Question

A 3-year $1000 face value bond pays an annual coupon of 2% and has a ytm of 3%. What is this bond's price? What is this bond's duration? Answer this question the long way, e.g., calculate the bond price as the present value of future cash flows. Use the related expression for duration from the lectures. Do not use the complex formulas for bond price and duration from the textbook or the TVM function on your calculator. You must show your work – the numbers in the formulas – to receive full credit.

Answer 1

Bond price

K = N

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

k=1

K =3

Bond Price =∑ [(2*1000/100)/(1 + 3/100)^k]     +   1000/(1 + 3/100)^3

k=1 = 20/(1+0.03)^1+20/(1+0.03)^2+(1000+20)/(1+0.03)^3

Bond Price = 971.71

Bond duration= = 1/971.71*(20*1/(1+0.03)^1+20*2/(1+0.03)^2+(1000+20)*3/(1+0.03)^3) =2.9406