# Present Value of a Perpetuity Formula

## Formula and Use

The present value of a perpetuity formula shows the value today of an infinite stream of identical cash flows made at regular intervals over time.

The formula discounts the value of each cash flow back to its value at the start of period 1 (present value).

### Excel Function

The Excel PV function can be used instead of the present value of a perpetuity formula, and has the syntax shown below.

`PV(i, n, pmt, FV, type)`

*The FV and type arguments are not used when using the Excel present value of a perpetuity function.

## Present Value of a Perpetuity Formula Example

If a payment of 4,000 is received each period for ever, and the discount rate is 5%, then the value of the payments today is given by the present value of a perpetuity formula as follows:

```PV = Pmt / i
PV = 4,000 / 5%
PV = 80,000.00
```

The same answer can be obtained using the Excel PV function as follows:

```PV = PV(i, n, pmt)
PV = PV(5%,999,-4000)
PV = 80,000.00```

The Excel formula requires a value for n. Although the value should be infinite, a value of 999 is used as an approximation in the formula.

The present value of perpetuity formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.