Question

A corporate pension plan has to make the following payments over the next few years:

Year	1	2	3	4
Amount ($ million)	16	20	26	34

The appropriate interest rate is 6%.

1. What is the present value of the liability (in $ million)?

2. What is the duration of the liability?

Answer 1

(1)-Present value of the liability

Year	Annual Payments ($ in Millions)	Present Value Factor at 6%	Present Value
1	16	0.94340	15.09
2	20	0.89000	17.80
3	26	0.83962	21.84
4	34	0.79209	26.93
	TOTAL		$81.66

“The Present value of the liability will be $81.66 Million”

(2)-Duration of the liability

Year (1)	Annual Payments ($ in Millions) (2)	Present Value Factor at 6% (3)	Present Value (4) = (3) x (2)	Weight (5)	Duration (6) = (1) x (5)
1	16	0.94340	15.09	0.18485	0.18
2	20	0.89000	17.80	0.21799	0.44
3	26	0.83962	21.83	0.26734	0.80
4	34	0.79209	26.93	0.32981	1.32
	TOTAL		81.66	1.0000	2.74

“The Duration of the liability will be 2.74 Years”

NOTE

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.