# NETPV Function

Returns the net present value as a percent.

 Category: Financial

## Syntax

### Required Arguments

#### r

is numeric, the interest rate over a specified base period of time expressed as a fraction.

 Range r >= 0

#### freq

is numeric, the number of payments during the base period of time that is specified with the rate r.

 Range freq > 0 Note The case freq = 0 is a flag to allow continuous discounting.

#### c0,c1,...,cn

are numeric cash flows that represent cash outlays (payments) or cash inflows (income) occurring at times 0, 1, ...n. These cash flows are assumed to be equally spaced, beginning-of-period values. Negative values represent payments, positive values represent income, and values of 0 represent no cash flow at a given time. The c0 argument and the c1 argument are required.

## Details

The NETPV function returns the net present value at time 0 for the set of cash payments c0,c1, ...,cn, with a rate r over a specified base period of time. The argument freq>0 describes the number of payments that occur over the specified base period of time.
The net present value is given by the equation:
$equation$
The following relationship applies to the preceding equation:
$equation$
Missing values in the payments are treated as 0 values. When freq>0, the rate r is the effective rate over the specified base period. To compute with a quarterly rate (the base period is three months) of 4 percent with monthly cash payments, set freq to 3 and set r to .04.
If freq is 0, continuous discounting is assumed. The base period is the time interval between two consecutive payments, and the rate r is a nominal rate.
To compute with a nominal annual interest rate of 11 percent discounted continuously with monthly payments, set freq to 0 and set r to .11/12.

## Example

For an initial investment of \$500 that returns biannual payments of \$200, \$300, and \$400 over the succeeding 6 years and an annual discount rate of 10 percent, the net present value of the investment can be expressed as follows:
`   value=netpv(.10,.5,-500,200,300,400);`
The value returned is 95.98.