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A project table can contain perfectly calculated ratios and still support the wrong choice. The missing information may be in the feasible set: whether both proposals can coexist, whether the budget can fund a larger alternative, or whether one proposal depends on another.
State the decision before sorting the table
Write the valuation date, covered cash-flow perspective, rate assumptions and constraints. A ranking of independent proposals is different from a choice between mutually exclusive machines. A budget of whole projects is different from an allocation that permits fractions.
| Can both be selected? | Independence, exclusivity and interactions |
| Can the larger option be funded? | Initial and any later-period budgets |
| Can a fraction be selected? | Indivisibility or divisibility |
| Are the values compatible? | Dates, risk assumptions and cash-flow boundaries |
Separate percentage return from value under a rate
In an original one-period case, A costs 100 and returns 140, while B costs 1,000 and returns 1,200. Their IRRs are 40% and 20%. At a stated common 10% discount rate, A has NPV 27.272727 and B 90.909091.
| A | 40% | 27.272727 |
| B | 20% | 90.909091 |
Under the fictional assumption that both are individually feasible and only one can be chosen, the rate rank and value rank differ. The result does not prove either forecast. It shows why an absolute value question cannot be replaced by a percentage rank.
The scale example keeps that comparison separate from a real project recommendation. A budget that cannot fund B changes the feasible choices before any ranking rule is applied.
Test a whole-project budget as combinations
Now use a different original case: budget 100; independent whole projects A cost 60 with NPV 40, B cost 50 with NPV 32, and C cost 50 with NPV 32. A has the highest NPV-to-cost ratio, but choosing it leaves 40 that cannot fund either other proposal.
B and C together cost 100 and have total entered NPV 64. The greedy ratio choice A has value 40. The arithmetic is not a dispute about whether the ratio was calculated correctly; it is a consequence of indivisibility and the feasible combinations.
| A | 60 | 40 | Yes |
| B + C | 100 | 64 | Yes |
| A + B | 110 | 72 | No |
| Empty set | 0 | 0 | Yes |
The bounded combination calculator checks all subsets of up to twelve independent projects. It does not enforce dependencies, exclusivity groups or future-period budgets. Add those constraints to the actual model rather than treating an exact search of an incomplete feasible set as a complete decision.
Keep the imported amounts defined
Read whether a figure is gross present value, net present value, revenue or contribution. If an NPV already includes an initial cost, subtracting that cost again double counts it. If displaced sales avoid variable costs, their net contribution effect differs from lost gross revenue.
Use the incremental cash-flow bridge and model-review log to retain those definitions. The article Use a small counterexample to check a finance rule explains how to test an overbroad statement before relying on it.
Report a result that another analyst can challenge
A useful conclusion names the objective, assumptions and feasible set: B+C maximizes the sum of entered NPVs in this independent whole-project example. It does not claim the forecasts are certain or every operational condition was modeled. This distinction makes a review more informative than a single highlighted ratio.
Frequently asked questions
Does the highest profitability index always solve a budget?
No. Whole-project combinations, dependencies and timing can defeat a greedy ratio order. Evaluate the feasible set under the actual constraints.
Does higher NPV mean an investment is guaranteed to succeed?
NPV is conditional on the supplied cash flows, rate and model boundary. The calculation does not establish forecast accuracy or all real constraints.
Sources
- CFA Institute: capital investments and allocation · cfainstitute.org · Retrieved
