In more detail
The formula is NPV = Σ CFₜ / (1 + r)^t, with the outlay as a negative cash flow at t = 0. The discount rate r is the return you could earn elsewhere at similar risk (the opportunity cost of capital), so money today is worth more than money later. A positive NPV means the project beats that alternative by that amount in today's money; a negative NPV means it falls short. NPV falls as the discount rate rises, and the rate at which it reaches zero is the IRR.
Why it matters
NPV answers "how much richer does this make me?" in money, which makes it the standard test for investments with costs now and benefits later. The result is very sensitive to the chosen rate and to optimistic cash-flow forecasts.
Example
Paying $1,000 now for $450 a year over three years, discounted at 10%:
−1,000 + 409.09 + 371.90 + 338.09 = $119.08
| Discount rate | NPV |
|---|---|
| 0% | $350.00 |
| 5% | $225.46 |
| 10% | $119.08 |
| 20% | −$52.08 |
At 10% it is worth doing; if your alternative earns 20%, it is not.
Common confusion
NPV is an amount of money at a chosen rate; IRR is a rate. Prefer NPV when the two disagree.