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Define both ratios under stated conditions
I_0 > 0 is the only initial outlay, and NPV = PV_future − I_0 under this simple convention.
| Ratio | Value | Zero-NPV threshold |
|---|---|---|
| Gross receipt-PV ratio | 1.2 | 1 |
| Net NPV-to-outlay ratio | 0.2 | 0 |
Identify what remains the same
Subtracting one preserves rankings when both conventions use the same project definitions and positive initial outlays. It changes the numerical threshold, so an unlabelled comparison with one or zero can produce a mistaken statement.
Do not extend the identity to every financing schedule
Additional outlays, different dates or a different denominator require a defined convention. A label such as profitability index is insufficient to reconstruct the equation if those details are absent.
Keep a ratio from replacing feasible-set analysis
Even a correctly computed ratio does not automatically solve an indivisible capital budget. Evaluate actual feasible combinations and dependencies. The counterexample below uses a fixed net-ratio convention and still defeats a greedy ranking.