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 at an annual interest rate of 9.4% and that at the end of the investment horizon 5 year bond will be selling to offer a yield to maturity of 11.2%. What is the total return for this bond?

Answer 1

Answer : Total Return of the Bond is 50.5 %.

Calculation And Explanation:

Face Value of Bond = $ 1,000 ( Assumed )

Coupon Rate = 9 %

Coupon = Face Value * Coupon Rate

= 1,000 * 9 %

= $ 90

The investor expects that he can reinvest the coupon @ 9.4 % after five years of holding bond, investor is getting 5 coupon payments, given the reinvestment rate is 9.4% or 0.094 , we will calculate the future value of annuity

Future Value of annuity = (Equal Coupon Amount / Reinvestment rate ) * [ (1 + Reinvestment rate )n - 1 ]

= (90 / 9.4 %) * [ (1 + 9.4 %)5 - 1 ]

= 957.4468 * [ (1 + 0.094)5 - 1 ]

= 957.4468 * 0.5671

= 542.97 or $ 543

Now we will calculate the price of the bond having remaining two years and yield to maturity @ 11.2 % or 0.112 as

Bond Price = Present value of Coupon for year 1+ Present value of ( coupon + Principal ) at year 2

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

= 90 / (1+ rate)1 + [(90+1000) / ( 1 + rate )2]

   = 90 / (1+0.112)1  + [1090 / (1 + 0.112)2]

= 80.9353 + 881.4891

= $ 962.4244 or $ 962

Now we will calculate Total receipt at the end of investment horizon

Total receipt at the end of the investment horizon = The future value of 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) / Initial investment

= (1,505-1000) / 1,000 = 50.5%.