Question

Suppose a​ ten-year, $1000 bond with an 8.5% coupon rate and semiannual coupons is trading for $1035.32

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)

b. If the​ bond's yield to maturity changes to 9.1% ​APR, what will be the​ bond's price

Answer 1

a. Use RATE function in EXCEL to find the yield to maturity

=RATE(nper,pmt,pv,fv,type)

Please note that the payments are semi-annual

nper=10 years*2=20

pmt=semi-annual coupon=(coupon rate*face value)/2=(8.5%*1000)/2=85/2=42.5

pv=1035.32

fv=1000

=RATE(20,42.5,-1035.32,1000,0)=3.99%

Yield to maturity=2*3.99%=7.98%

b. If yield to maturity changes to 9.1%, then Use PV function in EXCEL to find the price of the bond

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

rate=9.1%/2=4.55%

nper=20

pmt=42.5

fv=1000

=PV(4.55%,20,42.5,1000,0)=$961.14

Price of the bond=$961.14