NPV and IRR Calculator
Paste a list of cash flows, one per line with the initial outlay first, set a discount rate, and get the net present value, the internal rate of return (with a warning when there is more than one), the profitability index and the simple and discounted payback periods. The NPV profile chart shows where NPV crosses zero. Free, no sign-up.
Your cash flows
Outflows are negative: -40000 then 8000, 9200 and so on. Period 0 is not discounted. Enter 0 for a period with no cash flow.
6 cash flows
Period 0 is not discounted; the cash flow in period t is divided by (1 + rate)^t. Excel's NPV() function discounts its first value by one period, so NPV(rate, later flows) + period-0 flow equals this result.
Results
$1,922.06
Net present value (NPV)
9.6345%
Internal rate of return (IRR) — per period
1.0481
Profitability index
4.06 periods
Payback period
4.81 periods
Discounted payback
The NPV is positive: at this discount rate the cash flows are worth more than they cost.
Period by period
| Period | Cash flow | Discount factor | Present value | Cumulative cash flow | Cumulative PV |
|---|---|---|---|---|---|
| 0 | -$40,000.00 | 1 | -$40,000.00 | -$40,000.00 | -$40,000.00 |
| 1 | $8,000.00 | 0.925926 | $7,407.41 | -$32,000.00 | -$32,592.59 |
| 2 | $9,200.00 | 0.857339 | $7,887.52 | -$22,800.00 | -$24,705.08 |
| 3 | $10,000.00 | 0.793832 | $7,938.32 | -$12,800.00 | -$16,766.75 |
| 4 | $12,000.00 | 0.73503 | $8,820.36 | -$800.00 | -$7,946.39 |
| 5 | $14,500.00 | 0.680583 | $9,868.46 | $13,700.00 | $1,922.06 |
How to Use the NPV and IRR Calculator
- 1. List the cash flows. One per line, starting with period 0 — usually the initial outlay, entered as a negative number. Enter 0 for a period with nothing. You can paste a spreadsheet column.
- 2. Set the discount rate. This is the rate for one period: if your periods are years, it is an annual rate. It is the return you require or the cost of the money, not something the calculator can pick for you.
- 3. Read the NPV. Positive means the discounted inflows exceed the outlay at your rate; negative means they fall short.
- 4. Check the IRR and the chart. The IRR is the rate at which NPV is exactly zero. The chart plots NPV across a range of rates, so you can see where it crosses the axis.
- 5. Compare payback and profitability index. Both are quick screens; the table shows the working period by period.
NPV, IRR and the Other Measures
Net present value discounts each cash flow back to period 0 and adds them: NPV = Σ CFt ÷ (1 + r)t, summed from t = 0. The period-0 flow is not discounted. Accepting a project with a positive NPV is the standard textbook rule, because it earns more than the discount rate demands.
- IRR is the rate r at which NPV equals zero. It is found numerically: the calculator scans rates from −99% to 10,000% per period and refines each sign change by bisection, so it cannot diverge or jump to a wrong root.
- Profitability index is the present value of the later cash flows divided by the initial outlay, which equals 1 + NPV ÷ outlay. Above 1 means a positive NPV; it is shown only when period 0 is an outflow.
- Payback period is how long until cumulative cash flow turns positive, interpolating inside the period. It ignores the time value of money and everything after payback.
- Discounted payback does the same with each flow discounted at your rate, so it is always longer than simple payback.
Excel's NPV() is not the same
Excel's NPV function treats its first value as arriving at the end of period 1, so it discounts every value, including the first, by at least one period. To match this calculator in a spreadsheet, use NPV(rate, flows after period 0) + the period-0 flow. The IRR here uses all the roots in range; Excel's IRR returns one root, found by iteration from a 10% guess, and the calculator reports the root nearest that guess as the headline value.
Worked Example
An outlay of 40,000 returns 8,000, 9,200, 10,000, 12,000 and 14,500 over five years. At an 8% discount rate the present values add to 41,922.06, so the NPV is 41,922.06 − 40,000 = 1,922.06 and the profitability index is 1.0481. The IRR is 9.6345%: discounting at that rate brings NPV to zero, and because it exceeds 8% the NPV at 8% is positive. Cumulative cash flow turns positive during year 5, for a simple payback of 4.06 years; discounted at 8% it takes 4.81 years.
When the IRR Misleads
A set of cash flows whose sign changes more than once can have several IRRs, or none. Take −1,000, +2,600, −1,650: it has IRRs of 10% and 50%, and the NPV at 8% is −7.20. A project with a late cleanup cost or a mid-life refit can look like this. The calculator counts the sign changes and lists every root it finds; when there is more than one, base the decision on NPV at your discount rate.
- Scale. IRR is a percentage, so a small project can have a high IRR and a small NPV. Use NPV to compare projects of different size.
- Reinvestment. IRR implicitly assumes interim flows are reinvested at the IRR itself. NPV assumes reinvestment at the discount rate, which is usually more realistic.
- Timing. Periods must be equal in length. If cash arrives monthly, the rate must be monthly too.
Frequently Asked Questions
- How do you calculate NPV?
- Divide each cash flow by (1 + r)t, where r is the discount rate per period and t the period number, then add the results. The initial outlay is period 0 and is negative. The table in the calculator shows each discounted flow and the running total.
- What is a good IRR?
- One that exceeds your hurdle rate — the minimum return you require, such as the cost of financing or the return on the best alternative. There is no universal good IRR; compare it with the discount rate and, for risk, with similar projects.
- Should I use NPV or IRR to choose between projects?
- NPV is generally preferred. IRR can rank mutually exclusive projects wrongly when they differ in size or timing, and it can give several answers or none for cash flows that change sign more than once. IRR is still useful as a rate you can compare with your cost of capital.
- Why does my spreadsheet NPV differ from this one?
- Excel and Google Sheets NPV() assume the first value comes at the end of period 1. If your first value is the period-0 outlay, add it outside the function: NPV(rate, later flows) + outlay. Then the two agree.
- Can a project have more than one IRR?
- Yes. By Descartes' rule of signs, the number of positive IRRs cannot exceed the number of sign changes in the cash flows. A conventional project — one outflow followed by inflows — has a single IRR. Flows like −1,000, +2,600, −1,650 have two.
- What does a profitability index above 1 mean?
- That the present value of the future cash flows exceeds the initial outlay, so NPV is positive. An index of 1.05 means each unit invested returns 1.05 units in present-value terms. It is useful for ranking projects when capital is limited.