Question

Q1.  Suppose a​ ten-year,  bond with a face value of $1000 an coupon rate 8.4% p.a. and semiannual coupons is trading for 1034.59

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 remember the payments are semi-annual

nper=2*10=20 periods

pmt=semi-annual coupon rate=(coupon rate*face value)/2=(8.4%*1000)/2=84/2=42

pv=1034.59

fv=face value=1000

=RATE(20,42,-1034.59,1000,0)=3.95%

Yield to Maturity=2*3.95%=7.89%

b. if yield to maturity is 9.1%, to find the price of the bond, use PV function in EXCEL

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

rate=9.1%/2=4.55%

nper=20

pmt=42

fv=1000

=PV(4.55%,20,42,1000,0)=$954.67

The price of the bond=$954.67