Question

Problem #6:

A 3 year bond has annual coupons of 7.5%, and a face/redemption value of $100. If the bond YTM is 7.75%, find the Macauley duration for the bond.

Answer 1

Macaulay Duration = Time Weighted Present Value of Cash Flows,

Bond Par Value = $100

Coupon Payment = $7.50

Time Period = 3 years

YTM = 7.75%

Calculating Bond Price,

using TVM Calculation,

PV = [FV = 100, PMT = 7.50, N = 3, I = 0.0775]

PV = $99.35

Macaulay Duration = [1(7.50)/(1.0775) + 2(7.50)/(1.0775)² + 3(107.50)/(1.0775)3]/99.35

Macaulay Duration = 2.79 years