economics · cashflow
Payback Period (Simple & Discounted)
Simple: t = C0/CF. Discounted: t solves CF×[1-(1+r)^-t]/r = C0 (same equation as npv_cashflow, solved for t)
click formula to derive ↑
Inputs
$
$/yr
fraction
years
Description
Computes both the simple payback period (years to recover the investment, ignoring time value of money) and the discounted payback period (years to recover it in present-value terms) for a level annual cash flow. Both outputs come from the same annuity relationship npv_cashflow and irr use, so all three stay consistent with each other.
Variables
| Symbol | Unit | Description |
|---|---|---|
| t_simple | years | Simple Payback Period |
| t_disc | years | Discounted Payback Period |
| C0 | $ | Up-front capital cost incurred at time zero. |
| CF | $/yr | A single level (uniform) net cash flow received at the end of each year, pre-tax. |
| r | fraction | Annual discount rate used only for the discounted payback output; the simple payback output ignores it entirely. |
| n | years | Project life, used only to flag when a computed payback exceeds it. |
Assumptions
- Cash flow is a single uniform (level) amount received at the end of each year.
- Discounted payback uses the same discrete/annual discounting convention as npv_cashflow and irr.
- Cash flow is in nominal, pre-tax dollars.
- Payback is measured from time zero (the investment date), not from first production or any other reference point.
Limitations
- Payback period ignores all cash flow after the payback point entirely — a project with a fast payback but a short subsequent life can have a lower NPV than one with a slower payback and a long tail; use alongside npv_cashflow, not as a substitute.
- Simple payback specifically ignores the time value of money altogether and will understate the true recovery time relative to discounted payback whenever r > 0.
- Assumes a level cash flow, not a declining production-revenue stream; a genuinely declining stream reaches its (higher, front-loaded) cumulative cash sooner than this level-annuity approximation implies in early years.
Use Cases
- → Liquidity / capital-recovery screening: Estimate how quickly a project returns its capital outlay, independent of its full-life profitability — useful when capital availability, not total value, is the binding constraint.
- → Risk-tolerance check: Compare simple vs. discounted payback to see how much of a project's apparent quick recovery is an artifact of ignoring the time value of money.
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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