with the borrowed capital.

Requires early retirement of some bonds

Sinking fund provisions require the issuer to retire some of the bonds before maturity. This may be done either by repurchasing them in the open market or by purchasing them from investors at a specified price, depending on which price is lower. When the issuer purchases directly from investors, the bonds are chosen randomly based on their serial numbers. If all of the bonds have not been retired before maturity, the issuer typically makes a bullet payment in the amount of the outstanding bonds to retire the issue.

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Callable Debt

Call price

Some bonds have a provision that gives the issuer an option to repurchase the bonds from investors at a specified price. The price is referred to as the "call" price. Let's use an example to explain the process.

Example

If a company issues bonds when interest rates are relatively high, the debt is considered expensive to the company when interest rates move to lower levels. The price of a bond in the open market represents the present value of the payments that the bond is expected to make over the maturity of the instrument.

Bonds pay higher interest rate

A callable bond allows the issuer to repurchase the old bonds at a price that is usually lower than market price. Thus, investors may not get the full market value for the bonds as they would in an open market transaction. Investors require issuers to compensate them for the possibility that the bonds may be called. Issuers compensate investors in callable bonds most often by paying a higher interest rate than they would pay on bonds of similar risk without the call provision. In some callable bond situations, the borrower issues lowerpriced debt, then uses the proceeds to call the higher-priced bonds. We will discuss the pricing of bonds in more detail in Unit Three.

CLASSIFYING DEBT SECURITIES According to investor's rights to make claims

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Debt securities are often classified according to the investors' rights to make claims on specific assets or cash flows in the event of default or bankruptcy by the firm. "Secured" debt securities are backed by more than just the company name. In general, debt instruments that have specific backing, or collateral, will pay a lower rate of interest than those not backed by specific assets.

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According to relative priority of claims


Debt securities also may be classified by the relative priority of the debt security claims on the assets of the issuer in a reorganization or bankruptcy by the firm.

Claims on Assets Debt securities that are classified by their claims on specific assets fall into five categories: 1. Mortgage bonds 2. Collateral trust bonds 3. Guaranteed bonds 4. Debentures 5. Asset-backed securities Mortgage Bonds Backed by fixed assets

A mortgage bond gives the bondholders a lien, or claim, against the pledged assets (generally property owned by the firm). In other words, the bondholder has a legal right to sell the mortgaged property to satisfy unpaid obligations to the bondholders. Even though the bondholders have a right to this asset, it is unusual for the assets to be sold. In most default cases, the company undergoes a financial reorganization that provides a settlement of the debt for the bondholders. The mortgage provides a strong bargaining position for the bondholders in the reorganization negotiations. Generally, mortgage bonds pay the lowest rate of interest, all other factors being equal.

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Collateral Trust Bonds Backed by other assets

Some companies do not own any fixed assets (such as property or equipment) to which a mortgage can be attached. Many of these companies are holding companies that own the securities of other companies. These holding firms can satisfy their debt holders' demands for backing by issuing collateral trust bonds. The issuer pledges whatever assets (stocks, notes, bonds) are necessary to provide security and collateral for investors. These investors have claim on the collateral assets in the case of default. Once again, default generally results in some type of reorganization rather than a direct sell-off of the assets. Guaranteed Bonds

Backed by another firm's guarantee

Bonds that are backed with the guarantee of a firm other than the issuer are called guaranteed bonds. In most cases, a parent company will guarantee the bonds of a subsidiary. The guarantee may be for the interest payments on the bonds, the principal repayment, or both. This arrangement provides security for the investors buying the bond and lowers the interest rate the issuer pays. In case of default, the guarantor provides the necessary funds to satisfy the investors. Debentures

Backed by earnings potential

Debentures are not secured by any specific assets owned by the issuer. Only the earnings potential of the issuer backs these debt instruments. The investor in debentures is a general creditor of the company. In the event of default or bankruptcy, debenture holders have a claim on the assets of the defaulting firm only after all of the secured bondholders have been satisfied. In a financial reorganization, these bondholders have relatively little bargaining power.

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Debenture holders do have claim on assets before equity holders. To compensate investors for these disadvantages, debentures typically pay a higher rate of interest, all other factors being equal. Asset-backed Securities Backed by cash flows from high-quality loan pool

Lending institutions pool high-quality loans that they have made and use them as collateral for raising capital through the sale of asset-backed securities. Investors buying the securities receive their earnings from the interest and principal payments generated by the loans in the pool. There are many types of asset-backed securities. The most common assets being securitized include automobile loans, credit card receivables, residential and commercial mortgages, and computer and truck leases.

Process of securitization

The term "securitization" refers to the process of packaging groups of small, illiquid assets into a marketable security with an active secondary market. Let's summarize the process of securitization, which involves several participants. n

n

n

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The party who creates the loans to be pooled is called the originator. This is typically a lending or financing institution that wishes to sell its claim on a future set of cash flows (interest on the loans or leases plus principal repayment) for an immediate cash payment. The issuer of the asset-backed security is usually a trust created by the originator for this special purpose. The issuer acquires the assets from the originator and pools them together as marketable securities. The issuer raises money for this purchase by selling the securities to investors. One party acts as the servicer to look after the day-to-day details of the loans. Most often, the originator fills this role to maintain its relationship with its customers. The investment bank acts as the trustee for the transaction. Its role is essentially a policing one to ensure that the security holders are being treated fairly, that the assets are being collected, and that investors are paid on time.

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The enhancer serves to guarantee against default for the underlying assets. This ensures that the investors will receive interest and principal payments in a timely manner. An investment bank or insurance company fulfills the role of enhancer. Finally, the investment bank that assists in the issue of the assetbacked securities helps provide liquidity in the secondary market. This allows investors to buy and sell the securities on the secondary market in a timely manner and at fair prices.

Relative Priority of the Claim An alternative method for classifying debt securities is by the priority of the claim on the assets of the issuer in a reorganization or bankruptcy. Senior and subordinated debt

The terms "senior debt" and "subordinated debt" refer to the relative position of the bondholders in a reorganization or bankruptcy. Senior debt has the highest priority. Generally, secured debt is senior; however, the prospectus specifies the claims to which the investor is entitled. (See Unit One in the Equity Financing workbook for more information about the prospectus.) Subordinated bonds are usually last in the line of creditors for a claim on the assets of the issuer. The terms "senior" and "subordinated" are sometimes used with the classification system that describes claims on assets. For example, a subordinated debenture has claim after senior debentures. Remember, the issuer pays a higher rate of interest to compensate investors for relinquishing their claims on specific assets.

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UNIT SUMMARY

In this unit, we introduced some key ideas necessary to understand debt financing. We looked at two sources of debt capital: debt markets and bank financing. n

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The debt market is where borrowers needing capital sell securities to investors willing to lend capital. We introduced some of the key terms used in debt markets, the participants, and the major national and international markets. Bank financing involves a loan arranged directly between the company needing capital and the financial institution willing to lend that capital.

We discussed the provisions for paying off debt. You learned how interest payments compensate investors for the use of their funds and explored the factors affecting interest rates. We explained that interest payments can be made at a fixed rate, floating rate tied to a benchmark rate, or implied in the price of a zero-coupon bond selling at a discount. We also explained bullet, sinking fund, and callable debt provisions for repaying the principal. Finally, we looked at two methods for classifying debt securities: one based on the investors' claims on assets or cash flows; the other based on the relative position of the bondholders in a reorganization or bankruptcy. We summarized the rights of investors holding mortgage bonds, collateral trust bonds, guaranteed bonds, debentures, and assetbacked securities. We also summarized the process of securitization. You now have a broad understanding of the fundamentals of debt and are ready to focus on the issuer's concerns in raising capital through the debt markets. In Unit Two, we will look at the process of issuing debt.

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You have completed Unit One, Fundamentals of Debt Financing. Please complete the Progress Check to test your understanding of the concepts and check your answers with the Answer Key. If you answer any questions incorrectly, please reread the corresponding text to clarify your understanding. Then, continue to Unit Two, Raising Debt Capital.

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4 PROGRESS CHECK 1 Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page. Question 1: A corporation that sells bonds to fund an expansion of operations is: ____ a) directly negotiating a debt agreement. ____ b) issuing securities that represent loans. ____ c) securitizing loans for sale in the secondary market. ____ d) selling ownership interest in the company. Question 2: The major advantage of the Eurobond market is that: ____ a) the bonds are traded in London and Luxembourg. ____ b) the markets are not directly controlled by any government entity. ____ c) issuers can borrow in many currencies. ____ d) Eurobonds make only one interest payment per year. Question 3: Many floating rate instruments use a benchmark rate of interest to determine the rate paid by the instrument. Which of the following is most commonly used as a benchmark in the Euromarkets? ____ a) Prime rate ____ b) London Interbank Bid Rate (LIBID) ____ c) London Interbank Offered Rate (LIBOR) ____ d) Eurocurrency rate Question 4: Which type of bond requires the issuer to pledge a fixed asset (such as property or equipment) as security for the bond? ____ a) Mortgage bond ____ b) Collateral trust bond ____ c) Guaranteed bond ____ d) Debenture v.07/06/94 p.01/10/00

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ANSWER KEY

Question 1: A corporation that sells bonds to fund an expansion of operations is: b) issuing securities that represent loans.

Question 2: The major advantage of the Eurobond market is that: b) the markets are not directly controlled by any government entity. This is an advantage because Euromarket issues have relatively few regulations and are not subject to taxation.

Question 3: Many floating rate instruments use a benchmark rate of interest to determine the rate paid by the instrument. Which of the following is most commonly used as a benchmark in the Euromarkets? c) London Interbank Offered Rate (LIBOR) Other common benchmarks include the U.S. Treasury rate, prime lending rate, HIBOR, and SIBOR.

Question 4: Which type of bond requires the issuer to pledge a fixed asset (such as property or equipment) as security for the bond? a) Mortgage bond

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PROGRESS CHECK 1 (Continued)

Question 5: When investors refer to a debt security's term, or tenor, they are discussing its: ____ a) par value. ____ b) basis points. ____ c) interest payments. ____ d) maturity.

Use the following example to respond to Questions 6 and 7. Casaco Homebuilding, based in Venezuela, plans to issue dollar-denominated bonds in the U.S. to fund a new, 200-home housing development outside of Caracas. Question 6: In terms of its effects on the capital structure of Casaco, how would you classify this transaction? ____ a) Primary market transaction ____ b) Eurodollar transaction ____ c) Secondary market transaction ____ d) Open-economy transaction

Question 7: In which type of market is Casaco issuing its bonds? ____ a) Foreign market of the U.S. ____ b) Foreign market of Venezuela ____ c) Euromarket ____ d) Domestic market

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ANSWER KEY

Question 5: When investors refer to a debt security's term, or tenor, they are discussing its: d) maturity. Maturity, term, and tenor all refer to the length of time before a debt becomes due for repayment.

Question 6: In terms of its effects on the capital structure of Casaco, how would you classify this transaction? a) Primary market transaction Primary market transactions (new issues of debt) directly affect the capital structure of the borrower, whereas secondary market trades among investors have no direct effect on the capital structure of the original issuer.

Question 7: In which type of market is Casaco issuing its bonds? a) Foreign market of the U.S. Casaco's issue would be considered the foreign component of the U.S. national market because Casaco is domiciled outside the country where the securities will trade.

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Question 8: The major advantage of bank financing over capital from debt markets is: ____ a) greater liquidity for the investor. ____ b) the borrower generally pays a lower interest rate for bank financing. ____ c) the terms of the loan may be easier to renegotiate. ____ d) bank financing does not link interest payments to any benchmark rate.

Question 9: What is the effect of a good Standard and Poor's credit rating on a borrower's interest payments, all other factors being equal? ____ a) It increases the interest payment. ____ b) It decreases the interest payment. ____ c) There is no effect.

Question 10: Select four factors that affect the rate of interest a firm will pay to borrow funds. ____ a) Interest paid on short-term U.S. securities ____ b) Trends in the company's industry ____ c) Credit standing ____ d) Expectations of future level of inflation ____ e) Macroeconomic conditions in the bond market ____ f) Expectations of future consumerism ____ g) Length of the borrowing

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ANSWER KEY

Question 8: The major advantage of bank financing over capital from debt markets is: c) the terms of the loan may be easier to renegotiate. This flexibility stems from the ongoing relationship between the bank and the company and the greater ease in negotiating with one or a few parties, rather than a large pool of investors.

Question 9: What is the effect of a good Standard and Poor's credit rating on a borrower's interest payments, all other factors being equal? b) It decreases the interest payment. A borrower with a good credit rating would pay a lower interest rate and, therefore, have lower interest payments.

Question 10: Select four factors that affect the rate of interest a firm will pay to borrow funds. a) Interest paid on short-term U.S. securities c) Credit standing d) Expectations of future level of inflation g) Length of the borrowing

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Question 11: If a borrower pays interest at the rate of LIBOR plus 100 basis points, it means that the: ____ a) rate of interest will remain fixed during the period of the agreement. ____ b) funds are borrowed at a discount from face value and repaid at face value. ____ c) rate is based on the Treasury yield. ____ d) interest rate will be reset for each interest-paying period.

Question 12: One advantage of issuing callable bonds is that: ____ a) the company can refinance high-priced debt in a period of falling interest rates. ____ b) investors are willing to buy the bonds at a discount. ____ c) the gradual repayment of principal reduces the cost of retiring the issue. ____ d) the issuer must pay higher interest rates than similar bonds without the call provision.

Question 13: If your car loan has been "securitized," that means: ____ a) you are using it as collateral for a loan. ____ b) it has been pooled with other loans into a marketable security. ____ c) the originator continues to hold its claim on your interest and principal payments. ____ d) it has a relatively high position in the line of creditors.

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ANSWER KEY

Question 11: If a borrower pays interest at the rate of LIBOR plus 100 basis points, it means that the: d) interest rate will be reset for each interest-paying period.

Question 12: One advantage of issuing callable bonds is that: a) the company can refinance high-priced debt in a period of falling interest rates. When interest rates drop, callable debt enables companies to repurchase expensive debt at a lower-than-market price.

Question 13: If your car loan has been "securitized," that means: b) it has been pooled with other loans into a marketable security.

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Question 14: DFA Company issues $1,000 bonds to investors and receives $960 from each investor at the time of the transaction. DFA Company pays no interest during the life of the bond and returns $1,000 to the investor at maturity. The interest rate is: ____ a) calculated as a ratio of the difference between the original amount paid by investors and the face value divided by the face value. ____ b) implied by the rate of return earned by the investor. ____ c) zero because no interest payments were made. ____ d) discounted at maturity.

Question 15:

Select two ways that debt securities may be classified.

____ a) Level of interest rates ____ b) Relative priority of debt security investors ____ c) Credit rating of the investors ____ d) Claims on specific assets ____ e) Lien vs. non-lien securities ____ f) Relative collateral value of assets

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ANSWER KEY

Question 14: DFA Company issues $1,000 bonds to investors and receives $960 from each investor at the time of the transaction. DFA Company pays no interest during the life of the bond and returns $1,000 to the investor at maturity. The interest rate is: b) implied by the rate of return earned by the investor.

Question 15:

Select two ways that debt securities may be classified. b) Relative priority of debt security investors d) Claims on specific assets

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Unit 2

UNIT 2: RAISING DEBT CAPITAL

INTRODUCTION

In Unit One, we described two common ways of raising capital in the debt market: bank financing and selling debt securities in the public market. Another method for raising debt capital is by placing securities privately. The size of the company and its creditworthiness are the most important factors in determining a company's debtraising options. The advantages and disadvantages of each process often dictate which method a company uses. In this unit, we briefly describe each process and highlight the relative advantages, disadvantages, and costs associated with each method for raising debt capital.

UNIT OBJECTIVES

When you complete Unit Two, you will be able to: n

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Identify differences between methods of raising debt capital Recognize the process for raising debt capital through public offerings, private placement, and bank financing Compare the advantages, disadvantages, and costs of each method of raising debt capital

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RAISING DEBT CAPITAL

ISSUING DEBT SECURITIES

Two methods for issuing debt securities are public offering and private placement. In this section, we discuss the process for each type of offering.

Public Offering Issue process

In a public offering, a company offers its debt securities to all participants in the market. There are several steps in the public debt offering process.

Select investment bank

1. The issuer selects an investment bank to manage the offering. If the issue is large, or is to be placed in several markets, the investment bank may assemble a syndicate, or group, of investment banks. A syndicate helps to ensure that the entire issue can be placed with investors and spreads the underwriting risk among several underwriters. In a syndicate, one investment bank is chosen to be the lead, or managing, underwriter.

Discuss financing needs

2. The issuer and the investment bank (or syndicate) meet to discuss the financing needs of the company. In most cases, the two parties have an ongoing relationship, so the investment bank is familiar with the issuer and its needs.

Prepare registration statement

3. The issuer and the investment bank prepare a registration statement and submit it to the appropriate government regulatory agency. The registration statement may take three or four weeks to complete.

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Conduct "due diligence"

4. Because the investment bank serves both the issuer and the investor, it must maintain certain ethical standards. The bank must preserve confidentiality for the issuer at the same time it supports the investor's need for disclosure. The process of discovering for investors all relevant information about the issuer and its operations is called "due diligence." The investment bank managing the issue will investigate and verify all of the company's claims about its operations and finances, both quantitative and qualitative. One might say that the due diligence process requires the investment bank to become the "devil's advocate" in questioning the issuer's claims.

Generate interest

5. To help sell the issue, the investment bank (or syndicate) begins to generate interest in the debt securities among its investor clients. The investment bank may hold informational meetings with groups of clients or contact them individually through brokers.

Price and sell the issue

6. After receiving approval from the regulatory agency, the issuer and the investment bank set a date for the issue to be sold. On this date, known as the pricing day, the issuer and the investment bank complete the final prospectus, price the securities, prepare a "tombstone" to announce the issue, and complete the sale of the securities to the investors.

Issuing costs

The underwriting fees for a public issue of debt usually depend on the maturity of the securities being sold. Fees range from 40 – 50 basis points, for a short-term issue, to 85 – 90 basis points for thirtyyear bonds. Underwriters charge these fees up front and often deduct them from the proceeds of the issue. Other expenses include registration fees, legal expenses, printing expenses, rating agency fees, and other miscellaneous expenses. Expenses for offerings range from $350,000 to nearly $500,000. There are some economies of scale in these expenses because larger issues commit a relatively smaller proportion of proceeds to expenses.

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Tenor and size

Securities in public issues range in maturity from two to thirty years, but most of them are under ten years in tenor. Issue sizes usually range from $100 million to $500 million. Investors perceive smaller issues to be less liquid than larger issues.

Investors / issuers

Institutional investors dominate the market, but many individual investors buy debt instruments. Individual investors in the public market often seek a recognizable company name, which effectively limits public offerings to larger, more established firms. Small or new companies often find that their investment bank cannot place their entire issue with investors and that the costs of the issue are prohibitive. In addition, public debt securities require a public credit rating, a process that many smaller companies find too expensive.

Advantages

A public issue of debt securities gives the company more flexibility in terms of its operations. Although the issuer is required to make public disclosure of its financial and operating conditions, it generally has to maintain few minimum operating and financing covenants (requirements).

Disadvantages

In times of distress, it is hard to renegotiate the terms of publiclytraded instruments without entering some type of bankruptcy protection. Because many investors may own the securities, it is difficult to gain a consensus on suitable terms.

Euromarket issues

The process we have discussed in this section focuses on a domestic issue — a company issuing in its own domestic market. Many firms have found that the Euromarket provides an adequate pool of investors at a lower cost to the issuer. The Euromarket has effectively eliminated much of the government registration process — shortening the issue process by several weeks. The public disclosure requirements for financial and operating reporting are usually less stringent as well. This competition has forced many domestic markets to simplify their registration and reporting requirements.

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Private Placement Another method companies use to issue debt securities is private placement. In a private placement, a company places its debt directly with private investors without a public registration of the offering. Let's look at the process for a private offering. Issue process

1. As with a public offering, the issuing company selects an investment bank to manage the process. 2. The investment bank provides the following services: n

n

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Assists the issuer in planning the financial strategy and determining its financial needs Prepares a placement memorandum, which is a marketing book and credit analysis of the company Circulates the placement memorandum among potential investors to help generate interest in the issue Assists in preparing documents which describe the details of the loan agreement Acts as a placement agent working on a "best efforts" basis to sell the securities to investors. The investment bank does not underwrite the issue, but it does try its best to find sufficient investors to provide the required amount of capital.

Issuing costs

The costs and fees for private placements generally are less than for public issues. Placement fees run from 25 – 50 basis points. Legal and other expenses usually range between $50,000 and $100,000 per issue.

Tenor and size

Private market issues, like public issues, range in maturity from less than one year up to thirty years, with most issues being less than ten years. The size of the issue is more flexible than in the public markets.

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Investors

Investors in the private placement market tend to be large institutional investors and very wealthy individual investors. Depending on the type of security issued, the institutional investors may include insurance companies, pension funds, commercial finance companies, leveraged buyout firms, banks, trust funds, and mutual funds.

Covenants

Investors often require a set of covenants for the company issuing securities. These covenants dictate minimum and maximum levels for key financial and operational ratios such as debt-to-equity ratio, interest coverage ratio, and fixed payment coverage ratio. The covenants negotiated between the investors and the issuer usually depend on the industry in which the issuer conducts its business. Failure to meet specified covenants often gives investors the right to return bonds to the issuer. However, in times of distress, issuers often are able to renegotiate the terms with the investors.

Credit rating system

A credit rating system for private placement issues in U.S. markets, similar to the public issues systems, has been established by the National Association of Insurance Commissioners (NAIC). Companies use this rating system to determine the rate they will pay on privately-placed instruments. As with public issues, higher-rated securities will pay lower interest rates, all other factors being equal. A rating generally is not required because most investors in privatelyplaced debt make their own determination of credit quality.

Advantages

The private placement market offers issuers several advantages. n

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Private issues require no public disclosure. The issuer can maintain confidentiality because the securities are sold to a small group of institutional investors. The issuer can control the marketing process, effectively targeting particular types of investors. The issuer can sell securities with unusual terms or structures because the investors are sophisticated.

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Issuers need less lead time (4-8 weeks) to bring a private placement issue to market than to bring a public placement issue to market (12-16 weeks).

Disadvantages

One disadvantage of the private placement market is a lack of liquidity for the securities. The lack of a secondary market forces issuers to pay higher interest rates than similar issues in the public market.

SEC Rule 144A

The regulatory agency for the U.S. market, the Securities and Exchange Commission (SEC), passed Rule 144A to increase liquidity in the private placement market. Rule 144A allows for the resale of privately-placed securities (previously restricted in the U.S. market). However, the rule limits secondary market buying and selling to qualified institutional buyers (QIBs) that have at least $100 million of invested funds in their portfolio. Rule 144A issues often require additional legal and rating agency fees, but the issues are still competitively priced for many issuers. Rule 144A has provided many foreign issuers the opportunity to access U.S. capital markets without having to conform to the relatively tough U.S. accounting and disclosure standards. Many Latin American companies have been able to place issues with U.S. investors through Rule 144A. The interest rates being paid on Rule 144A issues are very competitive with other issues.

BANK FINANCING

In addition to issuing securities through public offerings or private placements, companies can raise debt capital by arranging for bank financing. Lead bank in a syndicate

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Many debt financings are simply loan agreements between a company and a bank, or bank syndicate. The lead manager, or loan arranger, is the bank that assumes primary responsibility for working out terms of the loan and for bringing other banks (known as participating banks) to share in the loan. Generally, banks handle a small loan request on their own and include other banks for the larger debt needs of a company. ver. 1.0

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Bank financing process


Let's look at the steps in the bank financing process. 1. The borrowing company selects a bank to serve as the lead manager. Generally, the company chooses a bank with which they already have a relationship. 2. The lead manager and the company negotiate the amount of the loan, the interest rate (or rates) to be paid, banking fees, and other details concerning the arrangement — based on the demand for the loan by prospective participating banks. 3. The bank develops a placement memorandum that describes the borrower's financial condition and the details of the loan. 4. Prospective participating banks review the placement memo to determine if they want to participate in the syndicate.

Underwritten loans

The loan is fully underwritten if the lead manager guarantees the full amount of the loan. If demand for the loan by prospective participating banks is insufficient, the lead manager may have to provide the additional capital for the borrower.

"Best efforts" loans

A "best efforts" offering of a syndicated loan requires that managing banks try their best to find enough lenders to complete the syndicate and provide the necessary capital. If demand for the loan is low, the amount of the loan may be renegotiated with the borrowing company.

Periodic costs

The borrower incurs periodic costs and up-front costs. The periodic costs may include: n

The interest paid on the amount of the credit being used For example, a syndicate provides a line of credit for $100 million. If the borrower currently is using only $40 million, the interest payment will be based on the $40 million being used. Interest rates may be fixed or floating, depending on the agreement. Most rates are set as a premium from a benchmark rate (e.g., LIBOR + 50 basis points). ver. 1.0 v.07/06/94 p.01/10/00


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A commitment fee, ranging from 25 – 75 basis points on the unused portion of the credit A small agent fee paid to the bank for its services

Up-front costs

Up-front fees include a one-time fee of 50 – 250 basis points on the total amount of the loan. The borrower pays this up-front fee to the lead bank for organizing and managing the loan. The managing bank generally passes along a portion of this fee to other participating banks. The syndicate agreement specifies the allocation of the upfront fee.

Size and tenor

The size of syndicated loans is flexible, depending on the needs of the borrowing company. The maturity of the loans is also flexible, but the most common syndicated loans are for less than seven years.

Restrictive covenants

Syndicated bank loans typically are more restrictive than private placement for the borrowing company in terms of the covenants for the agreement. However, if the company has a relationship with the lead manager, it usually can renegotiate the terms of the agreement when the company's prospects change.

Advantages and disadvantages

Larger companies often arrange syndicated bank lines of credit as collateral for issuing securities in the debt markets. Syndicated loans are common for smaller, less established companies. Lenders generally charge higher interest rates than companies pay for private placements or public issues because of the perceived credit risks. However, the process of arranging a syndicated loan takes much less time, and has lower up-front expenses than other methods of raising debt capital.

UNIT SUMMARY

In this unit, we have reviewed the three primary methods companies use to raise debt capital. Key features, advantages, and disadvantages of each method are summarized in the chart on page 2-10.

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METHOD


KEY FEATURES

ADVANTAGES

DISADVANTAGES

Issuing Debt Securities 1. Public Offering

Large pool of investors Issue size from $100MM to $500MM

Few minimum operating and financing covenants to maintain Liquidity for investors

Issuers: Large established companies

High costs Difficult to renegotiate terms Difficult and expensive for small companies

Large secondary market 2. Private Placement

Investment bank works on best efforts basis Flexible issue size

Less costly than public issue Faster than public issuing process

Illiquidity forces company to pay higher interest rates Restrictive covenants

No public disclosure

No public registration requirements

Control of marketing process

Restricted secondary market Accessible to foreign issuers

Easy to renegotiate terms

Small group of sophisticated investors

Marketability of securities with unusual structures or terms

Agreement between company and bank or syndicate

Flexible size and maturity for loans

Most restrictive covenants of all three methods

Loans underwritten or on best efforts basis

Easy to renegotiate terms

Requires higher interest rate than private and public placement

Bank Financing 3. Bank Loans

Common for small, new companies

Faster, less expensive process than issuing debt securities

You have completed Unit Two, Raising Debt Capital. Please complete the Progress Check to test your understanding of the concepts and check your answers with the Answer Key. If you answer any questions incorrectly, please reread the corresponding material. Then, continue to Unit Three, Valuing Debt.

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✔ PROGRESS CHECK 2 Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page.

Question 1: Which method for raising debt capital places the least restrictive financial and operational covenants on the borrower? _____a) Public offering _____b) Private placement _____c) Bank financing

Question 2: Which of the three methods for raising debt capital attracts large institutional investors and wealthy individual investors? _____a) Public offering _____b) Private placement _____c) Bank financing

Question 3: The purpose of conducting "due diligence" before a public offering is to: _____a) maintain confidentiality for the issuer. _____b) rate the borrower's creditworthiness. _____c) investigate and verify the issuer's claims. _____d) simplify the registration process.

Question 4: ABC Tool and Die Company is a small company with a brief history and no track record. The business is growing and needs additional capital to finance an expansion of operations. Management has decided to raise the capital through debt financing. Which method will it use? _____a) Public offering _____b) Private placement _____c) Bank financing v.07/06/94 p.01/10/00

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ANSWER KEY

Question 1: Which method for raising debt capital places the least restrictive financial and operational covenants on the borrower? a) Public offering

Question 2: Which of the three methods for raising debt capital attracts large institutional investors and wealthy individual investors? b) Private placement

Question 3: The purpose of conducting "due diligence" before a public offering is to: c) investigate and verify the issuer's claims.

Question 4: ABC Tool and Die Company is a small company with a brief history and no track record. The business is growing and needs additional capital to finance an expansion of operations. Management has decided to raise the capital through debt financing. Which method will it use? c) Bank financing

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Question 5: Select the major disadvantage of bank financing. _____a) Length of time to arrange _____b) Difficult to renegotiate _____c) Limitations on size and tenor _____d) Higher interest rates

Question 6: Select one advantage that a private debt placement has over a public debt offering. _____a) It allows more flexibility for the issuer in its operations. _____b) The lead time for bringing an issue to market is shorter. _____c) It increases the liquidity for the securities. _____d) There is a large pool of secondary market investors.

Question 7: In the U.S. debt markets, Rule 144A of the Securities and Exchange Commission (SEC) has: _____a) provided access to the U.S. market for many foreign issuers. _____b) increased the liquidity for many privately-placed debt issues. _____c) limited buying and selling of privately-placed securities to qualified institutional buyers (QIBs). _____d) accomplished all of the above.

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ANSWER KEY

Question 5: Select the major disadvantage of bank financing. d) Higher interest rates

Question 6: Select one advantage that a private debt placement has over a public debt offering. b) The lead time for bringing an issue to market is shorter.

Question 7: In the U.S. debt markets, Rule 144A of the Securities and Exchange Commission (SEC) has: d) accomplished all of the above.

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Question 8: Identify the activities associated with each method of raising debt capital. Mark "O" for public offering, "P" for private placement, and "B" for bank financing. _____a) Prepare a marketing book and credit analysis _____b) Prepare a registration document _____c) Sell securities only on "best efforts" basis _____d) Pay interest on the amount of credit being used _____e) Prepare a tombstone and final prospectus _____f) Make a public disclosure of financial and operating conditions _____g) Use NAIC ratings system to determine interest rate _____h) Select a lead manager _____i) Payment of up-front organizational and management fee

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Question 8: Identify the activities associated with each method of raising debt capital. Mark "O" for public offering, "P" for private placement, and "B" for bank financing. P a) Prepare a marketing book and credit analysis O b) Prepare a registration document P c) Sell securities only on "best efforts" basis B d) Pay interest on the amount of credit being used O e) Prepare a tombstone and final prospectus O f) Make a public disclosure of financial and operating conditions P g) Use NAIC ratings system to determine interest rate B h) Select a lead manager B i) Payment of up-front organizational and management fee

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Unit 3

UNIT 3: VALUING DEBT

INTRODUCTION

In Unit Two, we described three methods for issuing debt. Now we will focus on methods for comparing and pricing debt securities. In this unit, you will learn how to calculate the rate of return, or yield, earned by investors as well as how to find the price at which a bond should be selling. Investors use these calculations to determine which debt instrument provides the highest rate of return on their investment. Issuers use these calculations to find the lowest cost borrowing alternative. Finally, we will show how analysts use duration to measure the sensitivity of bond prices to changes in interest rates. It is important that you feel comfortable using your calculator to make future value and present value computations. You may want to review the concepts of future and present value before trying the calculations required in this unit. Unit Three, Time Value of Money, in the Basics of Corporate Finance workbook is a good place to begin your review.

UNIT OBJECTIVES

When you complete Unit Three, you will be able to: n

Select and calculate appropriate measures of yield

n

Determine the price and discount yield of zero-coupon bonds

n

Determine the price of a debt security that makes periodic coupon payments

n

Calculate the duration of a bond

n

Calculate the duration of a portfolio

n

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Use modified duration to estimate the sensitivity of a bond's price to changes in interest rates

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CALCULATING YIELD Income from a debt security

Let's begin this section by emphasizing a key point about debt securities. The owner of a debt security has three potential sources of income: 1. Contractual interest payments (coupon payments) 2. Income generated from the reinvestment of coupon payments 3. Capital gain or loss incurred when selling the security There are several yield measures, each with a specific definition and calculation method based on different assumptions about income. This section will help you to differentiate among the types of yield and understand their uses and functions. The four types of yield we will look at are current yield, yield-to-maturity, yield-to-call, and realized compound yield.

Example bond

Selling at a premium / discount

Throughout this section, we will illustrate the yield calculations with a hypothetical bond from XYZ Corporation. The bond has these characteristics: Years to maturity

= 7

Coupon rate

= 5%

Payment frequency

= Semiannual

Market price

= $842.60

Redemption value (Face or par value)

= $1,000.00

This bond is said to be selling at a discount, because the market price is less than the par value. A bond with a market price greater than the par value is selling at a premium.

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Current Yield Annual coupon interest and market price

Current yield relates the annual coupon interest to the market price of the security. The formula for calculating current yield is:

Current yield = Annual coupon interest / Market price

For our XYZ Corporation bond, the current yield is: Current yield

= = =

(.05 x $1,000) / $842.60 $50 / $842.60 0.0593 or 5.93%

In other words, investors are earning 5.93% on their investment. Compared to coupon rate

The current yield is always higher than the coupon rate for bonds selling at a discount to par value. For bonds selling at a premium, the current yield is always less than the coupon rate. Many secondary market bond quotations list a bond's current yield as well as its pricing information.

Weakness

One weakness of the current yield calculation is that it includes only one of the three sources of potential income: the periodic interest payment. It does not account for the reinvestment of interest payments or for any capital gains or losses. For example, an investor who buys the XYZ Corporation bond for $842.60 and holds it until maturity will realize a capital gain of $157.40 ($1,000.00 – $842.60). The current yield does not take the capital gain into account.

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Yield-to-maturity Present value of cash flows and market price

The yield-to-maturity is the discount rate that equates the present value of the future cash flows generated by the bond with the current market price of the bond. To calculate the yield-to-maturity (discount rate), we begin with the formula for pricing a bond (see below) and solve for R.

MxT

P =

Σ i=1

(C / M) F ___________ + _____________ [1 + (R / M)]i [1 + (R / M)]M x T

Where: P C T M R F

= = = = = =

Market price of the bond Annual coupon payment Number of years until maturity Number of coupon-paying periods per year Yield-to-maturity Face value of the bond

Please note that all calculations in this unit are presented as performed on a financial calculator. Solving this equation with a pencil may be difficult; therefore, we recommend that you use a financial calculator. (Before the invention of hand-held calculators, analysts worked by trial and error until they found a close approximation of R.) Before you begin, check the owner's manual for your financial calculator. Most machines require that either the present value or the coupon payments and future value of the instrument be entered as negative numbers. The last coupon and principal payment (future value) may have to be combined into one cash flow.

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Example

3-5

Let's calculate the yield-to-maturity for the XYZ Corporation bond (page 3-2). 1. Since the bond has seven years until maturity and is a semiannual bond, we input 14 for the number of interest paying periods. Enter 14 and press the N key. 2. Enter the current market price of $842.60 as the present value of the instrument. Press the PV key. 3. Enter the size of each coupon payment as $25 (0.05/2 x $1,000). Press the PMT key. 4. Input the par value of $1,000 as the future value. Press the FV key. 5. Press the I key or I% key. You should have a solution of R = 3.99%. 6. Multiply 3.99 by 2 to arrive at the yield-to-maturity of 7.98%. (Because we are working with a semiannual instrument, we need to convert this to an annual rate.) Investors are earning a 7.98% rate of return on their investment in the XYZ Corporation bond.

Fullydiscounted yield

Technically, the fully-discounted yield for a security making semiannual coupon payments is the compounded semiannual return. In our example, the true yield is (1.0399)2 – 1 = 8.14%.

Bond equivalent yield

In practice, however, analysts simply multiply the semiannual rate by two, as we did above, to arrive at 7.98%. This is called the bond equivalent yield (BEY). The BEY is the rate of return that investors compare with the yield on other instruments and to the quote on zerocoupon securities (including U.S. Treasury bills).

Comparative advantages

The yield-to-maturity improves upon the current yield measure because it accounts for the capital gain of $157.40. Yield-to-maturity also considers the reinvestment of interest payments. However, this measure assumes that interest payments are reinvested at exactly the yield-to-maturity rate (in this case, 7.98%). If that assumption is not valid, then yield-to-maturity comparisons may not be appropriate.

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Yield-to-call Assumes issuer calls bond

Yield-to-call is conceptually similar to yield-to-maturity. The major difference is that yield-to-call assumes the issuer will call the bond at the first opportunity. The yield-to-call calculation is the same as the yield-to-maturity calculation except that the number of interest paying periods until the first opportunity to call is used instead of the number of periods until maturity. Yield-to-call, like yield-to-maturity, assumes that interest payments are reinvested at the same rate as the yield-to-call rate. Another weakness of yield-to-call is that it does not consider what happens to the proceeds of the bond if it is called. The bond purchaser often has an investment horizon that is longer than the period until first call. This measure does not allow a direct comparison with investment opportunities for such an investor.

Realized Compound Yield Different reinvestment rate

The final measure, realized compound yield, adjusts for interest payments that are reinvested at a different rate than the yield-tomaturity. To calculate the realized compound yield, take the following steps: 1. Compute the total dollars to be received in the future from the investment. To do this, find the future value of the coupon payments reinvested at the appropriate rate. Using an annuity for the period that the payments are to be received, enter the amount of the payment and the number of payments. Use the reinvestment interest rate as the discount rate to calculate the future value of the annuity. Add the face value of the bond to this amount to compute the total dollars to be received.

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2. Enter this total as the future value of the investment in your calculator. 3. Enter the amount paid for the bond as the present value of the investment. (Your calculator may require that this number be entered as a negative number.) 4. Enter the number of coupon-paying periods. 5. Press the I (or I%) key to find the realized compound yield. If the coupon period is semiannual, multiply this yield by 2 to find the annual realized compound yield. Example

We can use the XYZ Corporation bond to illustrate the calculation. Remember that the bond has the following characteristics. Years to maturity

= 7

Coupon rate

= 5%

Payment frequency

= Semiannual

Market price

= $842.60

Redemption value (Face or par value)

= $1,000.00

If we reinvest the coupon payments at an annual rate of 4% and we hold the bond to maturity, what is the realized compound yield? 1. The first step is to find the future value of the coupon payments. Holding the bond until maturity, we would receive 14 payments of $25 and reinvest them at a 2% semiannual rate. Find the future value as you would for any other annuity. Enter in your calculator 14 payments of $25 with an interest rate of 2%. Make sure that the calculator knows that the payments are received at the end of each period. Pressing the future value key should give you $399.35 for the value of the coupon payments received and reinvested. 2. Enter $1,399.35 ($399.35 + $1,000) as the future value of the investment.

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3. Enter $842.60 as the present value (the amount that we paid for the bond). 4. Enter 14 as the number of coupon-paying periods. 5. Press the IRR key to get the semiannual rate of 3.69%. Multiply by 2 to get the annual realized compound yield of 7.38%. Assuming you reinvest your coupon payments at a 4% rate, you will earn 7.38% on your investment in the XYZ Corporation bond. One problem with realized compound yield is that the analyst may not know the reinvestment rate. When comparing investments, analysts can use the same arbitrary reinvestment rate for all investment alternatives. Usually, they use the yield-to-maturity for comparison purposes if they do not know the reinvestment rate.

Summary As you can see from the calculations, it is important to select the appropriate yield measure when calculating your rate of return. The chart below summarizes the different yields we calculated for our sample investment in XYZ Corporation bond.

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TYPE OF YIELD

DESCRIPTION

Current Yield

Relates annual coupon interest to market price

RATE OF RETURN 5.93%

Rate of return higher than coupon rate because bond sells at a discount to par value

7.98%

Rate of return higher than current yield because it accounts for capital gain of $157.40

7.38%

Rate of return lower than yield-to-maturity because it assumes lower reinvestment rate (4%)

Does not account for reinvested interest payments or capital gains/losses Yield-tomaturity

Relates present value of future cash flows to market price Assumes reinvestment rate = yield-to-maturity

Yield-to-call

IMPLICATIONS

Similar to yield-tomaturity Assumes issuer will call bond at first opportunity

Realized Compound Yield

Adjusts for interest payments reinvested at a different rate than yield-to-maturity

Please complete Practice Exercise 3.1 to check your understanding of calculating yield. Then, continue to the next section of Unit Three which covers methods for pricing common bond instruments.

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PRACTICE EXERCISE 3.1 Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page. Use the following data to answer Questions 1 and 2. Years to maturity Coupon rate Payment frequency Market price Redemption (face) value

= = = = =

6 5.5% Semiannual $955.60 $1,000.00

Question 1: What is the current yield for the bond? _______________________________

Question 2: Calculate the yield-to-maturity for the instrument. _______________________________

Question 3: The yield-to-maturity calculation shows a higher rate of return than the current yield calculation because yield-to-maturity: ____ a) compounds the semiannual payments. ____ b) assumes interest payments are reinvested at the coupon rate. ____ c) includes the income from a capital gain. ____ d) factors in the accumulated interest between coupon-paying periods. Question 4: You expect Quickly Company to repurchase its bonds at the first opportunity. Which measure would you use to calculate the yield of the Quickly Company bonds? ____ a) Realized compound yield ____ b) Yield-to-call ____ c) Yield-to-maturity ____ d) Current yield

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ANSWER KEY

Question 1: What is the current yield for the bond? Current yield

= =

$55 / $955.60 5.76%

Question 2: Calculate the yield-to-maturity for the instrument. Enter into your financial calculator: Number of payments (12) Present value ($955.60) Future value ($1,000) Coupon payments ($27.50) Press the I% key to find the answer:

3.20% x 2 = 6.40%

Question 3: The yield-to-maturity calculation shows a higher rate of return than the current yield calculation because yield-to-maturity: c) includes the income from a capital gain. The current yield calculation results in a lower rate of return because it only accounts for one of the three sources of potential income from debt securities: the contracted interest payments. The yield-to-maturity calculation figures in the capital gain when the security matures and assumes that interest payments are reinvested at a rate equaling the yield-to-maturity.

Question 4: You expect Quickly Company to repurchase its bonds at the first opportunity. Which measure would you use to calculate the yield of the Quickly Company bonds? b) Yield-to-call Rather than calculating and discounting the cash flows for the entire life of the instrument, yield-to-call calculates the rate of return using the number of interestpaying periods until the first opportunity to call.

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CALCULATING PRICE

Next, we will focus on the methods analysts use to price common bond instruments. The basic idea throughout this section is to find the present value of future cash flows generated by the security. We will demonstrate price calculations for zero-coupon securities, which make no interest payments, and for fixed income securities, which make fixed income payments.

Zero-coupon Securities Two cash flows

Zero-coupon bonds are the easiest instruments to value because there are only two cash flows: the price paid for the bond and the price received when the bond is redeemed. We want to find the price to be paid for the bond.

Price and yield based on days to maturity

U.S. Treasury bills, and other zero-coupon money market instruments quoted at a discount from their face value, typically have short-term maturities. Their price and yield calculations are based on the number of days until the security matures. The formula for finding the price of a money market security quoted on a discount basis is:

P = F [1 - ((R x DM) / DY )] Where: P = F = DM = DY = R

Example

=

Current price of the security Face value of the security Number of days until the security matures Number of days in quoted year that security is priced Discount yield used to price the security

This example will show you how to use the formula. Suppose that we have a Treasury bill, quoted on a 360-day year, with a face value of $1,000, priced to yield at 6.5% annually, that is held for 123 days. What is the price for this instrument?

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P

=

F [1 - ((R x DM ) / DY)]

P

=

$1,000 [ 1 - (0.065 x 123 / 360)]

P

=

$1,000 [ 1 - 0.0222]

P

=

$1,000 [ 0.9778]

P

=

$977.78

We expect the security to sell for $977.78 in the money market. The financial section of the newspaper usually quotes prices on a percentage basis. In this case, the security has a quoted price of 97.78 or 97.78% of $1,000 (face value). Note that most money market instruments, including U.S. Treasury bills, are quoted on a 360-day year (DY). Some short-term corporate securities use the 365-day year. Be sure to check the details so that your pricing computation is accurate. Discount Yield Rate to price the security

Sometimes we may know the price of the security but want to find the discount yield used to price the instrument. The discount yield is the rate that is used to discount the cash flows of the zero-coupon security. To calculate the rate, we use the pricing formula and solve for R. R = [(F - P) / F] x ( DY / DM)

The variables are the same as in the pricing formula (see page 3-13). Example

This example will help you understand the discount yield calculation. Suppose that a $1,000 security, quoted on a 360-day year, with 45 days until maturity, is priced at $994 in the market. What was the discount yield used to price the security? R

=

R

=

[(F - P) / F] x (DY / DM ) [($1,000 - $994) / $1,000] x (360 / 45)

R

=

[0.0060] x (8.00)

R

=

0.0480 or 4.80%

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The discount yield used to price the security is 4.80%. Investors may say that the security is priced to yield 4.80%. Converting the discount yield

Investors may need to convert the discount yield to allow direct comparison with other securities. There are three standard calculations for converting the discount yield: true yield, money market yield, and bond equivalent yield. 1. True (Actual) Yield

365-day basis

If a zero-coupon security is quoted on a 360-day basis, you may want to convert the yield-to-maturity to a 365-day basis to compare the return with another security. This conversion to a 365-day annual rate is often called the true (actual) yield of the instrument. To make this conversion, use the following formula:

i = [(P s - Pb ) / Pb ] x (365 / DH ) Where: i

=

Simple annual interest (rate of return) earned on a 365-day year basis

Ps

=

Price at which security was sold

Pb

=

Price at which security was bought

DH

=

Number of days security was held

For example, suppose an investor purchases a 90-day U.S. Treasury bill for $9,600 and sells it after 30 days for $9,700. What is the rate of return (or simple interest) earned by the investor? i

=

[(P s - Pb ) / Pb ] x (365 / DH )

i

=

[($9,700 - $9,600 ) / $9,600 ] x (365 / 30)

i

=

[0.0104] x (12.1667)

i

=

0.1267 or 12.67%

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If the investor holds the bill until maturity, the face value of the security is used as the selling price when calculating the simple interest. 2. Money Market Yield Short-term interest bearing instrument

The term money market yield (MMY), or Certificate of Deposit (CD) equivalent yield, refers to the rate of return earned on a shortterm interest-bearing instrument quoted on a 360-day year. Use the following formula to convert the discount yield to a money market yield: MMY = 360 x [R / (360 - (DH x R))] Where: MMY =

The money market yield

R

=

The discount yield

DH

=

Number of days that the security was owned

3. Bond Equivalent Yield Longer-term, interest bearing instrument

For a valid comparison with bonds that pay semiannual interest on a 365-day basis, many analysts convert the discount yield for money market securities to a bond equivalent yield (BEY). Use the following formula to make this conversion: BEY

= 365 x [R / (360 - (DH x R))]

You can use this formula for instruments with less than six months until maturity. For securities of longer tenor, you need to adjust for the compounding effect of the bond equivalent yield. You have just learned how to calculate prices for zero-coupon securities. Next, we will see how analysts price the second common bond instrument mentioned earlier, fixed-income securities.

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Fixed-income Securities Fixed periodic payments

Many debt securities make periodic interest payments to investors during the life of the instrument. In this section, we will discuss the process for calculating the price of instruments with fixed coupon payments. On page 3-4, we presented a general formula for calculating the price of a bond. MxT

P =

Σ i=1

(C / M) F ___________ + ______________ [1 + (R / M)]i [1 + (R / M)]M x T

The formula allows you to visualize the bond price calculation. We will demonstrate the pricing calculation using a financial calculator. Example

Consider a semiannual bond that has eight years left until maturity. It has a face value of $10,000 and makes coupon payments at an annual rate of 5.5%. If the bond is priced to yield 6.0% annually, at what price will we expect to sell the bond? 1. Because it is a semiannual bond, the number of coupon-paying periods is 16. Enter this information in your calculator. 2. The coupons are $275 for each period. 3. Enter 3.0% (6.0% / 2) as the yield. 4. Enter $10,000 as the future value. 5. Press the present value key to find the bond price of $9,685.97. Remember that the coupon rate and the yield-to-maturity should be consistent (i.e. semiannual coupon payments should be discounted with a semiannual rate).

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Accumulated Interest Accrued interest paid to seller

To find the true selling price of securities that make periodic interest payments, you make one further adjustment. Since a bond or note often sells on a date other than the one on which interest is paid, the buyer pays the seller the accrued interest earned since the last interest payment. Otherwise, the new owner would receive the entire coupon payment for a bond owned for only part of the coupon period. To calculate the accumulated interest, adjust the coupon payment by the number of days that the security was held in the coupon period. The formula is:

AI Where: AI = C = M = DH = DC =

=

(C /M) x (DH / DC )

Accumulated interest on the security Annual coupon payment Number of coupon paying periods per year Number of days that the security was held Number of days in the coupon period*

* For semiannual bonds, the number of days in the coupon period varies from 181 to 184, depending on the dates that the coupon is paid. For example, if the coupon payments are made on May 15 and November 15, there are 184 days from May 15 to November 15 and 181 days from November 15 to May 15. Example

We will demonstrate the accumulated interest calculation using a bond with the following characteristics: Par value Coupon rate Payment frequency Days until the next coupon payment Days in the coupon period

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= $10,000 = 9.8% = Semiannual = 130 = 182

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Use the formula with $980 as the annual coupon payment ($10,000 coupon x .098 coupon rate), and 52 (182 day coupon period minus 130 days remaining in the period) as the number of days that the security has been held. AI

=

(C / 2) x (DH / 182)

AI

=

($980 / 2) x (52 / 182)

AI

=

$140.00

The buyer of the security adds $140.00 to the quoted price of the security to compensate the seller for the 52 days the seller owned the security. Example

Let's look at another example of an accumulated interest calculation. What is the accumulated interest for a $1,000 face value, 6.5% annual bond, quoted on a 360-day basis that was held for 270 days since the last coupon payment? In this case, the annual coupon payment is $65 dollars and DH = 270. The computation is: AI

=

(C / 1) x (DH / 360)

AI

=

($65) x (270 / 360)

AI

=

$48.75

The previous owner receives the market price plus $48.75 to compensate for the accumulated interest earned since the last coupon payment. Summary In this section, you learned how to calculate the price and the discount yield for zero-coupon securities. You saw how the discount yield may be converted for comparison purposes using three standard calculations: true yield, money market yield, and bond equivalent yield. You also learned how to price a fixed-income security by calculating the present value of the instrument.

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Please complete Practice Exercise 3.2 to check your understanding of calculating the price of zero-coupon and fixed income securities. Then continue your study with the next section of Unit Three on the use of duration to track the sensitivity of bond prices to changes in interest rates.

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PRACTICE EXERCISE 3.2 Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page. Question 5: A zero-coupon security with 90 days until maturity (on a 360-day year basis) is priced to yield 5.75%. If the face value of the bond is $1,000, what is the market price we would expect for the security? _______________________________

Question 6: What is the discount yield earned on a U.S. Treasury bill purchased at $980, held for 60 days, and then sold for face value of $1,000? _______________________________

Question 7: What is the money market yield (MMY) equivalent for a zero-coupon security that has a discount yield of 5.50% and is held for 45 days? _______________________________

Question 8: What is the accumulated interest on a security that makes an annual coupon payment of $75, if there are 265 days left in a 365-day coupon-paying period? _______________________________

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ANSWER KEY Question 5: A zero-coupon security with 90 days until maturity (on a 360-day year basis) is priced to yield 5.75%. If the face value of the bond is $1,000, what is the market price we would expect for the security? P

= = = =

F [1 – ((R x DM) / DY )] $1,000 [1 – ((0.0575 x 90) / 360)] $1,000 [1 – 0.0144] $985.625

Question 6: What is the discount yield earned on a U.S. Treasury bill purchased at $980, held for 60 days, and then sold for face value of $1,000? i

= = = =

[(F – P) / F] x (DY / DM ) [($1,000 – $980) / $1,000] x (365 / 60) [0.02] x (6.08333) 12.17%

Question 7: What is the money market yield (MMY) equivalent for a zero-coupon security that has a discount yield of 5.50% and is held for 45 days? MMY

= = = =

360 x [R / (360 – (DH x R))] 360 x [0.055 / (360 – (45 x 0.055))] 360 x 0.0001538 5.54%

Question 8: What is the accumulated interest on a security that makes an annual coupon payment of $75, if there are 265 days left in a 365-day coupon-paying period? AI

= = =

(C / M) x (DH / DC ) ($75 / 1) x (100 / 365) $20.55

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DURATION Average maturity of bond's cash flows

Participants in the bond market use the concept of duration to assess interest rate risk and to implement portfolio and hedging strategies. Analysts use duration to track the sensitivity of bond prices to changes in interest rates. Duration measures the average maturity of a bond's cash flows.

Macauley Duration Duration represents the weighted average life of the bond. The weights are the present value of the individual cash flows divided by the current price of the bond. Known as Macauley duration, the formula for calculating the duration of a bond is:

T

D

=

å t

[ CFt / (1 + y)t ] _______________________________

t=1

P

Where:

Example

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D

=

Duration of the security

t

=

Time in years until each payment is made

T

=

Time in years until the security matures

CFt

=

Cash flow (coupon or principal) payments made by the security

y

=

Yield-to-maturity of the security. If the coupons are semiannual, then this rate needs to be a semiannual rate (y / 2).

P

=

Price of the security

To illustrate the duration calculation, we will calculate the duration of a three-year note that pays semiannual coupons and has the following characteristics: •

Percentage selling price of 95.65

•

Annual coupon rate of 7%

•

Annual yield-to-maturity (bond equivalent yield) of 8.678%

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Adjust annual coupon rate for semiannual payments

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Because the coupons are paid semiannually, it is necessary to convert the bond equivalent yield of 8.678% to a fully-compounded annual discount rate. To do this, we divide the bond equivalent yield by two, add one, square the result, and subtract one. Fully-compounded annual discount rate (1 + 0.04339)2 - 1

=

[(0.08678 / 2) + 1]2 - 1

=

0.0887 = 8.87%

The fully-compounded annual discount rate is 8.87%. We will use this rate to discount the bond's cash flows. You can see the results arranged in Figure 3.1. (1)

(2)

(3)

(4)

Cash Flow

Present Value at Semiannual Rate

Present Value / Bond Price

(5) (1) x (4) Timeweighted Value

0.5

3.50

3.3545

0.0351

0.0175

1.0

3.50

3.2150

0.0336

0.0336

1.5

3.50

3.0813

0.0322

0.0483

2.0

3.50

2.9531

0.0309

0.0617

2.5

3.50

2.8303

0.0296

0.0740

3.0

103.50

80.2159

0.8386

2.5159

95.6501

1.0000

2.7510

Time

Total

Figure 3.1: Duration for a Three-year Coupon Bond

Explanation of the table

An explanation of each column will help you understand the calculations. (1) Time:

The time in years from the present time until each coupon payment; the first coupon is paid in 0.5 years, and so on

(2) Cash Flow:

The cash flows in percentage terms that are made by the bond; note that at the end of the third year, the bond makes a last coupon payment plus the principal payment

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(3) Present Value at Semiannual Rate:

Each cash flow discounted at the appropriate rate (in this case, it is the fully-compounded annual rate of 0.0887); the present value of the first semiannual coupon is [3.5 / (1.0887)0.5 ] = 3.3545. The sum of the values in Column 3 should be equal to the market price of the bond. (There may be a slight rounding error.)

(4) Present Value / Bond Price:

Weights for each cash flow are determined by dividing the present value of the cash flow by the market price of the bond (95.65). The calculation for the first cash flow is 3.3545 / 95.65 = 0.0351. The weights in Column 4 should add up to 1.0.

(5) Time-weighted Value:

The time until the cash flow is received (Column 1) is multiplied by the weight for the cash flow (Column 4). The first calculation is 0.0351 x .05 = 0.0175. The sum of the time-weighted values in Column 5 is the weighted average life (duration) of the bond. In this example, the duration of the 3-year coupon bond is 2.7510 years.

Two points

There are two important points to consider when calculating the duration of a bond:

Appropriate discount rate

1. The discount rate used when discounting cash flows must be appropriate for the type of bond. For example, the annual bond equivalent yield (BEY) is the correct rate to use for an annual coupon bond. For a semiannual bond, we convert the BEY to a fully-compounded annual rate before discounting the cash flows.

Consistent use of percentages or dollars

2. It is important to be consistent in the use of percentages or dollar values for cash flows and prices. Either one is appropriate, but do not mix them!

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Example

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Another example of a duration calculation follows. What is the duration of a three-year Eurobond, with a coupon rate of 7.5% and a percentage price of 96.50? First, we calculate the BEY (yield-to-maturity) of the security. Using your financial calculator, enter the appropriate dates for maturity, the coupon rate of 7.5%, and the percentage price of 96.50. The yield-tomaturity should be 8.8797%. This is the appropriate rate to use to discount annual cash flows of the Eurobond. We can now build the worksheet and fill in the information as we make the calculations. (1)

(2)

Time

Cash Flow

1.0 2.0 3.0

(3) Present Value at Annual Rate

7.50 7.50 107.50

Total

(4) Present Value / Bond Price

(5) Timeweighted Value

6.8883 6.3266 83.2851

0.0714 0.0656 0.8631

0.0714 0.1311 2.5892

96.5000

1.0001

2.7917

Figure 3.2: Duration for a Three-year Eurobond

The duration of this Eurobond is 2.7917 years. Use the totals to ensure that the calculation is correct. The sum of the values in Column 3 equals the quoted percentage price of the Eurobond. The sum of the weights in Column 4 equals 1.0. Duration of a Perpetuity The duration of a perpetuity with equal payments is calculated as (1 + r) / r where r equals the yield of the security. For example, consider a perpetuity that is priced to yield 10% annually. The duration would be: (1 + r) / r (1 + 0.10) / 0.10 = 11 years

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Even though the instrument makes an annual payment forever, the duration is only 11 years. That is because the early payments dominate the present value calculation. (A payment received in 90 years carries very little weight in the calculation of present value.)

Modified Duration Measures price sensitivity to yield changes

Modified duration helps bond portfolio analysts estimate the percentage price change of a bond given a change in yield (interest rates). We calculate modified duration by dividing the Macauley duration by one plus the yield with which the bond is priced. The formula is: DM = D / (1 + (BEY / M))

Example

Returning to the three-year coupon bond example in Figure 3.1, we find the bond's modified duration by dividing its Macauley duration of 2.7510 by 1 + 0.04339, the semiannual yield with which the bond was priced. DM

=

2.7510 / (1 + .04339)

=

2.6366

The resulting quotient of 2.6366 is the modified duration. Estimate percentage price change

To estimate the percentage price change in the bond, analysts multiply the negative modified duration by the yield change. Percentage price change = - Modified duration x Yield change

Example

To illustrate this calculation, we estimate the percentage price change for our example from Figure 3.1. Suppose that the yield for similar bonds increases from an annual yield of 8.678% to 8.8% (a yield change of 8.80% – 8.678% = 0.122%). We calculate the percentage price change as: Percentage price change

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= - 2.6366 x 0.122% = - 0.3217%

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Given a 0.122% increase in the yield, we would expect a percentage price change of -0.3217. We, therefore, estimate that the example bond's percentage price will fall from 95.60 to 95.2783.

Duration of a Portfolio Equal to desired holding period

Investors protect security portfolios against the risk of changing interest rates by holding securities with an average duration that is equal to the investor's desired holding period. The effect is to hold the investor's total return constant, regardless of any interest rate changes. To limit risk, the portfolio manager pays for the more stable rate of return on the portfolio with a lower expected return.

Weighted average of all bonds

The duration of the portfolio is a weighted-average of the duration of each of the bonds held in the portfolio. For example, suppose an investor has a portfolio with 86.6% of the funds invested in four-year notes with a duration of 3.6554 years and 13.4% of the funds invested in ten-year bonds with a duration of 8.9652 years. The duration of the portfolio is: Dp = (3.6554)(0.866) + (8.9652)(0.134) = 4.3669 years

The weights are the percentage of the total portfolio invested in each security.

Duration Relationships Influences on duration calculation

As you can see from the calculations, duration is influenced by three important relationships: •

Maturity date

•

Coupon rate

•

Yield-to-maturity

Duration is positively correlated with maturity, but it moves in the opposite direction of coupon rates and yield-to-maturity.

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Maturity

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•

A bond's duration generally increases with the time to maturity, holding the coupon rate constant. Duration is a measure of the average maturity of the bond's payments, and the largest payment is generally made at maturity. Therefore, an increase in the time to maturity will increase the duration of the instrument. The duration of a zero-coupon bond equals the time to maturity. One cash flow is received when the bond matures in the amount of the face value. Compared to coupon bonds of the same maturity, zerocoupon bonds have the greatest duration and, therefore, have the greatest sensitivity to changes in market interest rates.

Coupon rate

•

A bond's duration is lower when the coupon rate is higher. High coupon rate bonds produce higher cash flows during the life of the bond and, therefore, duration is weighted toward the early or middle years. For low coupon bonds, duration is weighted more heavily toward the final payment at maturity.

Yield-tomaturity

•

The duration of a coupon bond is higher when the bond's yield-tomaturity is lower, all other factors remaining constant. Recall that our calculation of duration requires that the cash flows be discounted by the yield-to-maturity rate (bond equivalent rate). A smaller discount rate places less value on earlier cash flows in the discounting process.

Analysts use duration to track the sensitivity of bond prices to changes in interest rates.

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Example

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Suppose that you have to decide whether to invest in a bond with an 8% coupon rate with a 20-year maturity or a 12% coupon rate bond with a 25-year maturity. Which bond will have the larger increase in price if interest rates decline? The bond with the shorter maturity (8% coupon rate for 20 years) has a longer duration than the bond with the greater maturity (12% for 25 years) and, thus, is the most price sensitive. It is helpful to remember these relationships as you study duration. They will help to ensure that your thinking and assumptions are reasonable when you analyze fixed-income securities. Convexity

Analyze price / yield relationship

We are concluding this unit with an illustration of duration and a brief introduction to the concept of convexity. The term convexity is used by bond analysts to describe the curvature of the priceinterest rate relationship for a particular security. Convexity refers to the non-linear relationship between the change in a bond's price and a change in interest rates. This is shown in Figure 3.3.

Figure 3.3: Convexity of Bonds A and B

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Relationship between interest rate and market price

3-31

This graph plots the relationship between interest rates and market prices for two securities (Bond A and Bond B). Bond A is a straight bond, while Bond B has a call feature that allows the issuer to call the bond at a certain price. The market price for Bond B will not rise above the call price, regardless of the interest rate. Once interest rates reach a certain level, the issuer will call the bonds (buy them back) and the investor will lose the opportunity for a higher price on the bond. The call price is indicated at the point where the curve for Bond B flattens out (point B). You can see in the figure that the degree of curvature for Bond B is greater than for Bond A. You can say that Bond B has higher convexity than Bond A and, therefore, higher risk. In general, callable and putable bonds have higher convexity than straight bonds, all other factors being equal. A bond's convexity is used by bond investors to determine the effect a change in interest rates will have on the value of the bonds held in the portfolio. Calculating the convexity of the bonds gives the investor information necessary to hedge the risk of a change in interest rates.

Slope of the tangent line is the duration

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Our duration calculation was an estimate of the slope of the tangent line at the point of the curve corresponding to the market price of the bond. For the bond in the example on page 3-24, we calculated the tangent line corresponding to the percentage price of 95.65. This slope indicates the responsiveness of a security's price to a change in interest rates. Convexity measures the degree to which the bond's duration will change on the graph. We will not demonstrate the calculation of convexity in this course. The main point to remember is that convexity refers to the degree of curvature found in the priceinterest rate relationship of a bond.

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Summary You have completed this brief introduction to the concepts of duration and convexity. You have seen how duration is used to measure the average maturity of a bond's cash flows. Convexity refers to the relationship between bond prices and changes in interest rates. Please complete Practice Exercise 3.3 and then continue to the unit summary and final Progress Check for Unit Three.

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PRACTICE EXERCISE 3.3 Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page. Question 9: Duration is a measure analysts use to estimate the: ____ a) future value of a bond's cash flows. ____ b) average maturity of a bond's cash flows. ____ c) fully-discounted yield-to-maturity. ____ d) time in years until a bond matures. Question 10: Estimate the duration of the bond by entering the information in the following table. The bond has an annual coupon rate of 5.0% and makes semiannual payments. It has two years until maturity and is currently selling for a percentage price of 96.00. Price: ______________________

BEY: ___________________

Coupon: ____________________

Discount Rate: ____________

Maturity: ____________________

TIME

CASH FLOW

PRESENT VALUE AT SEMIANNUAL RATE

VALUE / BOND PRICE

TIME-WEIGHTED VALUE

0.5 1.0 1.5 2.0

____________

____________

TOTAL

Duration = __________________________Years

Question 11: What is the modified duration of this bond? _______________________________

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ANSWER KEY Question 9: Duration is a measure analysts use to estimate the: b) average maturity of a bond's cash flows. Duration represents the weighted average life of the bond. The weights are the discounted cash flows of the bond divided by the price of the bond.

Question 10: Estimate the duration of the bond by entering the information in the following table. The bond has an annual coupon rate of 5.0% and makes semiannual payments. It has two years until maturity, and is currently selling for a percentage price of 96.00. Price: 96.00 Coupon: 5.00% 7.3117% Maturity: 2 Years

BEY: 7.1827% Discount Rate:

Make sure that you have calculated the correct discount rate. Find the yield-tomaturity of the bond on your calculator. That rate should be 7.1827. Convert this to an equivalent semiannual discount rate. 0.071827 / 2 = 0.0359135 (1 + 0.0359135)2 – 1 = 0.073117 = 7.3117% Use this rate to discount the cash flows and your table should look like this: VALUE / BOND PRICE

TIME-WEIGHTED VALUE

2.4133

0.0251

0.0126

2.50

2.3297

0.0243

0.0243

1.5

2.50

2.2489

0.0234

0.0351

2.0

102.50

89.0081

0.9272

1.8543

96.0000

1.0000

1.9263

TIME

CASH FLOW

0.5

2.50

1.0

PRESENT VALUE AT SEMIANNUAL RATE

TOTAL

Duration =

1.9263

Years

Question 11: What is the modified duration of this bond? DM

= = =

D / (1 + (BEY / M)) 1.9263 / (1 + 0.35914) 1.8595

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PRACTICE EXERCISE 3.3 (Continued)

Question 12: What will be the percentage price change of the bond if the yield decreases from 5.0% to 4.7%? _______________________________

Question 13: What is the duration of the following portfolio? % of Portfolio 44.5% 36.2% 19.3%

Security 2-year notes 5-year notes 10-year bonds

Duration 1.8500 4.7465 9.3254

_______________________________

Question 14: When planning a hedging strategy, investors use convexity to describe the: _____ a)

change in interest rates relative to the duration of a bond.

_____ b) difference between a straight bond and a callable bond. _____ c) relationship between market price and duration. _____ d) price-yield relationship of a bond.

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ANSWER KEY Question 12: What will be the percentage price change of the bond if the yield decreases from 5.0% to 4.7%? Percentage price change = – Modified duration x Yield change = – 1.7972 x (0.3) = 0.5392% With a percentage price change of 0.5392%, the bond's percentage price is estimated to increase from 96.00 to 96.5392.

Question 13: What is the duration of the following portfolio? % of Portfolio 44.5% 36.2% 19.3% D

Security 2-year notes 5-year notes 10-year bonds

Duration 1.8500 4.7465 9.3254

= (0.445)(1.8500) + (0.362)(4.7465) + (0.193)(9.3254) = 4.3413 years

Question 14: When planning a hedging strategy, investors use convexity to describe the: d) price-yield relationship of a bond.

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UNIT SUMMARY

In this unit, we discussed three ways to evaluate debt securities: n

Yield

n

Price

n

Duration

Yield

Yield is the rate of return earned by investors of debt securities. We presented four different types of yield: current yield, yield-tomaturity, yield-to-call, and realized compound yield. We identified their assumptions about income, discussed their relative strengths and weaknesses, and demonstrated how to calculate each type of yield.

Price

We demonstrated the methodologies for pricing two types of bond instruments: money market discount instruments and debt instruments making a fixed interest payment. The discount yield is the rate used to price most money market discount instruments. The actual yield, money market yield, and bond equivalent yield convert the discount yield to allow for valid comparisons with other debt instruments. For securities that make periodic interest payments, the true selling price includes an adjustment for the accrued interest earned by the seller.

Duration

Duration is a way to measure a bond's price volatility in response to a change in interest rates. Duration represents the weighted average life of the bond. The weights are based on the present value of the individual cash flows relative to the present value of the total cash flows (current price of the bond). There are three important relationships to remember: 1. The longer the duration, the greater the impact of a change in interest rates on price. 2. The duration of a coupon bond is higher when the bond's yield-tomaturity is lower. 3. The higher the coupon rate, the lower the duration.

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Convexity, or the degree of curvature of the graph of a security, helps to illustrate the concept of duration. The slope of the tangent line at any point on the curve indicates how responsive the security's price is to a change in interest rates. Calculating convexity provides investors with information to hedge the risk of a change in interest rates. You have completed Unit Three, Valuing Debt. Please complete the Progress Check to test your understanding of the concepts and check your answers with the Answer Key. If any of your answers are incorrect, please reread the corresponding text. Then, continue to Unit Four, Debt Instruments.

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4 PROGRESS CHECK 3 Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page.

Question 1: A $1,000 U.S. Treasury bill, quoted on a 360-day year with 60 days until maturity, has a market price of $989.50. What was the discount yield used to price the security? ____________________________________

Use the following data to answer Questions 2 – 4. Years to maturity Years to call Coupon rate Payment frequency Market price Face value

= = = = = =

10 3 5% Semiannual $902.10 $1,000.00

Question 2: What is the current yield for the bond? ____________________________________

Question 3: Calculate the yield-to-call. ____________________________________

Question 4: The bond is not called and you hold it until it matures at the end of Year Ten. You reinvest the coupon payments at an annual rate of 6%. Calculate the annual realized compound yield for your investment. Future value of the coupon payments: ___________________________ Realized coupon yield: ______________________________________

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ANSWER KEY Question 1: A $1,000 U.S. Treasury bill, quoted on a 360-day year with 60 days until maturity, has a market price of $989.50. What was the discount yield used to price the security? R = = = =

[(F - P) / F] x (DY / DM) [($1,000 - $989.50) / $1,000] x (360 / 60) [0.0105] x (6.00) 0.063 or 6.3%

Question 2: What is the current yield for the bond? Current yield

= =

$50 / $902.10 5.54%

Question 3: Calculate the yield-to-call. Enter into your financial calculator: Number of payments (6) Present value (-$902.10) Future value ($1,000) Coupon payment ($25) Press the I% key to find the answer:

4.39% x 2 = 8.78%

Make sure that you entered the number of payments until the first opportunity to call (in three years) and not the number of interest paying periods until maturity (20).

Question 4: The bond is not called and you hold it until it matures at the end of Year Ten. You reinvest the coupon payments at an annual rate of 6%. Calculate the annual realized compound yield for your investment. Using a financial calculator: First, calculate the future value of the coupon payments reinvested at 6%. Enter number of payments (20) Coupon payment ($25) Reinvestment rate [3%, or (0.06 / 2)] Press the future value key to find the answer: $671.76 Now calculate the realized coupon yield. Enter the future value of the investment [$1,671.76, or ($671.76 + $1,000)] Present value (-$902.10) Number of payments (20) Press the I% key to find the answer: 3.13% x 2 = 6.27%

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Question 5: What is the true yield earned on a U.S. Treasury bill with a $10,000 face value, purchased for $9,650.00 and held for 90 days until maturity? ____________________________________

Question 6: What is the bond equivalent yield for a zero-coupon security that has a discount yield of 6.2% and is held for 60 days? ____________________________________

Use the following data to answer Questions 7-9. Years to maturity Coupon rate Payment frequency Face value

= = = =

12 5% Semiannual $10,000.00

Question 7: If the bond is priced to yield 6.4% annually, at what price would we expect to sell the bond? ____________________________________

Question 8: This bond is selling at a: ____ a) premium. ____ b) discount.

Question 9: You have held this bond for 73 days out of a total of 182 days in the current coupon period. How much accumulated interest would you have to add to the bond's $8,839.65 selling price? ____________________________________

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ANSWER KEY

Question 5: What is the true yield earned on a U.S. Treasury bill with a $10,000 face value, purchased for $9,650.00 and held for 90 days until maturity? i

= = = =

[(PS - PB) / PB] x [365 / DH] [($10,000 - $9,650) / $9,650] x [365 / 90] 0.0363 x 4.0556 0.1471 or 14.71%

Question 6: What is the bond equivalent yield for a zero-coupon security that has a discount yield of 6.2% and is held for 60 days? BEY = = = =

365 x [R / (360 - (DH x R))] 365 x [0.062 / (360 - (60 x 0.062))] 365 x [0.062 / 356.28] 6.35%

Question 7: If the bond is priced to yield 6.4% annually, at what price would we expect to sell the bond? Enter into your financial calculator: Number of payments (24) Coupon payments [$250 or (0.05 / 2 x $10,000)] Discount yield [3.2% or (6.4% / 2)] Future value ($10,000) Press the present value key to find the bond price: $8,839.65

Question 8: This bond is selling at a: b) discount. The market price is less than the face value.

Question 9: You have held this bond for 73 days out of a total of 182 days in the current coupon period. How much accumulated interest would you have to add to the bond's $8,839.65 selling price? AI = = =

(C / M) x (DH / DC) (500 / 2) x (73 / 182) $100.27 ver. 1.0

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Question 10: Estimate the duration of a bond by filling in the information on the following worksheet. The bond makes annual payments at the coupon rate of 6% and has two years until maturity. It is currently selling for a percentage price of 97.2.

TIME

Price:

Maturity:

_

Coupon:

BEY:

_

CASH FLOW

PRESENT VALUE AT ANNUAL RATE

VALUE / BOND PRICE

TIME-WEIGHTED VALUE

1.0 2.0

________

________

________

TOTAL

Duration =

Years

Question 11: The duration of a bond is related to its maturity, coupon rate, and yield-tomaturity. Holding other factors constant, as a bond's coupon rate increases, you would expect the duration to: ____ a) increase. ____ b) decrease. ____ c) remain the same.

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ANSWER KEY

Question 10: Estimate the duration of a bond by filling in the information on the following worksheet. The bond makes annual payments at the coupon rate of 6% and has two years until maturity. It is currently selling for a percentage price of 97.2. Price:

97.20

Coupon:

6%

Maturity: 2 years a BEY: 7.5607%

a

The annual bond equivalent yield (yield-to-maturity) is the correct discount rate to use for an annual coupon bond. Enter into your financial calculator: Number of payments (2) Coupon payment (6.00) Present value (97.20) Future value (100.00) Press the I% key to find the bond equivalent yield: 7.5607%. Use this rate to discount the cash flows and your table should look like this.

TIME

CASH FLOW

1.0

6.0

2.0

106.0

TOTAL

Duration:

1.9426

PRESENT VALUE AT ANNUAL RATE

VALUE / BOND PRICE

TIME-WEIGHTED VALUE

5.5782

0.0574

0.0574

91.6218

0.9426

1.8852

97.2000

1.0000

1.9426

Years

Question 11: The duration of a bond is related to its maturity, coupon rate, and yield-tomaturity. Holding other factors constant, as a bond's coupon rate increases, you would expect the duration to: b) decrease. Duration moves in the opposite direction of coupon rates.

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Unit 4

UNIT 4: DEBT INSTRUMENTS

INTRODUCTION In this unit, you are introduced to some common debt securities that are issued and traded in the short-, medium-, and long-term markets. We will present the attributes of each instrument and describe the issuers and the investors who use the instrument. We also will describe the special characteristics of some complex debt instruments trading in the markets today.

UNIT OBJECTIVES When you complete this unit, you will be able to:

Identify the markets in which debt instruments are issued and traded

Recognize the characteristics of different debt instruments

SHORT-TERM MARKETS One year or less

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The short-term market is often called the money market, or cash market. Securities issued in short-term markets generally mature in one year or less. The most common instruments are:

Treasury bills

Banker's acceptances

Commercial paper

Certificates of deposit

Repurchase agreements

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All short-term securities have active secondary markets; some instruments are more liquid than others, however.

Treasury Bills Backed by U.S. government

Treasury bills are short-term securities that are issued by the U.S. Treasury Department and backed by the full faith and credit of the U.S. Government. The Treasury Department holds a monthly auction to issue three-month, six-month, and 52-week securities.

Quoted on discount basis

Treasury bills are zero-coupon instruments; therefore, they are quoted on a bank discount basis. Treasury bill quotes are based on a 360-day year. Other Treasury securities are quoted on a price basis, which makes it difficult to directly compare Treasury bills with other Treasury instruments.

Large, liquid market

The market for Treasury bills is large and very liquid. The backing of the U.S. government makes these instruments popular for riskadverse investors.

Investors

Most investors in Treasury bills are institutional; however, some large individual investors participate in the Treasury bill market.

Banker's Acceptance Bank guarantees payment of time draft

A banker's acceptance (BA) is a time draft, or a bill of exchange, that directs the accepting bank or trust company to pay a third party a stated sum on a specified future date. When the bank or trust company accepts the time draft, it guarantees payment, thereby creating a negotiable instrument.

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Noninterest bearing security

Banker's acceptances are noninterest-bearing securities that are sold at a discount and redeemed at face value at maturity. Typical tenors range from two to six months. Since BAs are considered slightly less risky than commercial paper (see page 4-4), they sell at slightly lower yields.

Example

BAs are used to finance international trade, especially for smaller companies. To illustrate the use of a banker's acceptance, consider a U.S. company that would like to import shoes manufactured in Brazil. If the U.S. company is too small to enter the open market for debt financing to purchase the shoes, it may use a banker's acceptance as an alternative. The importer's bank writes a letter of credit for the amount of the sale and sends it to the Brazilian exporter. At the time the shoes are exported, the Brazilian company uses this letter to draw a time draft on the importer's U.S. bank. The exporter takes the draft to its local bank and receives immediate payment for the goods, less the discount charged by the local bank. The Brazilian bank sends the time draft to the importer's U.S. bank which stamps the draft "accepted." This means that the U.S. bank guarantees repayment of the amount of the time draft at the specified maturity date.

Two choices for investor

After the draft has been accepted, the Brazilian bank has two choices.

Redeem at discount before maturity

1. It can demand immediate payment less a discount from the U.S. bank. The U.S. bank will make the payment, then either hold the acceptance as an investment or sell it to another investor.

Redeem at full value at maturity

2. The Brazilian bank may hold the acceptance as part of its investment portfolio and present it to the accepting bank for repayment at maturity. In this case, the U.S. bank will return the security to the Brazilian bank.

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Regardless of who owns the acceptance, payment on the loan is backed by the pledge of the importer, secured by the goods purchased with the loan, and guaranteed by the importer's bank. Generally, the accepting bank determines the rate at which the BA can be sold in the market. This rate is determined by the creditworthiness of the borrower plus a spread (usually between 10 and 30 basis points) charged by the bank for creating the acceptance. Liquid market

Dealers who buy and sell the drafts have created an active secondary market for banker's acceptances, which creates liquidity for investors. An acceptance is often bought and sold by many investors before it matures. The major investors in banker's acceptances include banks, money market funds, corporations, and other foreign institutional investors. Commercial Paper

Unsecured promissory note

Commercial paper (CP) is an unsecured promissory note issued for a specific amount that matures on a specific date. It is sold on a discount basis, with the investor receiving face value at maturity.

Short maturities

The maximum maturity on commercial paper is 270 days in order to avoid the costly and time-consuming SEC registration process required for securities with longer maturities. Most commercial paper is issued with 30-day maturities. Companies that issue commercial paper usually do not have sufficient funds in 30 days to repay the loan and, therefore, they expect to "roll over" the paper (issue new commercial paper to pay off the maturing securities).

Interest rates

The interest rates paid on commercial paper depend on:

Maturity

Amount the borrower wishes to raise

General level of interest rates

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Market less liquid

Due to the possibility of default, rates generally are slightly higher than the rate paid on U.S. Treasury bills. Many issuers back their securities with a bank line of credit. Since investors typically hold commercial paper until maturity, liquidity is a problem in the secondary market. This also causes rates to be higher.

Issuers

Issuers of commercial paper are generally companies with high credit ratings. Most investors will not purchase the commercial paper of companies with lower ratings. Traditionally, large, well-established industrial and manufacturing firms issued commercial paper. Today, financial companies are large issuers; banks, foreign companies, government agencies, and sovereigns also have begun to enter the market. Many financial companies sell their paper directly to investors, while manufacturing and other companies use dealers. The commercial paper market is now larger than any other money market security, including the U.S. Treasury bill market.

Investors

The majority of investors in commercial paper are institutional investors, including money market funds, pension funds, commercial bank trust departments, and some non-financial firms seeking short-term investments.

Certificate of Deposit Financing for financial institutions

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A certificate of deposit (CD) is a certificate issued by a bank or thrift that indicates a specified sum of money has been deposited at the issuing depository institution. Financial institutions use CDs to raise funds to finance their activities. CDs have a minimum maturity of 14 days, with most tenors in the one- to six-month range. Some five-year and seven-year CDs exist, but they are not common.

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Issued at face value

DEBT INSTRUMENTS

Certificates of deposit are issued at face value. Shorter-term instruments (less than one year) pay interest at maturity, while longer instruments make semiannual interest payments. CD rates are quoted on a 360-day year basis. Yields on CDs are determined by the:

General level of interest rates

Credit rating of the issuer

Supply and demand for the securities

Interest rates

Rates are higher for CDs than for Treasury bills because of the credit risk associated with the issuer and the lower level of liquidity in the secondary market. Because most CDs have face values over $100,000, they usually attract institutional investors.

Innovations

Recent additions to the CD market include floating rate CDs, Yankee CDs, and Euro CDs.

Floating rate CDs are quoted on a spread off a benchmark rate such as Treasury bills or LIBOR. Most are 6-month instruments, with a 30-day interest rate reset. Issuers pay accrued interest at the reset date. Foreign banks issue Yankee CDs in the U.S. market. Euro CDs are dollar-denominated instruments issued by U.S. and European banks in the Euromarket.

Repurchase Agreements Short-term sale and repurchase of a security

A repurchase agreement (or "repo") is a common investment vehicle for lenders with funds available for very short-term investments. A repo involves the sale of a security with a commitment to repurchase the same security at a designated date and price. It is actually a collateralized loan, with the collateral being the security that is sold and repurchased. ver. 1.0 v.07/06/94 p.01/10/00

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Interest rate

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The difference between the sale price and the purchase price is the interest cost of the loan. Repo interest rates closely follow the interest rates being paid on other money market securities. Interest rates for repos are quoted on a 360-day year basis. From the borrower's point of view, the rate paid on a repo is usually less than the rate paid on bank financing. For the investor, repos provide an attractive rate of return on a short-term secured loan with a highly liquid secondary market.

Issuers

Primary users of repurchase agreements are government securities dealers who need short-term funds. For example, consider a government securities dealer who needs $10 million to purchase a particular Treasury security that the dealer plans to hold overnight. To obtain financing for the purchase, the dealer can arrange a bank loan, use the dealer's own funds, or enter a repo using other securities in the dealer's portfolio as the collateral.

Investors

The lender in the repurchase agreement may be any entity with excess funds for short-term investment. Common lenders in the repo market are municipal governments, other securities dealers, and government agencies. Corporations with excess cash also enter the repo market to earn interest on their holdings, even if the investment period is only one day. One-day repurchase agreements are called "overnight repos." Repos that are arranged for longer periods are referred to as "term repos."

MEDIUM-TERM MARKETS From one to ten years

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Medium-term market maturities are generally greater than one year, but less than ten years; however, there is some overlap with shortterm and long-term instruments. For example, some CDs may have maturities of greater than one year, and some bonds may have maturities of less than ten years.

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Two types of instruments are often classified as medium-term securities: U.S. Treasury notes and medium-term notes.

U.S. Treasury Notes Coupon-paying notes

U.S. Treasury notes are coupon-paying securities (with maturities of two to ten years) issued by the U.S. Treasury Department. The full faith and credit of the U.S. government backs these securities. The Treasury Department issues the notes through a monthly or quarterly auction, depending on the maturity of the security. U.S. Treasury notes pay semiannual interest and repay the face value at maturity.


The market for Treasury notes is large and very liquid. Investors can easily buy and sell securities at fair prices. Most investors are institutional; however, there are some individual participants.

Medium-term Notes Similar to commercial paper

Medium-term Notes (MTNs) began as an extension of commercial paper, providing longer maturities for issuers and investors who wanted the characteristics of commercial paper for longer investment periods.

Sold off the shelf

Issuers offer medium-term notes by filing a shelf registration with the SEC (per Rule 415). The registration specifies the maximum amount of debt to be raised through the issue and the time period during which it will be offered. A medium-term note program usually offers securities with a range of maturities and a different rate associated with each tenor. An investment banker, acting as a dealer for the issuer, posts rates for the different maturities and sells the paper "off the shelf" to investors. The notes are sold on a best efforts basis and continuously offered to investors during the time specified by the registration.

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Investors choose which maturity and rate best meet their investment needs and buy the selected securities from the dealer. The issuer may encourage investors to buy a particular maturity by offering it at a better yield than other tenors. Interest rates

Most MTNs are interest-bearing securities, paying a semiannual coupon. The interest rate is quoted on a 360-day year basis. The notes sell at par, with the interest rate fixed at the time of purchase. The maturity of the security, the overall level of interest rates, and the credit rating of the investor determine the rate. Usually, the rate is quoted as a spread over Treasury instruments of similar tenor.

Innovations

Floating rate MTNs (with rates reset monthly, quarterly, or semiannually) have become more common. Other innovations include credit-supported MTNs, collateralized MTNs, and multicurrency MTNs. Medium-term notes have become an important source of capital for Latin American and Asian companies hoping to gain access to U.S. capital markets. Euro MTN programs are becoming popular because investors in those markets have created demand for the issues.

Issuers

Typical issuers are companies with high credit ratings. The process for rating MTNs is the same as that used for rating corporate bonds (discussed in Unit One). The wide investor base for MTNs includes both institutions and individuals. Investors in MTNs are fairly sophisticated and require a variety of features being offered in the market.

LONG-TERM MARKETS More than ten years

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Instruments with maturities of greater than ten years typically are associated with long-term capital markets. However, there is often overlap among instruments. Some MTNs exist with 20-year or 30year maturities; some corporate bonds may have seven-year or even five-year maturities. Thus, divisions between short-term, mediumterm, and long-term instruments often are not clear.

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In this section, we will discuss some of the major categories of bonds trading in the long-term markets. These include U.S. Treasury bonds, corporate bonds, municipal bonds, Eurobonds, and Brady bonds.

U.S. Treasury Bonds Coupon-paying securities

The U.S. Treasury Department issues bonds with maturities of 10, 20, and 30 years. It offers the securities at a monthly or quarterly auction, depending on the maturity of the instrument. Treasury bonds are coupon-paying instruments, with semiannual interest payments, that repay the face value at maturity. The bonds are backed by the full faith and credit of the U.S. government.


The secondary market for Treasury bonds is large and very liquid. Most investors are institutional, although there are some individual participants in the long-term market.

Corporate Bonds Large market with variety of issues

The corporate bond market is very large and includes a wide variety of instruments. In Unit One, we discussed several methods for paying off debt and for providing security for debt instruments. In the corporate bond market, these features are combined to form an almost endless number of different debt securities that meet the needs of both issuers and investors.

Interest rates

The overall level of interest rates and the issuer's credit rating generally determine the interest rates paid on corporate bonds. Most domestic corporate bonds make semiannual coupon payments; however, there are many exceptions. Most corporate bond issues are underwritten.

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Straight and plain vanilla debt

After analysts carefully evaluate and estimate the value of each bond feature, they combine the estimated values to find the value of the entire instrument. The terms "straight debt" and "plain vanilla debt" refer to simple bonds that make periodic interest payments and repay the entire face value at maturity. These bonds are the easiest to evaluate. The entire range of possibilities cannot be covered in this course, but the discussions on "valuing debt" in Unit Three should give you an adequate background to begin to evaluate a wide variety of instruments.

Floating rate notes

Another common type of corporate bond is the floating rate note (FRN). As the name suggests, these securities have a floating interest rate payment, usually benchmarked against a market rate such as LIBOR or Treasuries plus a spread. The spread is determined by the credit rating of the company, the maturity of the instrument, plus a possible liquidity premium. FRNs have a wide range of maturities that fall into both the medium-term and long-term markets. FRN rates can be set either before the coupon payment period (predetermined) or at the time the coupon is due (postdetermined or "back-end" set).

Municipal Bonds State, county, city bonds

Municipal bonds are securities issued by government entities other than the U.S. government. They include state, county, and city governments.

No federal taxes

The distinguishing feature of municipal bonds is that interest payments are not subject to taxation by the U.S. government, which makes them attractive to many investors with tax concerns.

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Finance capital projects

DEBT INSTRUMENTS

Local governments issue most municipal bonds to finance capital projects. Two types are general obligation bonds and revenue bonds. 1. General obligation bonds (GOBs) are backed by the full faith and credit of the local government. The ability of the government entity to collect taxes to repay the bonds provides security for investors. 2. Revenue bonds are backed by the income generated by the project for which the bonds provided funding. For example, the expected revenue from a toll bridge may be used to provide security for the bond.

Sovereign / provincial bonds

Although technically not municipal bonds, many governments outside the United States also issue bonds to raise funds for their operations. These sovereign and provincial bonds are generally backed by the full faith and credit of the issuing government. However, returns earned on these bonds by U.S. investors are subject to U.S. taxation.

Eurobonds Issued in Euromarket

Eurobonds are securities issued in the unregulated Euromarket. These bonds are listed and traded on exchanges in London and Luxembourg. Most issuers are large, widely recognized companies with high credit ratings. Unlike most domestic corporate bonds, Eurobonds make annual coupon payments.

Investors

Since Eurobonds are not registered, the primary investors traditionally have been individuals seeking to avoid taxes. Eurobond markets are often considered fickle, probably because many individual investors buy securities on name recognition rather than credit rating. Recently, institutional investors have become an important part of the market.

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Because institutional investors tend to be sophisticated, there are many innovative instruments traded in the Eurobond market. Both fixed and floating rate instruments are common; zero-coupon instruments are also issued in the Eurobond market. The U.S. dollar is the most common currency issue, but Eurobonds also are issued in most European and some Asian and Latin American currencies.

Brady Bonds Restructures problem bank loans

In 1989, the U.S. Treasury Department devised the Brady Plan to help developing countries restructure troublesome bank loans. The plans are negotiated individually among the country, its creditor banks, the World Bank, and the International Monetary Fund. Essentially, the country agrees to a program of economic reforms designed to control inflation, restore currency values, create jobs, and make other relevant economic changes. In return, the creditor banks forgive a percentage of the bank loans due them from the country and work to reduce interest rates on the outstanding debt to ease the strain on the debtor country.

Loans exchanged for Brady bonds

The creditor banks exchange the remainder of the bank loans for marketable securities known as Brady bonds. Because the Brady bonds have a secondary market, the creditor bank can sell the bonds to other investors.

Backed by Treasury bonds

To make bonds attractive to investors, the Brady Plan added credit enhancements by collateralizing the principal of the bonds with U.S. Treasury bonds. Even though they are backed by Treasury securities, the bonds have been more volatile in their pricing and yields.

Interest rates

The credit rating of the government issuing the bonds generally determines the rates paid on Brady bonds. Bonds from the highestrated countries have been the most liquid; however, some investors seek higher returns with lower-rated bonds.

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The highest-rated bonds trade at spreads of about 200 basis points above Treasury securities of similar tenor. Lower-rated debt may see spreads as high as 1000 basis points above Treasuries. Brady bonds usually make periodic coupon payments; however, some special features may occur with stronger credits. The Brady Plan provides developing countries with access to a larger investor base for their capital-raising needs. While the program began with several Latin American countries, several African, Eastern European, and Asian developing countries are beginning to negotiate Brady Plans.

COMPLEX DEBT SECURITIES Difficult to evaluate

The market for complex debt instruments has grown exponentially as investors have become more sophisticated and issuers' needs have become more difficult to meet. In this section, we introduce some securities with special features that make them difficult for analysts to evaluate. These include equity-linked debt and dual currency debt. Analysts value these complex securities by breaking them into their basic parts and evaluating each part separately. The purpose of this section is to introduce these securities, rather than to demonstrate the evaluation process.

Equity-linked Debt Incentive to investors

Companies with lower credit ratings often need to provide investors with incentives to purchase their debt securities at reasonable rates. One common incentive links the debt to the company's equity by providing investors with an opportunity to participate in the earnings of the company. Companies use two basic methods to link debt with equity: convertible debt and warrants. ver. 1.0 v.07/06/94 p.01/10/00

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Convertible Debt Exchangeable for equity, assets, or alternative debt

Convertible debt gives a bondholder the option of exchanging the bond for a predetermined number of shares in the issuing company. Sometimes the bondholder can convert the debt into the shares of another company. This may occur when another company provides a guarantee for the bonds of the issuer. Some bonds are convertible into other assets, such as commodities like gold or oil. Other convertible bonds may allow conversion from fixed-rate debt to floating debt. Most of these conversions occur at a time that is most advantageous for the bondholders. Usually the conversion rates, regardless of the asset being converted, are preset at the time the bonds are issued. Warrants

Right to purchase shares

The other type of equity-linked debt instruments have warrants attached. A warrant is a negotiable certificate that gives the owner the right to purchase a predetermined number of shares of the issuing company at a specified price during a specified period.

Detachable from original bond

Warrants have value as stand alone securities, and often are separated from the bonds to which they were originally attached. This "detachability" provides investors with greater flexibility than investors in convertible bonds. Investors can detach the warrants and sell either the bonds or the warrants as their investment needs change. The secondary market for some warrants is very active and liquid. A company also may issue warrants that are not attached to bonds. These are called "naked warrants."

Lowers interest rate

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The purpose of attaching warrants is to lower the interest rate the issuer pays on the debt. When warrants are removed, bonds often trade at deep discounts to face value because the interest rate is much lower than the prevailing rate for bonds of similar maturity and risk.

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Most investors will value warrants and bonds separately, even if they do not plan to detach them. Typically, investors exercise the warrants when the market price of the stock is greater than the exercise price. Many warrants expire with no value because the stock price never exceeds the exercise price during the life of the warrant. Companies issue most convertible bonds or bonds with warrants as straight debt. Typically, they pay semiannual coupons with the face value repaid at maturity.

Dual Currency Debt Some debt instruments are linked to other assets or securities to create hybrid securities. One common hybrid is the dual currency bond. Interest and principal paid in different currencies

Dual currency bonds make interest payments in one currency and repay the principal in another currency. This structure is designed to meet expected cash flows the company will generate from the use of capital raised by the bonds.

Issuers

Companies with operations in more than one country and earnings in more than one currency are typical issuers of dual currency bonds. These bonds allow issuers to take advantage of the relatively low level of interest rates associated with strong currencies which, in turn, lowers their overall costs of borrowing. The redemption rate usually is set at the time the bonds are issued, so that exchange rates are known to the investors. The bonds are usually straight debt instruments, with semiannual coupon payments.

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UNIT SUMMARY In this unit, we discussed the attributes of common and complex debt instruments. We organized our presentation of the most common debt instruments by the market in which the securities are issued and traded.

Short-term markets Short-term market securities are those with maturities of less than one year. The safety of U.S. government backing has created a large and very liquid market for Treasury bills. Banker's acceptances are zero-coupon securities created by banks as a means of financing international trade. Banks also issue certificates of deposit to raise funds to finance their activities. Commercial paper is an unsecured promissory note for a specific amount with a specific maturity that typically is issued by companies with high credit ratings. The commercial paper market has become the largest of all the money markets. A repurchase agreement (repo) is a collateralized loan backed by the security being sold and repurchased. The tenor of repos is usually overnight.

Medium-term markets U.S. Treasury notes and medium-term notes are the most widely known medium-term securities. U.S. Treasury notes are couponpaying securities with a large, very liquid market. Medium-term notes have the characteristics of commercial paper and are offered "off the shelf" with a range of maturities and yields.

Long-term markets Long-term market securities, those with maturities of greater than ten years, include U.S. Treasury bonds, corporate bonds, municipal bonds, Eurobonds, and Brady bonds.

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Large markets exist both for Treasury bonds and for the many types of corporate bonds. Municipal bonds are tax-free bonds used to finance the capital projects of city, county, and state governments. Eurobonds include many innovative instruments issued in the unregulated Euromarket. Brady bonds convert the bank loans of developing countries into marketable securities backed by U.S. Treasury bonds. We introduced two types of complex instruments that are becoming wide spread in debt markets: equity-linked debt and dual currency debt.

Equity-linked debt Equity-linked debt allows investors to participate in the earnings of the issuing company. They do so either by converting the company's bond into a predetermined number of shares (convertible debt) or by purchasing or holding warrants that give the owner the right to purchase a predetermined number of shares at a specified price.

Dual currency debt Companies with multinational operations may issue dual currency bonds that pay interest in one currency and repay the principal in another.

You have completed Unit Four, Debt Instruments. Please complete the Progress Check to test your understanding of the concepts and check your answers with the Answer Key. Then, continue to Unit Five, Derivative Securities.

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✔ PROGRESS CHECK 4

Directions: Determine the correct answer to each question. Check your answers with the Answer Key on the next page. If you answer any questions incorrectly, read the appropriate text again. Question 1: Which of the following is a medium-term debt instrument? ____ a) U.S. Treasury note ____ b) Banker's acceptance ____ c) Commercial paper ____ d) Certificate of deposit Question 2: A bond is issued to replace bank loans and is collateralized by U.S. Treasury bonds. This is a: ____ a) Eurobond. ____ b) Yankee bond. ____ c) Foreign bond. ____ d) Brady bond. Question 3: The term "money market" refers to: ____ a) long-term markets. ____ b) debt markets. ____ c) short-term markets. ____ d) medium-term markets. Question 4: Which of the following U.S. Treasury issues has the longest maturity? ____ a) Treasury bonds ____ b) Treasury bills ____ c) Treasury notes

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ANSWER KEY Question 1: Which of the following is a medium-term debt instrument? a) U.S. Treasury note

Question 2: A bond is issued to replace bank loans and is collateralized by U.S. Treasury bonds. This is a: d) Brady bond.

Question 3: The term "money market" refers to: c) short-term markets. Money market securities generally have a maturity of one year or less.

Question 4: Which of the following U.S. Treasury issues has the longest maturity? a) Treasury bonds Treasury bonds have maturities of 10, 20, and 30 years.

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Question 5: In the example of a U.S. company importing shoes manufactured in Brazil, the issuer of the banker's acceptance is the: ____ a) Brazilian bank. ____ b) Brazilian shoe company. ____ c) U.S. importer. ____ d) U.S. bank.

Question 6: Which of the following is sold to investors off the shelf? ____ a) U.S. Treasury notes ____ b) Brady bonds ____ c) Medium-term notes ____ d) Commercial paper

Question 7: If tax avoidance is a goal of your investment plan, you may invest in: ____ a) municipal bonds and commercial paper. ____ b) commercial paper and Eurobonds. ____ c) Eurobonds and municipal bonds. ____ d) municipal bonds and medium-term notes.

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ANSWER KEY Question 5: In the example of a U.S. company importing shoes manufactured in Brazil, the issuer of the banker's acceptance is the: d) U.S. bank. When the U.S. bank stamps the time draft "accepted" and guarantees payment, it creates the banker's acceptance.

Question 6: Which of the following is sold to investors off the shelf? c) Medium-term notes Medium-term notes are offered continuously to investors with a range of maturities and rates. From choices displayed "on the shelf," investors choose the security which best meets their investment needs.

Question 7: If tax avoidance is a goal of your investment plan, you may invest in: c) Eurobonds and municipal bonds. Municipal bonds are not subject to taxation by the U.S. government. Eurobonds are not registered with any government and are often used to avoid taxes.

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Question 8: A corporation with excess cash agrees to an overnight purchase and resale of a certain security at specific prices. This corporation is investing in a: ____ a) repurchase agreement. ____ b) commercial paper. ____ c) certificate of deposit. ____ d) corporate bond.

Question 9: The term "straight debt" refers to corporate bonds that: ____ a) are benchmarked against a market rate plus a spread. ____ b) are backed by the funds generated by the capital project for which the bonds provide funding. ____ c) pay periodic interest and repay the face value at maturity. ____ d) pay no interest and are sold on a discount basis.

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ANSWER KEY

Question 8: A corporation with excess cash agrees to an overnight purchase and resale of a certain security at specific prices. This corporation is investing in a: a) repurchase agreement.

Question 9: The term "straight debt" refers to corporate bonds that: c) pay periodic interest and repay the face value at maturity.

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Question 10: Jonas Manufacturing is a U.S. company with a Brazilian subsidiary. Jonas-Brazil wants to issue debt to finance a new production process. To lower borrowing costs by taking advantage of U.S. interest rates, JonasBrazil may issue: _____ a) a dual-currency bond. _____ b) a Brady bond. _____ c) a Eurobond. _____ d) commercial paper.

Question 11: Both warrants and convertible debt link a company's debt to its equity. What is the difference between the two types of equity-linked debt? _____ a) Companies with low credit ratings issue convertible debt, whereas companies with high credit ratings issue warrants. _____ b) Convertible debt allows a bondholder to exchange the debt for shares of the company, while warrants grant the bondholder the right to purchase shares. _____ c) Warrants are exchangeable for other assets like gold or oil, while convertible debt provides access to the assets of the company. _____ d) Convertible bonds make interest payments in one currency and repay the principal in a second currency.

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DEBT INSTRUMENTS

ANSWER KEY Question 10: Jonas Manufacturing is a U.S. company with a Brazilian subsidiary. Jonas-Brazil wants to issue debt to finance a new production process. To lower borrowing costs by taking advantage of U.S. interest rates, JonasBrazil may issue: a) a dual-currency bond.

Question 11: Both warrants and convertible debt link a company's debt to its equity. What is the difference between the two types of equity-linked debt? b) Convertible debt allows a bondholder to exchange the debt for shares of the company, while warrants grant the bondholder the right to purchase shares.

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Unit 5

UNIT 5: DERIVATIVE SECURITIES INTRODUCTION During the past three decades, the sophistication level of issuers and investors in capital markets has increased significantly. These participants have learned to identify and quantify different types of risk inherent in their issues and investments. This ability to measure risk has spurred the development of many derivative instruments designed to manage these risks. These instruments are referred to as "derivatives" because their values are derived from the value of the underlying assets from which they are created. Derivative instruments serve a very important function in today's capital markets. They allow investors to limit their downside loss potential in exchange for the opportunity to capture possible upside profits. Derivative instruments help to limit the volatility inherent in a potential investment. Because of their widespread use in connection with other debt and equity securities, both as hedging instruments and as speculative instruments, we are providing a short introduction to some of the most common derivatives. In this unit, we will briefly introduce options, swaps, and forward agreements. For a more complete discussion and explanation of these and other derivative instruments, we recommend that you study the appropriate workbooks covering those instruments. If you have studied the Basics of Corporate Finance workbook, the sections on options and swaps may be familiar. This is a good opportunity to review the concepts as you prepare for more advanced courses on capital markets.

UNIT OBJECTIVES After you complete this unit, you will be able to:

Recognize terminology associated with options trading

Recognize payoff profiles for call options and put options

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Identify the characteristics of interest rate swaps, currency swaps, and forward agreements

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DERIVATIVE SECURITIES

OPTIONS An option contract between a buyer (holder) and a seller (writer) describes the rights of the option holder and the obligations of the option writer. The purchase price of an option is called the premium. This is the compensation that the holder of the option pays to the writer for the rights described in the option contract. Calls and puts

There are two types of options: call options and put options. Call options

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give the holder the right to buy an asset for a specified price on or before a given expiration (maturity) date.

Put options

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give the holder the right to sell an asset for a specified price on or before a given expiration (maturity) date.

The specific asset named in the option contract is called the underlying asset. The price at which the underlying asset may be bought is called the exercise or strike or contract price. Purchasing (or selling) the underlying asset of an option contract is referred to as exercising the option. The key thing to remember is that the holder of the option has the right (but not the obligation) to exercise the option. In the money / Out of the money

An option is "in the money" when exercising the option would produce profits for the holder. An option is "out of the money" during the time when exercising would not be profitable for the holder. This means that a call option on a stock is in the money when the exercise price is below the market price of the stock; a put option is profitable when the exercise price is above the market price of the stock.

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American / European

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Options may be either American or European. American options give the holder the right to exercise the option at any time up to the expiration date. European options give the holder the right to exercise the option only on the expiration date.

Background and Markets When options were first traded, contracts were arranged between pairs of investors and customized to meet specific needs. These customized contracts could vary according to exercise price, expiration date, and underlying asset. Because of these infinite possibilities, it was nearly impossible for a secondary options trading market to exist. Investors would enter into customized agreements according to their investment needs; if their needs changed, it was difficult to find another investor to buy the option contract. Secondary markets

This lack of liquidity and standardization was one of the driving forces behind the creation of the Chicago Board Options Exchange (CBOE) in 1973. The CBOE enacted rules to standardize option contracts in order to restrict the number of contract types that would trade on the exchange. Soon, other option exchanges were created. This led to a broader standardization of option contracts and was the key to creating a secondary market for options and increasing the liquidity of option contracts. Customized option contracts are still available to investors — they are traded in over-the-counter (OTC) markets. These customized options are usually considerably more expensive than the standard option contracts because of the lack of liquidity.

Standardized contracts

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The first standardized contracts were for the purchase or sale of common stock. However, investors soon created demand for options on a variety of financial and physical assets, including options on:

Common stock

Stock indices

Debt instruments

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Interest rate futures

Foreign currency futures

Agricultural commodities

Precious metals

These options are now written and traded by investors on several different exchanges. Since stock options are the most commonly traded options, we will use them as examples. The basic principles of options are the same, regardless of the underlying asset. Option Clearing Corporation (OCC)

Another important event occurring with the establishment of standardized option contracts was the creation of the Option Clearing Corporation (OCC). The OCC is the clearinghouse for options trading. It is the single guarantor of all the options listed on the options exchange. With the OCC in place, an option buyer need not be concerned with counterparty risk (lack of performance, for example).

Payoff Profile for Calls and Puts The following abbreviations will be used in this section for the diagrams and formulas concerning options and their uses. S

= Current stock price

ST = Stock price at time T X

= Exercise price

C

= Price of call option

P

= Price of put option

Call Options A call option gives the holder the right to buy an asset for a specified price on or before a given expiration (maturity) date. The payoff profile (gain or loss) for the holder and writer of a call option is shown in Figure 5.1. ver. 1.0 v.07/06/94 p.01/10/00


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Figure 5.1: Payoff Profile for Call Holder and Call Writer

Payoff for call option holder

The diagram on the left side of Figure 5.1 is the payoff for the holder of a call option. The solid line represents the payoff for the call option. The dashed line is the payoff of the option, net the cost of the option. If the price of the stock never rises above the exercise price, the holder of the option is only liable for the premium paid to buy the call option. This payoff of the option is also expressed using the following mathematical relationship: Call payoff = MAX (0, S - X)

When written out, this means that the payoff to the holder of a call option is the maximum of 0 (zero) and the difference between the price of the underlying stock (S) and the exercise price (X) of the option. Example

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Here is an example of how this works. LDM Company has a call option with an exercise price of $30. If the stock price (S) of LDM Company is less than $30, the option is out of the money, and the payoff of the option is $0. If the stock price rises above $30, the option is in the money, and the payoff for the call option is the price of the stock minus the exercise price (S - X). For instance, if the stock rises to $42, the option payoff is $42 - $30 = $12 per share.

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An option buyer is able to participate in any price change in the underlying asset without having to buy the asset itself, which would require a substantially larger investment. The option's cost (premium) is usually only a small fraction of the underlying asset's market price. Most stock options are written for a block of shares, such as 100. With an American option, the payoff profile is valid anytime during the life of the option. In other words, the holder of the option can exercise the option and claim the payout. In a European option, the only stock price we can consider is the price at the time the option expires. Payoff for a call option writer

The diagram on the right side of Figure 5.1 is the payoff profile for the call option writer. In this case, the writer receives the price of the call option up-front. Essentially, the writer is making a bet that the price of the underlying stock will not rise above the exercise price. If the bet is correct, the holder of the option will never exercise the option and the writer has the premium as profit. Options trading is a zero-sum transaction — any profits gained by one counterparty are exactly matched by losses incurred by the other counterparty. If the price of the stock is greater than the exercise price on the option plus the premium, the holder of the option will most likely exercise the option. In this case, the writer is obligated to sell the shares of stock to the holder at the exercise price. If the writer did not own the underlying stock when the option was written (called writing a naked option), then the writer has to buy the stock at the current market price and sell it to the holder of the option at the exercise price. The writer's loss will be the difference in the two prices (net of the premium received for the call option). Put Options A put option gives the holder the right to sell an asset for a specified price on or before a given expiration (or maturity) date. The payoff profiles for the holder and writer of a put option are given in Figure 5.2. ver. 1.0 v.07/06/94 p.01/10/00


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Figure 5.2: Payoff Profile for Put Holder and Put Writer

Maximum payoff for put holder

The figure on the left is the payoff profile for the holder of a put option. The maximum profit is the exercise price of the put option less the price paid for the option. This would occur if the stock price fell to $0. The mathematical relationship is: Put payoff = MAX (0, X - S)

With a put option, the option is in the money when the underlying stock price is less than the exercise price. The payoff to the holder is the difference between the exercise price and the underlying stock price less the amount paid for the put option. Once again, the solid lines represent the payoff of the put option; the dashed lines are payoff, net the price paid for the option. Example

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As an example, LDM Company put options have an exercise price of $45. As long as the stock price of LDM remains below $45, these put options are in the money. If the stock price is at $32, the payoff for the holder of a put option would be $45 - $32 = $13 per share. If the investor paid $90 for the put option contract, and it was for 100 shares, the net payoff would be ($13 x 100) - $90 = $1,210.

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Payoff for put writer


The profits for the writer of a put option are exactly the opposite of the holder of the put. Essentially, the writer of the put is betting that the price of the stock will rise above the exercise price. If that occurs, the writer's payoff is the put option premium. If the stock price is not above the exercise price, the writer of the put is obligated to purchase the underlying stock for the exercise price. This position (called writing a naked put) is somewhat risky, and most investors combine writing puts with other strategies to limit their potential losses. The transactions for put options work in the same way as the transaction for call options. Investors' accounts with brokers are credited and debited for the net amount of each option transaction. In the world of finance, very few option contracts are completed. Usually, investors will close out their option positions by taking the opposite side of the transaction before the exercise date; that is, the holder of a call option will become the writer of an identical option shortly before the exercise date.

OCC processing

Option transactions take place electronically through the OCC and its member brokers. The clearinghouse processes all transactions and acts as the counterparty on both sides of an option contract to ensure performance. If an option holder exercises an option, the OCC randomly assigns an exercise notice to a broker's account that reflects the writing of the same option. The broker then assigns the notice to one of its clients (option investors) on either a random or a "first in-first out" basis.

Margin money and margin calls

Investors are required to post margin money with their brokers to assure performance of their obligations. The broker can then deposit or withdraw the funds from the investor's account to correspond with the profit or loss on the option transactions. If an investor's account balance becomes too low (a point where the broker no longer feels that the investor can meet the possible obligations), the investor will receive a margin call. A margin call requires the investor to deposit more funds into the margin account.

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SWAPS Reduces exposure to rate changes

A swap is an exchange of cash flows between two counterparties. The purpose of a typical swap is to reduce the exposure a company may have to a change in interest rates or a change in the exchange rate between two currencies. The two most commonly used swaps are interest rate swaps and foreign currency swaps.

Interest Rate Swaps Fixed / Floating rate securities

In Unit Four, we discussed several types of debt securities. Most of these instruments make fixed coupon payments at some regular interval. However, many other debt instruments do not make fixed interest payments; the rates fluctuate based on a predetermined floating benchmark. These instruments are called floating rate securities.

London Interbank Offered Rate (LIBOR)

In Unit One, we defined a floating benchmark as an interest rate that is established by a third party. The most common benchmark used in floating rate instruments is the London Interbank Offered Rate (LIBOR). This is the rate that banks use to borrow from each other in the Eurodollar market.

Example of floating rate

Here is an explanation of how it works. Suppose that XYZ Corporation issues floating rate securities with an interest rate of LIBOR plus 50 b.p. (basis points – one basis point is 1/100 of 1% or 0.01%; 50 basis points equals 0.5%). The convention is that on the date the interest payment is due, the amount of the payment will be based on a rate equal to the current LIBOR plus 1/2%. In this case, if LIBOR is 5.25%, XYZ will pay interest based on a 5.75% rate. As LIBOR changes, so will the company's interest payments.

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Example of fixed / floating rate swap


Most interest rate swaps take place between two parties exposed to opposite types of interest rate exposure (risk). To illustrate the process, suppose that a savings and loan institution (S&L) is one of the counterparties. The assets of the S&L are predominantly longterm with fixed rates, such as conventional home mortgages, which pay roughly 8%. Its liabilities are mostly short-term, floating rate deposit accounts. If interest rates rise, the payments they are required to make on the deposits will increase, but the interest the S&L receives from the mortgages remains the same. The S&L is exposed to interest rate risk. On the other side of the swap is DEF Corporation, which has longterm non-callable bonds as liabilities. The interest rate on the bonds is 8%. DEF has invested in short-term, floating rate assets at roughly LIBOR + 0.5% as part of its portfolio. A fall in interest rates will cause losses for DEF and, therefore, it is also exposed to interest rate changes – but its exposure is opposite that of the S&L. A swap could work as follows. The S&L agrees to make fixed-rate payments to DEF Corporation based on some agreed upon amount (known as the notional principal) at a fixed interest rate. In return, DEF makes floating rate payments to the S&L based on the notional principal at LIBOR plus a premium of 50 b.p. The swap transaction is illustrated in Figure 5.3.

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Figure 5.3: Fixed / Floating Interest Rate Swap

Both parties reduce exposure

The swap has allowed both parties to minimize interest rate exposure. DEF Corporation now receives 8% fixed-rate payments from the S&L and pays its bondholders a fixed rate of 8%. The S&L receives a floating rate payment of LIBOR + 50 b.p. from DEF, which matches the floating rate that the S&L is paying its depositors on their accounts. The swap has helped both parties reduce their interest rate exposure by matching the assets and liabilities of both parties. There are two other points about interest rate swaps that you should remember.

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No exchange of principal

First, even though the payments are based on a notional principal, that principal is never exchanged between the counterparties. In our example, if the notional principal was US $10,000,000, the fixed rate payment made by S&L to DEF Corporation would be $800,000 each year for the period of the swap. The payment made by DEF to the S&L would be based on LIBOR. If LIBOR was 7.25%, then DEF's payment would be LIBOR + 0.50% = $775,000.

Decrease basis points

Second, it is possible for a company to cut basis points off the interest payments of its debt by using swaps. This occurs when the differential spreads of borrowing costs between companies with differing credit ratings are significantly different.

Example

Consider this example of how the rates may be reduced. These are the rates available in the market to XYZ Corporation and LDM Corporation: XYZ Corp. LDM Corp.

Fixed Rate 8.00% 10.50%

Floating Rate LIBOR + 1% LIBOR + 2%

Because XYZ has a better credit rating, its borrowing costs are lower than those for LDM. However, note that LDM pays 2.5% more than XYZ for fixed-rate debt, but only 1% more for floatingrate debt. A swap can be designed to take advantage of the difference and lower the borrowing costs for both companies. Suppose that XYZ is currently paying 8% to bondholders but needs 10-year floating-rate financing; LDM is currently paying LIBOR plus 200 b.p. but needs 10-year fixed-rate financing. XYZ Corporation needs floating rate financing and would have to pay LIBOR + 1% in the market; LDM Corporation needs fixed rate financing and would have to pay 10.5% in the market. The two companies negotiate through an intermediary to design a swap that will provide each company with the type of financing it needs at a lower cost than it can get in the market.

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LDM Corporation agrees to pay XYZ Corporation fixed rate payments of 8.0%. XYZ agrees to pay LDM a floating rate of LIBOR + 0.5%. You can see the cash flows in Figure 5.4.

Figure 5.4: Cash Flows for Interest Rate Swap

This table helps organize the cash flows: Cash Flow

XYZ

Payment to investors Pays in swap Receives in swap Net payment

Benefits of the swap

- 8.00% - LIBOR + 0.50% +8.00% - LIBOR + 0.50%

LDM - LIBOR + 2.00% - 8.00% +LIBOR + 0.50% - 9.50%

Let's see how each company benefits from the swap.

Rate available in market

XYZ LIBOR + 1.0% Floating

Net payment in swap

LIBOR + 0.5%

Savings

0.5% Floating

LDM 10.50% Fixed 9.50%

a

1.0% Fixed

Both companies now have the type of financing they need — and at a lower cost than if the swap agreement had not been arranged!

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Banks as intermediaries


In the example, we said that LDM and XYZ arranged the swap through an intermediary. Most companies lack the resources and expertise to find suitable counterparties and evaluate their creditworthiness. A large, money-center bank will act as an intermediary in most swap transactions. The bank serves as a clearinghouse for the interest payments and guarantees performance by each counterparty. From the company's perspective, the swap is essentially made with the bank — it may not know or even care who the counterparty is. Of course, the bank charges a fee for providing these services, usually in the form of a few basis points added to the overall rate that is paid in the swap. The bank usually receives a fee from both counterparties, so the all-in-cost of the interest payments for each company will include the fees paid to the bank. Currency Swaps

Exchange of cash flows in different currencies

A currency swap is an exchange of cash flows denominated in one currency for the cash flows in a different currency. The driving force behind the swap may be that a company is able to borrow in one currency at a lower rate than in another currency. Let's look at an illustration that shows how a currency swap might work.

Example

Consider a German company and a U.S. corporation that are trying to raise financing for their respective businesses in their home currencies. The German company has borrowed in the Deutsche mark (DM) bond market extensively in the past few months. This means that there could be a relative overabundance of DMdenominated debt issued by German companies and investors' demand is low. However, there is relatively little DM-denominated debt issued by U.S. corporations in that market. This situation may mean that a U.S. company could issue bonds at a lower rate than the German firm in the DM market.

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In the US$ market, investors perceive that the German company is a better credit risk than the U.S. corporation, and the German company could issue bonds at a lower rate in the US$ market. This is an opportunity for a swap to occur between the two companies. The German company could issue in the US$ market and the U.S. corporation could issue in the DM market. The two companies would exchange initial receipts from the bond issues (they would most likely be equal) and the U.S. company would then pay the interest and repay the principal of the US$-denominated bonds issued by the German company. The German company would do likewise on the DM-denominated bonds. Remember that the swap only makes sense if both companies can lower their all-in-cost of borrowing funds. Also remember that a bank or some other intermediary will usually be part of the arrangement and will charge fees for its service.

FORWARD AGREEMENTS Contract to deliver asset on a future date

A forward (or, more specifically, a forward agreement) is an agreement which obligates the seller to deliver a specified asset to the buyer on a specified future date. It obligates the buyer to pay the seller the contract price upon delivery of the asset. Forward contracts are similar to futures contracts, but have fewer features. We won't discuss futures in this course, but it is accurate to consider forward contracts as simplified futures contracts.

Value for Buyer / Seller Begins with zero value for both parties

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When a forward contract is first written, the convention is to specify a contract price that has zero value for both the buyer and seller. This contract price is determined by a process often referred to as price discovery. (See page 5-16)

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Value fluctuates

Although the contract initially has zero value for either party, the contract's value fluctuates based on the value of the underlying asset. If the value of the underlying asset falls relative to the contract price, the forward contract has positive value to the seller in the contract. The seller purchases the asset at the current market price and sells it to the buyer on the specified forward date for the contract price. The contract has negative value to the buyer who is obligated to pay a price for the asset that is higher than the market price.

Zero-sum situation

The reason that the contract has positive (or negative value) is that as the market price changes relative to the contract price and the time left until the forward date decreases, the probability that the price can recover is diminished. The contract is considered to be a zero-sum situation; positive value to one party is offset by negative value to the other party.

Price Discovery Cost of carry

Forward contract prices for physical assets, such as commodities, are determined by a complex process involving expected supply and demand for the asset. Most forward contract prices for financial assets (such as stocks or bonds) are determined by a methodology known as cost of carry.

Example

We can illustrate cost of carry with an example. Consider a stock that pays no dividend. The one-year interest rate is 7.5%, and the current market price (spot price) is $60. How do we determine the contract price for a one-year forward agreement to buy or sell the stock? In other words, at what contract price will the forward agreement have an initial value of zero to all buyers and sellers?

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Let's see what happens if the contract price is set at the same price as the spot price of the stock ($60). ■

The buyer of the forward contract borrows the stock from a third party and immediately sells it for the spot price of $60.

■

The buyer invests the $60 for one year at 7.5%.

■

At the end of the year, the buyer collects $64.50 from the investment, buys the stock for $60 (the contract price of the forward agreement), and returns the stock to the third party.

■

Regardless of what happens to the price of the stock during the year, the buyer earns $4.50 in certain profit.

At a contract price of $60, the forward agreement has an immediate value of $4.50 for the buyer of the contract. Since the contract price cannot have value for either party, the contract price for the forward agreement cannot be the spot price of the stock on the day the contract is set (in this case, $60). The concept of cost of carry does not allow for this arbitrage opportunity. The cost of carry for the asset is the one-year interest rate. Correct contract price

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To find the correct contract price, we multiply the spot price of the asset by 1 plus the cost of carry. In the example, the contract price is $60 x (1 + .075) = $64.50. At this price, the forward contract has zero value to both buyers and sellers when the agreement is made.

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As time progresses, it is likely that the spot price of the underlying asset will change. Let's continue with our example. It is six months since the original contract was made, and the market price of the stock is $65. Interest rates are now at 3.60% for six months — the amount of time left until the forward agreement expires. How do we revise the value of the original one-year agreement after the first six months? ■

Establish the forward price (contract price) for a new sixmonth forward contract for the same stock. Based on our calculation, the contract price will be $65 x (1.0360) = $67.34.

■

The buyer of the original one-year contract becomes the seller of a new six-month contract and locks in a certain profit.

■

At the end of the year, the original buyer is both a buyer and a seller of the asset and, therefore, is indifferent to the price of the asset at that time.

■

The original buyer fulfills the original one-year agreement by purchasing the stock for $64.50, and also fulfills the new sixmonth contract by selling the stock for $67.34. The original buyer has locked in a certain profit of $2.84 (the difference between the two prices).

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Present value of original contract

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The present value of the profit is $2.84 / 1.036 = $2.74. This means that, with six months left in the agreement, the value of the original contract is a positive $2.74 for the buyer of the contract. Remember, the seller of the original contract now has a negative value of $2.74. The value to the buyer of a forward contract may be summarized by the formula: V =

(F - C) / (1 + r)

Where: F = Current forward price C = Forward price of the original contract r = Rate of interest for the remaining life of the contract

In the example, the calculation would be: V = ($67.34 - $64.50) / (1.036) = $2.74

Closing forward contract positions

In addition to showing how forward contracts are valued, this example also illustrates how investors close out forward contract positions. Many buyers and sellers of forward contracts do not actually want to buy or sell the underlying securities; they use the contracts to hedge other investments. Therefore, it is common for buyers and sellers to take the offsetting position (buyers become sellers and vice versa) close to the time when the original contract expires. In the example, the offsetting position allows the buyer of the original contract to lock in the profit of $2.74. The original seller may also close out his/her position at this time, but at a cost of $2.74. Other types of forward agreements specify a rate of currency exchange or a rate of interest to be paid at some later date. These forward contracts are more complicated to price and are covered in more detail in the Forwards and Futures workbook.

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UNIT SUMMARY Options

An option is a contract between a buyer and a seller. A call option gives the buyer the right to buy an asset. A put option gives the buyer the right to sell an asset. The underlying asset is the specific asset named in the option contract. Exercising the option is either the buying or the selling of the underlying asset. An option is in the money when it produces a profit at the time of exercise. An option is out of the money when it does not produce a profit at the time of exercise. An American option gives the right to exercise the option at any time up to the expiration date. European option gives the right to exercise the option only on the expiration date. The Option Clearing Corporation (OCC) is the clearinghouse for options trading. All option investors post margin money with brokers to assure performance of investors' obligations. A margin call requires the deposit of additional funds into the margin account.

Swaps

A swap is an exchange of cash flows between two counterparties. An interest rate swap is used by a company to meet the need for fixed or floating interest rates at lower rates than may be available in the market. A foreign currency swap is a method for companies to borrow at a lower rate in one currency than in another currency. Swaps are arranged through an intermediary and are intended to reduce the borrowing costs for both counterparties.

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Forward agreement

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A forward agreement is a contract which obligates the seller to deliver a specified asset to a buyer on a specified future date. The contract is priced so that, initially, it has zero value for both the buyer and the seller. The market interest rate is the cost of carry that is used to determine the contract price and the current value of a forward agreement. Forwards are used to hedge other investments and, therefore, forward positions are usually closed out with offsetting contracts.

Congratulations! You have completed the Debt Financing course. Please complete the final Progress Check which follows. We have introduced you to some of the more common instruments and provided you with the necessary tools to evaluate different investment or borrowing alternatives. This knowledge will serve as a foundation for future courses related to corporate finance and the capital markets. The index and glossary are provided to help you use this workbook as an easy reference tool.

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✔ PROGRESS CHECK 5

Directions: Select the correct answer for each question. Check your solution with the Answer Key on the next page. If you are not able to complete the Progress Check correctly, read the appropriate text again. Question 1: On the expiration date of an option: ____ a) a call holder will exercise the option if the spot price is higher than the exercise price. ____ b) a call holder will not exercise the option if the premium paid for the option is lower than the spot price minus the exercise price. ____ c) a call holder will not exercise the option if the spot price is lower than the exercise price plus the premium paid for the option. ____ d) a call writer will exercise the option if the spot price is lower than the exercise price plus the premium received for the option. Question 2: A buyer of a call option will break even when the strike price: ____ a) equals the exercise price. ____ b) exceeds the exercise price. ____ c) equals the exercise price plus the premium. ____ d) goes below the exercise price plus the premium. Question 3: If the spot price of the underlying asset is higher than the exercise price of a call option, but lower than the exercise price of a put option, then: ____ a) both the call and the put options are in-the-money. ____ b) the call option is in-the-money, and the put option is out-of-themoney. ____ c) the call option is out-of-the money, and the put option is in-themoney. ____ d) both the call and the put options are out-of-the-money.

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ANSWER KEY

Question 1: On the expiration date of an option: a) a call holder will exercise the option if the spot price is higher than the exercise price.

Question 2: A buyer of a call option will break even when the strike price: c) equals the exercise price plus the premium.

Question 3: If the spot price of the underlying asset is higher than the exercise price of a call option, but lower than the exercise price of a put option, then: a) both the call and the put options are in-the-money.

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Question 4: Match the profit payoffs on options in Column B with each type of options trader in Column A. Column A ______ Call holder

Column B a)

______ Call writer ______ Put writer ______ Put holder b)

c)

d)

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ANSWER KEY

Question 4: Match the profit payoffs on options in Column B with each type of options trader in Column A. Column A c

Call holder

a

Call writer

d

Put writer

b

Put holder

Column B a)

b)

c)

d)

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Question 5: A European option is a right to: ____ a) buy a specified underlying asset, at a specified price, before a given date. ____ b) buy or sell a specified underlying asset, at a specified price, up to a given date. ____ c) sell a specified underlying asset, at a specified price, on a given date. ____ d) buy or sell a specified underlying asset, at a specified price, on a given date. Question 6: What is the profit for a writer of a call option that expires out-of-themoney? ____ a) Difference between the strike price and the price of the underlying asset ____ b) Premium paid for the call option ____ c) Amount of the strike price ____ d) No profit for an unexercised option

Question 7: Option investors are required to: ____ a) buy or sell the underlying asset on the exercise date. ____ b) maintain margin accounts with brokers to assure the performance of their obligations. ____ c) buy or sell the underlying asset if the option is in-the-money on the exercise date. ____ d) close out option positions by taking the opposite side of the transaction before the exercise date.

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ANSWER KEY

Question 5: A European option is a right to: d) buy or sell a specified underlying asset, at a specified price, on a given date.

Question 6: What is the profit for a writer of a call option that expires out-of-themoney? b) Premium paid for the call option

Question 7: Option investors are required to: b) maintain margin accounts with brokers to assure the performance of their obligations.

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Question 8: In an interest rate swap transaction, the notional principal is: ____ a) exchanged between the two parties at the beginning of the agreement and again on the maturity date. ____ b) loaned by one counterparty to the other in exchange for either fixed or floating rate interest. ____ c) rarely exchanged between the counterparties. ____ d) different for both counterparties.

Question 9: Consider the rates available in the market to Alpha Corporation and Beta, Inc. Alpha Corporation Beta, Inc.

Fixed Rate 8.00% 9.25%

Floating Rate LIBOR + 0.75% LIBOR + 1.25%

Currently, Alpha Corporation is paying 8.00% to bondholders, but it wants to replace this fixed rate financing with floating rate financing. Beta, Inc. pays LIBOR + 1.25% to investors in need of fixed rate financing. Beta agrees to pay Alpha fixed rate payments of 8%; Alpha agrees to pay Beta floating rate payments of LIBOR + 0.50%. How much will each company save on the financing it needs by entering into a fixed / floating rate swap transaction? Alpha _____________% Beta _____________%

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ANSWER KEY

Question 8: In an interest rate swap transaction, the notional principal is: c) rarely exchanged between the counterparties.

Question 9: Consider the rates available in the market to Alpha Corporation and Beta, Inc. Alpha Corporation Beta, Inc.

Fixed Rate 8.00% 9.25%

Floating Rate LIBOR + 0.75% LIBOR + 1.25%

Currently, Alpha Corporation is paying 8.00% to bondholders, but it wants to replace this fixed rate financing with floating rate financing. Beta, Inc. pays LIBOR + 1.25% to investors in need of fixed rate financing. Beta agrees to pay Alpha fixed rate payments of 8%; Alpha agrees to pay Beta floating rate payments of LIBOR + 0.50%. How much will each company save on the financing it needs by entering into a fixed / floating rate swap transaction? Alpha

0.25%

a

Beta

0.50%

a

Cash Flow

Alpha Corporation

Payment to investors Pays in swap Receives in swap Net payment

- 8.00% - LIBOR + 0.50% +8.00% - LIBOR + 0.50%

Rate available in market Net payment in swap Savings

Beta, Inc. - LIBOR + 1.25% - 8.00% +LIBOR + 0.50% - 8.75%

LIBOR + 0.75% Floating LIBOR + 0.50% a 0.25% Floating

9.25% Fixed 8.75% a 0.50% Fixed

Alpha Corporation saves .25% and Beta, Inc. saves .5% by entering into an interest rate swap to get the type of funding they need. ver. 1.0 v.07/06/94 p.01/10/00


5-31


Question 10: The spot price for XYZ stock is $45. The one-year interest rate is 6.75%. Calculate the contract price for a one-year forward agreement with XYZ stock as the underlying asset: $ _________________________________

Question 11: After six months, the price of the stock has moved to $42.00 and six month interest rates are 3.5%. The result of this change in rates is that the: ____ a) buyer may purchase an offsetting six-month contract to lock in a profit. ____ b) seller may purchase an offsetting contract to limit the loss, and the buyer may purchase an offsetting six-month contract to lock in a profit. ____ c) seller may purchase an offsetting six-month contract to limit the loss. ____ d) seller may offset the contract to lock in a profit and the buyer may offset to limit the loss.

Question 12: ABC Company has fixed-rate government bonds and wants to retain these low-risk bonds in its portfolio. However, the company thinks interest rates are going up and wants to increase the yield on the bonds. The best counterparty for an interest rate swap is an investor with: _____ a) floating interest rate bonds who thinks interest rates are going down and wants to exchange receipts. _____ b) fixed interest rates bonds who thinks interest rates are going up and wants to exchange receipts. _____ c) fixed interest rate bonds who thinks interest rates are going up and wants to sell the bonds. _____ d) floating interest rate bonds who thinks interest rates are going down and wants to exchange bonds.

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ANSWER KEY

Question 10: The spot price for XYZ stock is $45. The one-year interest rate is 6.75%. Calculate the contract price for a one-year forward agreement with XYZ stock as the underlying asset: $ 48.04 $45 x 1.0675 = $48.04

Question 11: After six months, the price of the stock has moved to $42.00 and six month interest rates are 3.5%. The result of this change in rates is that the: d) seller may offset the contract to lock in a profit and the buyer may offset to limit the loss.

Question 12: ABC Company has fixed-rate government bonds and wants to retain these low-risk bonds in its portfolio. However, the company thinks interest rates are going up and wants to increase the yield on the bonds. The best counterparty for an interest rate swap is an investor with: a) floating interest rate bonds who thinks interest rates are going down and wants to exchange receipts.

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Appendices

APPENDIX

GLOSSARY Accumulated Interest

The amount of interest earned between coupon payments

Banker's Acceptance (BA)

Marketable security, issued on a discount basis, that represents a time draft that a bank has agreed to pay unconditionally on the maturity date

Basis Point

One one-hundredth of one percent; also called a "tick"

Bond

A debt obligation or agreement issued by a firm or government, usually with a maturity of at least five years

Bond Equivalent Yield

The semiannual internal rate of return multiplied by two, for a bond making two coupon payments per year. Several formulas can be used to convert other yields to a bond equivalent yield.

Brady Bond

A bond created to exchange foreign bank loans into marketable securities. Brady bonds are partially collateralized by U.S. government securities.

Broker

An intermediary arranging the meeting of issuers and investors to complete the sale of securities

Bulldog Bond

A British sterling-denominated bond trading inside the U.K., but issued by a company outside the U.K.

Bullet Payment

A loan repayment convention in which the entire principal is repaid at the end of the loan agreement

Callable Bond

A bond that gives the issuer the option of repurchasing it from investors before maturity

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GLOSSARY

Call Option

A contract that gives the holder the right to buy an asset for a specified price on or before a given expiration (maturity) date

Certificate of Deposit (CD)

A security issued by a financial institution, backed by a specified amount of money held on deposit at the institution

Collateral

An asset owned by a borrower that is used to provide security for lenders in a loan agreement

Collateral Trust Bond

A bond backed by the issuer's pledge of specific securities held by the issuer

Commercial Paper (CP)

A short-term security issued by a corporation on a discount basis, secured only by the general earning ability of the company

Convexity

The curvature exhibited in the price-interest rate relationship graph of a bond

Corporate Bond

A bond issued by a corporation

Coupon

The payment of interest to an investor holding a bond. The coupon is usually determined by multiplying a coupon rate by the principal amount of the bond.

Coupon Rate

The rate of interest being paid on a bond

Covenants

A set of minimum and maximum levels for key financial and operational ratios that a company must maintain during the tenor of a loan agreement

Credit Rating

An evaluation, by independent sources, to determine the ability of an issuer to repay its debt obligations

Current Yield

Relationship between annual coupon interest and the market price of a debt security ver. 1.0 v.07/06/94 p.01/10/00

GLOSSARY

G-3

Dealer

An intermediary that purchases securities from investors and sells them to other investors

Debenture

A bond backed only by the full faith and credit of the issuer

Derivative

An instrument with a value that is derived from the value of the underlying security

Discount Yield

The discount rate used to price a short-term zero-coupon security; the rate on which these instruments are quoted

Domestic Market

A subdivision of the internal, or national market where the issuers of securities are residents of that country

Dual Currency Debt

Debt securities that have more than one currency involved in the coupon payments and the principal repayment

Duration

A measurement of a bond's price volatility in response to a change in interest rates. Calculated as the weighted average of the time until maturity of each of the expected cash flows of a debt security.

Equity-linked Debt

Debt securities that give the investor some opportunity to exchange or convert the debt securities into equity securities of the issuing company

Eurobond

A bond issued in the Euromarket, usually to avoid government registration and regulation. Most Eurobonds are issued in bearer form by companies with high credit ratings; the bonds make annual interest payments, as opposed to many other bonds that make semiannual payments.

Euromarket

A subdivision of the international market; it is specifically a market that does not come under the jurisdiction of any single government or government entity

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GLOSSARY

Face Value

The amount of money to be repaid to the lender in a loan or through the sale of security; also known as the par value or principal

Foreign Market

A subdivision of the internal, or national, market where the issuers of securities are not residents of that country

Forward Contract

An agreement between the seller and a buyer. In the contract, the seller is obligated to deliver a specified asset to the buyer on a specified date. The buyer is obligated to pay the seller a specified price (the contract price) upon delivery of the asset.

Guaranteed Bond

A bond backed by the guarantee of repayment by an entity other than the issuer. In many cases, the guarantor is the parent company of the issuer.

Individual Investor

Refers to smaller investors, usually single persons, that buy securities for their own portfolios

Institutional Investor

An investor with large amounts of capital with which to purchase securities; includes mutual funds, pension funds, insurance companies, and banks

Internal Market

See National Market

International Market

From the perspective of a single country, it is considered the securities that are trading outside of that country; also called the external market or off-shore market

Investor

An entity that provides capital by purchasing marketable securities

Issuer

An entity in need of capital that provides marketable securities for sale to investors

LIBOR

The London Interbank Offered Rate; the rate of interest that banks lend money to each other in the Eurodeposit market ver. 1.0 v.07/06/94 p.01/10/00

GLOSSARY

G-5

Liquidity

The ease with which marketable securities may be sold for cash at a fair price

Loan

A debt agreement between two parties: a borrower and a lender

Maturity

The length of time remaining in a loan or debt security before the agreement expires

Medium-term Note (MTN)

A type of security with many different features, designed to help issuers and investors meet needs. Usually the notes are issued with a shelf registration that allows them to be continuously offered to investors. Most MTNs make semiannual coupon payments.

Money Market Yield (MMY)

The rate of return earned on a 360-day year basis. Most shortterm, interest bearing securities are priced using a money market yield; also known as the CD-equivalent yield.

Mortgage Bond

A bond backed by the issuer's pledge of specific physical assets, such as property or equipment

Municipal Bond

A bond issued by a state, county, or other local government entity

National Market

From the perspective of a single country, it is considered the securities that are trading within that country; also known as the internal market

Note

A debt obligation or agreement issued by a firm or government, usually with a maturity of one to five years

Par Value

The amount of money to be repaid to the lender in a loan or through the sale of securities; also known as the face value or principal

Portfolio

A collection of marketable securities held by a single investor, individual or institutional

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GLOSSARY

Principal

The amount of money to be repaid to the lender in a loan, or through a sale of securities; also known as the face value or par value

Private Placement

The offering of securities to a select group of investors

Public Offering

The offering of marketable securities to all investors participating in the market

Put Option

A contract that gives the holder the right to sell an asset for a specified price on or before a given expiration (maturity) date

Realized Compound Yield

Makes the assumption that interest payments made by the debt security are reinvested at some rate, and compounded throughout the tenor of the security

Retail Market

The part of the securities market that targets individual investors

Rule 144A

Part of the U.S. Securities and Exchange Commission's (SEC) code governing the issuing of marketable securities. Specifically, this rule outlines the regulations concerning the private placement of securities to qualified institutional buyers (QIBs).

Samurai Bond

A yen-denominated bond issued by a company outside Japan, but trading inside Japan

Securitization

The process of packaging small, rather illiquid, assets into a larger, more marketable security

Senior Debt

Refers to the relative position of the bondholders, should the issuer be forced into reorganization or bankruptcy. Senior debt bond holders would be among the first creditors to be repaid.

Sinking Fund

A type of loan agreement in which the borrower, in addition to making periodic interest payments, repays part of the principal at intervals throughout the time of the loan agreement

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GLOSSARY

G-7

Straight Debt

Bonds that make periodic interest payments and repay the entire face value at maturity

Subordinated Debt

In the event of the issuer's reorganization or bankruptcy, the subordinated debt holders' claims are met after the senior debt holders

Swap

An exchange of cash flows between two counterparties. The counterparties may exchange flows in different currencies (currency swap) or exchange floating interest rate payments for fixed rate payments (interest rate swap).

Syndicate

A group of banks participating in the issue of marketable securities or the arrangement of a loan agreement

Tenor

The total length of time that a debt agreement is in force

Treasury Bill

A short-term, zero-coupon security issued by the U.S. government

Treasury Bond

A medium-term, coupon-paying security issued by the U.S. government

Treasury Note

A medium-term, coupon paying security issued by the U.S. government

True Yield

Simple annual interest (rate of return) earned on a zero-coupon security, calculated on a 365-day basis

Underwriter

A specific role an investment banker takes in the process of issuing marketable securities. As an underwriter, the bank purchases the securities directly from the issuer, then resells them to investors.

Warrants

A negotiable certificate giving the holder the right to purchase a predetermined number of shares of the issuing company's stock, at a specified price, on or before a specified date

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G-8

GLOSSARY

Wholesale Market

The part of the securities market that targets institutional investors; also called the institutional market

Yankee Bond

A dollar-denominated bond issued by a company outside the U.S., but trading in a U.S. market

Yield-to-call

The discount rate that equates the market price of a security with the present value of the future cash flows, up to the date of first call, generated by the security

Yield-tomaturity

The discount rate that equates the market price of a security with the present value of the future cash flows generated by the security

Zero-coupon Security

A type of marketable security in which the investor makes no periodic interest payments, receives somewhat less than face value at the time of issue, and repays the face value at maturity

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INDEX A Accumulated Interest B Banker's Acceptance (BA) Basis Point Bond

Bond Equivalent Yield Brady Bond Broker Bulldog Bond Bullet Payment

3-18, 3-19

4-1—4-4, 4-17 1-1, 1-12, 1-13, 2-3, 2-5, 2-8, 2-9, 4-4, 4-14, 5-9, 512, 5-14 1-2, 1-3, 1-5—1-7, 1-12—1-15, 1-17, 1-19, 2-3, 2-6, 3-1—3-9, 3-13, 3-16—3-20, 3-23—3-32, 3-37, 4-7, 4-10—4-16, 4-18, 5-10, 5-14—5-16 3-5, 3-15, 3-16, 3-19, 3-23—3-27, 3-29, 3-37 4-10, 4-13, 4-14, 4-17, 4-18 1-3, 2-3, 5-8, 5-20 1-5 1-14

C Callable Bond Call Option Certificate of Deposit (CD) Collateral Collateral Trust Bond Commercial Paper (CP) Convexity Corporate Bond Coupon

Current Yield

1-15 5-1, 5-2 3-16, 4-5, 4-6, 4-7 1-8, 1-15, 1-17, 1-18, 4-6, 4-7, 4-9, 4-13, 4-17 1-16, 1-17, 1-20 4-3—4-5, 4-8, 4-17 3-30, 3-32, 3-38 1-14, 4-9—4-12, 4-17, 4-18 1-12, 3-1—3-9, 3-17—3-19, 3-23—3-25, 3-27, 3-29, 3-37, 4-8—4-12, 4-14, 4-16, 4-17, 5-9 1-12, 3-2, 3-3, 3-7, 3-9, 3-17—3-19, 3-23, 3-24, 3-26, 3-28—3-30, 3-37 2-4, 2-6, 2-9, 2-10 1-10, 2-4, 2-6, 4-5, 4-6, 4-9, 4-11, 4-13—4-15, 4-18, 5-12 3-2, 3-3, 3-5, 3-9, 3-37

D Dealer Debenture Derivative Discount Yield Domestic Market Dual Currency Debt Duration

1-3, 4-4, 4-5, 4-7—4-9 1-16—1-20 5-1 3-1, 3-13—3-16, 3-19, 3-37 1-5, 2-4 4-14, 4-16, 4-18 3-1, 3-23—3-32, 3-37, 3-38

Coupon Rate Covenants Credit Rating

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I-2

INDEX

E Equity-linked Debt Eurobond Euromarket

4-14, 4-15, 4-18 1-6—1-9, 3-26, 4-10, 4-12, 4-13, 4-17, 4-18 1-6, 1-7, 1-12, 2-4, 4-6, 4-12, 4-18

F Face Value Foreign Market Forward Contract

1-2, 1-13, 1-14, 3-4, 3-6, 3-13, 3-14, 3-16, 3-17, 3-19, 3-29, 4-3, 4-4, 4-6, 4-8, 4-10, 4-15, 4-16 1-5, 1-7 5-15—5-19

G Guaranteed Bond

1-16, 1-17, 1-20

I Individual Investor Institutional Investor Internal Market International Market Investor

Issuer

1-4, 2-4, 2-6, 4-2, 4-12 1-4, 2-6, 2-7, 4-4—4-6, 4-12, 4-13 See National Market 1-5, 1-6, 1-8, 1-20 1-2—1-15, 1-17—1-20, 2-2—2-7, 2-10, 3-1, 3-3, 3-5, 3-6, 3-15—3-17, 3-28, 3-37, 3-38, 4-1—4-5, 4-7— 4-16, 4-18, 5-1, 5-3, 5-4, 5-7, 5-8, 5-13—5-15, 5-19, 5-20, 5-29, 5-30 1-2—1-11, 1-13—1-20, 2-2—2-7, 2-10, 3-1, 3-6, 3-9, 4-1, 4-4—4-10, 4-12, 4-14—4-16, 5-1

L LIBOR Liquidity Loan

1-12, 1-13, 2-8, 4-6, 4-11, 5-9—5-13, 5-29 1-19, 2-7, 2-10, 4-4—4-6, 4-11, 5-3 1-1—1-4, 1-8, 1-9, 1-11—1-14, 1-18, 1-20, 2-5, 2-7—2-10, 4-4, 4-6, 4-7, 4-13, 4-17, 4-18, 5-10

M Maturity

Medium-term Note (MTN) Money Market Yield (MMY) Mortgage Bond Municipal Bond

1-2, 1-8, 1-11—1-15, 2-3, 2-4, 2-9, 2-10, 3-2—3-4, 3-6, 3-7, 3-13, 3-14, 3-16, 3-17, 3-23, 3-26, 3-28— 3-30, 3-32, 4-3—4-6, 4-8—4-11, 4-15—4-17, 5-2, 5-4, 5-6 4-8—4-10, 4-18 3-13, 3-15, 3-16, 3-19, 3-37 1-16, 1-20 4-10—4-12, 4-17

ver. 1.0

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INDEX

I-3

N National Market Note

1-5, 1-8, 1-20 1-2, 1-3, 1-17, 3-18, 3-23, 3-24, 3-28, 4-4, 4-8, 4-9, 4-11, 4-17

P Par Value Portfolio Principal Private Placement Public Offering Put Option

1-2, 3-2, 3-3, 3-5, 3-7, 3-9, 3-18 2-7, 3-1, 3-23, 3-27, 3-28, 4-3, 4-7, 5-10 1-1, 1-2, 1-7, 1-9, 1-12, 1-14, 1-17—1-20, 3-4, 3-23, 3-24, 4-13, 4-16, 4-18, 5-10, 5-12, 5-15 2-1, 2-2, 2-5—2-7, 2-9, 2-10 2-1, 2-2, 2-4, 2-5, 2-7, 2-10 5-1, 5-2, 5-4, 5-6—5-8, 5-20

R Realized Compound Yield Retail Market Rule 144A

3-2, 3-6—3-9, 3-37 1-4, 2-7

S Samurai Bond Securitization Senior Debt Sinking Fund Straight Debt Subordinated Debt Swap Syndicate

1-5 1-18, 1-20 1-19 1-14, 1-20 3-31, 4-11, 4-16 1-19 5-1, 5-9—5-15, 5-20 1-7, 1-8, 2-2, 2-3, 2-7—2-10

T Tenor Treasury Bill Treasury Bond Treasury Note True Yield

1-2, 2-4, 2-5, 3-16, 4-3, 4-5, 4-8, 4-9, 4-14, 4-17 3-5, 3-13—3-15, 4-1, 4-2, 4-5, 4-6, 4-17 4-10, 4-13, 4-17, 4-18 4-8, 4-17 3-5, 3-15, 3-19

U Underwriter

2-2, 2-3

W Warrants Wholesale Market

4-4, 4-15, 4-16, 4-18 1-4

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Y Yankee Bond Yield-to-call Yield-to-maturity Z Zero-coupon Security

INDEX

1-5 3-2, 3-6, 3-9, 3-37 3-2, 3-4—3-6, 3-8, 3-9, 3-15, 3-17, 3-23, 3-26, 3-28, 3-29, 3-37

1-13, 1-20, 3-1, 3-5, 3-13—3-16, 3-19, 3-20, 3-29, 4-2, 4-13, 4-17

ver. 1.0

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