Suppose that an investor with a five-year investment horizon is considering purchasing a seven-year 9% coupon bond selling at par. The investor expects that he can reinvest the coupon payments at an annual interest rate of 9.4% and that at the end of the investment horizon two-year bonds will be selling to offer a yield to maturity of 11.2%. What is the total return for this bond?

The total return for this bond is 50.5% over five-year investment horizon.

Explanation:

Assume the face value of the bond is $1,000. As the bond is bought at par, initial investment is equal to face value which is $1,000.

So we have Coupon payment = $1,000 * 9% = $90

+ After five years of holding bond, he is getting 5 coupon payments, given the reinvestment rate is 9.4%, the future value of these 5 coupon payments at the end of investment horizon (which is at the end of year 5) is calculated as:

(90/9.4%) * [ (1+9.4%) ^5 - 1 ] = $543.

+ The price of the two-year remaining bond at the yield to maturity of 11.2%, at the end of the investment horizon, is calculated as: 90/1.112 + 1,090/1.112^2 = $962. (as there is one coupon payment of $90 in one-year time and one coupon payment plus principle repayment of $1,090 in two year time)

=> Total receipt at the end of the investment horizon = The future value of these 5 coupon payments at the end of investment horizon + The price of the two-year remaining bond at the end of the investment horizon = $543 + $962 = $1,505.

=> Total return = Total receipt at the end of the investment horizon / Initial investment = 1,505/1,000 = 50.5%.