A pension consists of a stream of payments to an individual beginning at a designated future date. The present value of such pension payments is based on the number of payments, the amount of each payment, and the risk associated with the receipt of each payment. The underlying premise of the present value calculation is that a dollar held today has a higher value than a dollar received any time in the future.

## Calculating Present Value of a Lump Sum or Changing Payments

The present value calculation should be performed using a spreadsheet, and all assumptions regarding interest rates, payment amounts and time frame should be entered separately into the spreadsheet. The present value of a future payment equals: P / (1 + r)^n, where "P" represents the payment amount, "r" represents the discount rate, and "n" represents the number of time periods until the payment is received. Of these variables, the discount rate is the only one that is subjective. It's best to use the risk-free rate, which is usually the yield on a Treasury bill with a maturity closest to the the number of time periods until the payment is received. Once the present value of each pension payment is calculated, calculate the sum total of the present values, which results in the present value of the pension.

## Present Value of an Annuity

Calculating the present value of a pension for which the payments are all identical, referred to as an annuity, is simpler. First, insert the assumptions regarding payment amount, interest rate and number of years. The present value of an annuity equals: [(P/r) x (1/(1+r)^n)], and should be entered into the spreadsheet this way, linking to cell numbers where applicable. If the pension is paid into perpetuity, the formula is: P/r. So, if the payment amount was entered into cell A:1, and the discount rate was entered into cell A:2, in cell A:3 you would enter "=A:1/A:2". The result is the present value.