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Internal Rate of Return

9 min read 5 practice questions
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On this page 9 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Quick check
  8. Study tools
  9. Sources & references

In 30 seconds

The is the that makes a project's net present value equal zero — the rate at which the money a project brings in exactly covers the money it costs. In plain words, it is the annual rate the project itself earns. The is simple: accept the project when its IRR beats the , and reject it when it does not. IRR reports a percentage, while net present value reports dollars, and a high percentage does not always mean the biggest value.

Why this matters

Every project — a new machine, a food cart, a rental property — asks the same question: is it worth the money? IRR turns that question into a single, easy-to-read number: the annual percentage rate the project itself earns. Because people already think in percentages from savings accounts and loans, IRR is one of the most common ways managers talk about whether an investment earns its keep. The rule is direct: if the project earns more than the money funding it costs, it is worth taking; if it earns less, the project cannot even pay for its own funding. Understanding IRR lets you follow real business conversations and size up any opportunity that promises future money in exchange for money spent today.

The college version

What IRR is: the rate the project itself earns

Two sources that agree give this lesson its working definition. OpenStax Principles of Finance defines the internal rate of return as the discount rate that makes a project's discounted inflows exactly equal its discounted outflows — in other words, the rate at which the project's net present value equals zero. Corporate Finance Institute states the same idea in plainer terms: IRR is the discount rate that makes a project's NPV zero, and it is the expected annual rate of return earned on a project or investment. The working definition used here combines them: IRR is the discount rate that makes a project's net present value equal zero, and in words, it is the annual rate the project itself earns. The one-period version needs nothing more than simple arithmetic. Suppose a project costs $500 today and returns $575 one year later. The gain is $75, and $75 is 15 percent of $500, so the project earns 15 percent on the money it uses — its IRR is 15 percent. The definition checks out: discount the $575 back one year at 15 percent ($575 ÷ 1.15 = $500), and the present value of the inflow exactly equals the outflow, which is what an NPV of zero means. That is also why IRR is called internal: it comes entirely from the project's own cash flows, with no outside rate plugged in.

The decision rule: compare IRR with the cost of capital

IRR by itself is just a number. It becomes a decision when it is compared with the cost of capital — the return the company must pay the people who supply its money. OpenStax states the rule directly: if the IRR is greater than the cost of capital, a project should be accepted; if it is less, the project should be rejected. CFI's version is the same: IRR is compared with the company's hurdle rate or cost of capital, and the project is accepted when the rate reaches that benchmark and rejected when it falls below. The logic is plain. If a project earns 15 percent while its funding costs 10 percent, the project brings in enough to pay the funders their 10 percent and still leaves something over — it adds value. If the project earns 8 percent while funding costs 10 percent, the project cannot even cover the cost of the money it uses; every dollar of return is outweighed by what the funding costs. The cost of capital is a sibling topic handled in its own lesson; it turns up here only as the benchmark that IRR must beat.

IRR versus NPV: a rate versus a dollar amount

IRR and net present value evaluate the same project but answer different questions. NPV (a sibling topic, referenced here only) is a dollar amount: a project's discounted expected inflows minus its discounted outflows, accepted when positive because the project adds value in today's dollars. IRR is the percentage rate at which that NPV equals zero. NPV answers 'how much value does this project add?' IRR answers 'what annual rate does this project earn?' In most cases the two point the same way — a project with a strongly positive NPV usually also carries an IRR well above the cost of capital — which is why companies commonly report both, often alongside other measures such as payback period. But a percentage and a dollar amount are different units and cannot be compared directly: '15 percent' and '$45' are not rivals; they are two views of the same project.

Where IRR can mislead: projects of different sizes

IRR has a well-documented blind spot: it ignores scale. OpenStax lists overlooking differences in scale among the method's disadvantages — IRR converts cash flows to percentages and ignores differences in the size of projects. CFI makes the same warning: a very small investment can carry a very high rate of return, so managers sometimes choose a lower percentage that offers higher dollar value. Original example: Project A costs $1,000 and returns $1,150 after one year — a 15 percent IRR and $150 of value added. Project B costs $100 and returns $120 — a 20 percent IRR and $20 of value added. Ranked by rate, Project B wins; ranked by the dollars actually created, Project A wins by a wide margin. OpenStax's guidance for choosing among competing projects is to take the one with the highest NPV, because NPV estimates how much value a project creates. That is the honest framing of IRR: it is the project's own speedometer — one clear number for the rate — but it is not the whole dashboard. Size, dollar value, and risk live on other instruments, and a driver who watches only the speedometer misses the fuel gauge.

Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of a project as a machine with a slot for money in and a chute for money out. You put $500 in today; a year later $575 comes out. The internal rate of return is the annual percentage rate the machine earns on the money you fed it — 15 percent in this case. It is one number that summarizes the whole deal, so you do not have to add up each year's cash by hand to know whether the project is earning its keep. But the number is a forecast, not a fact: it is computed from your best guesses about what the project will actually bring in, and optimistic guesses produce an optimistic rate.

Picture it like this

IRR is the project's own speedometer. One glance tells you the rate the project is going — 15 percent — without any arithmetic on your part. Managers like it for exactly that reason: a single, familiar number that anyone can compare with the cost of capital, the way a driver compares their speed with the limit.

Where the picture stops working

A speedometer measures the speed you are actually moving; IRR is an estimate built from predicted cash flows, so it is only as good as the predictions. And the speedometer is one gauge among several: it does not say whether the trip is worth taking, how much fuel it burns, or whether another route is better. A small project can show a very high rate while adding very little value, so the speedometer has to be read alongside the other instruments.

Worked example

Lena runs a small bakery and is weighing a used espresso machine. The machine costs $500, and she expects it to bring in $575 in extra sales over the next year. What is the project's IRR? The profit is $575 − $500 = $75. As a percentage of the $500 invested, that is $75 ÷ $500 = 0.15, or 15 percent — the IRR. Check the definition: discount the $575 back one year at 15 percent, $575 ÷ 1.15 = $500, which exactly equals the machine's cost, so the net present value is zero. Lena can earn 10 percent by leaving the money in her savings account, so her cost of capital is about 10 percent. Since 15 percent beats 10 percent, the IRR rule says buy the machine: it earns more than the money costs.

Key takeaway

IRR is the project's own rate — the discount rate that makes a project's net present value zero. Accept when it beats the cost of capital, reject when it does not, and remember the rate is not the whole picture: size and dollar value matter too.

Quick check

3 questions here, of 5 in this lesson’s practice set. Answers stay hidden until you check.

Question 1 of 3foundational

What does the internal rate of return (IRR) of a project measure?

Choose an answer, then check it.
Question 2 of 3intermediate

A taco stand costs $500 to set up and is expected to bring in $575 one year later. What is the project's internal rate of return?

Choose an answer, then check it.
Question 3 of 3intermediate

A company's cost of capital is 9%, and a proposed project has an IRR of 12%. What should the company do, and why?

Choose an answer, then check it.
Practice all 5

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Practice this lesson
Study tools & related lessonsYou’ll learn to · Common mistakes · Easily confused · Key vocabulary · Related

You’ll learn to

  • Define the internal rate of return as the discount rate that makes a project's net present value equal zero, using the working definitions from OpenStax and CFI.
  • Explain in plain words what IRR means: the annual rate the project itself earns on the money it uses.
  • Apply the decision rule with original one-period examples: accept when IRR exceeds the cost of capital, reject when it does not.
  • Distinguish IRR, a percentage rate, from net present value, a dollar amount.
  • Explain why ranking projects of different sizes by IRR alone can mislead, and what to check instead.

Common mistakes

  • Treating IRR as the dollar profit.

    IRR is a percentage rate. In the espresso-machine example, $75 is the profit and 15 percent is the rate; mixing the two units leads to false comparisons.

  • Assuming IRR already includes the cost of capital.

    IRR is computed from the project's own cash flows alone. Comparing it with the cost of capital is the decision-maker's step — that comparison is the decision rule.

  • Picking the project with the highest IRR without looking at size.

    A $100 project can show 20 percent while a $1,000 project shows 15 percent; the bigger project may still add far more value. Check the dollar value (NPV) before choosing.

  • Expecting IRR to be accurate when the cash-flow guesses are shaky.

    IRR is computed from predicted cash flows. If the predictions are optimistic, the rate is optimistic too — the number is only as good as the estimates that go in.

Easily confused

IRR — a percentage rate: the annual rate the project itself earns. vs. NPV — a dollar amount: the value the project adds in today's dollars.

Same project, two units. A rate says how fast the money grows; a dollar amount says how much value is created. They usually agree on accept or reject, but they cannot be compared directly.

IRR — the rate the project earns. vs. Cost of capital — the rate the money funding the project costs.

The decision rule compares the two: accept when the earned rate beats the required rate.

One-period IRR — simple arithmetic: (amount returned − amount invested) ÷ amount invested. vs. Multi-period IRR — found by trial and error or a financial calculator.

The simple division in this lesson works only when all the cash arrives in a single period; longer projects need the iterative method.

Key vocabulary

Internal rate of return (IRR)
The discount rate that makes a project's net present value equal zero — the annual rate the project itself earns on the money it uses.
Net present value (NPV)
A dollar amount: the present value of a project's expected cash inflows minus the present value of its outflows.
Discount rate
The interest rate used to translate future dollars into their value today.
Cost of capital
The return a company must pay the people who supply its money; the benchmark an IRR must beat.
Cash inflow
Money a project brings in, such as sales revenue from a new machine.
Cash outflow
Money a project requires, such as the upfront cost of buying the machine.
Initial investment
The money paid up front to start a project.
Decision rule
A simple yes-or-no standard for acting on a number, such as accepting a project when its IRR exceeds the cost of capital.

Sources & references

  1. Principles of Finance, Section 16.3: Internal Rate of Return (IRR) Method — OpenStax, Rice University
  2. Internal Rate of Return (IRR): An Analyst's Guide to IRR — Corporate Finance Institute (CFI)
  3. Principles of Finance, Section 16.5: Choosing between Projects — OpenStax, Rice University
  4. Principles of Finance, Section 16.2: Net Present Value (NPV) Method — OpenStax, Rice University
  5. Capital Budgeting Best Practices — Corporate Finance Institute (CFI)

EliExplains lessons are original prose written from the open, credible references above. See Copyright & Licensing.

Researched 2026-08-21

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