Question

What is the price of a 5​-year, 8.1 % coupon​ rate, $1000 face value bond that pays interest quarterly if the yield to maturity on similar bonds is 11.5 %​?

Answer 1

Since, the payment is paid quarterly

No. of periods = 5*4 = 20 periods

Quarterly YTM = 11.5%/4 = 2.875%

Face value of the bond = 1000

Annual coupon rate = 8.1%, therefore, quarterly coupon rate = 8.1%/4 = 2.025%

Quartely coupon Payment = 2.025%*1000 = $20.25

Following are the cashflows till 20th period:

C(1) =C(2) =.....=C(19) = 20.25 and C(20)= 1020.25

The formula to calculate the present value of bond is given by below equation:

PV = 872.0675398

We can also use Financial calculator(BA II Plus)

N =20, I/Y = 2.875, PMT = 20.25, FV=1000 CPT --> PV = 872.0675398

Answer -> $872.0675398