Question

Suppose that an investor with a 10-year investment horizon is considering purchasing a 20-year 8% coupon bond selling for $900. The par value of the bond is $1000. The original YTM on the bond is 10%, but the investor expects that he can reinvest the coupon payments at an annual interest rate of 7% and that at the end of the investment horizon this 10-year bond will be selling to offer a yield of 9%. What is the total return for this bond

Answer 1

Answer:

8.67%

Explanation:

PMT (Semi-annual coupon) = par value*coupon rate/2 = 1,000*8%/2 = 40

N (No of coupons paid) = 10*2 = 20

Rate (Semi-annual reinvestment rate) = 7%/2 = 3.5%

Future value of reinvested coupons = FV(PMT, N, Rate)

Future value of reinvested coupons = FV(40, 20, 3.5%)

Future value of reinvested coupons = $1,131.19

FV = 1,000

PMT (Semi-annual coupons) = 40

N (No of coupons pending) = 10*2 = 20

Rate (Semi-annual YTM) = 9%/2 = 4.5%

Price of the bond after 10 years = PV(FV, PMT, N, RATE)

Price of the bond after 10 years = PV(1000, 40, 20, 4.5%)

Price of the bond after 10 years = $934.96

Total amount after 10 years = Future value of reinvested coupons + Price of the bond after 10 years

Total amount after 10 years = $1,131.19 + $934.96

Total amount after 10 years = $2,066.15

Amount invested (Price of the bond now) = $900.

Total Annual Return = [(Total amount after 10 years / Amount invested)^(1/holding period)] -1

Total Annual Return = [($2,066.15/$900)^(1/10)] -1

Total Annual Return = [2.295722^0.1] - 1

Total Annual Return = 1.08665561792 - 1

Total Annual Return = 0.08665561792

Total Annual Return = 8.67%