Project Management guide · Cost and resources
Net Present Value (NPV) for Projects: Formula and Example
Net present value (NPV) is the total value, in today's money, of all a project's future cash inflows and outflows. Future cash flows are discounted at a chosen rate; if the result is positive, the project is expected to create more value than it costs.
Key takeaways
- NPV discounts future cash flows to today's money.
- Discount factor = 1 / (1 + r)^t.
- Accept projects with positive NPV; prefer the higher NPV between alternatives.
- Always test sensitivity to the discount rate and cash flow estimates.
The formula
NPV = sum of [cash flow in year t / (1 + r)^t] - initial investment
- r is the discount rate per period, such as 8% (0.08).
- t is the period number, starting at 1 for the end of year one.
- The discount factor for year t is 1 / (1 + r)^t.
Worked example
A project costs $100,000 today and returns $40,000 at the end of each of the next three years. The discount rate is 8%.
| Year | Cash flow | Discount factor at 8% | Present value |
|---|---|---|---|
| 0 | -$100,000 | 1.00000 | -$100,000.00 |
| 1 | $40,000 | 1 / 1.08 = 0.92593 | $37,037.04 |
| 2 | $40,000 | 1 / 1.1664 = 0.85734 | $34,293.55 |
| 3 | $40,000 | 1 / 1.259712 = 0.79383 | $31,753.29 |
| NPV | $3,083.88 |
Undiscounted, the project returns $120,000 for $100,000, a gain of $20,000. Once the time value of money is included, the gain is about $3,084. At a 10% discount rate the NPV falls to about -$526, so the decision depends on the rate.
Decision rules
| NPV | Decision |
|---|---|
| Positive | Accept: the project earns more than the required return |
| Zero | Break even at the required return |
| Negative | Reject on financial grounds, unless there are strong non-financial reasons |
When comparing mutually exclusive projects, prefer the one with the higher NPV, assuming similar risk.
NPV and IRR
The internal rate of return (IRR) is the discount rate at which NPV equals zero. In the example the IRR is about 9.7%: above an 8% required return (so NPV is positive) but below 10% (so NPV is negative). Use IRR alongside NPV, but rely on NPV when the two disagree on mutually exclusive choices.
How to calculate NPV step by step
- List the cash flows for each period, including the initial investment.
- Agree the discount rate with finance.
- Calculate the discount factor for each period: 1 / (1 + r)^t.
- Multiply each cash flow by its factor.
- Add the present values together.
- Check the result's sensitivity to the rate and the cash flows; see sensitivity analysis.
Common mistakes
- Discounting the year-zero investment.
- Using profit instead of cash flow.
- Ignoring running costs or end-of-life costs.
- Using an inconsistent period (monthly cash flows with an annual rate).
- Note that the Excel NPV function assumes the first value is at the end of period one, so add year-zero outflows separately.
Free templates for this topic
Frequently asked questions
What is net present value?
The sum of a project's future cash flows discounted to today's value, minus the initial investment.
What does a positive NPV mean?
The project is expected to earn more than the required rate of return, so it adds value.
What does a negative NPV mean?
The project's returns, in today's money, do not cover its costs at the chosen discount rate.
How do you calculate a discount factor for NPV?
Discount factor = 1 / (1 + r)^t. At 8% for year two it is 1 / 1.1664 = 0.85734.
What discount rate should be used for NPV?
Usually a rate set by finance, often based on the cost of capital or a required return, sometimes adjusted for risk.
What is the difference between NPV and IRR?
NPV is a money value at a given rate. IRR is the rate at which NPV is zero.
What is the difference between NPV and ROI?
NPV accounts for the timing of cash flows; simple ROI does not. See return on investment.
How do you calculate NPV in Excel?
Use =NPV(rate, cash flows for years 1 to n) and then add the year-zero cash flow, which is usually negative.
Is NPV used in project selection?
Yes, it is one of the most common financial measures in business cases and portfolio decisions.
Why is future money worth less in net present value?
Because money today can be invested to earn a return, and because of inflation and risk.
Is NPV on the PMP exam?
Project selection methods such as NPV, IRR and payback are commonly covered in PMP preparation materials at a conceptual level.