Question

Assume you have a liability with three required payments: $3,000 due in 1 year; $2,000 due in 2 years; and $1,000 due in 3 years.

(a) What is the Macaulay duration of this liability at a 20% (annually compounded) rate of interest? (b) What about at a 5% (annually compounded) rate of interest?

Answer 1

a) Macaulay duration @ 20% or 0.20 interest rate(i) annually

Years	Cash flow	Present value (P. V) factor (1/(1+i)^n)	Present value (P. V) of cash flow (Cash flow * P. V. Factor)	Weight of P. V. Of cash flow	Duration (Year * Weight of P. V of cash flow)
1	$3,000	(1/(1+0.20)^1) = 0.8333	$2,500	0.56	0.56 (0.56*1)
2	$2,000	(1/(1+0.20)^2) = 0.6944	$1,389	0.31	0.62 (0.31*2)
3	$1,000	(1/(1+0.20)^3) = 0.5787	$578	0.13	0.39 (0.13*3)
		Total	$4,467	1	1.57

Duration = 1.57 years

b) Macaulay duration @ 5% or 0.05 interest rate(i) annually

Years	Cash flow	P. V. Factor (1/(1+i)^n)	P. V. Of cash flow (Cash flow * P. V. Factor)	Weight of P. V. Of cash flow	Duration (years * P. V. Of cash flow)
1	$3,000	(1/(1+0.05)^1) = 0.9524	$2,857	0.51	0.51
2	$2,000	(1/(1+0.05)^2) = 0.9070	$1,814	0.33	0.66
3	$1,000	(1/(1+0.05)^3) = 0.8638	$864	0.16	0.48
		Total	$5,535	1	1.65

Duration = 1.65 years