Calculadora de TIR (3 períodos)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
TIR: r tal que VPL = 0 (bissecção)
About this calculator
The IRR (Internal Rate of Return) Calculator for 3 periods helps you find the discount rate that makes the Net Present Value (NPV) of a three-cash-flow stream equal to zero. The IRR represents the expected profitability of an investment, making it a key metric to compare projects of different sizes. If the IRR exceeds the required rate of return (hurdle rate), the project is considered viable.
The calculation uses the bisection method, a numerical technique that iteratively tests rates until the NPV approaches zero. The NPV is the sum of discounted cash flows: for each period, the cash flow is divided by (1 + rate) raised to the period. The algorithm searches for the root between 0% and 1000% (or another defined limit), ensuring accuracy even when no exact solution exists.
Use this calculator when analyzing investments with three cash flows, such as a project requiring an initial outlay (negative flow) and generating two future returns (positive flows). Common examples include purchasing equipment that reduces costs over two years, or a small business with an initial investment and profits in the following two years. This tool is useful for entrepreneurs, investors, and finance students.
Caution: The IRR may not exist or may be multiple if there is more than one sign change in the cash flows. For conventional flows (one negative, then positives), the IRR is unique. Additionally, the IRR should not be used to compare projects with different durations without considering the reinvestment of intermediate cash flows. Always compare the IRR with the investor's hurdle rate.
Frequently asked questions
What does IRR mean?
IRR stands for Internal Rate of Return. It is the discount rate that makes the present value of cash inflows equal to the present value of outflows, resulting in an NPV of zero.
How to interpret the calculated IRR?
If the IRR is higher than the required rate of return (hurdle rate), the project is viable; if lower, it is not. The higher the IRR, the more profitable the project.
Can I use this calculator for flows with more than 3 periods?
No, this version is limited to exactly 3 cash flows. For more periods, use a generic IRR calculator.
What if the calculator does not find an IRR?
If no IRR is found, it means no discount rate makes the NPV zero (e.g., all flows positive or all negative). Check the signs of the cash flows.
Does IRR consider reinvestment of flows?
IRR assumes that intermediate cash flows are reinvested at the IRR itself, which may not be realistic. For greater accuracy, use the modified IRR (MIRR).