Why does my series have no IRR?

Because the money only goes one way. A break-even rate exists only where cash goes out and later comes back, so a series of pure inflows or pure outflows has none.

Is a higher IRR always better?

No. It ignores scale, so a tiny project with a huge percentage return can be worth far less money than a large one with a modest return. Compare NPV when the sizes differ.

Investmentreturns

IRR Calculator

The rate at which a project exactly breaks even, found by root-find rather than approximation. Where the cashflows never change sign there is no such rate, and this says so instead of returning a number.

Also called: internal rate of return calculator, project irr.

Internal rate of return

17.09%

17.09% a period. That clears your hurdle rate. At your hurdle of 10% the project is worth $16,986.54.

NPV at your hurdle rate

$16,986.54

Total put in

$100,000.00

Total taken out

$150,000.00

Against your hurdle

That clears your hurdle rate.

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

IRR is the discount rate that makes net present value zero. There is no closed form, so it is solved numerically. Two failure modes matter: a series that only ever pays out, or only ever takes in, has no IRR at all; and a series that changes sign more than once can have several, in which case a single figure is misleading. This brackets the root before solving, which is what lets it decline rather than guess.

IRR is the rate at which the discounted cashflows sum to exactly zero

C_t: The cashflow in period t (currency)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

worked by hand

Cashflows, starting with period 0: -1000, 600, 600
Hurdle rate to compare against: 10%

Internal rate of return13.07%

The rate at which -1000 + 600/(1+r) + 600/(1+r)^2 = 0

Open this example

doubling in one period is 100%

Cashflows, starting with period 0: -100, 200
Hurdle rate to compare against: 10%

Internal rate of return100%

arithmetic identity

Open this example

Method and limits

What it assumes

Cashflows are evenly spaced. Use XIRR for real dates.

What it deliberately does not model

It implicitly assumes interim cash is reinvested at the IRR itself, which flatters high-return projects.
With more than one sign change several rates can satisfy the equation and only one is reported.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does my series have no IRR?: Because the money only goes one way. A break-even rate exists only where cash goes out and later comes back, so a series of pure inflows or pure outflows has none.
Is a higher IRR always better?: No. It ignores scale, so a tiny project with a huge percentage return can be worth far less money than a large one with a modest return. Compare NPV when the sizes differ.