Internal Rate of Return (IRR) Calculator

What Is the Internal Rate of Return (IRR)?

The Internal Rate of Return (IRR) 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 phrase “CF” you’ll see throughout this page is shorthand for Cash Flow, meaning the dollars coming in (or out) during a given year.

The IRR Formula

IRR is defined as the rate r that satisfies:

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

Where CF₀ is the initial outlay (a negative number) and CF₁ through CFₙ are future cash flows, which may be positive or negative. This calculator handles up to 15 years. The equation has no algebraic solution, so it is solved numerically by bisection: narrow the bracket, test the midpoint, repeat.

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 17.45%. If your required return (hurdle rate) is 12%, you should accept the project: the same cash flows discounted at 12% give a Net Present Value of +$6,549, so the project is worth about six and a half thousand dollars more than the money it ties up.

Note the total undiscounted inflow is $77,000 on a $50,000 outlay, a 54% gain. Nobody would call that a 54% return, because it took five years to arrive. IRR is what converts that lump gain into an annual rate you can compare against a hurdle.

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

Where you will actually meet it

Equipment purchases, rental property, private equity, and infrastructure bids. Private equity in particular lives and dies by IRR, which is also where its weaknesses get exploited: because IRR is sensitive to when money comes back, a fund can flatter its headline number by returning capital early through a dividend recapitalisation, without the underlying business having improved at all.

That sensitivity cuts the other way too. IRR says nothing about size. A 50% IRR on a $1,000 project and a 20% IRR on a $1,000,000 project are not close, and only the second one pays for anything. Read IRR next to NPV, never instead of it.