Question

Suppose a​ five-year, $1,000 bond with annual coupons has a price of $901.82 and a yield to maturity of 6.4%. What is the​ bond's coupon​ rate?

Answer 1

Given information

Face value of bond =$ 1000

Market price = $ 901.82

Yield to maturity(YTM) = 6.4%

Term of bond = 5 years

Yield to maturity means Value of discount rate for which intrinsic Value of the Bond equals its Market Price.

Hence Market price will be consider as Value of bond.

Value of bond = I (Present value of annuity at 6.4% for 5 years ) + F ( present value factor at 6.4% at 5th year)

where

I = annual interest payable on bond

F = Principal amount(par value) of the bond repayable at the time of maturity

V = Value of bond

Market price =I (PVAF 6.4% For 5 years) +F( PVF 6.4% At 5th year)

901.82 = I (4.1669) + 1000(0.7333)

901.82 = I (4.1699) + 733.31

I ( 4.1699) = 901.82-733.31

I ( 4.1699) = 168.503

Interest = 168.503/4.1699

= 40.44

Note : Interest is calculated by applying the coupon rate on face value of bond

Coupon rate = Interest / face value of bond *100

= 40.44/1000*100

= 4.04%

Finanl answer :

Bond Coupon rate = 4.04%