Question

6. Consider two different bonds, A and B. They both have a maturity of one year, and pay at maturity par value ($1,000) and a coupon. The two bonds have the same price of $900. Bond A has an annual YTM of 30% and bond B has an annual YTM of 15%. What is the coupon rate for the two bonds?

is there a way to do this question on a financial calculator? if not, please show how to do it by hand. thanks!

Answer 1

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =1

900 =∑ [(Coupon rate*1000/100)/(1 + 30/100)^k]     +   1000/(1 + 30/100)^1

k=1

Coupon rate% = 17

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-900

I/Y =30

N =1

FV =1000

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)/par value

=PMT(30/(100),1,-900,1000,)/1000

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =1

900 =∑ [(Coupon rate*1000/100)/(1 + 15/100)^k]     +   1000/(1 + 15/100)^1

k=1

Coupon rate% = 3.5

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-900

I/Y =15

N =1

FV =1000

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)/par value

=PMT(15/(100),1,-900,1000,)/1000