Question

Bond X is noncallable and has 20 years to maturity, a 9% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; 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 10.5%. 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

Answer :

Value of bond at the end of year 5 = Coupon * [ 1 - ( 1 + Yield rate )^(-Years remaining) ] / Yield rate + Face value of bond / ( 1 + Yield rate )^( Years remaining )

Coupon will be 9% of 1000 = $90

Yield rate = 10.5%

Years remaining = 15 years

Value of bond at the end of year 5 = 90 * [ 1 - 1.105^(-15) ] /.105 + 1000 / (1.105)^15

= 665.44 + 223.65

= $ 889.09

Value of bond today = 90* [ 1 - 1.09^(-5) ] /.09 + 889.09 / 1.09^5

= 350.07 + 577.85

= $927.92