8-15. Suppose you purchase a 30-year Treasury bond with a 5% annua

8-15. 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.

8-16. 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?

8-17. What is the price today of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium?

8-18. What is the price of a five-year, zero-coupon, default-free security with a face value of $1000?

8-19. What is the price of a three-year, default-free security with a face value of $1000 and an annual coupon rate of 4%? What is the yield to maturity for this bond?

8-20. What is the maturity of a default-free security with annual coupon payments and a yield to maturity of 4%? Why?

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8-21. Consider a four-year, default-free security with annual coupon payments and a face value of $1000 that is issued at par. What is the coupon rate of this bond?

8-22. Consider a five-year, default-free bond with annual coupons of 5% and a face value of $1000.

a. Without doing any calculations, determine whether this bond is trading at a premium or at a discount. Explain.

b. What is the yield to maturity on this bond?

c. If the yield to maturity on this bond increased to 5.2%, what would the new price be?

8-23. Prices of zero-coupon, default-free securities with face values of $1000 are summarized in the following table:

Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.50. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?

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