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How to use
Internal rate of return is the periodic discount rate that makes the net present value of a periodic cash-flow series equal zero. Some cash-flow patterns can have more than one valid rate, so this calculator searches for multiple roots rather than assuming IRR is always unique.
- Enter CF0, CF1, CF2… with their real signs, separated by commas or lines.
- At least one positive and one negative cash flow are required, with no more than 40 values.
- Calculate to display each IRR root found in the search interval from -99.9999% up to a decimal rate of 1,000,000.
How it is calculated
Example
Example: -1000, 400, 400, 400 gives a periodic IRR of about 9.70%. Cash flows with multiple sign changes can produce more than one root.
Important notes
This is a mathematical tool, not investment advice. It assumes equal periods and does not use actual dates, so it is not XIRR. A real root may not exist in the search range, and multiple roots are possible; interpret IRR alongside NPV and project assumptions.
Worked examples and interpreting results
Equally spaced flows of −1000 then 1100 have internal rate of return 10% per period. Flows −1000, 0, 1210 give the same rate.
| Case | Calculation | Result |
|---|---|---|
| One-period flow | (1100 ÷ 1000 − 1) × 100 | 10 % |
| Two-period flow | (√(1210 ÷ 1000) − 1) × 100 | 10 % |
How to check the result
Enter the initial flow first, then later flows with signs. The rate is per period and annual only for annual periods. Multiple sign changes can produce multiple solutions.
Frequently asked questions
Why can there be multiple IRRs?
Multiple sign changes in cash flows can make the NPV=0 equation have several real roots.
Is IRR always annual?
No. IRR has the same period as the cash-flow spacing; monthly flows produce a monthly IRR unless converted appropriately.
What is the difference between IRR and NPV?
IRR is the rate that makes NPV zero, while NPV is a currency value at a discount rate you choose. When project rankings conflict, NPV at the cost of capital is often more informative.