Question

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?

Extra information:

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?

Answer 1

Semi annual coupon = par value x annual coupon / 2 = 100 x 7% / 2 = 3.50

Cash flow timeline for a 7 year bond:

Year	Period	Cash flow
0.50	1	3.50
1.00	2	3.50
1.50	3	3.50
2.00	4	3.50
2.50	5	3.50
3.00	6	3.50
3.50	7	3.50
4.00	8	3.50
4.50	9	3.50
5.00	10	3.50
5.50	11	3.50
6.00	12	3.50
6.50	13	3.50
7.00	14	103.50

Part (1)

the coupons plus interest on coupons at the end of 5 years = FV (Rate, Nper, PMT, PV) = FV (9.4%/2, 2 x 5, 3.50, 0) = 43.41

Part (2)

Remaining life of the bond = 7 - 5 = 2 years = 2 x 2 = 4 semi annual

the value of the bond then = - PV (Rate, Nper, PMT, FV) = - PV (11.2% / 2, 2 x 2, 3.5, 100) = 92.66

Hence, the total return = (total proceeds on maturity / initial investment)^1/n - 1 = [(43.41 + 92.66) / 100]^1/5 - 1

= 6.35%