NETPV Function

Returns the net present value as a percent.

Category:

Financial

Syntax

NETPV(r,freq,c0,c1,...,cn)

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:

\begin{matrix} N E T P V (r, f r e q, c_{0}, c_{1}, . . ., c_{n}) = Σ_{i = 0}^{n} c_{i} x^{i} \end{matrix}

The following relationship applies to the preceding equation:

\begin{matrix} x = {\begin{matrix} \frac{1}{{(1 + r)}^{(1 / f r e q)}} & f r e q > 0 \\ ε^{- r} & f r e q = 0 \end{matrix} \end{matrix}

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.