Question

Suppose a​ ten-year,

$1,000

bond with an

8.2 %

coupon rate and semiannual coupons is trading for

$ 1,034.56.

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

9.3 %

​APR, what will be the​ bond's price?

Answer 1

Answer :

(a.) Calculation of Bond Yield to maturity :

Using Excel Function of Rate

=RATE(nper,pmt,pv,fv)

where nper is Number of years i.e 10 * 2 = 20 (As semi annual coupon payment)

pmt is Interest payment i.e 1000 * 8.2% =82/2 = 41 (As semi annual coupon payment)

pv is Current Market Price

= - 1034.56

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(20,41,-1034.56,1000)

therefore ,Yield to maturity is 3.849088% (Semiannual)

Yield to maturity is 3.849088% * 2 = 7.698176% or 7.70% (Annual)

(b.) Calculation of Price of Bond :

Price of Bond can be calculated using PV function of Excel :

=PV(rate,nper,pmt,fv)

where rate = yield to maturity i.e 9.3% / 2 = 4.65% (As semi annual coupon payment)

nper is Number of years i.e 10 * 2 = 20 (As semi annual coupon payment)

pmt is Interest payment i.e 1000 * 8.2% =82/2 = 41 (As semi annual coupon payment)

fv is the face value i.e 1000

=PV(4.65%,20,-41,-1000)

Price of Bond is $929.38