Question

Suppose a​ ten-year, $ 1,000 bond with an 8.1 % coupon rate and semiannual coupons is trading for $ 1, 035.42.

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

b. If the​ bond's yield to maturity changes to 9.6 % ​APR, what will be the​ bond's price? (round to the nearest cent)

Answer 1

Answer : (a.) Calculation's of Bond Yield to maturity :

Calculation of Yield to maturity :

Using Financial Calculator

=RATE(nper,pmt,pv,fv)

where nper is Number of years to maturity i.e 10 * 2 = 20 (As coupons are paid semiannually)

pmt is Interest payment i.e 1000 * 8.1% = 81 / 2 = 40.5 (Divided by 2 As coupons are paid semiannually)

pv is Current Market Price

= 1035.42

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(20,40.5,-1035.42,1000)

therefore ,Yield to maturity is 3.7941%(Semiannual)

Yield to maturity is 3.7941% * 2 = 7.59% (Annual)

(b.)  If the​ bond's yield to maturity changes to 9.6 % ​APR, calculation of​ bond's price:

or the purpose of calculaion of Yield to call we need to first estimate current market price

Using Financial Calculator

=PV(rate,nper,pmt,fv)

rate is the yield to maturity i.e 9.6%/2 = 4.8% (as coupons are paid semiannually)

where nper is Number of years to maturity i.e 10 * 2 = 20 (As coupons are paid semiannually)

pmt is Interest payment i.e 1000 * 8.1% = 81 / 2 = 40.5 (Divided by 2 As coupons are paid semiannually)

fv is face value

= - 1000

=PV(4.8%,20,-40.5,-1000)

therefore , Bond Price is $904.93