IRR Calculator

What is Internal Rate of Return (IRR)?

IRR is the discount rate at which the Net Present Value (NPV) of all cash flows from an investment equals zero. In plain terms: it is the annualized return rate your investment is expected to earn. If IRR > your cost of capital (or hurdle rate), the investment creates value and should be accepted. If IRR < cost of capital, reject it. IRR is the second most-used capital budgeting metric after NPV.

IRR Formula and Calculation Method

IRR has no closed-form algebraic solution. It is defined as the discount rate r that satisfies:

0 = −C₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ

This calculator uses the bisection method — it repeatedly halves the interval between a rate that makes NPV positive and one that makes it negative, converging to 5-decimal-place accuracy within 1,000 iterations. Excel uses Newton-Raphson (faster but can fail to converge); bisection is more reliable for unusual cash flow patterns.

What is MIRR — Modified Internal Rate of Return?

MIRR addresses two well-known flaws in standard IRR: (1) IRR assumes cash flows are reinvested at the IRR itself — unrealistic for high-IRR projects. (2) Multiple IRRs can exist when cash flows change sign more than once. MIRR uses two separate, realistic rates:

• Finance rate: Cost of borrowing for negative (outflow) cash flows.
• Reinvestment rate: Return expected on reinvested positive cash flows — typically your WACC or safe investment return.

MIRR formula: MIRR = (FV of positive CFs at reinvestment rate / PV of negative CFs at finance rate)^(1/n) − 1. MIRR is almost always lower than IRR and is the more conservative, realistic estimate of project return.

When IRR Fails — Key Limitations

• Multiple IRRs: When cash flows change sign more than once (e.g., year 3 has a large capex), there can be multiple valid IRRs. Use MIRR or NPV in this case.
• Mutually exclusive projects: A project with IRR 40% on a $10,000 investment may be less valuable than a project with IRR 20% on $1,000,000. NPV captures scale; IRR does not.
• Reinvestment assumption: Standard IRR assumes all cash flows are reinvested at the IRR rate — use MIRR with a realistic reinvestment rate for a more honest forecast.

How to Use This IRR Calculator

1. Enter your Initial Investment (negative cash flow in year 0).
2. Add Annual Cash Flows for each year of the investment period.
3. For MIRR, enter your Finance Rate (cost of capital) and Reinvestment Rate.
4. The calculator instantly shows IRR, MIRR, NPV, and a year-by-year discounted cash flow table.