IRR calculator

This IRR calculator determines the internal rate of return (IRR) by finding the discount rate that makes the net present value (NPV) of cash flows equal to zero.

Please note that Year 0 cash flow is the initial investment. Any intermediate cash flows that are left empty are assumed to be zero.

The calculator also detects multiple IRRs if they exist.

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What is IRR (Internal rate of return)?

Internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of cash flows equal to zero. In simpler terms, it’s the rate at which an investment breaks even in terms of NPV.

Mathematically, IRR is the solution to this equation:

NPV = \sum \frac{C_t}{(1 + IRR)^t} = 0

where:

• C_t​ = Cash flow at time t​
• IRR​= Internal rate of return
• t​= Year index (0, 1, 2, … n)

Example calculation

Scenario:

You invest $1,000 today (negative cash flow) and expect the following future cash flows:

• Year 1: $500
• Year 2: $400
• Year 3: $300

Step 1: Set up the IRR equation

0 = -1000 + \frac{500}{(1 + IRR)^1} + \frac{400}{(1 + IRR)^2} + \frac{300}{(1 + IRR)^3}

Step 2: Solve for IRR

Since this equation is nonlinear, IRR is found iteratively using trial-and-error or numerical methods (like Newton-Raphson).

Using a financial calculator or Excel (=IRR(A1:A4)) or Python:

IRR \approx 18.82\%

Interpretation of IRR

• If IRR > Required Return, the investment is profitable.
• If IRR < Required Return, the investment is not worth it.

For example, if your required return is 10%, an IRR of 18.82% means this is a good investment!