Question

14. An investor purchases a just issued 30-year, 10.500% semi-annual coupon bond at 104.079 percent of par value and sells it after 10 years. The bond’s yield to maturity is 9.584% at time of sale, and rises to 10.100% immediately after the purchase but before the first coupon is received. All coupons are reinvested to maturity at the new yield to maturity. Show the sources of return below.

Because the yield to maturity changed between bond purchase and sale, the final bond price is not on the constant yield price trajectory curve.   A capital gain or loss is realized on the sale. What is the capital gain or loss for this bond transaction?

Sale price of the bond after 10 years:

Answer 1

Total coupon payments: =10.5%*100/2*2*10=105.00000

Sale price of the bond after 10 years:

I/Y=10.1%/2

N=20*2

PMT=-10.5%*100/2

FV=-100

CPT PV=103.40845

Reinvestment income from coupons:

N=2*10

I/Y=10.1%/2

PMT=-10.5%*100/2

PV=0

CPT FV=174.51643

Reinvestment income=174.51643-105=69.51643

Total value at 10 years: =103.40845+69.51643+105=277.92488

Realized rate of return (horizon yield) at maturity:

N=10

FV=-277.92488

PMT=0

PV=104.079

CPT I/Y=10.32055%

capital gain=103.40845-104.079=-0.67055

SO there exists capital loss of 0.67055