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# Default and Interest-Rate Risk

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A14. (Stock valuation) Suppose Toyota has non-maturing (perpetual) preferred stock outstanding
that pays a \$1.00 quarterly dividend and has a required return of 12% APR (3% per quarter).
What is the stock worth?

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock
Exchange. Suppose PhilEl's bonds have identical coupon rates of 9.125% but that one issue
matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment

a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.
What is the fair price of each bond now?
c. Suppose that the yield to maturity for all of these bonds changed instantaneously again,
this time to 9%. Now what is the fair price of each bond?
d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same,
higher, or lower for longer- versus shorter-maturity bonds?

B18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the
\$1,000 principal in 10 years. You pay only \$500 for the bond.

a. You receive the coupon payments for three years and the bond defaults. After liquidating
the firm, the bondholders receive a distribution of \$150 per bond at the end of 3.5
years. What is the realized return on your investment?
b. The firm does far better than expected and bondholders receive all of the promised
interest and principal payments. What is the realized return on your investment?

B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its
common stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will
begin paying a \$1.00 per share dividend in two years and that the dividend will increase
6% annually thereafter. Bret Kimes, one of James' colleagues at the same firm, is less optimistic.
Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend
will be \$1.00, and that it will grow at 4% annually. James and Bret agree that the
required return for Medtrans is 13%

.C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated
the contingent returns given here.

a. Calculate the expected returns on the stock market and on Chicago Gear stock.
b. What is Chicago Gear's beta?
c. What is Chicago Gear's required return according to the CAPM?

REALIZED RETURN
State of the Market Probability that State Occurs Stock Market Chicago Gear
Stagnant 0.20 (10%) (15%)
Slow growth 0.35 10 15
Average growth 0.30 15 25
Rapid growth 0.15 25 35

#### Solution Preview

A14. (Stock valuation) Suppose Toyota has non-maturing (perpetual) preferred stock outstanding
that pays a \$1.00 quarterly dividend and has a required return of 12% APR (3% per quarter).
What is the stock worth?
Annual dividend on the stock = \$1.00*4=\$4.00
Value of a perpetual preferred stock = Annual dividend / Required rate of return = \$4.00 / 12% = \$33.33

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock
Exchange. Suppose PhilEl's bonds have identical coupon rates of 9.125% but that one issue
matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment
a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
Fair price of a bond = PV of coupon payment (an annuity) + PV of Principal payment on maturity (one time payment)
PV of an annuity = C/r*(1-1/(1+r)^n)
Where C=fixed payment = 9.125%*1000=\$91.25
r=interest rate = 8%
n= number of years = 1, 7 and 15 years for different bonds

PV of a single payment = P/(1+r)^n
Where P = Face value of Bond = \$1000

Fair price of 1 year bond = 91.25/8%*(1-1/(1+8%)^1) + 1000/(1+8%)^1=\$1010.42
Fair price of 7 year bond = 91.25/8%*(1-1/(1+8%)^7) + 1000/(1+8%)^7=\$1058.57
Fair price of 15 year bond = 91.25/8%*(1-1/(1+8%)^15) + 1000/(1+8%)^15=\$1096.29

b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%.
What is the fair price of each bond now?
Fair price of 1 year bond = 91.25/7%*(1-1/(1+7%)^1) + 1000/(1+7%)^1=\$1019.86
Fair price of 7 year bond = ...

#### Solution Summary

The solution discusses default and interest rate risks for Philadelphia Electric.

\$2.19