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Keep the cash-flow dates fixed
| Period | Cash flow |
|---|---|
| 0 | -100 |
| 1 | 230 |
| 2 | -132 |
Verify both roots by substitution
At 10%, the equation is −100 + 230/1.1 − 132/1.1² = 0. At 20%, it is −100 + 230/1.2 − 132/1.2² = 0. Numerical evaluation may show tiny floating-point residuals; these do not change the exact algebraic roots.
Read the value between and beyond the roots
The chart holds the schedule fixed and varies the per-interval discount rate. The displayed points are selected rate checks, with their exact calculated values in the accessible table.
Original three-date cash flows evaluated at rates from 0% through 30%; the curve is illustrative and the underlying point values are available. This is an illustrative example.
View the chart values
| Series | Discount rate (%) | NPV |
|---|---|---|
| NPV | 0 | -2 |
| NPV | 5 | -0.68027211 |
| NPV | 10 | -1.4210855E-14 |
| NPV | 15 | 0.18903592 |
| NPV | 20 | 1.4210855E-14 |
| NPV | 25 | -0.48 |
| NPV | 30 | -1.183432 |
Keep a root from becoming a ranking rule
NPV at 15% is approximately 0.189036, while at 0% it is −2. A single root does not summarize this sign pattern. The exercise does not establish a real project’s risk-adjusted discount rate or commercial desirability.