1 answer

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

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?


Answers

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

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