Question

. 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 15 years. The bond’s yield to maturity is 9.584% at time of sale, and falls to 9.200% immediately after the purchase but before the first coupon is received. All coupons are reinvested to maturity at the new yield to maturity. Does the investor realize a capital gain or loss on the sale, and by what amount (expressed as % of PAR)?

Answer #1

Total coupon payments: =10.5%*100/2*2*15=157.50

Sale price of the bond after 15 years:

I/Y=9.2%/2

N=15*2

PMT=-10.5%*100/2

FV=-100

CPT PV=110.46

Reinvestment income from coupons:

N=2*15

I/Y=9.2%/2

PMT=-10.5%*100/2

PV=0

CPT FV=325.77

Reinvestment income=325.77-157.50=168.27

Total value at 15 years: =110.46+168.27+157.50=436.23

Realized rate of return (horizon yield) at maturity:

N=15

FV=436.23

PMT=0

PV=-104.079

CPT I/Y=10.0247%

capital gain=110.46-104.079=6.38

So there exists capital gain of 6.38%

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