IRR Calculator
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Results
IRR 14.05% a year, NPV $1,626.24 at 8%, MIRR 10.4%, payback 3.25 years.
| Year | Cash flow | Cumulative | Discounted at 8% | Cumulative discounted |
|---|---|---|---|---|
| 0 | −$10,000.00 | −$10,000.00 | −$10,000.00 | −$10,000.00 |
| 1 | $2,500.00 | −$7,500.00 | $2,314.81 | −$7,685.19 |
| 2 | $3,000.00 | −$4,500.00 | $2,572.02 | −$5,113.17 |
| 3 | $3,500.00 | −$1,000.00 | $2,778.41 | −$2,334.76 |
| 4 | $4,000.00 | $3,000.00 | $2,940.12 | $605.36 |
| 5 | $1,500.00 | $4,500.00 | $1,020.87 | $1,626.24 |
How to use the IRR calculator
- Enter the initial investment, the money paid out at the start, as a positive number.
- Type the cash flows that follow, one per line, starting with period 1. Money you receive is positive; money you pay out is negative.
- Choose whether each line is a year, a quarter or a month. Rates are always entered and shown per year.
- Enter a discount rate for the NPV and the finance and reinvestment rates for the MIRR. The table shows how each cash flow is discounted.
IRR, NPV and MIRR formulas
IRR: the rate where NPV = 0
MIRR = (FV of inflows at the reinvestment rate ÷ PV of outflows at the finance rate)1/n − 1
Payback = last period with a negative running total + |that total| ÷ next cash flow
CFt is the cash flow in period t, with the initial investment as a negative CF0 at t = 0, and r is the rate per period. The IRR has no closed formula, so it is found numerically. The calculator also scans rates from −99% to +1,000% per period for every point where the NPV crosses zero, so it can tell you when there is no IRR or more than one. The MIRR fixes two weaknesses of the IRR by assuming cash received is reinvested at a rate you choose and outflows are financed at another. NPV here counts the first value as today; a spreadsheet's NPV function discounts every value it is given, so add the initial investment separately there.
Worked example
You invest $10,000 and expect $2,500, $3,000, $3,500, $4,000 and $1,500 at the end of the next five years. The IRR is the rate that discounts those five amounts back to exactly $10,000: 14.05% a year.
At an 8% required return, the NPV is $1,626.24, so the project beats that hurdle; the profitability index is 1.163. Reinvesting the cash you get back at 6% and financing the outlay at 8%, the MIRR is 10.4%, lower than the IRR because it doesn't assume the cash can be reinvested at 14.05%. The running total turns positive during year 4: the payback period is 3.25 years, or 3.79 years using discounted cash flows.
NPV at different discount rates
The example cash flows. The NPV falls as the rate rises and crosses zero at the IRR, 14.05%.
| Discount rate | NPV |
|---|---|
| 0% | $4,500.00 |
| 4% | $2,941.11 |
| 8% | $1,626.24 |
| 12% | $508.17 |
| 14% | $11.16 |
| 16% | −$449.70 |
| 20% | −$1,276.04 |
When there is no IRR, or more than one
A normal investment, money out first and money back later, has one sign change and one IRR. If the signs change more than once, for example a project that needs a large clean-up payment at the end, the NPV curve can cross zero several times. The flows −100, +230, −132 have IRRs of 10% and 20%; neither tells you much on its own. In that case, rely on the NPV at your required return, or the MIRR, which always gives a single answer. If the cash flows never change sign (all money out, or all money in), no IRR exists at all, and the calculator says so.
Tips for using IRR
- Compare with your cost of capital. An IRR above the return you require means a positive NPV at that rate.
- Don't rank projects of different sizes by IRR alone. A small project can have a high IRR but add less value than a larger one with a lower IRR. NPV shows the value in money.
- Timing matters. Moving the same cash a year earlier raises the IRR, even though the total received is unchanged.
- Garbage in, garbage out. The result is only as good as the cash flow forecast. Try a pessimistic case too.
For a single amount in and out, the ROI calculator is simpler. To analyze a rental, use the rental property calculator, which builds the cash flows for you. The present value calculator handles a single future sum or an annuity.
Frequently asked questions
What is IRR?
The internal rate of return is the discount rate at which the net present value of all the cash flows is zero. An investment of $10,000 that returns $2,500, $3,000, $3,500, $4,000 and $1,500 over five years has an IRR of 14.05% a year.
What is the difference between IRR and NPV?
NPV is a value in money at a rate you choose; IRR is the rate at which that value is zero. For the example cash flows, the NPV at 8% is $1,626.24. The NPV is positive at any rate below the 14.05% IRR and negative above it.
What is MIRR and why is it lower than IRR?
The modified IRR assumes cash you receive is reinvested at a rate you choose, and money you pay out is financed at another, instead of assuming reinvestment at the IRR itself. With 8% finance and 6% reinvestment, the example has an MIRR of 10.4% against a 14.05% IRR.
Can an investment have more than one IRR?
Yes, when the cash flows change sign more than once. The flows −100, +230 and −132 have two IRRs, 10% and 20%. In that case use NPV or MIRR to judge the investment. If the flows never change sign, there is no IRR at all.
How is the payback period calculated?
Add the cash flows period by period until the running total turns positive, then interpolate within that period. In the example, $1,000 is still unrecovered after year 3 and year 4 brings $4,000, so payback is 3 + 1,000 ÷ 4,000 = 3.25 years.