Payback Period Calculator
This calculator computes how long it takes for an investment to be recovered from net cash inflows. Use the simple method when inflows are approximately equal each period, or use the discounted method to account for the time value of money.
The discounted closed-form formula included here provides a fractional-year estimate for projects with uniform annual inflows. For uneven cash flows, use a period-by-period cumulative approach (spreadsheet recommended) or the project-level cash-flow tools linked in the citations.
Governance
Record 44236a1cdcae • Reviewed by Fidamen Standards Committee
Assumes identical annual net cash inflows. Returns the number of years required for cumulative nominal inflows to equal the initial investment.
Inputs
Results
Payback Period (years)
3.3333
| Output | Value | Unit |
|---|---|---|
| Payback Period (years) | 3.3333 | years |
Visualization
Methodology
Simple payback is calculated as Initial Investment divided by Annual Net Cash Inflow. It measures nominal years to recover the investment but ignores timing within the year and the time value of money.
Discounted payback applies the present value of an annuity formula and solves for the number of years n that satisfies the inequality PV(annuity up to n) equal o bigger than the Initial Investment. For constant annual inflow C and discount rate r, the closed-form solution used here is n = -ln(1 - r * I / C) / ln(1 + r), where I is the initial investment. This requires r bigger than 0 and r * I / C smaller than 1; when those conditions fail, discounted payback is undefined or indicates the project will not recover value under the given assumptions.
This tool assumes: (1) 'annual net cash inflow' is the net cash benefit available to repay the initial investment (after operating costs and taxes as applicable), (2) inflows occur once per period (year), and (3) for the discounted method inflows are identical each year. For uneven cash flows, perform a cumulative discounted sum by year and interpolate the fractional year when cumulative PV crosses the initial investment.
F.A.Q.
What if annual cash inflow is zero or negative?
If annual net cash inflow is zero or negative, simple payback is undefined (division by zero or negative recovery). For such cases the project does not recover its investment under the assumed steady inflow. Consider scenario analysis, operational changes, or a cash-flow table to inspect year-by-year outcomes.
How should I interpret fractional years in the result?
Fractional results indicate partial years required to recover the investment under the model's assumptions. For simple payback, fractional years are a linear interpolation within the year. For discounted payback, the closed-form solution yields a fractional year consistent with the continuous logarithmic solution for annuity recovery.
Can I use this for uneven cash flows or one-off receipts?
This calculator's methods assume equal annual inflows. For uneven cash flows, build a year-by-year table (or use a spreadsheet) to compute cumulative (nominal or discounted) cash flows by period and find the period where cumulative inflows meet the initial investment, interpolating within the year if needed. The citations include references and project-finance guidance for period-by-period evaluation.
What are the limits and numerical caveats of the discounted formula?
The closed-form discounted solution requires that discount rate is bigger than 0 and that discountrate x initial investment / annual cash inflow is less than 1. If discount rate is zero, discounted payback reduces to simple payback. If the condition fails, the annuity at the given discount rate never reaches the investment amount (project does not pay back under those assumptions). Always verify inputs and run sensitivity checks for discount rate and inflow size.
How do I adapt this to SaaS CAC payback or contribution-margin payback?
Treat 'Initial investment' as customer acquisition cost (CAC) and 'Annual net cash inflow' as per-customer contribution margin (revenue minus variable costs) on the same time basis. Ensure both values are comparable (monthly vs annual) and convert units before calculation.
Where can I learn more about present value and annuity formulas?
Authoritative educational materials on time value of money and project evaluation are available from university open-course materials and government energy and finance guidance linked in the citations. These resources explain derivations, assumptions, and recommended practices for capital budgeting.
Sources & citations
- MIT OpenCourseWare — Financial Management and Time Value of Money resources — https://ocw.mit.edu
- U.S. Department of Energy — Project finance and economic analysis guidance — https://www.energy.gov
- U.S. Securities and Exchange Commission — Investor education on financial statements and project evaluation — https://www.investor.gov
- National Institute of Standards and Technology (NIST) — https://www.nist.gov
- FASB — Financial Accounting Standards Board (GAAP) — https://www.fasb.org/
- SEC — Financial Reporting Manual — https://www.sec.gov/corpfin/cf-manual
- AICPA — American Institute of CPAs — https://www.aicpa-cima.com/
Further resources
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: 44236a1cdcaeWhat changed (latest)
v1.0.0 • 2025-11-15 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
What changed (latest)
v1.0.0 • 2025-11-15 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Engine
v1.0.0
Data
Baseline (no external datasets)
Content
v1.0.0
UI
v1.0.0
Governance
Last updated: Nov 15, 2025
Reviewed by: Fidamen Standards Committee (Review board)
Credentials: Internal QA
Risk level: low
Reviewer profile (entity)
Fidamen Standards Committee
Review board
Internal QA
Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person
Semantic versioning
- MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
- MINOR: New features or fields that do not change existing outputs for the same inputs.
- PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.
Review protocol
- Verify formulas and unit definitions against primary standards or datasets.
- Run golden-case regression suite and edge-case suite.
- Record reviewer sign-off with credentials and scope.
- Document assumptions, limitations, and jurisdiction applicability.
Assumptions & limitations
- Uses exact unit definitions from the Fidamen conversion library.
- Internal calculations use double precision; display rounding follows the unit's configured decimal places.
- Not a substitute for calibrated instruments in regulated contexts.
- Jurisdiction-specific rules may require official guidance.
Change log
v1.0.0 • 2025-11-15 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: 149b05bc9b52