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A pension plan is obligated to make disbursements of $1 million, 2 million and 1 million...

A pension plan is obligated to make disbursements of $1 million, 2 million and 1 million every six months during the next 1.5 years. What is the duration if the market interest rate is 10%?

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Answer #1

Given about a pension plan

disbursements of $1 million, 2 million and 1 million every six months during the next 1.5 years

Cash flow in 0.5 year = $1 million

Cash flow in 1 year = $2 million

Cash flow in 1.5 year = $1 million

Market interest rate r = 10%

Duration is calculated as below table:

PV of Cash flow = cash flow/(1 + r/2)^period

Total PV = sum of all PV = $3630277.51

weight = PV of cash flow/Total PV

duration of each Cash flow = year*weight

duration of the pension fund = sum of all duration = 0.99 years

Year Period Cash flow PV of Cash flow=cash flow/(1+r)^period weight = PV of coupon/Total PV Duration = weight*year
0.5 1 $ 10,00,000.00 $    9,52,380.95 0.2623 0.1312
1 2 $ 20,00,000.00 $ 18,14,058.96 0.4997 0.4997
1.5 3 $ 10,00,000.00 $    8,63,837.60 0.2380 0.3569
Total PV $ 36,30,277.51 Duration 0.99
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