Question

Suppose that an investor with a 10-year investment horizon is considering purchasing a 20-year 8% coupon bond selling for $900. The parvalue 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 horizonthis 10-year bondwill be selling to offer a yieldof 9%. What is the total return for this bond?

Step 1: Compute the total coupon payments plus the interest on coupons:

Step 2: Determine the projected sale price at the end of ten years:

Step 3: Adding the amounts in steps 1 and 2 gives total future dollars of how much?

Step 4: Obtain the semiannualtotal return:

Step 5: Obtain the annualtotal return:

Answer 1

Future value (FV) of reinvested coupons at the end of the `10-year holding period: PMT (semi-annual coupon) = par value*coupon rate/2 = 1,000*8%/2 = 40; N (number of coupons paid) = 10*2 = 20; rate (semi-annual reinvestment rate) = 7%/2 = 3.5%, solve for FV.

Future value = 1,131.19

Price of the bond after 10 years: FV (par value) = 1,000; PMT (semi-annual coupons) = 40; N (number of coupons pending after 10 years) = 10*2 = 20; rate (semi-annual YTM) = 9%/2 = 4.5%, solve for PV.

Price of the bond after 10 years = 934.96

Total amount after 10 years = 1,131.19 + 934.96 = 2,066.15

Amount invested = price of the bond now which is 900.

Total annual return = [(total amount after 10 years/amount invested)^(1/holding period)] -1 = [(2,066.15/900)^(1/10)] -1 = 8.67%