Payback period vs NPV
Payback is how long a project takes to hand back the cash it cost. NPV is what every remaining year is worth today. A $60,000 machine returning $18,000 a year pays back in 3.33 years. At 10 percent its NPV is $8,234.16, because the five receipts are worth $68,234.16 today.
| Payback period | Net present value | |
|---|---|---|
| What it returns | A date. 3.33 years on the $60,000 / $18,000 sheet. | An amount of money. $8,234.16 at 10 percent on that same sheet. |
| What happens after the cutoff | Ignored. By the end of year 4 the project has collected $72,000, and payback has already stopped. | Still counted. Year 5 is in the $68,234.16 present value of the receipts. |
| Waiting | Free, on plain payback. Discounted payback on the same receipts is 4.26 years. | Priced at the rate you type. Raise it and NPV falls. |
| Two projects, same payback | $25,000 a year on a $60,000 outlay pays back in 2.4 years whether the project then stops or runs three more years. | The project that keeps paying has the larger NPV. Payback cannot see the extra cash. |
| A different series, for rank | Silent on value. A date cannot be spent. | The $10,000 / five times $3,000 series is worth $1,372.36 at 10 percent. That is a ranking unit. |
| When you would pick it | Screening how long cash is tied up. | Choosing between projects, or judging one at the rate your money costs. |
On this page
A date against a surplus
A $60,000 machine returning $18,000 a year pays back in 3.33 years. Year 4 is the year the remaining outlay is recovered, a third of the way through that year's $18,000. By the end of year 4 the project has collected $72,000. Payback has already stopped.
Discount the same five receipts at 10 percent and they are worth $68,234.16 today. Subtract the $60,000 outlay and NPV is $8,234.16. The project still clears, and every year including the ones after 3.33 is in that figure.
Charge 10 percent inside the payback clock itself and discounted payback is 4.26 years, with a running total of $68,234.16 at the year it lands. Waiting is no longer free, and the tail after that date is still ignored.
How payback period works is the date. How NPV and IRR work is the surplus. Discounted against plain payback is the two clocks. A cash flow needs a date in both.
Same score, different cash
Two projects each cost $60,000 and each return $25,000 a year. Both pay back in 2.4 years. By the end of year 3 each has collected $75,000. One then stops. The other runs three more years. Payback scores them the same. NPV does not.
This is educational material, not financial advice.
Worked examples
Plain payback on \$18,000 a year
A machine costs $60,000 and brings in $18,000 a year for five years. How long before it has paid for itself?
- Run the cash total forward: after year 1, after year 2, after year 3. The cost is not covered yet.
- Year 4 opens with still to recover against that year's .
- The shortfall clears of the way through year 4, so payback is 3.33 years.
- By the end of year 4 the project has collected $72,000.
The machine pays for itself in 3.33 years. Cumulative cash at the end of the year payback lands in is $72,000.
NPV of the same machine at 10 percent
Same $60,000 outlay and five receipts of $18,000. What is NPV at 10 percent?
- Write the series: minus $60,000 at time zero, then five times $18,000.
- Discount the receipts at 10 percent. They are worth $68,234.16 today.
- Subtract the undiscounted outlay: NPV is $8,234.16.
NPV is $8,234.16 at 10 percent. The five receipts are worth $68,234.16 today against the $60,000 cost.
Discounted payback on the same receipts
Charge 10 percent for the wait, then ask the payback question of the same machine.
- The discounted receipts are $16,363.64, $14,876.03, $13,523.67, $12,294.24 and $11,176.58.
- The running total is still short of $60,000 after year 4.
- Discounted payback is 4.26 years, and the cumulative at that year is $68,234.16.
Discounted payback is 4.26 years. Cumulative discounted cash at the year it lands in is $68,234.16.
Two projects, the same 2.4 year payback
Two projects each cost $60,000 and each return $25,000 a year. How long is payback?
- Both collect in year 1 and by the end of year 2, so both are still short.
- Both clear that in year 3: of the year, so payback is 2.4 years.
- By the end of year 3 each has taken in $75,000.
Both pay back in 2.4 years. Cumulative cash at the end of year 3 is $75,000. What either project does after that date is invisible to payback.
NPV of the \$10,000 / \$3,000 series at 10 percent
A different project: $10,000 out, five times $3,000 in. What is NPV at 10 percent?
- The five discounted receipts add to $11,372.36.
- Take off the $10,000 outlay.
NPV is $1,372.36. This is a different series from the $60,000 machine, used here as a ranking unit, not as a second reading of the same project.
Common questions
If payback is 3.33 years and NPV is positive, which decides?
NPV, for a ranking. Payback is a screen for how long cash is tied up. The $8,234.16 surplus at 10 percent includes the years after 3.33, which is the part a project is bought for.
Why is discounted payback still not NPV?
Because it still stops. On this sheet it stops at 4.26 years. NPV keeps the rest of the discounted receipts.
Keep reading
- Profitability index vs NPV
- How the payback period works
- How NPV and IRR work
- Discounted vs plain payback
- NPV vs IRR: a value against a rate
- Payback period calculator and formula
- NPV calculator and net present value formula
- Payback: drag the annual cash
- NPV: drag the discount rate
- Cash flow, defined
- Present value, defined
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.