How to use the IRR calculator
The Cash flows tool works with equally spaced periods:
- Enter the cash flows in order. Period 0 is today and is normally the outlay, entered as a negative number. Money received is positive; a period with nothing happening is 0. The labels in the first column are optional.
- Choose the period length. If each row is a quarter or a month, the calculator also annualizes the IRR by compounding.
- Set the hurdle rate, the minimum return you require. It is used for the NPV and is marked on the chart.
- Set the two MIRR rates: the finance rate is what funding the outlays costs you, and the reinvestment rate is what you can realistically earn on cash as it comes in.
The XIRR (dates) tool is for cash flows on irregular dates. Enter each date as YYYY-MM-DD, with contributions negative and withdrawals or the current value positive. Rows can be in any order.
How IRR is calculated
The IRR is the rate that makes the present value of all the cash flows add up to zero:
Annualized IRR = (1 + IRRperiod)m − 1CFt is the cash flow in period t (t = 0, 1, 2 …) and m the number of periods in a year: 1 for years, 4 for quarters, 12 for months.
There is no algebraic solution for more than a few periods, so the rate is found numerically. This calculator scans every rate from −99% to +1,000% per period and refines each point where the NPV changes sign, which is how it can report all the IRRs rather than just one.
XIRR solves 0 = Σ CFi ÷ (1 + XIRR)(di − d0) ÷ 365n is the number of periods from the first to the last cash flow. In XIRR, di is the date of each cash flow and d0 the earliest date, with days counted as actual days divided by 365.
A worked example
A project costs $100,000 today and returns $20,000, $30,000, $35,000, $40,000 and $30,000 over the next five years. Those cash flows add up to $55,000.00 more than the outlay, or 1.55× the money paid in.
The IRR is 15.34%: at that discount rate the five inflows are worth exactly $100,000 today. Because it is above the 10% hurdle rate, the NPV at 10% is positive, at $15,219.40.
With a 8% finance rate and cash reinvested at 10%, the MIRR is 13.16%.
If the same five inflows arrived each quarter instead of each year, the IRR would be 15.34% per quarter, which compounds to 76.98% a year. Getting money back faster is worth a great deal.
The XIRR example is an account with two contributions in 2023 totaling $60,000.00, two withdrawals, and a final value of $65,000 in mid-2026. Measured over the actual 3.5 years, the XIRR is 12.57% a year.
IRR, MIRR and the reinvestment question
A single IRR is a clean summary, but it carries a hidden assumption: that every dollar the project pays out can be reinvested at the IRR. For a project earning 15.34%, that means finding other opportunities that also earn 15.34%, which is often unrealistic. MIRR makes the reinvestment rate explicit:
| Reinvestment rate | MIRR | IRR |
|---|---|---|
| 6% | 11.55% | 15.34% |
| 10% (example) | 13.16% | 15.34% |
| 15% | 15.20% | 15.34% |
The IRR does not move, because it ignores what happens to the cash after it leaves the project. The MIRR moves toward the IRR as the reinvestment rate approaches it. When the two figures are far apart, the IRR is overstating what the investment will really compound to.
When there is more than one IRR
The IRR is well behaved when the cash flows change sign once: money out, then money in. Projects with a large cost at the end, such as a mine that must be restored or a lease with a big final payment, change sign twice, and the NPV curve can cross zero twice.
The calculator counts the sign changes. By Descartes’ rule of signs, the number of IRRs is at most the number of sign changes and differs from it by an even number. Take an outlay of $100,000, income of $230,000 a year later and a $132,000 closing cost at the end of year two. The NPV is zero at 10.00% and again at 20.00%. Between the two the project creates value (the NPV at 15% is $189.04); outside them it destroys it. Neither rate can be compared with a hurdle on its own, so the NPV is the measure to rely on. Some cash flows have no IRR at all, and the calculator says so.
Reading the NPV profile
The chart plots the NPV at every annual discount rate from 0% to 30%, widened if needed to show the IRRs. For a conventional project the line slopes down: the higher the rate, the less the later cash flows are worth. The IRR is where the line crosses zero. Any hurdle to its left gives a positive NPV and any hurdle to its right a negative one. A steep line means the project’s value depends heavily on the discount rate, which is typical when most of the cash arrives late.
What this calculator does not include
- Cash flow quality. The result is only as good as the forecast. Use after-tax cash flows, not accounting profit.
- Project size. IRR is a percentage and says nothing about how much value is created. A small project can have a higher IRR than a large one that adds far more money. The NPV calculator compares projects on both measures.
- Touching roots. The scan finds rates where the NPV crosses zero. A rate where the curve only touches zero without crossing, which is rare, is not reported.
- Day-count choices. XIRR uses actual days divided by 365, as spreadsheet XIRR functions do. Leap years therefore add a day of growth.
- Risk. A higher IRR is not better if it comes with much more uncertainty. Set the hurdle rate to reflect the risk; our WACC calculator estimates a company’s cost of capital.