What the profitability index measures
The profitability index expresses a project's discounted benefits as a multiple of its cost. You discount every future cash flow back to today, add them up, and divide by the money you have to put in at the start. A PI of 1.24 says that each dollar committed buys $1.24 of present value, so 24 cents of that dollar is surplus.
Because the numerator and denominator use the same discount rate and the same currency, the index is dimensionless. That is what makes it a ranking tool. Net present value tells you how big a project's surplus is; the profitability index tells you how efficient that surplus is per unit of scarce capital. A $10 million project with a $1 million NPV and a $1 million project with a $500,000 NPV both pass the accept test, but their indices are 1.10 and 1.50, and if you can only fund one of them with a $1 million budget, the smaller one is plainly the better use of the budget.
The accept-or-reject signal is identical to net present value. Since PI = 1 + NPV/C₀ and C₀ is positive, PI > 1 happens exactly when NPV > 0. Anyone who tells you the two rules can disagree on a single stand-alone project is confusing the accept test with the ranking, where they genuinely can disagree.
The formula, term by term
Start with the numerator. Each future cash flow CFt is multiplied by the discount factor (1 + r)−t, which is the price today of a dollar delivered in year t. At a 10% discount rate that factor is 0.909091 for year 1, 0.826446 for year 2 and 0.751315 for year 3 — each year further out costs the project roughly another 9% of face value. Summing the discounted flows gives the present value of everything the project will produce.
The denominator, C₀, is the cash you commit at time 0. Include the purchase price, freight and installation, any non-recurring launch spend, and the working capital the project ties up. Do not include sunk costs: money already spent is not part of the decision, and putting it in the denominator will make a genuinely attractive project look unattractive.
Rearranging gives the identity PI = 1 + NPV/C₀. That single line explains everything about the measure's behaviour. The "1" is the return of your own capital; NPV/C₀ is the surplus expressed as a fraction of it. When NPV is zero the index sits exactly at 1.00 and the project earns precisely the discount rate, no more.
The discount rate you use should be the return required for risk of this kind. For a project that mirrors the firm's existing business, that is the weighted average cost of capital. For a riskier venture, add a premium — using a company-wide WACC on a project riskier than the company is the single most common way an unattractive project gets approved.
Worked example: a $250,000 line upgrade at 10%
A plant manager proposes a $250,000 packaging-line upgrade. After-tax cash flows are forecast at $70,000, $85,000, $95,000, $90,000 and $60,000 over five years, and the firm discounts projects of this risk at 10%.
- Discount year 1. 70,000 ÷ 1.10 = $63,636.36.
- Discount year 2. 85,000 ÷ 1.10² = 85,000 ÷ 1.21 = $70,247.93.
- Discount year 3. 95,000 ÷ 1.331 = $71,374.91.
- Discount year 4. 90,000 ÷ 1.4641 = $61,471.21.
- Discount year 5. 60,000 ÷ 1.61051 = $37,255.28.
- Add them. 63,636.36 + 70,247.93 + 71,374.91 + 61,471.21 + 37,255.28 = $303,985.69.
- Divide by the outlay. 303,985.69 ÷ 250,000 = PI = 1.2159.
- Cross-check with NPV. 303,985.69 − 250,000 = $53,985.69, and 1 + 53,985.69 ÷ 250,000 = 1.2159. The two routes agree, as the identity requires.
Read the answer as: every dollar of the $250,000 buys about $1.22 of present value, so the project produces roughly 21.6 cents of surplus per dollar committed. Those are the defaults in the calculator above, so you can change one input at a time and watch the index move.
How to read the number
PI > 1.00 — accept on a stand-alone basis. The project earns more than the discount rate. There is no universal "good" threshold above that, because the index already has the hurdle rate baked into it; a PI of 1.05 at a correctly-set 12% discount rate is a genuinely value-creating project, just a thin one.
PI = 1.00 — indifference. The project earns exactly the discount rate and NPV is zero. The discount rate at which this happens is the internal rate of return, which is why PI, NPV and IRR all cross their accept thresholds at the same rate for a conventional project.
PI < 1.00 — reject. The discounted inflows are worth less than the outlay.
Under capital rationing, rank projects by descending PI and take them from the top until the budget is exhausted. That greedy rule maximises total NPV when the projects are divisible or when they happen to fit the budget exactly. When they are lumpy and indivisible it can leave money on the table. Take an $800,000 budget and three projects: $600,000 at PI 1.30, $400,000 at PI 1.25, and $400,000 at PI 1.24. Starting with the highest index uses $600,000 and strands $200,000, for a surplus of 0.30 × 600,000 = $180,000. Skipping it and taking the two $400,000 projects uses the whole budget for 0.25 × 400,000 + 0.24 × 400,000 = $196,000. Check the top few feasible combinations by total NPV before signing.
One thin margin worth naming: a PI of 1.02 on a five-year project is inside the error bar of almost any cash-flow forecast. Treat anything under about 1.05 as a project whose approval rests on the forecast rather than on the arithmetic, and run the numbers again with pessimistic cash flows before committing.
Profitability index for a level five-year cash flow
| Annual cash flow | 6% | 8% | 10% | 12% | 15% |
|---|---|---|---|---|---|
| $20,000 | 0.842 | 0.799 | 0.758 | 0.721 | 0.670 |
| $24,000 | 1.011 | 0.958 | 0.910 | 0.865 | 0.805 |
| $26,000 | 1.095 | 1.038 | 0.986 | 0.937 | 0.872 |
| $28,000 | 1.179 | 1.118 | 1.061 | 1.009 | 0.939 |
| $30,000 | 1.264 | 1.198 | 1.137 | 1.081 | 1.006 |
| $35,000 | 1.474 | 1.397 | 1.327 | 1.262 | 1.173 |
The five-year annuity factors used are 4.212364 at 6%, 3.992710 at 8%, 3.790787 at 10%, 3.604776 at 12% and 3.352155 at 15%. Multiply the factor by the annual cash flow and divide by the outlay to reproduce any cell.
Mistakes that corrupt a profitability index
- Putting sunk costs in the denominator. Feasibility studies already paid for are gone. Only cash that is still avoidable belongs in C₀.
- Mixing pre-tax cash flows with an after-tax discount rate. The WACC is an after-tax rate, so the cash flows must be after tax too, or the index is inflated.
- Ranking mutually exclusive projects by PI. When you can only do one of two projects and there is no budget constraint, take the higher NPV. PI's scale-blindness is a feature only when capital is the binding constraint.
- Treating later outflows two different ways. A negative cash flow in year 3 can be discounted into the numerator (net-benefit convention, which this calculator uses) or added to the denominator (gross-benefit convention). Both are defensible; the resulting indices differ, so pick one and apply it to every project you are comparing.
- Ignoring project length. A one-year project with PI 1.15 and a ten-year project with PI 1.15 are not equally attractive if you can recycle the capital. Compare with equivalent annual value when lives differ materially.
- Double-counting working capital. If you put the working-capital injection in C₀, the release of it must show up in the final year's cash flow.
Where PI sits among the capital-budgeting rules
PI is one of four discounted rules you will see on the same approval memo. NPV is the theoretically correct measure of value added and should decide any unconstrained choice. IRR gives a rate that is easy to compare against a hurdle but misbehaves when a project has more than one sign change in its cash flows; the modified IRR repairs that by making the reinvestment assumption explicit. Discounted payback answers a liquidity question rather than a value question and ignores everything after the payback date.
PI earns its place only in one situation: capital rationing. When the budget is fixed, ranking by value per dollar of budget is exactly the right greedy heuristic, and it is the reason government benefit-cost analysis has used the same ratio for decades under the name benefit-cost ratio. Outside rationing, use NPV.
The index is only as good as the discount rate you feed it. Build that rate properly from the cost of equity and the after-tax cost of debt rather than reaching for a round number, and re-check the resulting project economics against the firm's actual return on invested capital: a portfolio of projects with indices near 1.00 will pull ROIC toward the cost of capital over time.
Key terms
- Capital rationing
- A fixed ceiling on total investment spending that is lower than the cost of all the projects clearing the hurdle rate. It can be imposed externally by lenders or internally by management.
- Discount factor
- (1 + r)−t, the present value today of one dollar delivered at the end of year t.
- Benefit-cost ratio
- The same ratio under its public-sector name, where discounted benefits are divided by discounted costs.