КФ / Лекции / Brealey Myers - Principles Of Corporate Finance 7th Ed (eBook)

Bond ratings are judgments about firms’ financial and business prospects. There is no fixed formula by which ratings are calculated. Nevertheless, investment bankers, bond portfolio managers, and others who follow the bond market closely can get a fairly good idea of how a bond will be rated by looking at a few key numbers such as the firm’s debt–equity ratio, the ratio of earnings to interest, and the return on assets.

Table 24.5 shows that bond ratings do reflect the probability of default. Since 1971 no bond that was initially rated triple-A by Standard and Poor’s has defaulted in the year after issue and fewer than one in a thousand has defaulted within 10 years of issue. At the other extreme, over 2 percent of CCC bonds have defaulted in their first year and by year 10 almost half have done so. Of course, bonds rarely fall suddenly from grace. As time passes and the company becomes progressively more shaky, the agencies revise downward the bond’s rating to reflect the increasing probability of default.

Since bond ratings reflect the probability of default, it is not surprising that there is also a close correspondence between a bond’s rating and its promised yield. For example, in the postwar period the promised yield on Moody’s Baa corporate bonds has been on average about .9 percent more than on Aaa’s.

Firms and governments, having noticed the link between bond ratings and yields, worry that a reduction in rating will result in higher interest charges.25 When the Asian currency crisis in 1998 led Moody’s to downgrade the Malaysian government’s risk rating, the government immediately canceled a much-needed $2 billion bond issue. Investors have a different concern; they worry that the rating agencies are slow to react when businesses are in trouble. When Enron went belly up in 2001, investors protested that only two months earlier the company’s debt had an investment-grade rating.

Junk Bonds

Bonds rated below Baa are known as junk bonds. Most junk bonds used to be fallen angels, that is, bonds of companies that had fallen on hard times. But during the 1980s new issues of junk bonds multiplied tenfold as more and more companies issued large quantities of low-grade debt to finance takeovers or to defend themselves against being taken over.

25They almost certainly exaggerate the influence of the rating agencies, which are as much following investor opinion as leading it.

The development of this market for low-grade corporate bonds was largely the brainchild of the investment banking firm Drexel Burnham Lambert. The result was that for the first time corporate midgets were able to take control of corporate giants, because they could finance this activity by issues of debt. However, issuers of junk bonds often had debt ratios of 90 or 95 percent. Many worried that these high levels of leverage resulted in undue risk and pressed for legislation to ban junk bonds.

One of the largest issuers of junk bonds was Campeau Corporation. Between 1986 and 1988 Campeau amassed a huge retailing empire by acquiring major department store chains such as Federated Department Stores and Allied Stores. Unfortunately, it also amassed $10.9 billion in debt, which was supported by just $.9 billion of book equity. So when in September 1989 Campeau announced that it was having difficulties meeting the interest payments on its debt, the junk bond market took a nosedive and worries about the riskiness of junk bonds intensified. Campeau’s own bonds fell to the point at which they offered a promised yield of nearly 50 percent. Campeau eventually filed for bankruptcy, and investors with holdings of junk bonds took large losses.

In 1990 and 1991 the default rate for junk bonds climbed to over 10 percent and the market for new issues of these bonds dried up. But later in the decade the market began to boom again and with increasing economic prosperity the annual default rate fell to below 2 percent before rising again in the new millenium.

Junk bonds promise a higher yield than U.S. Treasuries. When junk bonds were out of favor, their yields reached more than 9 percent above that of Treasuries, but the gap has since narrowed. Of course, companies can’t always keep their promises. Many junk bonds have defaulted, while some of the more successful issuers have called their bonds, thus depriving their holders of the prospect of a continuing stream of high coupon payments. Figure 24.8 shows the performance since 1977 of a portfolio of junk bonds and 10-year Treasury bonds. On average, the promised yield on junk bonds was 4.8 percent higher than that on Treasuries, but the annual realized return was only 1.9 percent higher.

Option Pricing and Risky Debt

In Section 20.2 we showed that holding a corporate bond is equivalent to lending money with no chance of default but at the same time giving stockholders a put option on the firm’s assets. When a firm defaults, its stockholders are in effect ex-

we assumed that the company made only a single issue of zero-coupon debt. But suppose instead that it issues a 10-year bond which pays interest annually. We can still think of the company’s stock as a call option that can be exercised by making the promised payments. But in this case there are 10 payments rather than just 1. To value the stock, we would have to value 10 sequential call options. The first option can be exercised by making the first interest payment when it comes due. By exercise the stockholders obtain a second call option, which can be exercised by making the second interest payment. The reward to exercising is that the stockholders get a third call option, and so on. Finally, in year 10 the stockholders can exercise the tenth option. By paying off both the principal and the last year’s interest, the stockholders regain unencumbered ownership of the company’s assets.

Of course, if the firm does not make any of these payments when due, bondholders take over and stockholders are left with nothing. In other words, by not exercising one call option, stockholders give up all subsequent call options.

Valuing the equity when the 10-year bond is issued is equivalent to valuing the first of the 10 call options. But you cannot value the first option without valuing the nine that follow.28 Even this example understates the practical difficulties, because large firms may have dozens of outstanding debt issues with different interest rates and maturities, and before the current debt matures they may make further issues. But do not lose heart. Computers can solve these problems, more or less by brute force, even in the absence of simple, exact valuation formulas.

In practice, interest rate differentials tend to be greater than those shown in Figure 24.9. High-grade corporate bonds typically offer promised yields about 1 percentage point greater than U.S. Treasury bonds. It is very difficult to justify yield

28The other approach to valuing the company’s debt (subtracting the value of a put option from riskfree bond value) is no easier. The analyst would be confronted by not one simple put but a package of 10 sequential puts.

Without a guarantee, the loan becomes an ordinary debt obligation of the firm. We know from Section 20.2 that

The loan’s value, assuming no chance of default, is exactly its guaranteed value; thus, the put value equals the difference between the values of a guaranteed and an ordinary loan. This is the value of the loan guarantee.

Thus, option pricing theory should lead to a way of calculating the actual cost of the government’s many loan guarantee programs. This will be a healthy thing. The government’s possible liability under existing guarantee programs has been enormous. In 1987, for example, $4 billion in loans to shipowners had been guaranteed under the so-called Title IX program to support shipyards in the United States.32 This program was one of dozens. Yet the true cost of these programs is not widely recognized. Because loan guarantees involve no immediate outlay, they do not appear in the federal budget. Members of Congress sponsoring loan guarantee programs do not, as far as we know, present careful estimates of the value of the programs to business and the present value of the programs’ cost to the public.

Calculating the Probability of Default

Banks and other financial institutions not only want to know the value of the loans that they have made but they also need to know the risk that they are incurring. Suppose that the assets of Backwoods Chemical have a current market value of $100 and its debt has a face value of $60 (i.e., 60 percent leverage), all of which is due to be repaid at the end of five years. Figure 24.10 shows the range

32The actual figure on March 31, 1987, was $4,497,365,297.98. Since 1987 these government guarantees to shipowners have been substantially reduced.

of possible values of Backwoods’s assets when the loan becomes due. The expected value of the assets is $120, but this value is by no means certain. There is a probability of 20 percent that the asset value could fall below $60, in which case the company will default on its debt. This probability is shown by the shaded area in Figure 24.10.

To calculate the probability that Backwoods will default, we need to know the expected growth in the market value of its assets, the face value and maturity of the debt, and the variability of future asset values. Real-world cases are likely to be more complex than our Backwoods example. For example, firms may have several classes of debt maturing on different dates. If so, shareholders have an option on an option. It may be worth their while to put up more money to pay off the shortterm debt and thus keep alive the chance that the firm’s fortunes will recover before the rest of the debt becomes due.

However, banks and consulting firms are now finding that they can use these ideas to measure the risk of actual loans.33 For example, by mid-2001 the fiber-optics company, Metromedia Fiber Network, was a company in difficulties. Revenues had expanded rapidly, but so had losses. By 2000 the company was making operating losses of $329 million on revenues of $188 million. The stock price had fallen from a high of $50 to under $2, while the company’s 8-year 10 percent notes were priced at 44 percent and offered a yield to maturity of 27 percent.

How close was Metromedia to default? Figure 24.11 provides an answer. The burgundy line shows the market value of Metromedia’s assets, and the blue line shows the asset value at which the company would choose to default on its debts. You can see that during the first half of 2001 the value of the company’s assets crept closer and closer to the default point.

33Banks are not just interested in the risk of individual loans; they would also like to know the risk of their entire portfolio. Therefore, specialists in credit risk also need to recognize the correlation between the outcomes. A portfolio of loans, all of which are to factory outlets in suburban Hicksville, is likely to be more risky than a portfolio with a wide variety of different borrowers.

Of course, nobody had a crystal ball that could foresee what would happen to Metromedia, but KMV, a consulting firm specializing in the assessment of credit risk, estimated the probability at each point that the company would default in the next year. Figure 24.12 shows how KMV progressively increased its assessment of the probability of default.

Bond dealers generally look at the yield to maturity on a bond. This is simply the internal rate of return y, the discount rate at which

The yield to maturity y is a complex average of the spot interest rates r1, r2, etc. Like most averages it can be a useful summary measure, but it can also hide a lot of interesting information. We suggest you refer to yields on stripped bonds as measures of the spot rates of interest.

When you invest in a bond you usually receive a regular interest payment and then the final principal payment. Duration measures the average time to each payment. It is a useful summary measure of the length of a loan. It is also important because there is a direct relationship between the duration of a bond and its volatility. A change in interest rates has a greater effect on the price of a bond with a longer duration.

The one-period spot rate r1 may be very different from the two-period spot rate r2. In other words, investors often want a different annual rate of interest for lending for one year than for two years. Why is this? The expectations theory says that bonds are priced so that the expected rate of return from investing in bonds over any period is independent of the maturity of the bonds held by the investor. The expectations theory predicts that r2 will exceed r1 only if next year’s one-period interest rate is expected to rise.

The expectations theory cannot be a complete explanation of the term structure if investors are worried about risk. Long bonds may be a safe haven for investors with long-term fixed liabilities. But other investors may not like the extra volatility of long-term bonds and may be concerned that a sudden burst in inflation could largely wipe out the real value of these bonds. Such investors will be prepared to hold long-term bonds only if they offer a liquidity premium—that is, a higher rate of interest.

Finally, we come to our third question: What determines the difference between interest rates on company and government debt? Company debt sells at a lower price than government debt. This discount represents the value of the company’s option to default. We showed you how the value of this option varies with the degree of leverage and the time to maturity.

Ratings are widely used as a guide to the risk of loans. However, banks and consulting firms also recognize that the option to default is a put option and they have been developing models to estimate the probability that the borrower will exercise its option to default.

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: Interpreting 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 liabilities:

S.M. Schaefer: “Immunisation and Duration: A Review of Theory, Performance and Application,” 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).

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?