economics · cashflow
Payback Period (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 simple and discounted payback period, plus the undiscounted Return on Investment (total return over the full pasted cash-flow sequence, as a fraction of capital invested), for an arbitrary year-by-year sequence of annual cash flows — the array-input counterpart of payback_period, for a genuinely variable or declining cash flow instead of a single level amount. Walks the pasted cash-flow sequence as a running (prefix) sum, since there is no closed-form solution once CF varies by period, and reports the fractional year the cumulative sum first reaches the initial investment. ROI reuses the same full-sequence cumulative sum the simple-payback calculation already accumulates internally, evaluated at its final (full-array) value rather than at the payback crossing point — not a separate formula, and answering a different question (total return, not time to recover capital), the same distinction payback_period's own ROI output draws against its two payback outputs.
Variables
| Symbol | Unit | Description |
|---|---|---|
| t_simple | years | Simple Payback Period |
| t_disc | years | Discounted Payback Period |
| ROI | fraction | Return on Investment (Undiscounted) |
| C0 | $ | Up-front capital cost incurred at time zero. |
| 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. |
| r | fraction | Annual discount rate used only for the discounted payback output; the simple payback output ignores it entirely. |
Assumptions
- Each row's cash flow is received at the end of that year, matching npv_cashflow_variable's timing convention exactly.
- Within the crossing year, that year's cash flow is treated as arriving evenly (linear interpolation) to produce a fractional payback year rather than only a whole-year answer.
- Cash flow is in nominal, pre-tax dollars.
- Payback is measured from time zero (the investment date).
- 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.
- ROI is computed over the full pasted cash-flow sequence, not just to the payback crossing point — it deliberately ignores the time value of money and the timing of cash flow, unlike either payback output.
Limitations
- Payback period ignores all cash flow after the payback point entirely, exactly as in payback_period — use alongside npv_cashflow_variable, not as a substitute.
- Simple payback ignores the time value of money altogether and will understate the true recovery time relative to discounted payback whenever r > 0.
- For a level (uniform) annual cash flow, payback_period's closed-form solution 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.
- ROI ignores timing entirely — two cash-flow sequences with identical total ROI can have very different NPVs if their cash arrives on different schedules; use alongside npv_cashflow_variable/irr_variable, not as a substitute for either.
Use Cases
- → Declining-production liquidity screening: Estimate how quickly a project with a genuinely declining annual cash flow returns its capital outlay, without approximating it as a level annuity.
- → Risk-tolerance check on an irregular cash flow: Compare simple vs. discounted payback for a cash flow stream with a ramp-up period or other year-to-year irregularity that a single level CF can't represent.
- → Type curve economics: Estimate payback 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 evaluate payback here.
- → Total-return sanity check: Get a simple, undiscounted 'cash-on-cash' return figure across the full pasted cash-flow sequence, useful as a quick sense-check alongside the time-value-aware NPV/IRR/PI results, not as a replacement for them.
Related Calculations
Region Notes
General
Payback screening thresholds are company- and risk-tolerance-specific rather than regionally standardized; some operators use payback only as a secondary screen alongside NPV/IRR rather than a primary decision criterion.
References
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