Question

Suppose you purchase a ten-year bond with 6% annual coupons.  You hold the bond for four years and sell it immediately after receiving the fourth coupon.  If the bond's yield to maturity was 5% when you purchased and sold the bond.

a.  What cash flows will you pay and receive from your investment in the bond per $100 face value?

We need to calculate how much we are willing to pay for the bonds by using the formula

Answer 1

a.Bond Price=Present Value of Future Cash flows

Present Value of Coupon Payments:

Uniform Series Present Worth Factor(USFWF)=(P/A,i,N)=(((1+i)^N)-1)/(i*((1+i)^N))

i=Yield to maturity=5%=0.05

N=Number of Years=10

Uniform Series Present Worth Factor(USFWF)=(P/A,5%,10)=(((1+0.05)^10)-1)/(0.05*((1+0.05)^10))=7.721735

Annual Coupon Payment =100*6%=$6

Present Value of Coupon Payments=6*7.721735=$46.33

Present Value of Maturity Payment

Payment at maturity =$100

Present Value of Maturity Payment=100/((1+i)^N)=100/(1.05^10)=$61.39

Cash flow paid at the time of purchase=46.33+61.39=$107.72

Amount receive from investment after 4 years

N=Number of years of future cash flows (to maturity)=10-4=6

Uniform Series Present Worth Factor(USFWF)=(P/A,5%,6)=(((1+0.05)^6)-1)/(0.05*((1+0.05)^6))=5.075692

Present Value of Coupon Payments=6*5.075692=$30.45

Present Value of Maturity Payment=100/((1+i)^N)=100/(1.05^6)=$74.62

Cash Flow received from investment after 4 years=30.45+74.62=$105.07