How to Calculate Internal Rate of Return (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. In plain terms, it's the annualized return your investment generates. The higher the IRR, the more attractive the investment.

The Concept

IRR solves for r in the NPV equation:

0 = CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ

Where CF is the cash flow at each period and r is the IRR.

There's no closed-form solution—IRR is found by trial-and-error (or iteration).

Step-by-Step Example

You invest $10,000 (CF₀ = −$10,000) and receive:

Year 1: $3,000
Year 2: $4,000
Year 3: $5,000
Year 4: $3,000

Total cash in: $15,000 on $10,000 invested.

Try r = 20%: NPV = −10,000 + 3,000/1.2 + 4,000/1.44 + 5,000/1.728 + 3,000/2.074 = −10,000 + 2,500 + 2,778 + 2,894 + 1,446 = −$382 (slightly negative, so IRR < 20%)

Try r = 18%: NPV ≈ +$180 (positive, so IRR > 18%)

IRR ≈ 19% (between 18% and 20%)

Decision Rule

If IRR > your required rate of return (hurdle rate): invest
If IRR < hurdle rate: pass
Compare projects: higher IRR is generally preferred

IRR vs. CAGR

IRR accounts for timing of cash flows (when you receive money matters), while CAGR assumes a single lump sum grows at a constant rate. For investments with multiple cash flows, IRR is the more accurate measure.

Use our IRR calculator for any investment cash flow schedule.