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Consol Bonds

Perpetual Life Corp. has issued consol bonds with coupon payments of $80. (Consols pay interest forever, and never mature. They are perpetuities.) If the required rate of return on these bonds at the time they were issued was 8 percent, at what price were they sold to the public? If the required return today is 12 percent, at what price do the consols sell?

16. Bond Pricing. Sure Tea Co. has issued 9 percent annual coupon bonds which are now selling at a yield to maturity of 10 percent and current yield of 9.8375 percent. What is the remaining maturity of these bonds?

17. Bond Pricing. Large Industries bonds sell for $1,065.15. The bond life is 9 years, and the yield to maturity is 7 percent. What must be the coupon rate on the bonds?

18. Bond Prices and Yields.

a. Several years ago, Castles in the Sand, Inc., issued bonds at face value at a yield to maturity of 8 percent. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 14 percent. What has happened to the price of the bond?

b. Suppose that investors believe that Castles can make good on the promised coupon payments, but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80 percent of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

19. Bond Returns. You buy an 8 percent coupon, 10-year maturity bond for $980. A year later, the bond price is $1,050.

a. What is the new yield to maturity on the bond?

b. What is your rate of return over the year?

20. Bond Returns. You buy an 8 percent coupon, 10-year maturity bond when its yield to maturity is 9 percent. A year later, the yield to maturity is 10 percent. What is your rate of return over the year?

21. Interest Rate Risk. Consider three bonds with 8 percent coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.

a. What will happen to the price of each bond if their yields increase to 9 percent?

b. What will happen to the price of each bond if their yields decrease to 7 percent?

c. What do you conclude about the relationship between time to maturity and the sensitivity of bond prices to interest rates?

22. Rate of Return. A 2-year maturity bond with face value $1,000 makes annual coupon payments of $80 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is

a. 6 percent

b. 8 percent

c. 10 percent

23. Rate of Return. A bond that pays coupons annually is issued with a coupon rate of 4 percent, maturity of 30 years, and a yield to maturity of 8 percent. What rate of return will be earned by an investor who purchases the bond and holds it for 1 year if the bond s yield to maturity at the end of the year is 9 percent?

24. Bond Risk. A bond s credit rating provides a guide to its risk. Long-term bonds rated Aa currently offer yields to maturity of 8.5 percent. A- rated bonds sell at yields of 8.8 percent. If a 10-year bond with a coupon rate of 8 percent is downgraded by Moody s from Aa to A rating, what is the likely effect on the bond price?

25. Real Returns. Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus a coupon payment of $60 at the end of the year. What real rate of return will you earn if the inflation rate is

a. 2 percent

b. 4 percent

c. 6 percent

d. 8 percent