Question

Bond X is noncallable and has 20 years to maturity, a 11% 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 9%. 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: Investor is willing to pay $1182.57 today

a) Calculation of Price Of Bond after 5 Years

Key Data

FV of the Bond = $1000

Coupon Rate = 11%

Coupon Amount= $1000* 11%= $110

Period(n) = 15 years

Redemption Amount = $1000 (assumed redeemed at par)

Discount Rate (r) =YTM = 9%

Solution

Price of bond is the present value of all future cashflow discounted at YTM

Price (P)= Coupon Amount*PVAF(r,n)+ Redemption Amount*PVIF(r,n)

= $110*PVAF(9%,15) + $1000*PVIF(9%,15)

= $886.68 + $ 274.53

= $ 1161.21(Approx)

B) Amount that investor will be ready to pay today for the bond will be

PV of all future cash flow i.e. Present Value of 1162.1 and interest amount of 110

Key Data

FV of the Bond = $1000

Coupon Rate = 11%

Coupon Amount= $1000* 11%= $110

Period(n) = 5 years

Redemption Amount = $1161.21 (price of the bond after 5 years)

Discount Rate (r) =YTM = 9%

Solution

Price (P)= Coupon Amount*PVAF(r,n)+ Redemption Amount*PVIF(r,n)

= $110*PVAF(9%,5) + $1161.21*PVIF(9%,5)

= $427.86 + $ 754.71

= $ 1182.57 (Approx).