IRR Calculator

What Is IRR?

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows from an investment equal to zero. It represents the annualized rate of return the project is expected to generate over its life.

If the IRR exceeds your hurdle rate (required rate of return), the investment is expected to create value. If the IRR is below the hurdle rate, the project is expected to destroy value. When IRR equals the hurdle rate, the NPV is approximately zero and you are indifferent.

How IRR Is Calculated

IRR is found by solving the equation where NPV equals zero:

0 = −C₀ + CF₁/(1+IRR)¹ + CF₂/(1+IRR)² + … + CF_n/(1+IRR)ⁿ

There is no closed-form solution for IRR, so it must be found numerically. This calculator uses a bisection algorithm that iteratively narrows the search range until it finds the rate where NPV is within $0.01 of zero.

IRR vs NPV

IRR gives an intuitive percentage return, making it easy to communicate and compare. NPV gives the dollar value created, making it better for comparing projects of different sizes.

For independent projects, they usually agree on accept/reject decisions. For mutually exclusive projects (choose one), NPV is preferred because IRR doesn’t account for scale differences — a small project with high IRR may create less total value than a large project with lower IRR.

Modified IRR (MIRR)

A key limitation of IRR is that it assumes intermediate cash flows are reinvested at the IRR itself, which may be unrealistically high. MIRR fixes this by using two separate rates:

• Reinvestment rate: The rate at which positive cash flows are compounded forward to the end of the project (typically the firm’s cost of capital).
• Finance rate: The rate at which negative cash flows are discounted back to the present (typically the firm’s borrowing cost).

MIRR = (FV of positive CFs / |PV of negative CFs|)^1/n − 1

MIRR provides a more realistic measure of return and always produces a unique solution, even when traditional IRR gives multiple values.

IRR Decision Rule

• IRR > Hurdle Rate: Accept the project — it creates value above your required return
• IRR < Hurdle Rate: Reject the project — it destroys value
• IRR = Hurdle Rate: Indifferent — the project earns exactly the required return (NPV ≈ 0)

For mutually exclusive projects, always rank by NPV rather than IRR. A higher IRR does not necessarily mean a better investment when project sizes or timelines differ.

Limitations of IRR

• Multiple IRRs: When cash flows change sign more than once (e.g., outflow → inflow → outflow), the NPV equation can have multiple roots. In such cases, IRR is unreliable — use MIRR or NPV instead.
• Reinvestment assumption: IRR assumes intermediate cash flows are reinvested at the IRR rate, which may be unrealistic. MIRR corrects for this.
• Scale problem: IRR doesn’t account for project size. A 50% IRR on a $1,000 project creates less value than a 20% IRR on a $1,000,000 project.
• No IRR: If all cash flows are the same sign, no IRR exists. The calculator detects this and displays “N/A”.