Definition
Net present value (NPV) is defined as the total present value (PV) of a time series of cash flows. It is a standard method for using the time value of money to appraise long-term projects.
Formula
Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms Rt/(1+i)t where:
t – the time of the cash flow
i – the discount rate (the rate of return that could be earned on an investment with similar risk.)
Rt – the net cash flow (the amount of cash, inflow minus outflow) at time t
What NPV Means
NPV is a decision model that measures how much value an investment or project creates for the firm’s owners above the opportunity cost contained in the discount rate. With a particular project, if Rt is a positive value, the project is in the status of discounted cash inflow in the time of t. If Rt is a negative value, the project is in the status of discounted cash outflow in the time of t. Projects with a positive NPV should be accepted. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. The following sums up the NPVs in various situations.
| If… | It means… | Then… |
| NPV > 0 | the investment would add value for the owners | the project may be accepted |
| NPV < 0 | the investment would subtract value from the owners | the project should be rejected |
| NPV = 0 | the investment would neither gain nor lose value for the owners | We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value above the opportunity cost of funds used to invest. Decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation. |
Harry White, PhD
Professor of Finance, Boise State University
June 2009