economics · cashflow
Profitability Index (Variable Cash Flow)
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Inputs
$
Paste one row per line — separate columns with a comma or tab: Net Cash Flow ($/yr)
⚠ Needs at least 2 valid rows to calculate — 0 so far.
fraction
Description
Computes the profitability index for an arbitrary year-by-year sequence of annual cash flows — the array-input counterpart of profitability_index, reusing npv_cashflow_variable's own arrayNPV equation directly, for a genuinely variable or declining cash flow instead of a single level amount.
Variables
| Symbol | Unit | Description |
|---|---|---|
| PI | — | Profitability Index |
| C0 | $ | Up-front capital cost incurred at time zero, before any cash flow begins. |
| CFₜ | — | One row per year, in order starting at year 1: that year's own net cash flow, pre-tax — same array shape as npv_cashflow_variable. Paste at least 2 years. |
| r | fraction | Annual discount rate, applied once per year (discrete, not continuous, compounding). |
Assumptions
- Each row's cash flow is received at the end of that year, matching npv_cashflow_variable's timing convention exactly.
- Cash flow is in nominal, pre-tax dollars.
- A single constant discount rate applies to every period.
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.
- No income, severance, or ad valorem tax deduction is applied.
- For a level (uniform) annual cash flow, profitability_index is simpler to use and produces an identical result — this tool's value is specifically for a genuinely variable or declining year-by-year stream.
Use Cases
- → Capital-constrained project ranking with a declining cash flow: Rank competing projects with genuinely declining production-revenue streams by value created per dollar invested, without approximating either as a level annuity.
- → Cross-check against variable-cash-flow NPV: Confirm that a project's PI and its NPV (from npv_cashflow_variable) at the same discount rate agree on accept/reject for the same year-by-year cash flow sequence.
Related Calculations
Region Notes
General
PI-based capital rationing is more common in portfolio/budget-constrained settings than in single-project accept/reject decisions, where NPV alone is typically sufficient.
References
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