economics · cashflow
Internal Rate of Return (IRR)
IRR = r such that -C0 + CF × [1-(1+r)^-n]/r = 0 (same equation as npv_cashflow)
click formula to derive ↑
Inputs
$
$/yr
years
Description
Computes the internal rate of return — the discount rate that makes NPV exactly zero — for a level annual cash flow over a fixed project life. Solves the identical annuity equation npv_cashflow uses, just for the rate instead of the value, so the two are guaranteed to agree.
Variables
| Symbol | Unit | Description |
|---|---|---|
| IRR | fraction | Internal Rate of Return |
| 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, pre-tax. |
| 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 for the full project life.
- Discounting is discrete/annual, matching npv_cashflow's convention exactly.
- Cash flow is in nominal (current, non-escalated), pre-tax dollars.
- The cash flow pattern has a single sign change (one outflow followed by level inflows), so exactly one IRR exists.
Limitations
- For a variable or declining cash flow stream, or one with multiple sign changes, IRR can have multiple roots or none — this tool assumes the conventional single-root case and does not detect multiple-IRR situations.
- IRR ignores the scale of the investment — a small project with a high IRR is not necessarily better than a large project with a lower IRR but higher absolute NPV; use alongside npv_cashflow, not instead of it.
- No income, severance, or ad valorem tax deduction is applied; a post-tax IRR would generally be lower.
Use Cases
- → Hurdle-rate comparison: Compare a project's IRR directly against the company's minimum acceptable rate of return without needing to pick a specific discount rate first.
- → Cross-check against NPV: Confirm that a project's IRR and its NPV at the company hurdle rate agree on accept/reject — a mismatch signals a data-entry or convention error, not a genuine conflict, for a conventional cash flow.
Related Calculations
Region Notes
General
IRR thresholds used as accept/reject screens vary by operator and are typically set well above the discount rate used for NPV to compensate for risks IRR itself doesn't capture (commodity price, execution, geologic uncertainty).
References
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