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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 £100 at maturity.

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

b.Is the term structure upwardor 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.

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?

8. You have estimated spot rates as follows:

1r1 5.00%

2r2 5.40

3r3 5.70

4r4 5.90

5r5 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

(c)must lie between the yield on a five-year zero-coupon bond and a five-year 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 sixyear 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 maturities. Calculate how their prices would change if their yields to maturity increased by one percentage point. Are longor short-term bonds most affected by the change in yields? Are highor low-coupon bonds most affected?

12.Assume the term structure of interest rates is upward-sloping. How would you respond to the following comment? “The present term structure of interest rates makes short-term debt more attractive to corporate treasurers. Firms should avoid new longterm 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 fiveyear 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 mediumand long-term bonds. Now assume that the price of the medium-term bond can either fall by $10.75 or

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. Suppose that the firm’s book balance sheet is

Backwoods Chemical Company (Book Values)

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 interest 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 Backwoods’s assets over the next year is normally distributed with a mean of 10 percent. What is the probability that Backwoods will default?

Rule 144A for bond issues in the United States. Rule 144A bonds can be bought and sold only by large financial institutions.4

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 international bond issues are sold throughout the world by syndicates of underwriters, mainly located in London. They include the London branches of large U.S., European, 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. government 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.5 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 denominated 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 regulation 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.

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.6 Continental Bank, which is the trust company for the Ralston

4We described Rule 144A in Section 15.5.

5Also, 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.

6In the case of international bond issues, there is a fiscal agent who carries out somewhat similar functions to a bond trustee.

T A B L E 2 5 . 1

Summary of terms of 91⁄2 percent sinking fund debenture 2016 issued by Ralston Purina Company.

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 document.7 Its main provisions are summarized in the prospectus to the issue.

7For example, the indenture for one J.C. Penney bond stated: “In any case where several matters are required 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 certified 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 certify or give an opinion as to such matters in one or several documents.” Try saying that three times fast.

Moving down Table 25.1, you will see that the Ralston Purina bonds are registered. This means that the company’s registrar records the ownership of each bond and the company pays the interest and the final principal amount directly to each owner.8

Almost all bonds issued in the United States are issued in registered form, but in many countries bonds may be issued in bearer form. In this case, the certificate constitutes the primary evidence of ownership so the bondholder must send in coupons to claim interest and must send the certificate itself to claim the final repayment of principal. International bonds almost invariably allow the owner to hold them in bearer form. However, since the ownership of such bonds cannot be traced, the IRS has tried to deter U.S. residents from holding them.9

The Bond Terms

Like most dollar bonds, the Ralston Purina bonds have a face value of $1,000. Notice, however, that the bond price is shown as a percentage of face value. Also, the price is stated net of accrued interest. This means that the bond buyer must pay not only the quoted price but also the amount of any future interest that may have accrued. For example, an investor who bought bonds for delivery on (say) June 11, 1986, would be receiving them 10 days into the first interest period. Therefore, accrued interest would be 10/360 9.5 .26 percent, and the investor would pay a price of 97.60 plus .26 percent of accrued interest.10

The Ralston Purina bonds were offered to the public at a price of 97.60 percent, but the company received only 96.725 percent. The difference represents the underwriters’ spread. Of the $86.4 million raised, about $85.6 million went to the company and $.8 million went to the underwriters.

Since the bonds were issued at a price of 97.60 percent, investors who hold the bonds to maturity receive a capital gain over the 30 years of 2.40 percent.11 However, the bulk of their return is provided by the regular interest payment. The annual interest or coupon payment on each bond is 9.50 percent of $1,000, or $95. This interest is payable semiannually, so every six months investors receive interest of 95/2 $47.50. Most U.S. bonds pay interest semiannually, but a comparable international bond would generally pay interest annually.12

The regular interest payment on a bond is a hurdle that the company must keep jumping. If the company ever fails to pay the interest, lenders can demand their

8Often, investors do not physically hold the security; instead, their ownership is represented by a book entry. The “book” is in practice a computer.

9U.S. residents cannot generally deduct capital losses on bearer bonds. Also, payments on such bonds cannot be made to a bank account in the United States.

10In the U.S. corporate bond market accrued interest is calculated on the assumption that a year is composed of twelve 30-day months; in some other markets (such as the U.S. Treasury bond market) calculations recognize the actual number of days in each calendar month.

11This gain is not taxed as income as long as it amounts to less than .25 percent a year.

12If a bond pays interest semiannually, investors usually calculate a semiannually compounded yield to maturity on the bond. In other words, the yield is quoted as twice the six-month yield. Because international bonds pay interest annually, it is conventional to quote their yields to maturity on an annually compounded basis. Remember this when comparing yields.