Net Present Value (NPV)
$$\text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$$
What is Net Present Value (NPV)?
Net Present Value (NPV) is the sum of all cash flows from an investment - positive (inflows) and negative (outflows) - each discounted back to their present value using a chosen rate. A positive NPV means the investment generates more value in present-dollar terms than it costs, creating wealth. A negative NPV means it destroys value at the given discount rate.
The discount rate used in NPV analysis represents the investor's required return or the company's opportunity cost of capital. This rate reflects the time value of money: a dollar received in the future is worth less than a dollar today because the dollar today could be invested to earn a return. Discounting converts all future cash flows into a common "present-day dollar" basis, making cash flows from different time periods directly comparable.
NPV and IRR are the two dominant discounted cash flow (DCF) methods and are mathematically linked: IRR is the specific discount rate at which NPV equals exactly zero. For a standard project (cash out first, cash in later), NPV is positive whenever the actual discount rate is below the IRR, and negative whenever it exceeds the IRR. NPV is preferred by financial academics because it measures absolute value creation in dollars, not just a percentage rate.
When to use Net Present Value (NPV)
Use NPV when comparing projects with different scales or very different cash flow timing, where IRR can mislead. NPV directly answers "how many dollars of value does this project create today?" and can be added across projects in a portfolio (IRR cannot be averaged). In capital budgeting, always pair NPV with a sensitivity analysis - known as an NPV profile - showing how the result changes as the discount rate varies. If NPV turns negative at only a small rate increase, the project is fragile.
Worked examples
| Project | CF Year 0 | CF Year 1 | CF Year 2 | CF Year 3 | Discount Rate | NPV |
|---|---|---|---|---|---|---|
| Factory expansion | -$500,000 | $150,000 | $200,000 | $250,000 | 10% | +$36,157 |
| Equipment upgrade | -$80,000 | $30,000 | $30,000 | $40,000 | 8% | +$6,427 |
| Marketing campaign | -$50,000 | $70,000 | $0 | $0 | 12% | +$12,500 |
| Rejected project | -$200,000 | $50,000 | $60,000 | $70,000 | 15% | -$30,812 |
Common pitfalls
NPV is only as reliable as its two inputs: the discount rate and the cash flow forecasts. Small changes in the discount rate can flip NPV from positive to negative on long-duration projects. Cash flow forecasts beyond 3-5 years are often highly speculative. Most critically, terminal value - the assumed value at the end of the explicit forecast period - typically accounts for 60-80% of total NPV in DCF models, making it the single most important and most uncertain input. Always stress-test terminal value assumptions separately.
Frequently asked questions
What is the difference between NPV and IRR?
NPV is an absolute dollar figure showing how much value a project creates at a chosen discount rate. IRR is the specific discount rate at which NPV = 0 - a percentage. Both are DCF methods and generally agree on accept/reject decisions. They can diverge when ranking competing projects of different scale or duration: NPV is academically preferred because it measures real dollar value added and is additive across a portfolio.
What discount rate should I use for NPV?
For corporate projects, the standard choice is the company's Weighted Average Cost of Capital (WACC) - the blended required return across debt and equity. For personal investments, use your required return or opportunity cost (e.g., the return you could earn in an index fund at similar risk). For public sector projects, governments often use a social discount rate of 3-8%. The discount rate is the single most debated input in NPV analysis.
Can NPV be negative and the investment still be worthwhile?
At a given discount rate, a negative NPV means the investment earns less than required and should be rejected. However, changing the discount rate can change the sign of NPV. If your actual cost of capital is lower than your initial assumption, the project may actually be positive-NPV. This is why IRR is useful alongside NPV: IRR tells you exactly what return the project earns, which you then compare to your actual cost of capital.