Sample Bond Valuation Questions
1) A 30-year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments.
a. What is the coupon payment for this bond?
b. What is the price of the bond?
2) Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.
a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?
b. If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?
3) Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond’s coupon rate?
4) Explain why the yield of a bond that trades at a discount exceeds the bond’s coupon rate.
5) Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.
a. Is this bond currently trading at a discount, at par, or at a premium? Explain.
b. If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for?
6) Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.
a. What was the price of this bond when it was issued?
b. Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?
c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?
7) Suppose you purchase a 10-year bond with 6% annual coupons. You hold the bond for four years, and sell it immediately after receiving the fourth coupon. If the bond’s yield to maturity was 5% when you purchased and sold the bond,
a. What cash flows will you pay and receive from your investment in the bond per $100 face value?
b. What is the internal rate of return of your investment?
8) Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%. You hold the bond for five years before selling it.
a. If the bond’s yield to maturity is 6% when you sell it, what is the internal rate of return of your investment?
b. If the bond’s yield to maturity is 7% when you sell it, what is the internal rate of return of your investment?
c. If the bond’s yield to maturity is 5% when you sell it, what is the internal rate of return of your investment?
d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain.
9) Suppose you purchase a 30-year Treasury bond with a 5% annual coupon, initially trading at par. In 10 years’ time, the bond’s yield to maturity has risen to 7% (EAR).
a. If you sell the bond now, what internal rate of return will you have earned on your investment in the bond?
b. If instead you hold the bond to maturity, what internal rate of return will you earn on your investment in the bond?
c. Is comparing the IRRs in (a) versus (b) a useful way to evaluate the decision to sell the bond? Explain.
10) Suppose the current yield on a one-year, zero coupon bond is 3%, while the yield on a five-year, zero coupon bond is 5%. Neither bond has any risk of default. Suppose you plan to invest for one year. You will earn more over the year by investing in the five-year bond as long as its yield does not rise above what level?
11) Explain why the expected return of a corporate bond does not equal its yield to maturity.
12) Grummon Corporation has issued zero-coupon corporate bonds with a five-year maturity. Investors believe there is a 20% chance that Grummon will default on these bonds. If Grummon does default, investors expect to receive only 50 cents per dollar they are owed. If investors require a 6% expected return on their investment in these bonds, what will be the price and yield to maturity on these bonds?
13) The Isabelle Corporation rents prom dresses in its stores across the southern United States. It has just issued a five-year, zero-coupon corporate bond at a price of $74. You have purchased this bond and intend to hold it until maturity.
a. What is the yield to maturity of the bond?
b. What is the expected return on your investment (expressed as an EAR) if there is no chance of default?
c. What is the expected return (expressed as an EAR) if there is a 100% probability of default and you will recover 90% of the face value?
d. What is the expected return (expressed as an EAR) if the probability of default is 50%, the likelihood of default is higher in bad times than good times, and, in the case of default, you will recover 90% of the face value?
e. For parts (b–d), what can you say about the five-year, risk-free interest rate in each case?
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