Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Simple payback
Simple mode
- Payback Period
- the years until the cash returned equals the amount invested
- Initial Investment
- the cost paid at the start
- Annual Cash Flow
- the net cash the investment returns each year, the same every year
Cash is counted at the end of each year. The project life sets the totals, not the payback.
Source: Uses the simple payback formula in NIST Handbook 135 (Kneifel and Webb, 2025), Equation 6-13 [1], and in OpenStax (Franklin and colleagues, 2019) [2].
Payback from year-by-year cash flows
Cash Flows mode
- Payback Period
- the full years before the crossing, plus the part of that year still owed
The part of the last year is the amount still owed ÷ that year's cash flow, as if the cash arrived evenly. NIST's handbook counts whole years and says the data seldom support a fraction. A year left out counts as zero, and rows for one year add up. A later cost that undoes payback moves it to where the cost is recovered for good. NIST's handbook says its software checks that payback, once reached, is not reversed.
Source: Based on the payback definition in NIST Handbook 135, Equation 6-11 [1], with the partial-year step in OpenStax [2][3].
Discounted payback
Discounted mode
- Discounted Payback Period
- the same crossing, counted in discounted cash
Each year's cash flow is first divided by (1 + rate)^year, so for a positive rate the discounted payback is the same as or longer than the simple one. The rate is yours to choose; with it cleared, the simple payback shows.
Source: Based on the discounted payback in NIST Handbook 135, Equation 6-11 with a discount rate [1], which the handbook calls the preferred way to compute payback.
Discounting one cash flow
Discounted mode
- PV
- the cash flow's value today
- CF
- one year's cash flow, counted at the end of that year
- rate
- the discount rate, as a decimal
- year
- the year it arrives
Source: Uses the single present value factor in NIST Handbook 135, Figure 3-1 [1].
Net present value
Discounted mode
- NPV
- the discounted cash flows less the investment
- CF
- each year's cash flow
- rate
- the discount rate, as a decimal
- Initial Investment
- the cost paid at the start
The sum runs over the project life with one annual figure, or over the years entered. Above zero, the cash flows beat the discount rate over those years.
Source: Uses the present value factors in NIST Handbook 135, Figure 3-1 [1]; OMB Circular A-94 calls the same quantity discounted net benefits [4].
Net profit and ROI
Every mode
- Net Profit
- what is left after the cost comes back
- Total Cash Flows
- the cash flows added over the project life, or the years entered
- Initial Investment
- the cost paid at the start
- ROI
- the return on the investment, in percent
ROI here covers the whole span; it is not a yearly return and is not discounted.
Source: Standard formula; no single publisher.
Sources
- Kneifel J, Webb D. Life Cycle Costing Manual for the Federal Energy Management Program (NIST Handbook 135), section 6.4 "Simple Payback (SPB) and Discounted Payback (DPB)", pp. 86-91; Figure 3-1, p. 25. National Institute of Standards and Technology, 2025 edition (August 2025).
- Franklin M, Graybeal P, Cooper D. Principles of Accounting, Volume 2: Managerial Accounting, section 11.2 "Evaluate the Payback and Accounting Rate of Return in Capital Investment Decisions". OpenStax, Rice University, 2019 (web edition read October 5, 2026).
- Dahlquist J, Knight R, and colleagues. Principles of Finance, section 16.1 "Payback Period Method". OpenStax, Rice University, 2022 (web edition read October 5, 2026).
- Office of Management and Budget. Circular A-94: Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs, section 5.a, p. 4. Revised November 9, 2023.
What this calculator does not cover
- It models when the cash comes back, not financing costs, taxes, inflation beyond the discount rate you enter, or a return adjusted for risk.
- NIST's handbook treats payback as relative to doing nothing: the investment is the extra cost of the project, and the cash flows are the extra net cash it brings.
- NIST's handbook says payback is not a valid way to choose among competing projects or to rank projects for funding, and OpenStax's finance text notes it has no clear acceptance criterion.
Sources checked on .