Two bonds have the following terms Bond A Bond B Principal 1

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?

Solution

a.
principal: 362.45 interest 910.79 total 1,273.24

c. the implied trade-off is that Bond B offers less interest, but if interest rates were to rise, its prices declines less. Bond B is safer.
d. The present value of the $4 foregone annually for ten years when the interest rate is 8 percent is $4(6.710)-$26.34
The value of the bond is reduced by this to $973.15