Question

Assume an investor with a 5 year investment horizon is considering purchasing an 8 year semiannual 5% coupon bond that is currently selling at 99. The investor expects to reinvest the coupons at 2% and that the bond will be selling to offer a yield to maturity of 6% in five years. What is the expected total return for this bond? Express your answer on a bond-equivalent basis and on an effective annual rate basis.

Answer 1

Face value = $100 (assumed)

Coupon rate= 5% paid semi annually.

Therefore, semi annual interest= $100*5%/2= $2.50

Maturity value of coupon invested at 2% per year (1% per HY) for 5 years (10 HYs)is the FV of annuity

= $2.50*PVA(1%,10)= $2.5*9.471305 = $23.68

Sale price after 5 years= $97.29 calculated using the PV function of Excel as follows:

Total proceeds after 5 years (F) = FV of interest reinvested + Sale price= $23.68 + $97.29= $120.97

Bond equivalent yield per year= {[(F/P)^(1/10)]-1}*2 = {[($120.97/$99)^(1/10)]-1}*2

={[1.221933 ^(1/10)]-1}*2 = (1.020246 -1)*2 = 4.049130%

Yield on Effective annual rate basis= [(F/P)^(1/5)]-1 =[($120.97/$99)^(1/5)]-1

=1.221933 ^(1/5)]-1 =1.04090119 – 1 = 4.090119%