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PV function

::: warning Note: This draft page is under construction 🚧 :::

Overview

PV (Present Value) is a function of the Financial category that can be used to calculate the present value of a series of future cash flows.

PV can be used to calculate present value over a specified number of compounding periods. A fixed interest rate or yield is assumed over all periods, and a fixed payment or deposit can be applied at the start or end of every period.

Usage

Syntax

PV(rate, nper, pmt, fv=0, type=FALSE) => pv

Argument descriptions

rate (number, required). The fixed percentage interest rate or yield per period.
nper (number, required). "nper" stands for number of periods, in this case the number of compounding periods to be taken into account. While this will often be an integer, non-integer values are accepted and processed.
pmt (number, required). "pmt" stands for payment, in this case the fixed amount paid or deposited each compounding period.
fv (number, optional). "fv" is the future value at the end of the final compounding period (default 0).
type (Boolean, optional). A logical value indicating whether the payment due dates are at the end (FALSE or 0) of the compounding periods or at the beginning (TRUE or any non-zero value). The default is FALSE when omitted.

Additional guidance

Make sure that the rate argument specifies the interest rate or yield applicable to the compounding period, based on the value chosen for nper.
The pmt and fv arguments should be expressed in the same currency unit.
To ensure a worthwhile result, one of the pmt and fv arguments should be non-zero.
The setting of the type argument only affects the calculation for non-zero values of the pmt argument.

Returned value

PV returns a number representing the present value expressed in the same currency unit that was used for the pmt and fv arguments.

Error conditions

In common with many other IronCalc functions, PV propagates errors that are found in any of its arguments.
If too few or too many arguments are supplied, PV returns the #ERROR! error.
If the value of any of the rate, nper, pmt or fv arguments is not (or cannot be converted to) a number, then PV returns the #VALUE! error.
If the value of the type argument is not (or cannot be converted to) a Boolean, then PV again returns the #VALUE! error.
For some combinations of valid argument values, PV may return a #NUM! error or a #DIV/0! error. In paticular, PV always returns a #DIV/0! error if the value of the rate argument is set to -1.

Details

If \text{type} \neq 0, \text{pv} is given by the equation: $$ \text{pv} = - \Biggl(\dfrac{(\text{fv} \times \text{rate}) + \bigl(\text{pmt} \times (1+\text{rate})\times \bigl({(1+\text{rate})^{\text{nper}}-1\bigr)\bigr)}}{\text{rate} \times (1+\text{rate})^{\text{nper}}}\Biggl)



* If $\text{type} = 0$, $\text{pv}$ is given by the equation:
$$ \text{pv} = - \Biggl(\dfrac{(\text{fv} \times \text{rate}) + \bigl(\text{pmt}\times \bigl({(1+\text{rate})^{\text{nper}}-1\bigr)\bigr)}}{\text{rate} \times (1+\text{rate})^\text{{nper}}}\Biggl)

For any \text{type}, in the special case of \text{rate} = 0, \text{pv} is given by the equation:


\text{pv} = -\text{fv} - (\text{pmt} \times \text{nper})

Examples

See some examples in IronCalc.

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