Question

Bond X is noncallable and has 20 years to maturity, a 7% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 9.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

$

Answer 1

Price of bond at end of 5 years =

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =15

Bond Price =∑ [(7*1000/100)/(1 + 9.5/100)^k]     +   1000/(1 + 9.5/100)^15

k=1

Bond Price = 804.3

Price to be paid today=

K = N

Bond Price =∑ [(Annual Coupon)/(1 + required rate)^k]     +   price at year 5/(1 + required rate)^N

k=1

K =5

Bond Price =∑ [(7*804.3/100)/(1 + 12/100)^k]     +   804.3/(1 + 12/100)^5

k=1

Bond Price = 659.33