Profitability index calculator

A project that costs $500,000 and whose future cash flows are worth $517,554 today has a profitability index of 1.035: it creates about 3.5 cents of value for every dollar invested. Ranking candidate projects by PI and funding them in that order is a common way to spend a fixed budget, and it can still miss the best combination. With a $1,000,000 budget, ranking three projects by PI and funding the top two creates $460,000 of value; taking the single largest project instead creates $500,000. The higher-PI combination loses to the lower-PI single project because it does not use the whole budget as well.

The calculator computes PI, NPV, IRR and payback from any cash flow schedule, and works through a multi-project ranking under a fixed budget so you can see both what PI recommends and where that recommendation can go wrong.

Who reaches for this

You enter the initial outlay and up to ten years of cash flow after it, plus a discount rate. The calculator discounts each year's cash flow to today, sums them, and divides by the outlay for PI. NPV, IRR, MIRR and payback are computed from the same numbers, so PI is never the only figure you see.

PI is one of five related numbers from a cash flow schedule. The IRR calculator covers the internal rate of return and the multiple-IRR problem, and the payback period calculator covers how long a project takes to recover its cost. All three pages use this same engine.

PI restates NPV as a ratio instead of a dollar figure. A $500,000 outlay with future cash flows worth $517,554 today has NPV = $517,554 − $500,000 = $17,554, and PI = $517,554 ÷ $500,000 = 1.035. The two formulas, present value of future flows over outlay, or 1 plus NPV over outlay, always agree.

A PI of 1 means the project exactly breaks even in present-value terms: it earns precisely the discount rate and adds nothing beyond it. Above 1, it adds value; below 1, it destroys it. A PI of 1.035 is a real number to report, not a rounding artifact: it says the project returns about 3.5% more, in today's dollars, than it costs.

PI and the reinvestment question

A ratio measure like PI implicitly assumes that whatever capital is not spent on one project is available for something else earning the discount rate, which is the same rate used to value the project itself. That assumption is much milder than IRR's assumption that leftover cash reinvests at the project's own rate of return, which is one reason PI and NPV tend to agree with each other far more often than IRR agrees with either. When PI and NPV point to different projects, as in the capital rationing case below, it is worth asking whether the budget itself is the binding constraint or whether it could reasonably be stretched, since the two measures are built for genuinely different situations.

NPV and PI can rank projects differently for the same reason IRR and NPV can: PI is a ratio and does not see the size of the project, while NPV is a dollar amount and does.

Project S creates 24.6 cents of value per dollar invested, well ahead of Project L's 6.8 cents. Project L still creates almost three times the total dollars. If capital is not the binding constraint and both projects are available, take both; if only one can be funded and there is enough budget for either, NPV says take L for the larger total value it creates. PI becomes the more useful number specifically when the budget cannot fund every attractive project and choices must be made between them.

When several independent projects compete for a limited pool of capital, called capital rationing, the common rule is to rank by profitability index and fund projects in that order until the budget is used up. It generally gets more total value from the budget than ranking by NPV, because NPV alone tends to favor large projects that can consume the whole budget on one investment.

Take four projects competing for a budget. Project S costs $50,000 with a PI of 1.246, Project L costs $500,000 with a PI of 1.068, Project F costs $1,200,000 with a PI of 1.011, and Project E costs $800,000 with a PI of 0.979, below 1 and so rejected outright regardless of budget. Ranked by PI: S, then L, then F.

With a $900,000 budget, taking S and L uses $550,000 and creates $46,085 of NPV; the remaining $350,000 does not fit Project F ($1,200,000) and would only go to Project E, whose PI is below 1 and should be rejected on its own merits. In this case PI ranking finds the best available combination, since nothing better fits the leftover budget.

PI ranking is a heuristic, not a guarantee, because projects are usually lumpy: they must be taken whole, and a budget rarely divides evenly among the highest-ranked ones. A textbook case shows exactly how it can go wrong.

With a $1,000,000 budget, ranking by PI takes Project B first, since its 1.70 is the highest, using $600,000 and creating $420,000. The remaining $400,000 exactly fits Project C, adding $40,000. The PI-ranked combination creates $460,000 in total, and uses the whole budget.

Project A alone, with a lower PI of 1.50, uses the same $1,000,000 budget and creates $500,000, $40,000 more than the PI-ranked combination. Project B's high PI is real, but taking it forces the budget's remaining dollars into Project C, a much weaker use of capital. A had a lower ratio and a better overall fit for the budget.

The lesson is not that PI ranking is wrong, but that it is a starting point. With a small number of candidate projects, it is worth checking a handful of alternative combinations against the budget by hand, particularly when a high-PI project's size does not divide the remaining budget cleanly. With many candidates, this becomes a proper capital-budgeting optimization problem, and PI ranking remains a fast, usually-good approximation of its answer.

Checking alternative combinations by hand

With a small number of candidate projects, checking PI ranking against the alternatives takes only a few minutes. List every combination of projects whose total outlay fits the budget, add up each combination's NPV, and compare the best one against what PI ranking picked. For the three-project example, there are only four combinations to check within a $1,000,000 budget: A alone, B and C together, B alone, and C alone. A alone and B-plus-C both use the full budget, so those two are the real contest, and A alone wins by $40,000.

As the number of candidate projects grows, the number of combinations grows quickly, and checking them by hand stops being practical. Larger capital rationing problems are usually solved with integer programming, which finds the combination of whole projects that maximizes total NPV subject to the budget constraint directly, rather than relying on a ranking heuristic. For a handful of projects, though, a short list of combinations checked by hand is often enough to catch a case like the one above before it becomes an expensive mistake.

Divisible vs. indivisible projects

PI ranking works perfectly when projects can be split into any size, for example buying a fractional share of a project or scaling an investment up or down continuously. Then funding the highest-PI projects first, and a fraction of the next one if the budget runs out partway through it, always maximizes total NPV for a given budget. Real capital projects are almost always indivisible: a company cannot build 62% of a warehouse or acquire 62% of a piece of equipment and expect a proportional 62% of the cash flows.

That indivisibility is exactly why the ranking rule can be led astray by a budget that does not divide evenly among the top-ranked projects. If the same three projects could be scaled to any size, PI ranking would allocate $1,000,000 across them in proportion to their ratios and reach the mathematically best answer. Because they cannot be scaled, the leftover budget after taking a high-PI project is often stranded in a weaker option, or left unused entirely.

Any PI above 1 is a project worth considering, since it means the project is expected to return more than its cost of capital in present-value terms. Beyond that threshold, there is no fixed target: a PI of 1.05 is a marginal project and a PI of 1.50 is a strong one, but which specific number is worth pursuing depends on what else competes for the same capital and how confident the cash flow forecasts are.

A very high PI on a small project and a modest PI on a large one are not directly comparable without knowing the budget and the alternatives, which is the theme of this whole page: PI is most useful as a ranking tool under a real constraint, and least useful as a number to judge on its own.

A useful habit, when a proposal arrives with a PI attached, is to ask two follow-up questions before treating the ratio as decisive: how large is the outlay behind it, and what else is competing for the same money right now. A PI of 1.05 on a project that is the only candidate for an otherwise idle budget is worth taking. The same 1.05 competing against a shortlist that includes several projects above 1.30 is a weak claim on scarce capital, even though the number itself has not changed.

PI in private equity and venture screening

Investors who see far more deals than they can fund use a version of the same logic. A ratio of expected present value to capital committed lets an investor compare a $200,000 check and a $5,000,000 check on the same footing, something a raw dollar return cannot do on its own. PI is not usually the final word in these settings either, since a fund also cares about how much total capital it can deploy and how concentrated its portfolio becomes, but as a first-pass filter across a large deal flow it plays the same role it plays in corporate capital budgeting: sorting a long list down to a shorter one worth a closer look.

PI is one of four related numbers from the same cash flow schedule, each covered in full on its own page.

A quick screen often runs payback first, for a sense of how exposed the capital is, checks NPV and IRR against the cost of capital for the accept-or-reject decision, and reaches for PI only when a budget forces a choice among several positive-NPV projects.

A worked walkthrough of the ranking rule

It helps to see the mechanics laid out step by step. Start with every candidate project's outlay and PI. Discard anything with a PI below 1, since no amount of budget makes a value-destroying project worth taking. Sort what remains from highest PI to lowest. Walk down the sorted list, adding each project's outlay to a running total, and stop taking a project the moment adding it would exceed the budget, moving on to check whether the next one on the list fits instead.

That walk-down is the ranking rule in full, and it is fast enough to redo by hand whenever a new project is proposed or the budget changes. The extra step worth adding, given the failure case above, is a second pass: once the ranking rule has produced its answer, check whether one or two of the largest rejected projects, taken alone or in a different combination, would use the budget better. That second pass is what catches a result like Project A beating the PI-ranked pair of B and C.

Most PI errors come from treating the ranking rule as infallible, or from confusing PI with a simple return percentage.

See the full return a project implies with the IRR calculator, or see how long it takes to recover its cost with the payback period calculator.