Question

A 3-year annual coupon bond has coupons of $12 per year starting one year from now and matures in 3 years for the amount $100. The yield to maturity is 11.8% (annual effective). Find the Macaulay duration of the bond.

Answer 1

Answer: Macaulay Duration = 2.6908154485 = 2.69

Explanation:

Macaulay Duration = Sum of Cash flows Present Value/ current bond price

Cash flows: year 1 = $12

Cash flows: year 2 = 12

Cash flows: year 3 = 100 + 12 = 112

Sum of Cash Flow PV = (1×12÷ (1.118)^1) + (2×12÷ (1.118)^2) +(3×112÷(1.118)^3)

Sum of Cash Flow PV = 270.37857712

Current Bond Price or Value = Face Value/ (1+r)^n + PV of Annuity

Current Bond Price or Value = 1000/ (1.118)^3 + (30×(1 - (1+0.118)^-3)/0.118

Current Bond Price or Value  = 100.48202201

Macaulay Duration = 270.37857712 ÷ 100.48202201

Macaulay Duration = 2.6908154485 = 2.69