economics · cashflow
Profitability Index
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Inputs
$
$/yr
fraction
years
Description
Computes the profitability index for a level annual cash flow — present value of future cash flows per dollar invested — reusing npv_cashflow's own annuityNPV equation directly (PI = (NPV+C0)/C0), so the two never silently disagree. Unlike NPV, which measures absolute value created, PI measures value created per dollar of capital committed — the standard metric for ranking projects under a capital constraint, where the biggest NPV isn't necessarily the best use of limited capital.
Variables
| Symbol | Unit | Description |
|---|---|---|
| PI | — | Profitability Index |
| C0 | $ | Up-front capital cost incurred at time zero, before any cash flow begins. |
| CF | $/yr | A single level (uniform) net cash flow received at the end of each year for the project life — same convention as npv_cashflow. |
| r | fraction | Annual discount rate, applied once per year (discrete, not continuous, compounding) — same convention as npv_cashflow. |
| n | years | Number of years the level annual cash flow is received. |
Assumptions
- Cash flow is a single uniform (level) amount received at the end of each year — same convention as npv_cashflow.
- Discounting is discrete/annual, matching npv_cashflow's convention exactly.
- Cash flow is in nominal, pre-tax dollars.
Limitations
- PI and NPV always agree on accept/reject for a single project, but can disagree on ranking when comparing multiple mutually exclusive projects of different sizes — PI can favor a smaller, higher-ratio project over a larger one with greater absolute NPV; which is 'correct' depends on whether capital is actually constrained.
- No income, severance, or ad valorem tax deduction is applied.
- For a genuinely variable or declining cash flow stream, use profitability_index_variable instead.
Use Cases
- → Capital-constrained project ranking: Rank competing projects by value created per dollar invested when total available capital, not project acceptability alone, is the binding constraint.
- → Cross-check against NPV: Confirm that a project's PI and its NPV at the same discount rate agree on accept/reject — a mismatch signals a data-entry error, not a genuine conflict.
Related Calculations
Region Notes
General
PI-based capital rationing is more common in portfolio/budget-constrained settings (e.g. a fixed annual drilling budget across many candidate projects) than in single-project accept/reject decisions, where NPV alone is typically sufficient.
References
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