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, ...)
Rate is the rate of discount over the length of one period.
Value1, value2, ... are 1 to 29 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 numbers, empty cells, logical values, or text representations of numbers are counted; arguments that are 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 1
The example may be easier to understand if you copy it to a blank spreadsheet.
How?- Create a blank spreadsheet.
- Select the example in the Help topic.
Selecting an example from Help
- Press CTRL+C.
- In the spreadsheet, select cell A1, and press CTRL+V.
- To switch between viewing the formula that returns the result and the result in the cell, select the cell and press F2 and then ENTER, or click Commands and Options on the spreadsheet toolbar, click the Formula tab, and look in the Formula in active cell (active cell) box.
| Data | Description |
|---|---|
| 10% | Annual discount rate |
| -10,000 | Initial cost of investment one year from today |
| 3,000 | Return from first year |
| 4,200 | Return from second year |
| 6,800 | Return from third year |
| Formula | Description (Result) |
| =NPV(A2, A3, A4, A5, A6) | Net present value of this investment (1,188.44) |
In the preceding example, you include the initial $10,000 cost as one of the values, because the payment occurs at the end of the first period.
Example 2
The example may be easier to understand if you copy it to a blank spreadsheet.
- Create a blank spreadsheet.
- Select the example in the Help topic.
Selecting an example from Help
- Press CTRL+C.
- In the spreadsheet, select cell A1, and press CTRL+V.
- To switch between viewing the formula that returns the result and the result in the cell, select the cell and press F2 and then ENTER, or click Commands and Options on the spreadsheet toolbar, click the Formula tab, and look in the Formula in active cell (active cell) box.
| Data | Description |
|---|---|
| 8% | Annual discount rate. This might represent the rate of inflation or the interest rate of a competing investment. |
| -40,000 | Initial cost of investment |
| 8,000 | Return from first year |
| 9,200 | Return from second year |
| 10,000 | Return from third year |
| 12,000 | Return from fourth year |
| 14,500 | 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) |
In the preceding example, you don't include the initial $40,000 cost as one of the values, because the payment occurs at the beginning of the first period.