NPV function
This article describes the formula syntax and usage of the NPV function 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.
Example
Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.
Data 
Description 

0.1 
Annual discount rate 

10000 
Initial cost of investment one year from today 

3000 
Return from first year 

4200 
Return from second year 

6800 
Return from third year 

Formula 
Description 
Result 
=NPV(A2, A3, A4, A5, A6) 
Net present value of this investment 
$1,188.44 
Example 2
Data 
Description 

0.08 
Annual discount rate. This might represent the rate of inflation or the interest rate of a competing investment. 

40000 
Initial cost of investment 

8000 
Return from first year 

9200 
Return from second year 

10000 
Return from third year 

12000 
Return from fourth year 

14500 
Return from fifth year 

Formula 
Description 
Result 
=NPV(A2, A4:A8)+A3 
Net present value of this investment 
$1,922.06 
=NPV(A2, A4:A8, 9000)+A3 
Net present value of this investment, with a loss in the sixth year of 9000 
($3,749.47) 