Payback Period Calculator
The discounted payback period (DPP) estimates how long it takes for the present value of cash inflows to equal the initial investment, expressed in years. Unlike the simple payback, DPP accounts for the time value of money by discounting future cash flows.
This tool computes DPP for projects with uniform periodic after-tax cash inflows. It also returns the undiscounted payback period for quick comparison and includes guards for edge cases (zero cash flow, zero discount rate, or impossible recovery).
Governance
Record f27945aff3cc • Reviewed by Fidamen Standards Committee
Inputs
Results
Discounted payback period (years)
4.03
Undiscounted payback period (years)
3.3333
Percent of initial investment recovered by undiscounted payback (%)
—
| Output | Value | Unit |
|---|---|---|
| Discounted payback period (years) | 4.03 | years |
| Undiscounted payback period (years) | 3.3333 | years |
| Percent of initial investment recovered by undiscounted payback (%) | — | % |
Visualization
Methodology
We assume evenly spaced, uniform cash inflows (same amount each period). For this case the cumulative present value of cash inflows up to time t is CF * (1 - (1+ r)^-t) / r where CF is the periodic cash inflow and r is the decimal discount rate per period.
To find the discounted payback time t (possibly fractional), we invert the cumulative present value formula to solve for t: t = -ln(1 - (Initial * r / CF)) / ln(1 + r). The calculator falls back to the undiscounted payback when the discount rate is zero, and returns Infinity when recovery is not possible under the provided inputs.
Worked examples
Example 1: Initial = 10,000, CF = 3,000 per year, r = 8% (0.08). Undiscounted payback = 3.333 years. Discounted payback calculated using the formula above is approximately 3.7 years.
Example 2: If CF = 0 the tool reports payback as not achievable. If r = 0 the discounted payback equals the undiscounted payback.
F.A.Q.
When should I use discounted payback instead of undiscounted payback?
Use discounted payback when the timing of cash flows matters and when you want to account for the time value of money. Undiscounted payback ignores discounting and can understate true payback time for remote cash flows.
Can I use this calculator for irregular or uneven cash flows?
This particular calculator assumes uniform periodic cash flows. For irregular series, use a dedicated irregular-cash-flow tool that discounts each period individually and computes cumulative discounted cash flows.
What does an Infinity result mean?
Infinity indicates that, under the given parameters, the present value of future cash inflows will never equal the initial investment (for example, cash flow is zero or too small relative to the investment and discount rate).
How should I interpret fractional years?
Fractional years indicate a partial period required for recovery. They are calculated by solving the discounted cumulative cash flow equation and represent the continuous-time equivalent under the uniform cash flow assumption.
Sources & citations
- NIST — Numerical Standards and Good Practices — https://www.nist.gov
- ISO — Quality Management Principles (relevant to model validation) — https://www.iso.org
- IEEE — Standards and Best Practices for Numerical Computing — https://standards.ieee.org
- OSHA — Guidance on Financial Decision Safety and Process Controls — https://www.osha.gov
- SEC — Non-GAAP Financial Measures Guidance — https://www.sec.gov/corpfin/non-gaap-financial-measures
- FASB — Financial Accounting Standards Board — https://www.fasb.org/
- CFA Institute — Global Investment Performance Standards (GIPS) — https://rpc.cfainstitute.org/gips-standards
Further resources
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: f27945aff3ccWhat changed (latest)
v1.0.0 • 2025-11-17 • 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 • 2025-11-17 • 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 17, 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 • 2025-11-17 • 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: e9e44e444080