How the Irr Calculator Works
The internal rate of return, or IRR, is the yearly return an investment earns. It is one number that sums up a whole series of cash flows: what you pay in at the start, and the money you get back over time. It is used to judge business projects, rental properties, private investments and any plan where the money comes back in uneven amounts. The IRR Calculator finds it for you.
What you enter
- Amount you invest at the start: the money you put in on day one.
- Cash you get back in each period: one number for every year (or quarter, or month), separated by commas. If you must put in more money later, enter that period as a negative number.
- How often the cash flows arrive: yearly, quarterly or monthly. The result is always shown as a yearly rate.
- Discount rate: the return you could earn elsewhere. It is used for the net present value, and to judge if the IRR is good enough.
What the IRR means
Money you get later is worth less than money you get now, because money in hand can earn a return. To compare cash flows at different times, each one is discounted back to today. The net present value (NPV) adds them up:
NPV = -investment + cash 1 / (1 + r) + cash 2 / (1 + r)^2 + cash 3 / (1 + r)^3 + ...
The IRR is the rate r at which the NPV is exactly zero. At that rate, the cash you get back, in today's money, is worth exactly what you paid. If you could earn more than the IRR elsewhere, the investment is not worth it. If you could earn less, it is.
How the calculator finds it
There is no simple formula for the IRR, so the calculator finds it by trial. It tests many rates, looks for the place where the NPV changes from positive to negative, and then narrows in on it very closely. If the cash flows are not in the usual pattern, it can find more than one answer, and it tells you.
A worked example
You invest $50,000. You get back $12,000, $15,000, $18,000, $20,000 and $22,000 over the next five years.
| Year | Cash flow | Worth today at 19.44% |
|---|---|---|
| 0 | -$50,000 | -$50,000 |
| 1 | $12,000 | $10,047 |
| 2 | $15,000 | $10,514 |
| 3 | $18,000 | $10,563 |
| 4 | $20,000 | $9,826 |
| 5 | $22,000 | $9,050 |
| Total | $0 |
At a rate of 19.44%, the five cash flows are worth exactly $50,000 today. So the IRR is 19.44%. In all, you put in $50,000 and get back $87,000, a profit of $37,000. That is $1.74 back for every $1 in. If your discount rate is 8%, the NPV is $17,934, which is positive, so the investment beats an 8% alternative.
Chart: NPV at different discount rates
The same example. The higher the discount rate, the lower the NPV. The IRR is where it reaches zero:
0% ████████████████████████████████████████ $37,000 5% ██████████████████████████ $24,275 10% ███████████████ $14,150 15% ██████ $5,985 19.4% (IRR, NPV is zero) 20% -$680 25% -$6,183
The calculator draws this curve for your own numbers, and marks the IRR where it crosses zero.
Other examples
- A single payment: invest $1,000 and get $1,100 after one year. The IRR is 10%.
- Even payments: invest $1,000 and get $500 a year for three years. The IRR is 23.38%.
- A loss: invest $1,000 and get $300 a year for three years, which is only $900. The IRR is negative, at -5.09%.
- Quarterly cash: invest $2,000 and get $150 each quarter, then $2,150 in the last. The rate is 7.5% a quarter, which is 33.55% a year when compounded.
Limits of the IRR
- It assumes you can reinvest the cash at the IRR. A very high IRR may be unrealistic if you cannot find another investment as good.
- It ignores the size of the project. A small investment with a 40% IRR may make less money than a big one with a 15% IRR. Look at the NPV and the profit too.
- More than one answer is possible. If the cash flows change from negative to positive more than once, such as a project with a big cleanup cost at the end, there may be several IRRs. The calculator warns you when this happens.
- Timing is assumed. Each cash flow is treated as arriving at the end of its period.
This tool gives an estimate for general information only. It is not financial or investment advice. Real cash flows will differ from your estimates.