Two bonds have the following terms:

Bond A

Principal ...$1,000

Coupon ...8%

Maturity ...10 years

Bond B

Principal ...$1,000

Coupon ...7.6%

Maturity ...10 years

Bond B has an additional feature: It may be redeemed at par after five years (i.e., it has a put feature). Both bonds were initially sold for their face amounts (i.e., $1,000).

a) If interest rates fall to 7 percent, what will be the price of each bond?

b) If interest rates rise to 9 percent, what will be the decline in the price of each bond from its initial price?

c) Given your answers to questions (a) and (b), what is the trade-off implied by the put option in bond B?

d) Bond B requires the investor to forgo $4 a year (i.e., $40 if the bond is in existence for ten years). If interest rates are 8 percent, what is the present value of this forgone interest? If the bond had lacked the put feature but had a coupon of 7.6 percent and a term to maturity of ten years, it would sell for $973.16 when interest rates were 8 percent. What, then, is the implied cost of the put option?