How do I calculate the payback period?

Add the yearly cash flows up until the running total reaches the cost, then work out how far into the year that happened. For a 100,000 investment returning 30,000, 35,000 and 40,000, the cumulative totals are 30,000, 65,000 and 105,000, so the cost is passed during year three with 35,000 of that year's 40,000 needed. That is 0.875 of the way through, giving a payback period of 2.88 years.

What is the difference between payback and discounted payback?

The plain figure adds the cash flows at face value; the discounted one reduces each year's amount by the discount rate before adding it. On the default example, 100,000 back from receipts of 30,000 to 50,000 takes 2.88 years undiscounted and 3.32 years discounted at eight percent. The difference of 0.44 years is the cost of waiting expressed in time, and it grows with both the rate and how far out the money arrives.

Why does this page give two answers instead of one?

Because the two are used for different purposes and a single figure hides the gap between them. The undiscounted version is the one in the United States federal energy management rule, which defines the estimated simple payback time as the years needed for cumulative savings to equal the investment cost without consideration of discount rates. The discounted version is the same sentence with the cost of money put back in. If they are close, waiting is cheap; if they are far apart, a fast-looking payback is being paid for by the rate.

What does the delay figure mean?

It is the discounted payback minus the undiscounted one, so it is the extra time the money takes to come back once the discount rate is allowed for, measured in years. It is zero whenever the discount rate is zero, because then every discount factor is exactly 1 and the two calculations are the same calculation. A large delay is a warning that a good part of the early receipts is really interest on the money rather than a return on the project.

Why is the answer not a whole number of years?

Because the recovery rarely lands exactly at the end of a year. The page assumes the cash arrives evenly through the crossing year and credits the fraction of it that was needed, which is why 100,000 against a third-year receipt of 40,000 comes out at 2.88 rather than 3. Rounding up to a whole year would be simpler but it would make two projects that differ by several months look identical, and the difference between them is exactly what this measure is being used to judge.

What happens if the cash flow never covers the cost?

The page reports an error rather than a figure, because there is no payback period to quote. This can happen at two different points and for two different reasons: either the flows never add up to the investment at all, or they do add up but not once they are discounted — 100,000 repaid exactly one year later covers the cost at a discount rate of zero and fails at five percent. Both are real answers, and the second one is the more informative of the two.

Payback Period Calculator

Result

2.88

Payback period, undiscounted

Payback period, discounted: 3.32
Extra time from discounting: 0.44

A payback period calculator answers the simplest question anyone asks about a purchase: how long until the thing has paid for itself? You enter what it costs and a list of what it brings in each year, and the page returns two answers rather than one. The first is the plain payback: add the yearly amounts up until they cover the cost, and that is how many years it took. The second discounts each year's amount before adding it, so it asks how long the money takes to come back once you allow for the fact that a pound or a dollar received in year four is worth less than one received today. The gap between the two is the third figure on the page, and it is the interesting one — it is what waiting costs, expressed in years rather than in money. Both answers are quoted to the fraction of a year in which the cumulative total crosses the cost, so a project that collects 40,000 in the year it goes over is credited with the part of that year it actually needed. The definition of the undiscounted version is not this page's invention: the United States federal energy management rule defines the estimated simple payback time as the number of years required for the cumulative value of savings to equal the investment costs, without consideration of discount rates. The discounted version is the same sentence with a discount rate put back in. A project can clear the first and fail the second, and when the flows never cover the cost under either reading the page reports an error instead of a number. Amounts carry no currency symbol.

The default project at six discount rates: what waiting costs in years

Discount rate (%)	Payback, undiscounted (years)	Payback, discounted (years)	Extra time (years)
0	2.88	2.88	0
4	2.88	3.08	0.2
8	2.88	3.32	0.44
12	2.88	3.59	0.71
16	2.88	3.91	1.03
20	2.88	4.29	1.41

The cash flows and the investment are the same in every row, so the only thing moving down the table is the discount rate — and the undiscounted column is therefore constant at 2.88 by construction, which is worth seeing once. Everything else in the table is that column being left behind. At a discount rate of zero the two payback columns are identical and the extra time is exactly zero; at four percent the discounted answer is already 0.20 years later, and by twenty percent it is 1.41 years later, which is more than half of the 2.88 the plain figure reports. Read the last column as the answer to a question the plain payback cannot ask: how much of this project's early speed is real, and how much of it is the discount rate being ignored.

Formula

Payback = the year the cumulative cash flow first reaches the investment (with or without discounting)

C: The initial investment, which must be greater than zero — a cost of nothing pays back instantly and has no period
CF(k): The cash flow received at the end of year k, or that flow discounted by the rate when the answer is the discounted one
Cumulative: The running total of the cash flows; payback is the moment it first equals or passes the investment
Fraction: The part of the crossing year that was actually needed, which is why the answer is not a whole number
Discount rate: The rate used for the discounted answer only; at zero the two answers are identical by construction

Use it as a first filter rather than a final answer. Payback is easy to explain and it speaks the language of a budget: a business that replaces equipment every few years cares a great deal about whether the new machine has paid for itself before it is replaced again, and that question is answered by the undiscounted figure. Its weakness is that it stops counting at the moment of recovery and ignores everything after, so a project with a fast payback and a short remaining life can beat one with a slower payback and decades of income left. That is why the page prints the discounted answer beside it: if the two are close, waiting is cheap and the simple figure is a fair summary; if the discounted answer is much later, a good part of the early receipts is being eaten by the cost of the money, and the fast-looking payback is not what it seems.

Worked examples

100,000 in, five annual receipts starting at 30,000
1. Cumulative, undiscounted: 30,000 then 65,000 then 105,000
2. The cost of 100,000 is passed during year 3, with 35,000 of the 40,000 that year needed
3. 35,000 ÷ 40,000 = 0.875, so payback is 2 + 0.875 = 2.88 years
4. Discounted at 8%: 27,777.78 then 57,784.64 then 89,537.93 then 122,614.27
5. Discounted payback is passed during year 4: 3 + (100,000 − 89,537.93) ÷ 33,076.34 = 3.32 years
6. Delay: 3.32 − 2.88 = 0.44 years
This is the page's default, and the pair of answers is the whole point: at eight percent the money takes almost half a year longer to come back than the plain arithmetic suggests. The interpolation step is worth reading twice, because it is the part that is easy to mis-state. During year three the project collects 40,000 and only needs 35,000 of it, so the recovery happens 0.875 of the way through that year, which is 2.875 years from today.
120,000 in, three flat receipts of 50,000
1. Cumulative, undiscounted: 50,000 then 100,000 then 150,000
2. The cost is passed during year 3 with 20,000 of that year's 50,000 needed: 2 + 0.4 = 2.40 years
3. Discounted at 10%: 45,454.55 then 86,776.86 then 124,342.60
4. Discounted payback: 2 + (120,000 − 86,776.86) ÷ 37,565.74 = 2.88 years
5. Delay: 2.88 − 2.40 = 0.48 years
Flat receipts make the arithmetic visible, and they also show how far the discounted total falls behind: the same three payments of 50,000 add up to 150,000 in plain money and only 124,342.60 once discounted at ten percent, which is barely above the 120,000 cost. A project like this is much closer to the edge than the undiscounted answer suggests.
100,000 recovered in a single year when the discount rate is zero
1. One payment of 100,000 at the end of year 1 covers the cost exactly
2. The crossing happens at the very end of year 1, so the fraction is 0 and payback is exactly 1 year
3. At a discount rate of zero every discount factor is 1, so the discounted answer must be identical
At a discount rate of zero the two answers are forced to agree, and this case checks that they do: every discounted flow equals the plain flow, the cumulative totals are equal at every step, and the delay is exactly zero. It is the boundary that makes the third figure meaningful, because a delay can only be read against a rate where there is no delay at all.

Limitations

Payback answers one question and ignores most of what matters. It stops the clock the moment the money is back, so it cannot tell a project that then earns for twenty years from one that stops earning the next day, and it will always prefer a short-lived quick return over a long-lived slow one. It also says nothing about size: a project that returns 1,000 after a year beats one that returns a million after two, on this measure. The cash flows are assumed to arrive at the end of each year and to be equal to what you typed, with no allowance for inflation, tax or the possibility that a risky project simply does not deliver. The interpolation within the crossing year is this page's convention rather than a rule from any standard — it assumes the money arrives evenly through that year, when in fact it may all arrive in the final month. Finally, if the cash flows never cover the investment the page reports an error rather than a number, because there is no payback period to quote; the limit is a useful answer in itself, since it means the project does not pay back at that discount rate within the horizon you entered.

Frequently asked questions

How do I calculate the payback period?: Add the yearly cash flows up until the running total reaches the cost, then work out how far into the year that happened. For a 100,000 investment returning 30,000, 35,000 and 40,000, the cumulative totals are 30,000, 65,000 and 105,000, so the cost is passed during year three with 35,000 of that year's 40,000 needed. That is 0.875 of the way through, giving a payback period of 2.88 years.
What is the difference between payback and discounted payback?: The plain figure adds the cash flows at face value; the discounted one reduces each year's amount by the discount rate before adding it. On the default example, 100,000 back from receipts of 30,000 to 50,000 takes 2.88 years undiscounted and 3.32 years discounted at eight percent. The difference of 0.44 years is the cost of waiting expressed in time, and it grows with both the rate and how far out the money arrives.
Why does this page give two answers instead of one?: Because the two are used for different purposes and a single figure hides the gap between them. The undiscounted version is the one in the United States federal energy management rule, which defines the estimated simple payback time as the years needed for cumulative savings to equal the investment cost without consideration of discount rates. The discounted version is the same sentence with the cost of money put back in. If they are close, waiting is cheap; if they are far apart, a fast-looking payback is being paid for by the rate.
What does the delay figure mean?: It is the discounted payback minus the undiscounted one, so it is the extra time the money takes to come back once the discount rate is allowed for, measured in years. It is zero whenever the discount rate is zero, because then every discount factor is exactly 1 and the two calculations are the same calculation. A large delay is a warning that a good part of the early receipts is really interest on the money rather than a return on the project.
Why is the answer not a whole number of years?: Because the recovery rarely lands exactly at the end of a year. The page assumes the cash arrives evenly through the crossing year and credits the fraction of it that was needed, which is why 100,000 against a third-year receipt of 40,000 comes out at 2.88 rather than 3. Rounding up to a whole year would be simpler but it would make two projects that differ by several months look identical, and the difference between them is exactly what this measure is being used to judge.
What happens if the cash flow never covers the cost?: The page reports an error rather than a figure, because there is no payback period to quote. This can happen at two different points and for two different reasons: either the flows never add up to the investment at all, or they do add up but not once they are discounted — 100,000 repaid exactly one year later covers the cost at a discount rate of zero and fails at five percent. Both are real answers, and the second one is the more informative of the two.

References

10 CFR 436.23 — Estimated simple payback time (the definition of payback without discounting) — U.S. Department of Energy rule, via the Electronic Code of Federal Regulations (United States)
10 CFR 436.14 — Methodological assumptions (how future cash flows are discounted to present values) — U.S. Department of Energy rule, via the Electronic Code of Federal Regulations (United States)
H.15 Selected Interest Rates — the published benchmark rates a computed rate is compared against — Board of Governors of the Federal Reserve System (United States)

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