Payback period calculator

How the payback period calculator works

The payback period is how long an investment takes to return its own cost. Enter the outlay and what the project brings in each year, and this returns both the simple figure and the discounted one, along with the thing the metric throws away.

For a steady stream the arithmetic is a single division. A 10,000 outlay returning 2,500 a year pays back in four years. Uneven flows need the interpolation below.

The formula for uneven flows

Add the inflows year by year until they cover the outlay, then work out where inside that year the line was crossed:

Payback = years until break-even + (unrecovered amount / cash flow in the recovery year)

WallStreetPrep publishes it in that form. Omni writes the same idea as X + Y/Z. calculator.net computes it and publishes neither.

On a 10,000 outlay returning 3,000, 4,000, 5,000 and 6,000: the first two years bring in 7,000, leaving 3,000 outstanding, and year three's 5,000 covers that three fifths of the way through. Payback is 2.6 years.

Discounting makes it longer, always

The discounted payback period is the same question asked of cash flows that have been discounted back to today. Plain payback treats a dollar in year five as worth a dollar now, which it isn't.

Because discounting shrinks every inflow, the discounted figure is never shorter than the simple one at any positive rate. That relationship holds no matter what the flows look like.

WallStreetPrep's example: a $20 million outlay against $5 million a year at 10%. Undiscounted it's exactly four years. Discounted, year one's $5 million is worth $4.5 million and year two's is worth $4.1 million, and break-even slips to roughly 5.4 years.

Omni publishes a closed form for the steady case that skips the table entirely:

DPP = -ln(1 - I x R / C) / ln(1 + R)

On those same numbers it returns 5.36 years against the table's 5.37. The small disagreement is real and worth knowing about: interpolation treats the recovery year as a straight line, while the logarithmic form treats the cash as arriving continuously. Neither is wrong; they're answering the question at slightly different resolutions.

What the metric deliberately ignores

Payback stops counting the moment the outlay is back. Everything after that point is invisible to it.

So a project returning 10,000 a year for two years and then nothing beats a project returning 6,000 a year for fifteen, on this measure alone. The first pays back faster and is worth far less.

That's why this tool shows the cash arriving after the payback point next to the payback figure. On the 3,000 / 4,000 / 5,000 / 6,000 example, payback lands at 2.6 years and 8,000 arrives afterwards, which is most of the project's value sitting in the part the metric discarded.

calculator.net puts the same limitation more generally, that neither version accounts for risk or for opportunity costs such as alternative investments and market volatility.

Two ways a project never pays back

The nominal flows may simply never add up to the outlay. Ten thousand out, a thousand a year back, four years: the answer is never, and no amount of arithmetic changes that.

The subtler case is a project that pays back nominally and not once discounted. A 1,000 outlay returning 500, 300 and 250 recovers 1,050 in nominal terms, so simple payback is under three years. Discounted at 12% those flows are worth about 864 in total, which never reaches 1,000. The tool distinguishes the two, because they mean different things.

A worked case

A 10,000 investment returning 3,000, 4,000, 5,000 and 6,000 over four years, with a 10% discount rate.

Discounting adds about five and a half months to the wait. And the 8,000 arriving after break-even happens to equal the project's entire net gain, which is a neat illustration of why payback is a screening tool rather than a verdict.

What this calculator does not do

It won't tell you whether a payback period is acceptable. That threshold is a policy choice that varies by industry and by how quickly the underlying technology dates.

It doesn't rank projects by value. Payback measures how long capital is exposed, which is a liquidity and risk question. For what a project is worth, the present value calculator discounts the flows at a rate you choose, and the IRR calculator solves for the rate the project earns.

Salvage value, tax and inflation aren't modelled. Fold them into the yearly figures you enter if they matter to your case.

Results are arithmetic on your inputs, not financial advice. For decisions about your money, speak to a licensed financial adviser.

Frequently asked questions

What is the payback period? The payback period is how long an investment takes to return its own cost. For a steady cash flow it is simply the initial investment divided by the yearly inflow, so a 10,000 outlay returning 2,500 a year pays back in 4 years.

How do you calculate payback with uneven cash flows? Add the inflows up year by year until they cover the outlay, then interpolate inside the year that closes the gap: whole years before break-even, plus the amount still unrecovered divided by the flow arriving in the recovery year. On a 10,000 outlay returning 3,000, 4,000, 5,000 and 6,000, the first two years cover 7,000 and the remaining 3,000 arrives three fifths of the way through year three, giving 2.6 years.

What is the discounted payback period? It answers the same question after discounting each inflow back to today, so it accounts for the time value of money that plain payback ignores. Because discounting shrinks every inflow, the discounted figure is always at least as long as the simple one at any positive rate. A 20 million outlay against 5 million a year pays back in 4 years simple and about 5.4 years discounted at 10 percent.

Is there a formula for discounted payback with a steady cash flow? Yes, and it avoids the year-by-year table entirely: DPP = -ln(1 - I x R / C) / ln(1 + R), where I is the investment, C the yearly cash flow and R the discount rate. On the 20 million against 5 million at 10 percent it gives 5.36 years. The interpolated table gives 5.37, because interpolation treats the recovery year as linear where the formula is continuous.

What does the payback period fail to capture? Everything that happens after payback. The metric stops counting the moment the outlay is back, so a project that repays quickly and then produces nothing scores better than one that repays slowly and then runs profitably for a decade. That is why this tool shows the cash arriving after the payback point next to the payback figure.

What is a good payback period? It depends entirely on the type of investment and what else the money could do, so there is no universal threshold. Firms usually set their own cutoff by category, with shorter requirements where technology dates quickly or the outlook is uncertain. A payback period is most useful compared against alternatives rather than judged on its own.

Should I use payback period or IRR and NPV? Payback is a liquidity and risk screen, not a profitability measure: it tells you how long your money is exposed. Net present value tells you what the project is worth and IRR tells you what rate it earns. Payback is quick and intuitive enough to filter options, and the decision itself is better made on net present value.

Can a project never pay back? Yes, in two different ways. The nominal cash flows may simply never add up to the outlay. Or they may cover it nominally but not once discounted, which happens when the inflows are spread far enough out that their present value falls short. This tool distinguishes the two cases, since they mean different things.

Sources

• WallStreetPrep on the discounted payback period, the source of the interpolation formula and the 20 million worked example
• Omni Calculator payback period, which publishes the closed form for a steady cash flow
• calculator.net payback period calculator, which names the risk and opportunity-cost limitations