Profitability Index Calculator
Calculate the Profitability Index (PI) to rank investment projects.
Understand when PI beats NPV for capital rationing decisions, with worked examples.
Profitability Index Formula
The Profitability Index (PI), also called the Benefit-Cost Ratio, measures the value created per dollar of capital invested. It is the Net Present Value (NPV) to investment ratio, normalized so that 1.0 is break-even.
Formula:
PI = (NPV + Initial Investment) ÷ Initial Investment
Or equivalently:
PI = 1 + (NPV ÷ Initial Investment)
The PI is simply the present value of future cash flows divided by the initial investment.
Decision Rules
| PI Value | Decision |
|---|---|
| PI > 1.0 | Accept, project creates value |
| PI = 1.0 | Break-even, neutral (accept if no better use of capital) |
| PI < 1.0 | Reject, project destroys value |
Calculating NPV from Cash Flows
If you don’t have NPV ready, calculate it first:
NPV = Σ [Cash Flow_t ÷ (1 + r)^t] − Initial Investment
Where:
- r = discount rate (required rate of return / cost of capital)
- t = time period (year 1, 2, 3, …)
- Initial Investment = cash outflow at time zero (negative in NPV)
PI vs NPV vs IRR: When to Use Each
| Method | Best For | Weakness |
|---|---|---|
| Net Present Value (NPV) | Single project, absolute value | Cannot rank different-sized projects |
| Internal Rate of Return (IRR) | Return percentage comparison | Can mislead with multiple cash flow signs |
| Profitability Index (PI) | Capital rationing, ranking many projects by value per dollar | Ignores absolute size of value created |
When PI Is Superior to NPV
Imagine you have $1,000,000 to invest and three choices:
| Project | Investment | NPV | PI |
|---|---|---|---|
| Project A | $1,000,000 | $240,000 | 1.24 |
| Project B | $500,000 | $175,000 | 1.35 |
| Project C | $500,000 | $160,000 | 1.32 |
NPV alone points at Project A, the biggest single number on the page. But the same budget buys B and C together, and that pair generates $335,000 of value against A’s $240,000. PI spots this because it measures value per dollar, and on that measure A is the weakest of the three.
That is capital rationing: the constraint is the budget, not the merit of any one project.
One caution. Ranking by PI and filling the budget from the top is a greedy rule, not a guaranteed optimum. It works cleanly here because B and C happen to consume the budget exactly. When the projects do not divide neatly you can be left holding cash that earns nothing, and a slightly worse-ranked combination that spends it all may win.
Worked Example
A company is evaluating a marketing initiative:
- Initial Investment: $150,000
- Discount Rate: 10%
- Expected Cash Flows: $55,000/year for 4 years
Step 1: Calculate NPV:
Year 1: $55,000 ÷ 1.10 = $50,000 Year 2: $55,000 ÷ 1.21 = $45,455 Year 3: $55,000 ÷ 1.331 = $41,323 Year 4: $55,000 ÷ 1.464 = $37,566 Total PV = $174,344 NPV = $174,344 − $150,000 = $24,344
Step 2: Calculate PI:
PI = ($24,344 + $150,000) ÷ $150,000 = 1.162
Interpretation: The project generates $1.162 in present value for every $1 invested. Approve.
Pro Tips
- PI is most useful when capital budgets are constrained: it helps maximize value per dollar deployed.
- For a single isolated project decision, NPV and PI always give the same accept/reject signal.
- PI ignores the absolute dollar size of value created: a large project with PI = 1.05 may be better than a tiny one with PI = 1.50 if you have the capital.
- Always pair PI with a sensitivity analysis on the discount rate: if the rate changes by 2%, does the project still clear PI > 1?
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