How do you compute the simple payback period with equal cash flows?

Use: simple payback (in periods) = initial investment ÷ cash flow per period. For example, if the outlay is 10,000 and each month returns 3,000, simple payback = 10,000 ÷ 3,000 = 3.33 months. Convert to years by dividing periods by 12 for monthly, 4 for quarterly, or using periods ÷ periods-per-year.

How do you compute the discounted payback period?

First convert the annual discount rate i to a per-period rate r using r = (1 + i)^(1/m) − 1, where m is the number of periods per year (12 monthly, 4 quarterly, 1 yearly). Then discount each period’s inflow CF_t to present value PV_t = CF_t ÷ (1 + r)^t, accumulate PV_t until the running total equals or exceeds the initial investment. The discounted payback is the first period where cumulative PV ≥ initial investment, with interpolation if it happens between periods.

How do you interpolate when break-even falls between two periods?

Let B be the unrecovered balance just before the break-even period k, and let PV_k be the discounted cash flow in period k. Fraction of period to recover = B ÷ PV_k. Discounted payback (in periods) = (k − 1) + B ÷ PV_k. The same linear interpolation applies to simple payback using nominal flows.

What if payback is not reached within the analysis horizon?

The calculator reports “Remaining Before Last Period” as the unrecovered balance at the end of the horizon (nominal for simple payback; present value for discounted payback) and indicates that payback is not achieved. “Recovered at Payback” is the cumulative amount recovered right at the break-even point (equal to the initial investment by construction).

How are rates, units, and rounding handled?

Cash flows are treated in the user’s currency (use ISO 4217 codes where relevant), time is in periods consistent with the selected periodicity, and annual rates are converted to effective per-period rates using r = (1 + i)^(1/m) − 1. Totals and periods are rounded to two decimals using round-half-even (banker’s rounding). Results in years are periods ÷ m with the same rounding. If cash flows are irregular, the same logic applies using the provided sequence instead of a fixed amount.

Payback Period Calculator - Simple & Discounted

Payback Period Calculator

Estimate how long it takes to recover an initial investment from incoming cash flows. Supports simple and discounted payback with fixed or irregular cash flows.

Initial Investment

Cash Flow Mode

Use when cash inflows are the same every period (e.g., monthly).

Periodicity

Cash Flow per Period

Analysis Horizon (periods)

Cash Flows (by period)

Discount Rate (annual)

Results

Simple Payback (periods)
Simple Payback (years) years
Discounted Payback (periods)
Discounted Payback (years) years
Recovered at Payback $
Remaining Before Last Period $

Estimate how quickly an investment is recovered using either:

Simple Payback (no discounting)
Discounted Payback (accounts for time value of money)

Works with fixed each period or irregular by period cash flows. Choose periodicity (monthly, quarterly, yearly) and an analysis horizon to cap the timeline.

How it works

1) Simple Payback

Equal cash flows:
Payback (in periods) = Initial investment ÷ Cash flow per period
Uneven cash flows:
Add cumulative cash flow each period until it ≥ initial investment.
Fraction in recovery period = Remaining amount ÷ Cash flow in recovery period

2) Discounted Payback

Convert annual discount rate to per-period rate:
r_period = r_annual ÷ periods_per_year
Discount each cash flow: PV_t = CF_t ÷ (1 + r_period)^t
Sum discounted cash flows until they offset the initial outlay.
Fraction in recovery period = Remaining ÷ Discounted CF in recovery period

Example

Initial investment: 10,000
Periodicity: Monthly
Cash flow per month: 3,000
Annual discount rate: 10%

Results:

Simple payback: 10,000 ÷ 3,000 ≈ 3.33 months (≈ 0.28 years)
Discounted payback: using 10% ÷ 12 per month → cumulative PV crosses 10,000 between months 3 and 4; fraction ≈ 1,147.6 ÷ 2,902.1 ≈ 0.40 → 3.39 months (≈ 0.28 years)

How to Use the

Frequently Asked Questions

Use: simple payback (in periods) = initial investment ÷ cash flow per period. For example, if the outlay is 10,000 and each month returns 3,000, simple payback = 10,000 ÷ 3,000 = 3.33 months. Convert to years by dividing periods by 12 for monthly, 4 for quarterly, or using periods ÷ periods-per-year.
First convert the annual discount rate i to a per-period rate r using r = (1 + i)^(1/m) − 1, where m is the number of periods per year (12 monthly, 4 quarterly, 1 yearly). Then discount each period’s inflow CF_t to present value PV_t = CF_t ÷ (1 + r)^t, accumulate PV_t until the running total equals or exceeds the initial investment. The discounted payback is the first period where cumulative PV ≥ initial investment, with interpolation if it happens between periods.
Let B be the unrecovered balance just before the break-even period k, and let PV_k be the discounted cash flow in period k. Fraction of period to recover = B ÷ PV_k. Discounted payback (in periods) = (k − 1) + B ÷ PV_k. The same linear interpolation applies to simple payback using nominal flows.
The calculator reports “Remaining Before Last Period” as the unrecovered balance at the end of the horizon (nominal for simple payback; present value for discounted payback) and indicates that payback is not achieved. “Recovered at Payback” is the cumulative amount recovered right at the break-even point (equal to the initial investment by construction).
Cash flows are treated in the user’s currency (use ISO 4217 codes where relevant), time is in periods consistent with the selected periodicity, and annual rates are converted to effective per-period rates using r = (1 + i)^(1/m) − 1. Totals and periods are rounded to two decimals using round-half-even (banker’s rounding). Results in years are periods ÷ m with the same rounding. If cash flows are irregular, the same logic applies using the provided sequence instead of a fixed amount.

Methodology & Sources

The calculator computes simple payback by dividing the initial outlay by the uniform periodic inflow, or by accumulating nominal flows for irregular series until break-even. Discounted payback follows discounted cash-flow practice: convert the stated annual discount rate i to an effective per-period rate r with r = (1 + i)^(1/m) − 1; discount each inflow CF_t to PV_t = CF_t ÷ (1 + r)^t; sum cumulatively until meeting the initial investment.

If break-even occurs within a period, linear interpolation uses unrecovered balance divided by the current period’s (discounted or nominal) inflow to compute the fractional period. If the analysis horizon ends before recovery, the remaining unrecovered balance is reported.

Currency handling follows ISO 4217 notation; time units are consistent with the chosen periodicity. Numerical outputs are rounded to two decimals using round-half-even to reduce bias. These procedures align with government and standards-body guidance that treats payback (simple and discounted) as supplementary measures within life-cycle cost analysis.

Bibliography

Joshua D. Kneifel, David Webb (2022). LIFE CYCLE COSTING MANUAL for the Federal Energy Management Program — National Institute of Standards and Technology https://www.nist.gov/publications/life-cycle-costing-manual-federal-energy-management-program
Accessed 2025-10-24
U.S. Department of Energy (2025). 10 CFR Part 436, Subpart A — Methodology and Procedures for Life Cycle Cost Analyses — Electronic Code of Federal Regulations (NARA/OFR) https://www.ecfr.gov/current/title-10/chapter-II/subchapter-D/part-436/subpart-A
Accessed 2025-10-24
(2017). ISO 15686-5:2017 — Buildings and constructed assets — Service life planning — Part 5: Life-cycle costing — International Organization for Standardization https://www.iso.org/obp/ui/
Accessed 2025-10-24
ASTM International (2017). ASTM E917-17e1 — Standard Practice for Measuring Life-Cycle Costs of Buildings and Building Systems — ASTM International https://www.astm.org/e0917-17e01.html
Accessed 2025-10-24

Payback Period Calculator

Results

Insights

How it works

1) Simple Payback

2) Discounted Payback

Example

How to Use the

Frequently Asked Questions

Methodology & Sources

Bibliography

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