What is the payback period formula?

Simple payback is the initial cost divided by the annual cash flow. Discounted payback solves the annuity: n = −ln(1 − C·r / F) ÷ ln(1 + r), where C is the cost, F the yearly flow and r the discount rate. Where C·r is at least F, the discounted stream never covers the cost.

Why is the discounted payback longer?

Because a dollar arriving in year six is worth less than one arriving now, so it takes more of them to repay the same cost. At 8% the gap on a four-year simple payback is about a year. The higher the rate, the wider it gets — and above a threshold the project never pays back at all.

What is a good payback period?

It depends on the asset’s life, not on a fixed number. A two-year payback on equipment that lasts three years is worse than a six-year payback on a roof that lasts thirty. Industrial rules of thumb of "under three years" exist because they screen out projects whose life is uncertain, not because three is meaningful.

Should I use payback or NPV?

Both, for different questions. Payback answers "when do I get my money back", which is a liquidity question. Net present value answers "does this make me richer", which is the investment question. Payback ignores every dollar after the break-even point, so it will always prefer the shorter, smaller project.

Payback Period Calculator

With initial cost 25000 usd, cash flow a year 6000 usd, discount rate 8 percent, project life 20 years, payback period comes to 5.27 years — discounted payback. It is reached in 5 steps, the last of which is (-log(1 - 0.3333333) / log(1 + 0.08)), and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Handbook 135, not an approximation fitted to it.

How long an investment takes to repay its own cost, both undiscounted and with the cost of capital applied — the two answers differ by years on a long project.

Formula and sources checked 2 September 2026 · How we check

Initial cost 25000, Cash flow a year 6000, Discount rate 8, Project life 20 years

5.27 years

Discounted payback for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

Initial costusdCash flow a yearusdNet of running costs. For an energy retrofit this is the saving on the bill, not the gross output.Discount ratepercentWhat the money would earn elsewhere. Set it to zero to see the simple payback alone.Project lifeyearsHow long the asset keeps producing the cash flow. A payback longer than this means it never repays.

Discounted payback

5.27 years

Simple payback: 25000 / 60004.167
Discounted payback: (-log(1 - 0.3333333) / log(1 + 0.08))5.268
Cash over the whole life: 6000 * 20120,000
Net gain over the life: 120000 - 25000$95,000
Return on the cost: 95000 / 25000 * 100380

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Worked example

A $25,000 outlay returning $6,000 a year pays back in 4.17 years if a dollar in 2031 is worth a dollar today. At an 8% cost of capital it takes 5.27 years — a year and three months longer, because the later dollars are worth less than the early ones. Over a twenty-year life the project returns $120,000 on a $25,000 cost.

How to work it out yourself

1.Use net cash flow, not revenue. The payback on a machine is what it earns after the power, the maintenance and the operator, and using the gross figure is the single most common way a payback comes out half what it should be.
2.Set the discount rate to what the money would actually earn — the cost of borrowing, or the return on the alternative project. Zero is a defensible answer only for cash that has nowhere else to go.
3.Check the payback against the asset’s life before believing it. A seven-year payback on a five-year roof is a project that never repays, and the simple payback figure will not say so on its own.
4.Payback ignores everything after the break-even day. Two projects with the same payback are not equally good if one keeps paying for fifteen more years, which is why it is a screening test and net present value is the decision.

Payback by annual cash flow

Payback by annual cash flow
Cash flow a year (usd)	Discounted payback	Simple payback	Discounted payback
3000	14.27 years	8.33	14.27
4000	9.01 years	6.25	9.01
5000	6.64 years	5	6.64
6000	5.27 years	4.17	5.27
8000	3.74 years	3.13	3.74
10000	2.90 years	2.5	2.9

The formula

Simple payback25000 / 6000
Discounted payback(-log(1 - 0.3333333) / log(1 + 0.08))
Cash over the whole life6000 * 20
Net gain over the life120000 - 25000
Return on the cost95000 / 25000 * 100

Source: NIST Handbook 135 — life-cycle costing manual for the federal energy management program, 10 CFR 436 subpart A — methodology for estimating life-cycle costs

Questions people actually ask

What is the payback period formula?: Simple payback is the initial cost divided by the annual cash flow. Discounted payback solves the annuity: n = −ln(1 − C·r / F) ÷ ln(1 + r), where C is the cost, F the yearly flow and r the discount rate. Where C·r is at least F, the discounted stream never covers the cost.
Why is the discounted payback longer?: Because a dollar arriving in year six is worth less than one arriving now, so it takes more of them to repay the same cost. At 8% the gap on a four-year simple payback is about a year. The higher the rate, the wider it gets — and above a threshold the project never pays back at all.
What is a good payback period?: It depends on the asset’s life, not on a fixed number. A two-year payback on equipment that lasts three years is worse than a six-year payback on a roof that lasts thirty. Industrial rules of thumb of "under three years" exist because they screen out projects whose life is uncertain, not because three is meaningful.
Should I use payback or NPV?: Both, for different questions. Payback answers "when do I get my money back", which is a liquidity question. Net present value answers "does this make me richer", which is the investment question. Payback ignores every dollar after the break-even point, so it will always prefer the shorter, smaller project.

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