PV function

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.

• For more information about the different types of errors that you may encounter when using IronCalc functions, visit our Error Types page.

Details

• If $\text{type}\ne 0$, $\text{pv}$ is given by the equation:

$$\text{pv}=-({\displaystyle \frac{(\text{fv}\times \text{rate})+(\text{pmt}\times (1+\text{rate})\times ((1+\text{rate}{)}^{\text{nper}}-1))}{\text{rate}\times (1+\text{rate}{)}^{\text{nper}}}})$$

• If $\text{type}=0$, $\text{pv}$ is given by the equation:

$$\text{pv}=-({\displaystyle \frac{(\text{fv}\times \text{rate})+(\text{pmt}\times ((1+\text{rate}{)}^{\text{nper}}-1))}{\text{rate}\times (1+\text{rate}{)}^{\text{nper}}}})$$

• 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.

Links

• For more information about the concept of "present value" in finance, visit Wikipedia's Present value page.
• See also IronCalc's FV, NPER, PMT and RATE functions.
• Visit Microsoft Excel's PV function page.
• Both Google Sheets and LibreOffice Calc provide versions of the PV function.