5. A zero-coupon bond with face value $1,000 and maturity of five years sells for $746.22. What is its yield to maturity? What will happen to its yield to maturity if its price falls immediately to $730?

9. A bond with an annual coupon rate of 4.8% sells for $970. What is the bond’s current yield?

12. You buy an eight-year bond that has a 6% current yield and a 6% coupon (paid annu-ally). In one year, promised yields to maturity have risen to 7%. What is your holding-period return?

14. Which security has a higher effective annual interest rate?

a. A three-month T-bill with face value of $100,000 currently selling at $97,645.

b. A coupon bond selling at par and paying a 10% coupon semiannually.

16. Consider a bond paying a coupon rate of 10% per year semiannually when the market interest rate is only 4% per half-year. The bond has three years until maturity.

a. Find the bond’s price today and six months from now after the next coupon is paid.

b. What is the total rate of return on the bond?

17. A 20-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is:

a. $950

b. $1,000

c. $1,050

22. A bond with a coupon rate of 7% makes semiannual coupon payments on January 15 and July 15 of each year. The Wall Street Journal reports the ask price for the bond on January 30 at 100.125. What is the invoice price of the bond? The coupon period has 182 days.

27. A 10-year bond of a firm in severe financial distress has a coupon rate of 14% and sells for $900. The firm is currently renegotiating the debt, and it appears that the lenders will allow the firm to reduce coupon payments on the bond to one-half the originally contracted amount. The firm can handle these lower payments. What are the stated and expected yields to maturity of the bonds? The bond makes its coupon payments annually.

32. A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five years at a call price of $1,100. The bond currently sells at a yield to maturity of 7% (3.5% per half-year).

a. What is the yield to call?

b. What is the yield to call if the call price is only $1,050?

c. What is the yield to call if the call price is $1,100 but the bond can be called in two years instead of five years?

35. Masters Corp. issues two bonds with 20-year maturities. Both bonds are callable at $1,050. The first bond is issued at a deep discount with a coupon rate of 4% and a price of $580 to yield 8.4%. The second bond is issued at par value with a coupon rate of 8.75%.

a. What is the yield to maturity of the par bond? Why is it higher than the yield of the discount bond?

b. If you expect rates to fall substantially in the next two years, which bond would you prefer to hold?

c. In what sense does the discount bond offer “implicit call protection”?