Question

Robert Smith just purchased a 10-year bond for $944. The bond has a coupon rate of 8% and pays coupons semiannually. Robert does not intend to hold the bond until maturity, instead, he plans to sell the bond in exactly 5 years. What is the price Robert can sell the bond for at this time?

Answer 1

Assuming that the market-rate of interest remains same after 5 years.

First we calculate the yield-to-maturity of the bonds when Robert purchased it.

We solve using a financial calculator,

N=20( Since, 10 years remain and hence 20 coupon payments)

FV=$1000

PV= - $944

PMT = $40 ( Since, 8% annual rate for semi-annual coupon payment)

Calculating, I/Y = 4.427% ( This is the semi-annual yield)

Annual yield = 2*4.427% = 8.8556%

Now, we calculate the PV of the bond after 5 years

We solve using a financial calculator,

N=10( Since 5 years remain and hence 10 coupon payments)

FV=$1000

PMT = $40 ( Since, 8% annual rate for semi-annual coupon payment)

I/Y = 4.427%

Calculating,

PV =$966.09

Hence, Robert can sell the bond for $966.09 after 5 years