Question

Suppose that an investor with a 5-year investment horizon is considering purchasing a 7-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 2-year bonds will be selling to offer a yield to maturity of 11.2%. What is the total return for this bond

Answer 1

50.34%

Step-by-step explanation:

initial investment = $1,000 (bond purchased at par value)

annual coupon = $1,000 x 9% = $90

period cash flow

year 0 -$1,000

year 1 $90

year 2 $90 + ($90 x 0.094) = $98.46

year 3 $90 + ($188.46 x 0.094) = $107.71524

year 4 $90 + ($296.17524 x 0.094) = $117.84

year 5 $90 + ($414.02 x 0.094) = $128.92

at the end of year 5, the investor will have $542.94, plus he/she will still own the bond

the price of the bond at year 5 will be:

0.112 = {90 + [(1,000 - MV)/2]} / [(1,000 + MV)/2]

0.112 x [(1,000 + MV)/2] = 90 + [(1,000 - MV)/2]

0.112 x (500 + 0.5MV) = 90 + 500 - 0.5MV

56 + 0.056MV = 590 - 0.5MV

0.556MV = 534

MV = 534 / 0.556 = $960.43

the investor's total return = [($542.94 + $960.43) / $1,000] - 1 = ($1,503.37 / $1,000) - 1 = 0.50337 x 100 = 50.34%