how to calculate an irr

What is IRR?

IRR stands for Internal Rate of Return. It is the discount rate that makes a project’s net present value (NPV) equal to zero. In plain English: IRR is the break-even growth rate of an investment based on its timing and size of cash flows.

If your required return (sometimes called hurdle rate) is below the IRR, the investment may be attractive. If your required return is above the IRR, the investment usually does not pass.

The IRR formula

IRR is the value of r that solves this equation:

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

Where:

• CF₀ is usually the initial investment (often negative).
• CF₁ ... CF_n are future cash flows.
• r is the periodic return rate we are solving for.

Unlike a simple average return, IRR respects time value of money: cash received earlier is worth more than cash received later.

How to calculate IRR step by step

1) List your cash flows in order

Put each cash flow in timeline order, starting with period 0. For example:

• Period 0: -10,000
• Period 1: +3,000
• Period 2: +4,200
• Period 3: +6,800

2) Set NPV equal to zero

Build the NPV equation using those cash flows and unknown rate r.

3) Solve for r (usually numerically)

There is no simple algebraic formula for most real cash-flow patterns, so calculators and spreadsheets use numerical methods (such as Newton-Raphson or bisection) to find the rate.

4) Interpret the result

If the IRR is 14%, it means the project’s implied return is about 14% per period (assuming the input periods are annual, then 14% per year).

Quick worked example

Suppose your cash flows are:

• -5,000 today
• +2,000 in year 1
• +2,100 in year 2
• +2,200 in year 3

You can test discount rates:

• At 5%, NPV is positive.
• At 15%, NPV is near zero.
• At 20%, NPV turns negative.

So IRR is between 15% and 20%, and a precise solver gives the exact estimate.

How to use the calculator above

• Enter cash flows, with negatives for outflows and positives for inflows.
• Choose periods per year to annualize the result correctly.
• Click Calculate IRR.
• Review the periodic IRR, annualized IRR, and residual NPV near zero.

If your timeline is monthly and you enter 12 periods per year, the tool converts periodic IRR to annualized IRR using:

Annualized IRR = (1 + periodic IRR)^{periods per year} - 1

IRR in Excel and Google Sheets

Equal time intervals

Use:

=IRR(A1:A6)

This assumes each period is equally spaced (monthly, yearly, etc.).

Irregular dates

Use:

=XIRR(values, dates)

XIRR is often more realistic when cash flows happen on specific calendar dates.

Common IRR mistakes

• Mixing time intervals: monthly and yearly flows in one IRR run without adjustment.
• Wrong sign convention: forgetting that investments paid out should be negative.
• Relying on IRR alone: high IRR on a tiny project can be less valuable than lower IRR on a larger one.
• Ignoring multiple IRRs: projects with alternating signs (e.g., - + - +) can produce more than one IRR.
• Assuming reinvestment at IRR: classic IRR can imply unrealistic reinvestment assumptions.

IRR vs NPV: which should you trust?

Use both, but when they conflict, finance teams often prioritize NPV because it measures actual value created in currency terms. IRR is still helpful for comparing efficiency and communicating returns as a percentage.

When MIRR may be better

MIRR (Modified Internal Rate of Return) can be more practical because it lets you set a financing rate and reinvestment rate explicitly. This can produce a more realistic performance metric than classic IRR in some cases.

Final takeaway

To calculate IRR, you are finding the discount rate that makes NPV equal zero. The process is simple conceptually, but usually solved numerically. Use consistent cash-flow timing, correct signs, and pair IRR with NPV for stronger decisions.