Internal Rate of Return (IRR) Calculator
Calculate the Internal Rate of Return (IRR) for an investment with up to 5 cash flows.
Determine if a project meets your required rate of return.
What Is the Internal Rate of Return (IRR)?
The Internal Rate of Return is the discount rate that makes the Net Present Value (NPV) of an investment equal to zero. In plain terms, it is the annualized rate of return an investment is expected to generate over its lifetime.
The IRR Formula
IRR is defined as the rate r that satisfies:
0 = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + CF₃/(1+r)³ + CF₄/(1+r)⁴ + CF₅/(1+r)⁵
Where CF₀ is the initial outlay (a negative number) and CF₁ through CF₅ are future cash inflows. Because this equation cannot be solved algebraically, it is solved numerically — this calculator uses a bisection search method.
The Decision Rule
Compare IRR to your hurdle rate (also called the required rate of return or cost of capital):
- IRR > Hurdle Rate → Accept the project. It creates value.
- IRR < Hurdle Rate → Reject the project. It destroys value.
- IRR = Hurdle Rate → Breakeven. Indifferent.
Worked Example
You invest $50,000 today and expect cash inflows of $15,000, $18,000, $20,000, $14,000, and $10,000 over five years. The IRR works out to approximately 18.7%. If your required return (hurdle rate) is 12%, you should accept the project.
IRR vs. NPV
Both IRR and NPV are used for capital budgeting, but they can disagree. NPV is generally preferred because:
- IRR assumes cash flows are reinvested at the IRR itself, which is often unrealistic
- A project can have multiple IRRs if cash flows change sign more than once (the multiple IRR problem)
- NPV directly measures the dollar value created
Practical Applications
IRR is used for evaluating equipment purchases, real estate investments, private equity deals, and infrastructure projects. It is especially useful for comparing projects of different sizes because it is expressed as a percentage, making it intuitive for stakeholders.
Limitations
IRR should not be used in isolation. It does not account for project scale (a 50% IRR on a $1,000 investment may be less valuable than a 20% IRR on $1,000,000). Always pair IRR analysis with NPV and payback period.