economics · cashflow
Internal Rate of Return (Variable Cash Flow)
click formula to derive ↑
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.
Description
Computes the internal rate of return for an arbitrary year-by-year sequence of annual cash flows — the array-input counterpart of irr, for a genuinely variable or declining cash flow instead of a single level amount. Bisects over the same arrayNPV equation npv_cashflow_variable uses, 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. |
| CFₜ | — | One row per year, in order starting at year 1: that year's own net cash flow, pre-tax. Paste at least 2 years, ideally a conventional pattern (an initial outflow at C0 followed by positive cash flows) so a single IRR exists — see limitations. |
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 (current, non-escalated), pre-tax dollars.
- The cash flow pattern has a single sign change (an initial outflow followed by cash inflows), so exactly one IRR exists.
- For a type-curve well, the cash-flow array's revenue rows are typically built outside this calculator from a decline-curve rate forecast (decline_hyperbolic/decline_harmonic) converted to volume × price, less operating cost; use economic_limit_rate to decide the last year worth including.
Limitations
- For a cash flow with multiple sign changes (e.g. a mid-life workover cost that turns a later year negative), IRR can have multiple roots or none — this tool assumes the conventional single-root case and does not detect or enumerate multiple-IRR situations.
- IRR ignores the scale of the investment and the absolute size of the cash flow stream — use alongside npv_cashflow_variable, not instead of it.
- No income, severance, or ad valorem tax deduction is applied; a post-tax IRR would generally be lower.
Use Cases
- → Declining-production hurdle-rate comparison: Compare a project with a genuinely declining or otherwise irregular cash flow against the company's minimum acceptable rate of return, without approximating it as a level annuity.
- → Cross-check against variable-cash-flow NPV: Confirm that a project's IRR and its NPV at the company hurdle rate (from npv_cashflow_variable) agree on accept/reject for the same year-by-year cash flow sequence.
- → Type curve economics: Evaluate IRR for a decline-curve-forecast well: use decline_hyperbolic/decline_harmonic (Reservoir) to project annual production, price and cost each year's volume by hand into a cash-flow array, then solve for IRR here.
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
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.