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Payback period calculator and formula

The payback period is how long a project takes to hand back the cash it cost. A $60,000 machine returning $18,000 a year pays for itself in 3.33 years. Payback stops counting there, and it treats a dollar in year 4 as a dollar today, so it screens projects rather than choosing between them.

Payback period

3.33 years

The $60,000.00 cost is back in hand by the end of year 4, when $72,000.00 has come in. What the project does after that is invisible to this measure.

Cash that clears the cost
$60,000.00
Cash arriving after payback
$30,000.00
Total cash over 5 years
$90,000.00
$
$
yr

The count stops at payback, so the later years never reach the headline.

The formula

t=n+C−∑k=1nCFkCFn+1t = n + \frac{C - \sum_{k=1}^{n} CF_k}{CF_{n+1}}

CC is the cash paid up front, CFkCF_k is the cash the project returns in year kk, and nn is the last full year at which the running total is still short of CC. The fraction finishes the job: what is still owed, over the cash arriving in the next year. When every year pays the same, this collapses to t=C/CFt = C / CF.

What this calculator works out

Enter what the project costs up front, the cash it returns each year, and how many years it runs. The result is the payback period: the moment the running total of cash returned equals the cash you put in.

The answer is a date, not a profit. At the payback point the project has given your money back and nothing more. Everything it earns after that is the actual gain, and payback does not look at it. That is why the breakdown under the result splits the cash into two parts, the part that clears the cost and the part that arrives afterwards.

The count runs on cash, not on accounting profit. Money that leaves the bank counts on the day it leaves, and money that arrives counts on the day it arrives.

The payback period formula

Keep a running total of the cash the project returns and stop when it reaches the cost:

t=n+C−∑k=1nCFkCFn+1t = n + \frac{C - \sum_{k=1}^{n} CF_k}{CF_{n+1}}

Read it in two pieces. The nn is the last full year where the running total is still short. The fraction is the slice of the following year needed to finish: the amount still outstanding, divided by the cash that year brings in. That fraction assumes cash arrives evenly through the year, which is the usual convention and the one this calculator uses. Assume instead that each year's cash lands in one lump at the year end and the answer rounds up to a whole number of years.

When every year pays the same amount, the sum collapses and the whole thing becomes one division, t=C/CFt = C / CF. A $60,000 outlay against $18,000 a year is 60000/18000=3.333360000/18000 = 3.3333 years. Uneven cash flows need the running total, which is what the formula above is doing.

The cash flows are net: what comes in less what has to be spent to keep it coming. A project that returns money but needs work done to it in year 3 has a smaller number in year 3, and that pushes the date out.

The two things payback cannot see

The first blind spot is everything past the cutoff. Payback measures how long your money is exposed and then stops. A project that pays back in two years and dies scores better than one that pays back in three and runs for twenty. Nothing in the arithmetic can tell those apart, because the arithmetic ends at the moment the running total crosses the cost.

The second blind spot is the waiting itself. A running total adds a dollar arriving in year 4 to a dollar arriving today as though they were the same dollar. They are not: money you already hold can be working, and money promised for year 4 might not arrive at all. This is the time value of money, and payback ignores it completely.

Discounting the cash flows before running the total fixes the second problem and leaves the first one standing. The second worked example below does exactly that, and it pushes the same machine's payback from 3.33 years to 4.26 years without the project's cash flows changing at all.

The measure that fixes both is net present value. It prices the waiting on every year and it counts every year, not just the ones before the cutoff. The net present value calculator runs that version of the question, and the IRR calculator asks it as a rate instead of an amount.

When payback is still worth asking

Payback survives because it answers a question the value measures do not: how long is the money at risk. A business that would not survive a long wait for its cash back cares about the date more than the surplus, and so does anyone putting money into a market that may look different in five years.

It is also cheap and hard to argue with. Net present value needs a discount rate, and two careful people can pick different ones and reach opposite conclusions. Payback needs no rate at all, which makes it a first screen that nobody can accuse of being tuned to a preferred answer. Use it to rule projects out quickly, then judge the survivors on value.

The cutoff a business applies is set by its own tolerance for liquidity risk, not by any external standard. Short cutoffs suit fast-moving equipment and uncertain later years. Long ones suit stable, long-lived assets.

A related question, in units rather than years, is how much you have to sell before the fixed costs are covered. The break-even calculator does that one.

Worked examples

A \$60,000 machine returning \$18,000 a year

A machine costs $60,000 up front and is expected to bring in $18,000 of net cash a year for five years. How long before it has paid for itself?

  1. Run the cash total forward: 1800018000 after year 1, 3600036000 after year 2, 5400054000 after year 3. The cost is not covered yet.
  2. Year 4 opens with 60000−54000=600060000 - 54000 = 6000 still to recover.
  3. That year brings in $18,000, so the shortfall clears 6000/18000=0.33336000/18000 = 0.3333 of the way through it.
  4. Payback is 3+0.3333=3.33333 + 0.3333 = 3.3333 years, which is 3 years and 4 months.

The machine pays for itself in 3.33 years. Payback lands a third of the way into year 4, by the end of which the project has collected $72,000 against the $60,000 it cost. What is left after the payback date is a further year and eight months of cash, and that is the part a project is bought for. The payback figure says nothing about it.

The same machine with the waiting priced in

Plain payback counts a dollar in year 4 as equal to a dollar today. Charge 10 percent a year for the waiting first, then ask the same question of the same $60,000 machine.

  1. Discount each year's $18,000 back to today: 18000/1.1=16363.6418000/1.1 = 16363.64, 18000/1.12=14876.0318000/1.1^2 = 14876.03, 18000/1.13=13523.6718000/1.1^3 = 13523.67, 18000/1.14=12294.2418000/1.1^4 = 12294.24, 18000/1.15=11176.5818000/1.1^5 = 11176.58.
  2. Run the total on those figures: 16363.6416363.64, then 31239.6731239.67, then 44763.3444763.34, then 57057.5857057.58 by the end of year 4, still short of 6000060000.
  3. Year 5 opens with 60000−57057.58=2942.4260000 - 57057.58 = 2942.42 left to recover, against $11,176.58 arriving that year.
  4. 2942.42/11176.58=0.26332942.42/11176.58 = 0.2633 of the year, so payback is 4+0.2633=4.26334 + 0.2633 = 4.2633 years.

Discounted payback is 4.26 years against 3.33 years for the same machine, nearly a year later, and not one of the project's cash flows changed. All five years are worth $68,234.16 in today's money against the $60,000 the machine cost, so the project still clears its outlay, but most of its life now goes on simply getting the money back. Plain payback treats waiting as free, and over a long project that is a large thing to treat as free.

Two projects, the same payback, very different value

Two projects each cost $60,000 and each return $25,000 of cash a year. Project A wears out at the end of year 3. Project B runs for six years. Payback scores them identically. Should you?

  1. Both collect 2500025000 in year 1 and 5000050000 by the end of year 2, so both are still 60000−50000=1000060000 - 50000 = 10000 short.
  2. Both clear that in year 3: 10000/25000=0.410000/25000 = 0.4 of the year, so payback is 2+0.4=2.42 + 0.4 = 2.4 years for each.
  3. By the end of year 3 each has taken in $75,000, and that is where Project A stops.
  4. Project B collects another $75,000 across years 4, 5 and 6. The payback count ended at 2.4 years, so none of it registers.

Both pay back in 2.4 years, and by the end of year 3 both have collected $75,000 against the $60,000 they cost. Project B then earns a further $75,000 that Project A never sees. Same score, and B collects twice the cash. Take the $60,000 cost off each and B's gain is six times A's, not twice it. Price the waiting in as well and the gap is wider still. Payback is not measuring value, so it cannot rank by value.

Using payback to choose rather than to screen

The mistake is treating the shortest payback as the best project.

Payback ranks by speed, and speed is not worth. On the two projects above it returns 2.4 years for both: one that stops at $75,000 of cash and one that goes on to collect another $75,000. Rank by payback and you are indifferent between them. Take the $60,000 cost off what each collects and one gains six times what the other does.

The same blind spot has a nastier version. A project with a large cost late in its life, a plant to strip out or a site to clear, can post an excellent payback and still destroy money, because the expensive year falls after the count has stopped. Payback never sees the bill.

The fix is not to abandon the measure. It is to use it in the order it works in: payback and the cutoff to remove projects that tie money up longer than the business can stand, then net present value on the ones that survive to decide which is actually worth doing. Screening first, choosing second. The two questions are different and only one of them is about value.

Common questions

What is a good payback period?

There is no standard number, because it is not a market rate. Each business sets its own cutoff from how long it can stand to have cash tied up and how confident it is about the later years. Fast-changing equipment and uncertain forecasts push cutoffs shorter, and stable long-lived assets allow longer ones. A cutoff is a screening threshold set inside the business, so comparing two firms' cutoffs says more about their appetite for risk than about their projects.

What is discounted payback and is it better?

It is the same count, run on cash flows that have been discounted back to today first, as in the second worked example. It is better in one way: it charges for the waiting, so the answer stops pretending a dollar in year 5 is a dollar now. It is no better in the other way, because it still stops counting at the cutoff and still ignores everything after it. Treat it as a sharper screen, not a decision rule.

Should payback use cash flow or profit?

Cash flow. Depreciation and similar charges reduce reported profit without any money leaving the bank, so a payback worked out from profit shows a longer wait than the real one. Writing the cost of a long-lived asset off against profit over several years while the cash leaves in one go is the standard treatment under IFRS and under United States accounting rules alike, and that gap is exactly what this measure cares about. Use net cash in and out, dated when it moves.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.