Goals & planning
Payback period & NPV calculator
How fast does a project pay itself back, and is it worth it on a discounted basis? Enter the outlay and yearly net cash flows for payback, discounted payback and NPV.
Payback period
4.56 yrs
Cumulative first ≥0 during year 5 (interpolated)
Discounted payback
5.53 yrs
Net present value (NPV)
$10,640.79
Total net cash flow
$150,000
End cumulative (undiscounted)
$50,000
End cumulative (discounted) = NPV
$10,640.79
Discounted-payback note
Cumulative first ≥0 during year 6 (interpolated)
Payback uses the FIRST time cumulative cash flow turns ≥0; the fraction is a linear interpolation assuming even in-year flows. Cash flows are your own assumptions, not forecasts.
Cash flow chart
- Yearly net flow
- Cumulative
- Cumulative discounted
- First payback
Year-by-year detail
| Year | Net cash flow | Discounted flow | Cumulative | Cumulative discounted |
|---|---|---|---|---|
| 0 | −$100,000 | −$100,000 | −$100,000 | −$100,000 |
| 1 | $12,000 | $11,111.11 | −$88,000 | −$88,888.89 |
| 2 | $18,000 | $15,432.10 | −$70,000 | −$73,456.79 |
| 3 | $24,000 | $19,051.97 | −$46,000 | −$54,404.82 |
| 4 | $28,000 | $20,580.84 | −$18,000 | −$33,823.98 |
| 5 | $32,000 | $21,778.66 | $14,000 | −$12,045.32 |
| 6 | $36,000 | $22,686.11 | $50,000 | $10,640.79 |
The formulas
Net present value NPV = −initial investment + Σ(year-t net cash flow ÷ (1 + r)^t), with r the annual discount rate and cash flows treated as year-end amounts. The plain payback period is the first time the cumulative undiscounted position (−outlay + Σ flows) turns ≥ 0; the discounted payback discounts each year's flow by (1+r)^t before accumulating, again taking the first crossing.
The fractional part of a payback year is a linear interpolation — the crossing year's cash flow is assumed to accrue evenly: payback = previous year-end + remaining gap ÷ that year's flow. If the cumulative position dips back below zero after first turning positive, the recorded payback still uses the first crossing and the page flags the relapse separately.
Plain vs discounted payback
Plain payback counts nominal money only: how long until the outlay comes back unchanged. It is intuitive but ignores the time value of money — year-1 cash and year-10 cash weigh the same. Discounted payback first converts future flows to present value, so late money shrinks; it is never shorter than the plain figure, and the gap widens with higher rates and later crossings.
At a 0% discount rate the two measures coincide. The higher the rate, the more distant cash flows are penalized and the more the discounted figure lags the plain one. Read them together: plain payback tells you how quickly cash comes back, discounted payback is closer to when the investment is truly earned back.
Reading the results
NPV > 0 means the discounted flows outweigh the outlay at your chosen rate — the rule of thumb is 'positive NPV is worth considering, negative means the money could earn your required return elsewhere'. It is still arithmetic on your assumptions: the cash flows are your estimates, not a market forecast, and the answer is sensitive to both the rate and the amounts.
The page also shows a per-year table and a chart: bars are each year's net flow (green positive, red negative), the two lines are cumulative undiscounted vs discounted position, the dashed line is the zero baseline and the marker is the first payback point. Any year may hold a negative flow (top-up investment, loss years); zero-flow years still compound into the totals.
Frequently asked
How exactly is the payback period computed?
Net cash flows accumulate from −initial investment; the first time the running total turns ≥ 0 is payback. The fraction is linear inside the crossing year — e.g. an 18k gap left after year 4 against a 32k year-5 inflow gives 4 + 18/32 ≈ 4.56 years.
Why is discounted payback always later?
Each year's flow is divided by (1+r)^t first, so distant money counts for less and the cumulative crossing arrives later. At a 0% rate the two measures are identical.
What if it never pays back inside the horizon?
The page plainly reports 'not recovered within the horizon' — no fake year, no negative payback. Under your cash-flow assumptions the outlay is not recovered; try extending the horizon or check whether a terminal salvage value is missing.
Can a year's cash flow be negative or zero?
Yes. A negative year means extra outlay or a net loss; zero means no net flow that year. If the cumulative position turns positive and later dips negative again, payback still uses the FIRST crossing and the page flags the relapse.
What discount rate should I use?
Your required return or cost of capital — enter 8 for 8%. Common anchors: a deposit-rate baseline for low-risk projects, your own opportunity cost for business ventures. 0 means no discounting, where discounted and plain figures coincide.
Does the currency selector convert anything?
No. The symbol (¥/$/€/£ or none) is display-only — no FX conversion happens. Keep the initial outlay and every yearly flow in the same currency.
Does a positive NPV guarantee a go?
No. NPV only answers 'do the discounted flows cover the outlay at this rate' — it says nothing about how reliable your estimates are or how risky the project is. Run optimistic/base/pessimistic sets and compare; scenarios can be saved locally in your browser.
Payback uses the first time cumulative cash flow turns non-negative; fractions are linear interpolations assuming even in-year flows. Your cash flows are assumptions, not market forecasts or promises. Everything is computed locally in your browser. Estimates only, not investment advice.