NPV function
This article describes the formula syntax and usage of the NPVfunction in Microsoft Excel.
Description
Calculates the net present value of an investment by using a discount rate and a series of future payments (negative values) and income (positive values).
Syntax
NPV(rate,value1,[value2],...)
The NPV function syntax has the following arguments:

Rate Required. The rate of discount over the length of one period.

Value1, value2, ... Value1 is required, subsequent values are optional. 1 to 254 arguments representing the payments and income.

Value1, value2, ... must be equally spaced in time and occur at the end of each period.

NPV uses the order of value1, value2, ... to interpret the order of cash flows. Be sure to enter your payment and income values in the correct sequence.

Arguments that are empty cells, logical values, or text representations of numbers, error values, or text that cannot be translated into numbers are ignored.

If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are ignored.

Remarks

The NPV investment begins one period before the date of the value1 cash flow and ends with the last cash flow in the list. The NPV calculation is based on future cash flows. If your first cash flow occurs at the beginning of the first period, the first value must be added to the NPV result, not included in the values arguments. For more information, see the examples below.

If n is the number of cash flows in the list of values, the formula for NPV is:

NPV is similar to the PV function (present value). The primary difference between PV and NPV is that PV allows cash flows to begin either at the end or at the beginning of the period. Unlike the variable NPV cash flow values, PV cash flows must be constant throughout the investment. For information about annuities and financial functions, see PV.

NPV is also related to the IRR function (internal rate of return). IRR is the rate for which NPV equals zero: NPV(IRR(...), ...) = 0.
Examples
Example 1
Use the embedded workbook shown here to work with examples of this function. You can inspect and change existing formulas, enter your own formulas, and read further information about how the function works.
EWA1
To work indepth with this workbook, you can download it to your computer and open it in Excel. For more information, see the article Download an embedded workbook from OneDrive and open it on your computer.
Example 2
EWA2