P 4. Two bonds have the following terms:
Bond A Bond B
Principal $1,000 Principal $1,000
Coupon 8% Coupon 7.6%
Maturity 10 years Maturity 10 years
Bond B has an additional feature: It may be redeemed at par after 5 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%, what will be the price of each bond?
b) If interest rates rise to 9%, what will be the decline in the price of each bond from the 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 10 years). If interest rates are 8%, what is the present value of this forgone interest? If the bond had lacked the put feature but had a coupon of 7.6% and a term to maturity of 10 years, it would sell for $973.16 when interest rates were 8%. What, then, is the implied cost of the put option?
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