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Fix the cash flows
Use the fictional schedule −1,000 now and +1,200 at time one. Hold those amounts and dates fixed while changing only the per-interval discount rate. This isolates a mathematical rate effect, not a full change in project risk.
Compare selected rates
| Rate | NPV |
|---|---|
| 5% | 142.857143 |
| 10% | 90.909091 |
| 15% | 43.478261 |
Explain the denominator
The future receipt is divided by 1 + r. For these nonnegative future amounts, reducing r raises their present value and therefore raises NPV. Using a rate too low would overstate value under this fixed schedule, not understate it.
Do not assume every schedule is monotonic
A later negative cleanup amount changes the profile and can alter the direction over some ranges. The earlier two-IRR example illustrates a different sign pattern. Inspect the actual future flows before extending this simple direction rule.