Question

A 2-year $1000 face value bond pays an annual coupon of 6% and has a ytm of 4%. 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. You must show your work – the numbers in the formulas – to receive full credit. The answers themselves are only worth 3 points total.

Answer 1

Calculation of bond price :-

Bond price for a 2-year bond = Coupon1/(1+ YTM) + Coupon 2/(1+YTM)^2 + Face value/(1+YTM)^2

Coupon amount = $1000*6% = $60

YTM = 4%

Face value = $1000

Bond price = 60/1.04 + 60/(1.04)^2 + 1000/ (1.04)^2 = 57.69+55.47+924.56 = $1,037.72

Calculation of duration

Duration for a 2 year bond = [(Time left in maturity * Coupon 1)/(1+YTM) + (Time left in maturity* Coupon 2)/(1+YTM)^2 + (Number of coupon payments * Par value)/ (1+YTM)^2] / Price of bond

Duration = [(2*$60)/1.04 + (1*$60)/(1.04)^2 + (2*1000)/(1.04)^2] / 1037.72 = ($115.38 + $55.47 + 1849.12) / 1037.72

Duration = 1.947 years