Question

16. Suppose that an investor with a five-year investment horizon is considering purchasing a seven-year 7% 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 on this investment? Hint: Draw the cashflows of the 7 year bond. Using Par Value of 100, investors pays 100 and receives 14 coupon payments and Par Value of 100 at the end of 7 years. Part 1: As the investor has hold the bond for 5 years, he will have received 10 coupon payments. With an reinvestment rate of 9.4% (s.a. compounding), what is the coupons plus interest on coupons at the end of 5 years? Part 2: At the end of year 5, what is the remaining life of the bond? With a yield to maturity of 11.2%, what is the value of the bond then? Total return of the investment is basically the sum of values from Part 1 and Part 2.

16. Suppose that an investor with a five-year investment horizon is considering purchasing a seven-year 7% 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 on this investment? Hint: Draw the cashflows of the 7 year bond. Using Par Value of 100, investors pays 100 and receives 14 coupon payments and Par Value of 100 at the end of 7 years. Part 1: As the investor has hold the bond for 5 years, he will have received 10 coupon payments. With an reinvestment rate of 9.4% (s.a. compounding), what is the coupons plus interest on coupons at the end of 5 years? Part 2: At the end of year 5, what is the remaining life of the bond? With a yield to maturity of 11.2%, what is the value of the bond then? Total return of the investment is basically the sum of values from Part 1 and Part 2.

Answer 1

On assuming, we have the face value of the bond is $1,000.

Bond is bought at par, initial investment = face value which is $1,000.

So, Coupon payment = $1,000 * 7% = $70

After five years of holding bond, he is getting 5 coupon payments

Reinvestment rate = 9.4%

The future value of these 5 coupon payments at the end of investment horizon

FV = (70/9.4%) * [ (1+9.4%)^5 -1 ] = $422

The price of the two-year remaining bond at the yield to maturity of 11.2%

At the end of the investment horizon = [(70/1.112) + (1,070/1.112)^2] = $928

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

= $422 + $928 = $1,350

Total return = Total receipt at the end of the investment horizon / Initial investment

= [(1,350/1,000)-1]*100

= 13.5%