# Valuation Measuring and managing the value ofpanies - Koller T.

ISBN 0-471-36190-9

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The coupon rate—that is, the historical (or imbedded) cost of debt—is irrelevant for determining the current cost of capital. Always use the most current market rate on debt of equivalent risk. A reasonable proxy for the risk of debt is Moody's or Standard & Poor's bond rating. If the bond rating is not available, calculate traditional financial ratios—times-interest-earned, debt-to-equity, and so on—to compare the entity you are valuing with known firms.

Most companies have variable-rate debt, either acquired through swaps, as an original security issue, or in the form of revolving bank loans. If the variable-rate loan has no cap or floor, then use the long-term rate, because the short-term rate will be rolled over and the geometric average of the expected short-term rates is equal to the long-term rate. If the variable-rate debt has a cap or floor, or if the interest payment is determined as a moving average of past rates, then an option is involved and the problem becomes more complicated. For example, if market rates have risen and a variable rate loan is ''capped out," then it becomes a subsidized form of financing that adds value to the company.

Below-Investment-Grade Debt

When dealing with debt that is less than investment grade, be aware of the difference between the expected yield to maturity and the promised yield to maturity. The promised yield to maturity assumes that all payments (coupons and principal) will be made as promised by the issuer. Consider the following simple example: A three-year bond promises to pay a 10 percent coupon at the end of each year, plus a face value of $1,000 at the end of the third year. The current market value of the bond is $951.96. What is the yield to maturity? It can be computed by solving the following formula:

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Where Bo = The current market value of noncallable, nonconvertible debt Coupon = The promised coupon paid at the end of time period t Face = The face value of the bond, promised at maturity y = The promised yield to maturity

The solution is y = 12 percent. This promised yield to maturity assumes that the debt is default-free. Suppose that there is a 5 percent chance that the bond will default and pay only $400.

If we were to rewrite the formula, putting the bond's expected payments rather than its promised payments in the numerator, we could calculate the market's expected rate of return as opposed to the promised rate of return implicit in the yield to maturity. As recomputed, the market expected rate of return on the risky debt would be 11.09 percent. The rate of return that the market expects to earn is 91 basis points lower than the promised yield to maturity. The promised yields on junk bonds are very different (frequently much higher) from the expected yields that the market anticipates on these risky securities.

Our problem is that we need to compute the expected yield to maturity, not the quoted, promised yield. We can do this if we have the current market price of the low-grade bond and estimates of its expected default rate and value in default. The necessary data are usually unavailable. Default rates on original issue corporate bonds in the United States are given in Exhibit 10.1. Original issue junk bonds (those with the lowest rating of CCC) have large default rates after a period of time (26.7 percent after 5 years, and 37.7 percent after 10 years).

Exhibit 10.1 Mortality Losses by Original Rating

1971-1999 (%of principal)

Years after issuance

1 2 3 4 5 6 7 8 9 10

AAA o.oo 0.00 0.00 0.00 0.01 0 01 0.01 0.01 0.01 0.01

AA 0.00 0.00 0.07 0.15 0.15 0.15 0.15 0.15 0.17 0.19

A 0.00 0.00 0.02 0.08 0.12 0.19 0.21 0.28 0.32 0.32

BBB 0.02 0.19 0.33 0.66 0.76 1.01 1.15 1.19 1 24 1.44

BB 0.25 0.70 2.68 3 91 5.05 5.92 6.98 7.12 7.90 9.52

B 0.67 2.65 6.97 10.91 13.90 15.72 17.24 18.39 19.05 19.60

CCC 1.02 12.00 21.39 25.30 26.68 31.52 33.98 35.75 35.75 37.73

Source: E. Altman, Defaults & Returns on High Yield Bonds: Analysis Through 1998 & Default Outlook for 1999-2000. New York University Salomon Center, laimary 1999.

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If the necessary data are not available, use the yield to maturity on BBB-rated debt, which reduces most of the effects of the difference between promised and expected yields.

Although the promised yield to maturity is not equivalent to the opportunity cost of capital for debt with high default risk, it can serve as a useful proxy for the market's estimate of default risk. Exhibit 10.2 shows the relationship between promised yields to maturity and maturity periods for portfolios of bonds varying in risk from default-free U.S. government obligations (U.S. Treasury strips) to CCC-rated corporate debentures.

Subsidized Debt

The coupon rate on subsidized debt such as industrial revenue bonds is below the market rate for taxable bonds of equivalent risk because they are tax-free to investors. The cost of capital for this type of debt is their current market yield to maturity, where known. If the bonds are not traded, their yield can be estimated by reference to similarly rated tax-free issues that are actively traded (or from similar new issues of tax-exempt debt).

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