Question

A $1000 bond with a coupon rate of 6.2% paid semiannually has eight years to maturity and a yield to maturity of 8.3%. If interest rates rise and the yield to maturity increases to 8.6%, what will happen to the price of the bond?

Answer 1

The price of a bond can be found by using PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

Here, the payments are semi-annual.

rate=yield to maturity/2=8.3%/2=4.15%

nper=number of periods=2*8=16

pmt=semi-annual coupon payment=(6.2%*1000)/2=$31

fv=$1000

=PV(4.15%,16,31,1000,0)=$879

PV=price of the bond=$879

If yield to maturity increases, the bond prices will fall. There is an inverse relationship that exists between yield to maturity and bond prices.

Now, the rate becomes=8.6%/2=4.3% and the remaining numbers remain to be the same.

=PV(4.3%,16,31,1000,0)=$863

Now, with an increase in the yield to maturity to 8.6% from 8.3%, the bond price fell to $863 from $879