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Write the two synthetic schedules
| Project | CF0 | CF1 | CF2 |
|---|---|---|---|
| A | −100,000 | 60,000 | 60,000 |
| B | −100,000 | 10,000 | 120,000 |
Solve the two quadratic checks
Let a = 1 + r. A satisfies a² − 0.6a − 0.6 = 0, giving IRR 13.066239%. B satisfies a² − 0.1a − 1.2 = 0, giving IRR 14.658561%.
Compare correctly computed values
At 10%, A has NPV 4,132.231405 and B 8,264.46281. B also has the higher correctly calculated IRR. These schedules therefore do not demonstrate a conflict between the two rankings.
Use a substitution check as a quality control
A reported rate of 12.7% for B is not its root. Recalculate the NPV at a reported rate before relying on a narrative about timing or ranking. This exercise is an arithmetic audit, not an investment recommendation.