Question

#5. Suppose that we invest in a bond with a 3-year horizon. We consider purchasing a bond with the face value of $1,000, the maturity of 20 years, and the coupon rate of 8%. The bond pays the coupons semi-annually. The price of the bond is $907.99 and the YTM is 9%. We expect that we can reinvest the coupon payments at an annual rate of 6%. At the end of the horizon, the 17-year bond will be selling to offer a YTM of 10%. What is the total return (ROR) of this bond?

Answer 1

First let us find the total coupon payments and the interest on interest
Reinvestment rate=6%/2=3%
n=3*2=6 periods
coupon=face value*(coupon rate/2)
=1000*(8%/2)=40
=Coupon*((1+rate)^n)-1)/rate
=40*((1+3%)^6)-1)/3%
=258.74
the price of bond after 3 years :
Price=(coupon*(1-((1+i)^-n))/i)+(issue price*(1+i)^-n)
Coupon=maturity value*coupon rate
=1000*(8%/2)=40
i=10%/2=5%
n=17*2=34 periods
issue price=1000
price of bond=838.07
total value=258.74+838.07=1096.81
return=((final/initial)^(1/n)]-1
=[(1096.81/907.99)^(1/6)]-1
=3.20%
annual return=3.2%*2=6.40%