Brealey, Myers. Principles of Corporate Finance. 7th edition

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Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 24. Valuing Debt

Companies, 2003

694 PART VII Debt Financing

Empirical tests of term structure theories are provided by Fama and Shiller, Campbell, and

Schoenholtz:

E. F. Fama: “The Information in the Term Structure,” Journal of Financial Economics,

13:509–528 (December 1984).

E. F. Fama: “Term Premiums in Bond Returns,” Journal of Financial Economics, 13:529–546

(December 1984).

R. J. Shiller, J. Y. Campbell, and K. L. Schoenholtz: “Forward Rates and Future Policy: Inter-

preting the Term Structure of Interest Rates,” Brookings Papers on Economic Activity,

1:173–217 (1983).

The following paper by Schaefer is a good review of duration and of how it is used to hedge fixed lia-

bilities:

S. M. Schaefer: “Immunisation and Duration: A Review of Theory, Performance and Appli-

cation,” Midland Corporate Finance Journal, 3:41–58 (Autumn 1984).

We referred briefly to modern models of the term structure, which exploit the relationship between the

price changes of bonds with different maturities. For more on this topic we suggest:

T. S. Y. Ho: “Evolution of Interest Rate Models: A Comparison,” Journal of Derivatives, 2:9–20

(Summer 1995).

The classic paper on the valuation of the option to default on corporate debt is:

R. Merton: “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal

of Finance, 29:449–470 (May 1974).

QUIZ

1. The real interest rate is determined by the demand for, and supply of, capital. Draw a

diagram showing how the demand by companies for capital and the supply of capital

by investors vary with the interest rate. Use this diagram to show the following:

a. What will happen to the amount of investment and saving if firms’ investment

prospects improve? How will the equilibrium interest rate change?

b. What will happen to the amount of investment and saving if individuals’ willingness

to save increases at each possible interest rate? How will the equilibrium interest rate

change? Assume firms’ investment opportunities do not change.

2. In 2001 Treasury 13 7/8s of 2011 offered a semiannually compounded yield of 8.04 per-

cent. Recognizing that coupons are paid semiannually, calculate the bond’s price.

3. Here are the prices in 1998 of four Scandinavian government bonds with similar

maturities:

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Bond Price (%)

Denmark 7s of 2007 116.58

Finland 6s of 2008 111.58

Norway 6 3/4s of 2007 108.15

Sweden 6 1/2s of 2008 113.19

a. If coupons are paid annually, which bond offered the highest yield to maturity?

Which had the lowest?

b. Which bonds had the longest and shortest durations?

4. a. What is the formula for the value of a two-year, 5 percent bond in terms of spot rates?

b. What is the formula for its value in terms of yield to maturity?

c. If the two-year spot rate is higher than the one-year rate, is the yield to maturity

greater or less than the two-year spot rate?

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 24. Valuing Debt

Companies, 2003

CHAPTER 24 Valuing Debt 695

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d. In each of the following sentences choose the correct term from within the

parentheses:

“The (yield-to-maturity/spot-rate) formula discounts all cash flows from one bond

at the same rate even though they occur at different points in time.”

“The (yield-to-maturity/spot-rate) formula discounts all cash flows received at the

same point in time at the same rate even though the cash flows may come from

different bonds.”

5. Construct some simple examples to illustrate your answers to the following:

a. If interest rates rise, do bond prices rise or fall?

b. If the bond yield is greater than the coupon, is the price of the bond greater or less

than 100?

c. If the price of a bond exceeds 100, is the yield greater or less than the coupon?

d. Do high-coupon bonds sell at higher or lower prices than low-coupon bonds?

e. If interest rates change, does the price of high-coupon bonds change

proportionately more than that of low-coupon bonds?

6. The following table shows the prices of a sample of strips of UK gilts (government

bonds) in December 1998. Each strip makes a single payment of at maturity.

£100

Maturity Price (£)

December 2000 90.826

December 2005 73.565

December 2006 70.201

December 2007 67.787

December 2028 29.334

a. Calculate the annually compounded, spot interest rate for each year.

b. Is the term structure upward- or downward-sloping?

c. Would you expect the yield on a coupon bond maturing in December 2028 to be

higher or lower than the yield on the 2028 strip?

d. Calculate the annually compounded, one-year forward rate of interest for

December 2005. Now do the same for December 2006.

7. a. An 8 percent, five-year bond yields 6 percent. If the yield remains unchanged, what

will be its price one year hence? Assume annual coupon payments.

b. What is the total return to an investor who held the bond over this year?

c. What can you deduce about the relationship between the bond return over a

particular period and the yields to maturity at the start and end of that period?

8. True or false? Explain.

a. Longer-maturity bonds necessarily have longer durations.

b. The longer a bond’s duration, the lower its volatility.

c. Other things equal, the lower the bond coupon, the higher its volatility.

d. If interest rates rise, bond durations rise also.

9. Calculate the durations and volatilities of securities A, B, and C. Their cash flows are

shown below. The interest rate is 8 percent.

Period 1 Period 2 Period 3

A40 40 40

B 20 20 120

C 10 10 110

10. a. Suppose that the one-year spot rate of interest at time 0 is 1 percent and the two-year

spot rate is 3 percent. What is the forward rate of interest for year 2?

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 24. Valuing Debt

Companies, 2003

696 PART VII Debt Financing

b. What does the expectations theory of term structure say about the relationship

between the forward rate and the one-year spot rate at time 1?

c. Over a very long period of time, the term structure in the United States has been

on average upward-sloping. Is this evidence for or against the expectations theory?

d. What does the liquidity-preference theory say about the relationship between the

forward rate and the one-year spot rate at time 1?

e. If the liquidity-preference theory is a good approximation and you have to meet

long-term liabilities (college tuition for your children, for example), is it safer to

invest in long- or short-term bonds? Assume inflation is predictable.

f. If inflation is very uncertain and you have to meet long-term real liabilities, is it

safer to invest in long- or short-term bonds?

11. a. State the four Moody’s ratings that are generally known as “investment-grade” ratings.

b. Other things equal, would you expect the yield to maturity on a corporate bond to

increase or decrease with

i. The company’s business risk?

ii. The expected rate of inflation?

iii. The risk-free rate of interest?

iv. The degree of leverage?

12. The difference between the price of a government bond and a simple corporate bond is

equal to the value of an option. What is this option and what is its exercise price?

13. How in principle would you calculate the value of a government loan guarantee?

PRACTICE

QUESTIONS

1. Why might Fisher’s theory about inflation and interest rates not be true?

2. Under what conditions can the expected real interest rate be negative?

3. A 6 percent six-year bond yields 12 percent and a 10 percent six-year bond yields 8 per-

cent. Calculate the six-year spot rate. (Assume annual coupon payments.)

4. Is the yield on high-coupon bonds more likely to be higher than that on low-coupon

bonds when the term structure is upward-sloping or when it is downward-sloping?

5. The one-year spot rate is percent, and the forward rate for a one-year loan ma-

turing in year 2 is percent. Similarly, percent, percent, and

percent. What are the spot rates , and ? If the expectations hypothesis

holds, what can you say about expected future interest rates?

6. Suppose your company will receive $100 million at but must make a $107 mil-

lion payment at . Assume the spot and forward rates from question 5. Show

how the company can lock in the interest rate at which it will invest at . Will the

$100 million, invested at this locked-in rate, be sufficient to cover the $107 million

liability?

7. Use the rates from question 5 one more time. Consider the following bonds, each with

a five-year maturity. Calculate the yield to maturity for each. Which is the better in-

vestment (or are they equally attractive)? Each has $1,000 face value and pays coupons

annually.

t ⫽ 4

t ⫽ 5

t ⫽ 4

, r

⫽ 8.2

⫽ 7.3f

⫽ 7.1f

⫽ 6.4

⫽ 6

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Coupon Price

5 92.07%

7 100.31

12 120.92

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 24. Valuing Debt

Companies, 2003

CHAPTER 24 Valuing Debt 697

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8. You have estimated spot rates as follows:

Year Spot Rate

1 r

⫽ 5.00%

2 r

⫽ 5.40

3 r

⫽ 5.70

4 r

⫽ 5.90

5 r

⫽ 6.00

a. What are the discount factors for each date (that is, the present value of $1 paid in

year t)?

b. What are the forward rates for each period?

c. Calculate the PV of the following Treasury notes:

i. 5 percent, two-year note.

ii. 5 percent, five-year note.

iii. 10 percent, five-year note.

d. Explain intuitively why the yield to maturity on the 10 percent bond is less than

that on the 5 percent bond.

e. What should be the yield to maturity on a five-year zero-coupon bond?

f. Show that the correct yield to maturity on a five-year annuity is 5.75 percent.

g. Explain intuitively why the yield on the five-year Treasury notes described in part

annuity.

9. Look at the spot interest rates shown in question 8. Suppose that someone told you that

the six-year spot interest rate was 4.80 percent. Why would you not believe him? How

could you make money if he was right? What is the minimum sensible value for the six-

year spot rate?

10. Look again at the spot interest rates shown in question 8. What can you deduce about

the one-year spot interest rate in four years if

a. The expectations theory of term structure is right?

b. The liquidity-preference theory of term structure is right?

c. The term structure contains an inflation uncertainty premium?

11. Look up prices of 10 U.S. Treasury bonds with different coupons and different maturi-

ties. Calculate how their prices would change if their yields to maturity increased by

one percentage point. Are long- or short-term bonds most affected by the change in

yields? Are high- or low-coupon bonds most affected?

12. Assume the term structure of interest rates is upward-sloping. How would you re-

spond to the following comment? “The present term structure of interest rates makes

short-term debt more attractive to corporate treasurers. Firms should avoid new long-

term debt issues.”

13. In Section 24.3 we stated that in 2001 the duration of the 4 5/8s of 2006 was 4.36 years.

Construct a table like Table 24.2 to show that this is so.

14. The formula for the duration of a perpetual bond which makes an equal payment each

year in perpetuity is (1 ⫹ yield)/yield. If bonds yield 5 percent, which has the longer du-

ration—a perpetual bond or a 15-year zero-coupon bond? What if the yield is 10 percent?

15. You have just been fired as CEO. As consolation the board of directors gives you a five-

year consulting contract at $150,000 per year. What is the duration of this contract if

your personal borrowing rate is 9 percent? Use duration to calculate the change in the

contract’s present value for a .5 percent increase in your borrowing rate.

16. Look at the example in Section 24.4 of the Treasury bill and the medium- and long-term

bonds. Now assume that the price of the medium-term bond can either fall by $10.75 or

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 24. Valuing Debt

Companies, 2003

698 PART VII Debt Financing

rise by $14.0. What can you say now about the relationship between the value of the

three bonds?

17. Explain carefully what factors determine the yield on corporate bonds.

18. Companies sometimes issue floating-rate bonds. In this case the interest rate might be

set at (say) 1 percent above the Treasury bill rate. Would you expect the price of a com-

pany’s floating-rate bonds to vary? If so, why?

19. Company A has issued a single zero-coupon bond maturing in 10 years. Company B

has issued a coupon bond maturing in 10 years. Explain why it is more complicated to

value B’s debt than A’s.

20. Company X has borrowed $150 maturing this year and $50 maturing in 10 years. Com-

pany Y has borrowed $200 maturing in five years. In both cases asset value is $140. Why

might X not default while Y does?

CHALLENGE

QUESTIONS

1. It has been suggested that the Fisher theory is a tautology. If the real rate of interest is

defined as the difference between the nominal rate and the expected inflation rate, then

the nominal rate must equal the real rate plus the expected inflation rate. In what sense

is Fisher’s theory not a tautology?

2. Find the arbitrage opportunity (opportunities?). Assume for simplicity that coupons

are paid annually. In each case the face value of the bond is $1,000.

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Bond Maturity (years) Coupon ($) Price ($)

A 3 zero 751.30

B 4 50 842.30

C 4 120 1,065.28

D 4 100 980.57

E 3 140 1,120.12

F 3 70 1,001.62

G 2 zero 834.00

3. The duration of a bond which makes an equal payment each year in perpetuity is (1 ⫹

yield)/yield. Prove it.

4. What is the duration of a common stock whose dividends are expected to grow at a con-

stant rate in perpetuity?

5. a. What spot and forward rates are embedded in the following Treasury bonds? The

price of one-year (zero-coupon) Treasury bills is 93.46 percent. Assume for simplic-

ity that bonds make only annual payments. Hint: Can you devise a mixture of long

and short positions in these bonds that gives a cash payoff only in year 2? In year 3?

Coupon (%) Maturity (years) Price (%)

4 2 94.92

8 3 103.64

b. A three-year bond with a 4 percent coupon is selling at 95.00 percent. Is there a

profit opportunity here? If so, how would you take advantage of it?

6. Look back at our example in Section 24.4 of the short-, medium-, and long-term bonds.

Remember that we said that the prices must stand in a particular relationship or there

would be an arbitrage opportunity. This means that we can take advantage of the risk-

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 24. Valuing Debt

Companies, 2003

CHAPTER 24 Valuing Debt 699

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neutral trick that we used to value options. Pretend that investors are risk-neutral. Now

answer the following questions:

a. Suppose that the price of the short bond is 98 and the price of the medium is 83.

What is the price of the long bond?

b. What are the possible future prices of these three bonds at the end of three months

if rates rise and if they fall?

c. What would be the expected return over the three months on each bond?

d. What is the probability of an interest rate rise?

e. Show that the expected return on each bond is equal.

7. Look up prices of 10 corporate bonds with different coupons and maturities. Be sure to

include some low-rated bonds on your list. Now estimate what these bonds would sell

for if the government had guaranteed them. Calculate the value of the guarantee for

each bond. Can you explain the difference between the 10 guarantee values?

8. Bond rating services usually charge corporations for rating their bonds.

a. Why do they do this, rather than charge those investors who use the information?

b. Why will a company pay to have its bonds rated even when it knows the service is

likely to assign a below-average rating?

c. A few companies are not willing to pay for their bonds to be rated. What can

investors deduce about the quality of these bonds?

9. Look back to the first Backwoods Chemical example at the start of Section 24.5. Sup-

pose that the firm’s book balance sheet is

Backwoods Chemical Company (Book Values)

Net working capital $ 400 $1,000 Debt

Net fixed assets 1,600 1,000 Equity (net worth)

Total assets $2,000 $2,000 Total value

The debt has a one-year maturity and a promised interest rate of 9 percent. Thus, the

promised payment to Backwoods’s creditors is $1,090. The market value of the assets is

$1,200, and the standard deviation of asset value is 45 percent per year. The risk-free in-

terest rate is 9 percent. Calculate the value of Backwoods debt and equity.

10. Refer again to question 9. Suppose that the continuously compounded return on Back-

woods’s assets over the next year is normally distributed with a mean of 10 percent.

What is the probability that Backwoods will default?

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 25. The Many Different

Kinds of Debt

Companies, 2003

CHAPTER TWENTY-FIVE

700

THE MANY

DIFFERENT KINDS

OF DEBT

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 25. The Many Different

Kinds of Debt

Companies, 2003

IN CHAPTERS 17 and 18 we discussed how much a company should borrow. But companies also need

to think about what type of debt to issue. They must decide whether to issue short- or long-term

debt, whether to issue straight bonds or convertible bonds, whether to issue in the United States or

in the international debt market, and whether to sell the debt publicly or place it privately with a few

large investors.

As a financial manager, you need to choose the type of debt that makes sense for your company.

For example, foreign currency debt may be best suited for firms with a substantial overseas business.

Short-term debt is generally used when the firm has only a temporary need for funds.

Sometimes

competition between lenders opens a window of opportunity in a particular sector of the debt mar-

ket. The effect may be only a few basis-points reduction in yield, but on a large issue that can trans-

late into savings of several million dollars. Remember the saying, “A million dollars here and a million

there—pretty soon it begins to add up to real money.”

Our focus in this chapter is on straight long-term debt.

We begin our discussion by looking at the

different types of bonds. We examine the differences between senior and junior bonds and between

secured and unsecured bonds. Then we describe how bonds may be repaid by means of a sinking

fund and how the borrower or the lender may have an option for early repayment. We also look at

some of the restrictive provisions that deter the company from taking actions that would damage the

bonds’ value. We not only describe the different features of corporate debt but also try to explain

why sinking funds, repayment options, and the like exist. They are not simply matters of custom;

there are generally good economic reasons for their use.

Debt may be sold to the public or placed privately with large financial institutions. Because pri-

vately placed bonds are broadly similar to public issues, we will not discuss them at length. However,

we will discuss another form of private debt known as project finance. This is the glamorous part of

the debt market. The words project finance conjure up images of multi-million-dollar loans to finance

huge ventures in exotic parts of the world. You’ll find there’s something to the popular image, but it’s

not the whole story.

Finally, we look at a few unusual bonds and consider the reasons for innovation in the debt markets.

If a company cannot service its debt, it will need to come to some arrangement with its creditors

or file for bankruptcy. In the appendix to this chapter we explain the procedures involved in such

cases. We will also consider the efficiency of the bankruptcy rules in the United States and look at

how some European countries handle the problem.

701

For example, Stohs and Mauer show that firms with a preponderance of short-term assets tend to is-

sue short-term debt. See M. H. Stohs and D. C. Mauer, “The Determinants of Corporate Debt Maturity

Structure,” Journal of Business 69 (July 1996), pp. 279–312.

The remark was made by the late Senator Everett Dirksen. However, he was talking billions.

Short-term debt is discussed in Chapter 30.

25.1 DOMESTIC BONDS AND INTERNATIONAL BONDS

A firm can issue a bond either in its home country or in another country. Of course,

any firm that raises money abroad is subject to the rules of the country in which it

does so. For example, any issue in the United States of publicly traded bonds needs

to be registered with the SEC. Since the cost of registration can be particularly large

for foreign firms, these firms often avoid registration by complying with the SEC’s

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 25. The Many Different

Kinds of Debt

Companies, 2003

Rule 144A for bond issues in the United States. Rule 144A bonds can be bought and

sold only by large financial institutions.

Bonds that are sold to local investors in another country’s bond market are

known as foreign bonds. The United States is by far the largest market for foreign

bonds, but Japan and Switzerland are also important. These bonds have a variety

of nicknames: A bond sold publicly by a foreign company in the United States is

known as a yankee bond; a bond sold by a foreign firm in Japan is a samurai.

There is also a large international market for long-term bonds. These interna-

tional bond issues are sold throughout the world by syndicates of underwriters,

mainly located in London. They include the London branches of large U.S., Euro-

pean, and Japanese banks and security dealers. International issues are usually

made in one of the major currencies. The U.S. dollar has been the most popular

choice, but a high proportion of international bond issues are made in the euro, the

currency of the European Monetary Union.

The international bond market arose during the 1960s because the U.S. govern-

ment imposed an interest-equalization tax on the purchase of foreign securities

and discouraged American corporations from exporting capital. Therefore both

European and American multinationals were forced to tap an international market

for capital.

This market came to be known as the eurobond market, but be careful

not to confuse a eurobond (which may be in any currency) with a bond denomi-

nated in euros.

The interest-equalization tax was removed in 1974, and there are no longer any

controls on capital exports from the United States. Since U.S. firms can now choose

whether to borrow in New York or London, the interest rates in the two markets are

usually similar. However, the international bond market is not directly subject to reg-

ulation by the U.S. authorities, and therefore the financial manager needs to be alert

to small differences in the cost of borrowing in one market rather than another.

702 PART VII

Debt Financing

We described Rule 144A in Section 15.5.

Also, until 1984 the United States imposed a withholding tax on interest payments to foreign investors.

Investors could avoid this tax by buying an international bond issued in London rather than a similar

bond issued in New York.

In the case of international bond issues, there is a fiscal agent who carries out somewhat similar func-

tions to a bond trustee.

25.2 THE BOND CONTRACT

To give you some feel for the bond contract (and for some of the language in

which it is couched), we have summarized in Table 25.1 the terms of an issue of

30-year bonds by Ralston Purina Company. We will look at each of the principal

items in turn.

Indenture, or Trust Deed

The Ralston Purina offering was a public issue of bonds, which was registered with

the SEC and listed on the New York Stock Exchange. In the case of a public issue, the

bond agreement is in the form of an indenture, or trust deed, between the borrower

and a trust company.

Continental Bank, which is the trust company for the Ralston

Brealey−Meyers:

Principles of Corporate

Finance, Seventh Edition

VII. Debt Financing 25. The Many Different

Kinds of Debt

Companies, 2003

Purina bond, represents the bondholders. It must see that the terms of the indenture

are observed and look after the bondholders in the event of default. A copy of the

bond indenture is included in the registration statement. It is a turgid legal docu-

ment.

Its main provisions are summarized in the prospectus to the issue.

CHAPTER 25

The Many Different Kinds of Debt 703

Listed New York Stock Exchange

Trustee Continental Bank, Chicago

Rights on default The trustee or 25% of the debentures outstanding may declare interest due

and payable.

Indenture modification Indenture may not be modified except as provided with the consent of two-

thirds of the debentures outstanding.

Registered Fully registered

Denomination $1,000

To be issued $86.4 million

Issue date June 4, 1986

Offered Issued at a price of 97.60% plus accrued interest (proceeds to Company

96.725%) through First Boston Corporation, Goldman Sachs and Company,

Shearson Lehman Brothers, Stifel Nicolaus and Company, and associates.

Interest At a rate of 9

⁄

2% per annum, payable June 1 and December 1 to holders

registered on May 15 and November 15.

Security Not secured. Company will not permit to have any lien on its property or

assets without equally and ratably securing the debt securities.

Sale and lease-back Company will not enter into any sale and lease-back transaction unless the

Company within 120 days after the transfer of title to such principal property

applies to the redemption of the debt securities at the then-applicable

option redemption price an amount equal to the net proceeds received by

the Company upon such sale.

Maturity June 1, 2016

Sinking fund Annually between June 2, 1996, and June 2, 2015, sufficient to redeem not less

than $13.5 million principal amount, plus similar optional payments. Sinking

fund is designed to redeem 90% of the debentures prior to maturity.

Callable At whole or in part at any time at the option of the Company with at least 30,

but not more than 60, days’ notice on each May 31 as follows:

1989 106.390 1990 106.035 1991 105.680

1992 105.325 1993 104.970 1994 104.615

1995 104.260 1996 103.905 1997 103.550

1998 103.195 1999 102.840 2000 102.485

2001 102.130 2002 101.775 2003 101.420

2004 101.065 2005 100.710 2006 100.355

and thereafter at 100 plus accrued interest; provided, however, that prior to

June 1, 1996, the Company may not redeem the bonds from, or in

anticipation of, moneys borrowed having an effective interest cost of less

than 9.748%.

TABLE 25.1

Summary of terms of 9

⁄2 percent sinking fund debenture 2016 issued by Ralston Purina Company.

For example, the indenture for one J.C. Penney bond stated: “In any case where several matters are re-

quired to be certified by, or covered by an opinion of, any specified Person, it is not necessary that all

such matters be certified by, or covered by the opinion of, only one such Person, or that they be certi-

fied or covered by only one document, but one such Person may certify or give an opinion with respect

to some matters and one or more such other Persons as to other matters, and any such Person may cer-

tify or give an opinion as to such matters in one or several documents.” Try saying that three times fast.