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E. (1) What is the value of a 13% coupon bond that is otherwise identical
to the bond described in Part D? Would we now have a discount or
a premium bond?
Answer: [Show S7-13 here.] With a financial calculator, just change the
E. (2) What is the value of a 7% coupon bond with these characteristics?
Would we now have a discount or premium bond?
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Answer: [Show S7-14 here.] In the second situation, where the coupon rate
E. (3) What would happen to the values of the 7%, 10%, and 13%
coupon bonds over time if the required return remained at 10%?
[Hint: With a financial calculator, enter PMT, I/YR, FV, and N; then
change (override) N to see what happens to the PV as it approaches
maturity.]
Answer: [Show S7-15 and S7-16 here.] Assuming that interest rates remain
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F. (1) What is the yield to maturity on a 10-year, 9%, annual coupon,
$1,000 par value bond that sells for $887.00? That sells for
$1,134.20? What does the fact that it sells at a discount or at a
premium tell you about the relationship between rd and the coupon
rate?
Answer: [Show S7-17 through S7–19 here.] The yield to maturity (YTM) is
the discount rate that equates the present value of a bond’s cash
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F. (2) What are the total return, the current yield, and the capital gains
yield for the discount bond? Assume that it is held to maturity and
the company does not default on it. (Hint: Refer to Footnote 7 for
the definition of the current yield and to Table 7.1.)
Answer: [Show S7-20 through S7-22 here.] The current yield is defined as
follows:
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G. What is price risk? Which has more price risk, an annual payment
1-year bond or a 10-year bond? Why?
Answer: [Show S7-23 and S7-24 here.] Price risk is the risk that a bond will
lose value as the result of an increase in interest rates. The table
below gives values for a 10%, annual coupon bond at different
values of rd:
H. What is reinvestment risk? Which has more reinvestment risk, a
1-year bond or a 10-year bond?
Answer: [Show S7-25 through S7-27 here.] Reinvestment risk is defined as
the risk that cash flows (interest plus principal repayments) will
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Optional Question
Suppose a firm will need $100,000 20 years from now to replace some
equipment. It plans to make 20 equal payments, starting today, into an
investment fund. It can buy bonds that mature in 20 years or bonds that
mature in 1 year. Both types of bonds currently sell to yield 10%, i.e., rd =
YTM = 10%. The company’s best estimate of future interest rates is that they
will stay at current levels, i.e., they may rise or they may fall, but the expected
rd is the current rd.
There is some chance that the equipment will wear out in less than 20
years, in which case the company will need to cash out its investment before
20 years. If this occurs, the company will desperately need the money that has
been accumulated—this money could save the business. How much should
the firm plan to invest each year?
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Answer: Start with a time line:
0 1 2 18 19 20
| | | • • • | | |
10%
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Optional Question
If the company decides to invest enough right now to produce the future
$100,000, how much is its outlay?
Answer: To find the required initial lump sum, we would find the PV of $100,000
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Optional Question
Can you think of any other type of bond that might be useful for this
company’s purposes?
Answer: A zero coupon bond is one that pays no interest—it has zero
coupons, and its issuer simply promises to pay a stated lump sum at
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Optional Question
What type of bond would you recommend that it actually buy?
Answer: It is tempting to say that the best investment for this company
would be the zeros, because they have no reinvestment risk. But
I. How does the equation for valuing a bond change if semiannual
payments are made? Find the value of a 10-year, semiannual
payment, 10% coupon bond if nominal rd = 13%.
Answer: [Show S7-28 and S7-29 here.] In reality, virtually all bonds issued
in the U.S. have semiannual coupons and are valued using the setup
shown below:
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J. Suppose for $1,000 you could buy a 10%, 10-year, annual payment
bond or a 10%, 10-year, semiannual payment bond. They are
equally risky. Which would you prefer? If $1,000 is the proper
price for the semiannual bond, what is the equilibrium price for the
annual payment bond?
Answer: [Show S7-30 and S7-31 here.] The semiannual payment bond
would be better. Its EAR would be:
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K. Suppose a 10-year, 10%, semiannual coupon bond with a par value
of $1,000 is currently selling for $1,135.90, producing a nominal
yield to maturity of 8%. However, it can be called after 4 years for
$1,050.
(1) What is the bond’s nominal yield to call (YTC)?
Answer: [Show S7-32 and S7-33 here.] If the bond were called,
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K. (2) If you bought this bond, would you be more likely to earn the YTM
or the YTC? Why?
Answer: [Show S7-34 and S7-35 here.] Since the coupon rate is 10% versus
L. Does the yield to maturity represent the promised or expected
return on the bond? Explain.
Answer: [Show S7-36 here.] The yield to maturity is the rate of return
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M. These bonds were rated AA– by S&P. Would you consider them
investment-grade or junk bonds?
Answer: [Show S7-37 and S7-38 here.] These bonds would be investment-
N. What factors determine a company’s bond rating?
Answer: [Show S7-39 and S7–40 here.] Bond ratings are based on both
qualitative and quantitative factors, some of which are listed below.
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O. If this firm were to default on the bonds, would the company be
immediately liquidated? Would the bondholders be assured of
receiving all of their promised payments? Explain.
Answer: [Show S7-41 through S7-44 here.] When a business becomes
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If the firm is deemed to be too far gone to be saved, it will be
liquidated and the priority of claims (as seen in Web Appendix 7C)
would be as follows:
1. Secured creditors.