How to use it
- On line 1 of Cash flows, one per line, type the amount you invest now as a positive number.
- On each following line, type the net cash of one year: money in is positive, money you put in is negative.
- Type the Discount rate per year, the return you could earn elsewhere.
- Read the Net present value, the Internal rate of return and the two payback periods, then the table.
How the net present value is calculated
Money received later is worth less than money received now, because it could have been invested in the meantime. The net present value discounts each year's cash flow by the discount rate and adds them up. The investment is paid at time zero, and the flow of year t is discounted by t years.
A positive NPV means the investment returns more than the discount rate. A negative NPV means it returns less.
NPV = Σ CF(t) ÷ (1 + r)^t, for t = 0, 1, 2, …
CF(0) = minus the investment
CF(t) = the net cash of year t
r = the discount rate as a fraction- For −1,000, 300, 400 and 500 at 10%: −1,000 + 300 ÷ 1.10 + 400 ÷ 1.21 + 500 ÷ 1.331 = −21.04.
- The first flow is at time zero and is not discounted.
The internal rate of return
The internal rate of return (IRR) is the discount rate at which the NPV is exactly zero. If the return you require is below the IRR, the textbook rule says the investment clears that hurdle. The calculator finds it by Newton's method, starting at your discount rate, and by scanning rates if Newton does not settle.
When the cash flows change sign more than once, the equation can have more than one solution, so there can be more than one IRR. The calculator shows the one nearest your discount rate and says so.
Payback and discounted payback
The payback period is the time until the running total of the cash flows turns from negative to zero or more. The year in which it happens is counted as a fraction: if the total is −300 at the end of year 2 and the year 3 flow is 500, the payback is 2 + 300 ÷ 500 = 2.6 years.
The discounted payback does the same with the discounted flows, so it is always longer than the plain payback when the rate is positive. It ignores money that comes after the payback point.
What this calculator does not include
- Taxes, fees and inflation. Enter the cash flows after them, or adjust the rate.
- Changes in the rate over the years: use one rate for the whole period.
- Cash flows that do not fall at year ends. The calculator treats each line as one period.
Worked example: invest 10,000, then 3,000, 4,000, 5,000 and 2,000 at 10%
The discounted flows are 2,727.27, 3,305.79, 3,756.57 and 1,366.03 after the investment. Added together and less the 10,000 invested now, they give the NPV of 1,155.66.
The running total is −10,000, then −7,000, −3,000 and 2,000 after year 3, so the payback is 2 + 3,000 ÷ 5,000 = 2.60 years. Discounted, the running total turns positive in year 4, giving 3.15 years.
| Figure | |
|---|---|
| Net present value at 10% | 1,155.66 |
| Internal rate of return | 15.32% |
| Payback, years | 2.60 |
| Discounted payback, years | 3.15 |
Frequently asked questions
What discount rate should I use?
Use the return you could get on a similar investment with the same risk, or the cost of the money you borrow. The result depends on the rate, so try a few to see how sensitive it is.
Why is my IRR missing?
The IRR is shown only when the cash flows change sign and some rate makes the NPV zero. If all flows after the investment are money put in, or none are, no IRR exists.
What is the difference between payback and discounted payback?
The plain payback counts the cash at face value. The discounted payback counts it at today's value, so it is longer because later money is worth less.
Why are there two IRRs?
When the cash flows change sign twice, such as an investment, then income, then a cost to close, the NPV can cross zero twice. Both rates are valid answers to the same equation.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you enter is sent to us.
Sources
- Wikipedia: Net present value (NPV formula with t = 0 for the first flow)
- Wikipedia: Internal rate of return (the rate that sets NPV to zero, multiple IRRs)
- Wikipedia: Payback period (uneven cash flows formula)
Figures and text last checked on Tuesday, November 10, 2026.