Find the internal rate of return from an initial investment and up to 8 annual cash flows with a fast bisection solver.
Enter your initial investment and up to 8 annual cash inflows. The calculator finds the discount rate that makes net present value equal zero, using a bisection search.
Formula: NPV = −I + Σ CF_t ÷ (1+r)^t = 0, solved for r. Example: −$10,000 then $3,000/year for 5 years → IRR 15.24%.
Getting an accurate internal rate of return from the calculator above takes less than a minute once you have your cash-flow numbers ready. The walkthrough below explains each field in plain language, shows you what to type, and teaches you how to read the result the way a finance professional would.
Pro tip: keep your time units consistent. If your cash flows are annual, the IRR is an annual rate. Mixing monthly cash flows with an annual interpretation, or vice versa, is one of the most common ways beginners misread the result.
The internal rate of return is one of the most widely used yardsticks in finance because it answers the question every investor asks first: what annualized return does this investment actually earn? Unlike a simple profit total, the IRR respects the time value of money, which is the principle that a dollar received today is worth more than a dollar received five years from now, because today’s dollar can be invested and put to work immediately.
Formally, the IRR is the discount rate at which a project’s net present value (NPV) equals zero. In other words, it is the break-even interest rate: the exact rate at which the present value of all future cash inflows precisely offsets the initial investment. If you borrowed money at exactly the IRR to fund the project, you would break even, not a cent richer and not a cent poorer. Any borrowing rate below the IRR leaves you with a surplus, which is why investors compare the IRR against their hurdle rate or cost of capital when making decisions.
The appeal of the IRR is that it expresses performance as a single, intuitive percentage. Saying a project earns 15.24 percent is instantly comparable to a savings account paying 4 percent, a stock portfolio averaging 9 percent, or a business loan charging 7 percent. Dollar-based NPV tells you how much value a project creates in absolute terms, but it cannot tell you the efficiency of the capital employed. IRR fills that gap, which is why corporate finance teams, real-estate investors, and venture capitalists quote it constantly.
The IRR also carries an important economic interpretation: it represents the project’s own internal compounding rate. Every dollar the project generates is implicitly assumed to be reinvested at the IRR itself. This assumption is harmless when the IRR is modest and realistic, but it can flatter extraordinary results. A project with a 60 percent IRR implicitly assumes you can keep reinvesting proceeds at 60 percent, which is rarely true in practice. Professionals handle this by cross-checking unusually high IRRs against NPV and, when needed, against the modified internal rate of return (MIRR).
Used wisely, the internal rate of return is a compact summary of a project’s economic merit: one number that blends the size of the investment, the size and timing of every cash flow, and the time value of money into a single decision-ready percentage.
The IRR is defined as the rate r that solves this equation:
NPV = -I + CF1/(1+r) + CF2/(1+r)^2 + … + CFn/(1+r)^n = 0
In this formula, I is the initial investment, CFt is the cash flow in year t, and n is the number of periods. Because r appears in the denominator of every term, there is no way to isolate it with basic algebra, so the rate must be found iteratively by trying candidate rates until NPV lands on zero. The two worked examples below show exactly how that trial process works with real numbers.
Worked example 1: even cash flows. You invest $10,000 today and receive $3,000 at the end of each year for 5 years. Try a 12 percent discount rate first. The present-value annuity factor is (1 – 1.12^-5)/0.12 = 3.604775, so the present value of the inflows is $3,000 x 3.604775 = $10,814.33, and NPV = $10,814.33 – $10,000 = +$814.33. Because NPV is positive, the true IRR must be higher than 12 percent. Try 16 percent: the annuity factor becomes (1 – 1.16^-5)/0.16 = 3.274294, giving a present value of $9,822.88 and NPV = -$177.12. Now NPV has flipped sign, so the IRR lies between 12 percent and 16 percent. Linear interpolation gives 12% + 4% x 814.33/(814.33 + 177.12), which is about 15.29 percent, and one more refinement lands on the exact IRR of 15.24 percent, matching the calculator’s result.
Worked example 2: uneven cash flows. You invest $50,000 today and expect $8,000 in Year 1, $12,000 in Year 2, $15,000 in Year 3, $18,000 in Year 4, and $20,000 in Year 5. Discounting each flow at 12 percent gives $8,000/1.12 = $7,142.86; $12,000/1.2544 = $9,566.10; $15,000/1.404928 = $10,676.55; $18,000/1.573519 = $11,439.33; and $20,000/1.762342 = $11,348.53. The total present value is $50,173.37, so NPV = +$173.37, which is slightly positive, meaning the IRR sits just above 12 percent. Repeating the calculation at 13 percent gives a present value of $48,768.19 and NPV = -$1,231.81. Interpolating: 12% + 1% x 173.37/(173.37 + 1,231.81), which is about 12.12 percent, the project’s IRR.
Notice the pattern in both examples: pick a rate, compute NPV, and adjust. A positive NPV means the trial rate was too low; a negative NPV means it was too high. Repeating this bracketing, called bisection, converges on the IRR quickly, and it is precisely the algorithm running inside the calculator above.
A small logistics company is considering a $40,000 rooftop solar installation for its warehouse. The system is expected to cut the electricity bill by a net $7,200 per year, after maintenance and insurance, for 8 years, after which the panels will be near the end of their warranted life. Management’s hurdle rate is 7 percent, which is the interest rate on the equipment loan that would finance the project. Should they proceed?
Running the numbers through the IRR calculator gives an initial investment of $40,000 and an annual cash flow of $7,200 for years 1 through 8. To verify by hand, discount the annuity at 9 percent: the factor is (1 – 1.09^-8)/0.09 = 5.534820, so present value = $7,200 x 5.534820 = $39,850.70 and NPV = -$149.30. That is slightly negative, so the IRR is a touch below 9 percent. At 8.9 percent the factor is 5.555573, present value = $40,000.13, and NPV is essentially zero, which means the IRR is approximately 8.9 percent.
Because 8.9 percent exceeds the 7 percent hurdle rate, the project earns about 1.9 percentage points more than its financing cost, so it clears the bar. But the margin is thin. If electricity savings came in just 15 percent lower, at $6,120 per year instead of $7,200, the IRR would fall to roughly 6.9 percent, below the hurdle rate, and the project would destroy value. Management’s sensible move is to approve the project while locking in the savings assumptions with a fixed-price maintenance contract and a conservative generation estimate, then re-run the calculator if any assumption changes.
A business has $25,000 to invest and must choose between two mutually exclusive projects.
Project A costs $25,000 and returns $9,000 per year for 4 years. Discounting at 16 percent: the annuity factor is (1 – 1.16^-4)/0.16 = 2.798181, present value = $9,000 x 2.798181 = $25,183.63, NPV = +$183.63. At 16.5 percent the factor is 2.770854, present value = $24,937.69, NPV = -$62.31. Interpolating gives an IRR of about 16.4 percent.
Project B also costs $25,000 but returns $4,000 in Year 1, $8,000 in Year 2, $12,000 in Year 3, and $16,000 in Year 4. At a 14 percent discount rate the present values are $3,508.77 + $6,155.59 + $8,099.66 + $9,473.11 = $27,237.13, so NPV = +$2,237.13. At 18 percent the total is $24,691.55, NPV = -$308.45. Interpolation yields an IRR of about 17.5 percent.
On IRR alone, Project B (17.5 percent) beats Project A (16.4 percent). A cross-check with NPV at a 10 percent hurdle rate confirms it: Project A’s NPV is $9,000 x 3.169865 – $25,000 = +$3,528.79, while Project B’s NPV is $30,192.68 – $25,000 = +$5,192.68. Both metrics agree, so choose Project B. Note, however, that IRR compares rates, not dollars: if Project A had cost $250,000 with the same 16.4 percent IRR, the dollar value it created could dwarf Project B’s despite the lower rate. Always pair IRR with NPV when project sizes differ.
1. Treating IRR like simple ROI. An IRR of 15 percent is not the same as a 15 percent total profit. IRR is an annualized, time-adjusted rate: earning 15.24 percent per year for five years on $10,000 turns it into about $20,345, a total gain of roughly 103 percent, far more than a simple 15 percent. Conversely, a project that returns your money plus 15 percent over ten years has an IRR under 1.5 percent. Always remember the rate compounds over the project’s life.
2. Ignoring the scale of the investment. A 40 percent IRR on a $1,000 project creates at most a few hundred dollars of value, while a 12 percent IRR on a $10,000,000 project can create millions. Ranking projects purely by IRR systematically favors small, quick wins over large, valuable ones. Use IRR for efficiency and NPV for absolute value, and never let a dazzling percentage blind you to tiny dollar stakes.
3. Forgetting the reinvestment assumption. The IRR calculation implicitly assumes every interim cash flow is reinvested at the IRR itself. If your project shows a 35 percent IRR but you can only reinvest spare cash at 6 percent in the real world, the true realized return will be well below 35 percent. For unusually high IRRs, sanity-check with the modified internal rate of return (MIRR), which lets you set a realistic reinvestment rate.
4. Missing multiple IRRs when cash flows change sign more than once. The classic pattern of money out followed by money in produces a single IRR. But projects with mid-life shutdowns, decommissioning costs, or phased investments, where cash goes out, comes in, then goes out again, can have two or more mathematically valid IRRs, or none at all. If your cash flows change sign multiple times, inspect the NPV profile directly instead of trusting a single percentage.
5. Comparing IRRs across different time horizons. A 20 percent IRR over 2 years and a 14 percent IRR over 15 years are not directly comparable. The longer project compounds its rate for far longer and may create much more wealth, while the shorter one frees up capital sooner for the next opportunity. When horizons differ, compare NPVs at your hurdle rate instead of ranking by the raw percentage alone.
Pair the IRR Calculator with these tools for a complete investment analysis: the Investment Calculator for projecting lump-sum and recurring investment growth, the Payback Period Calculator for measuring how quickly an investment returns its cost, or browse the full Financial Calculators collection.
This page’s IRR Calculator computes the internal rate of return: the discount rate r that solves NPV = -I + Sum CFt/(1+r)^t = 0, where I is the initial investment and CFt are up to 8 annual cash flows. Method: numerical bisection on NPV(r). Inputs: initial investment in dollars as a positive number, and annual cash flows per year. Outputs: IRR as a percentage, total cash inflows, and net profit at that rate. Decision rule: accept the project when the IRR exceeds the hurdle rate, also called the cost of capital. Worked reference values: -$10,000 followed by $3,000 per year for 5 years gives an IRR of 15.24 percent; -$50,000 with flows of $8,000, $12,000, $15,000, $18,000, and $20,000 gives an IRR of about 12.12 percent. Known limitations: assumes reinvestment at the IRR, can yield multiple or no solutions when cash flows change sign more than once, and ignores project scale.
The internal rate of return is the discount rate at which an investment’s net present value equals zero — the project’s break-even annualized return.
Anything above your cost of capital or hurdle rate. Higher is better, but only compare IRRs of similar-risk projects.
ROI is a single total-return percentage; IRR is an annualized rate that accounts for the timing of every cash flow.
Yes — if the cash flows never recover the investment, no IRR exists. Cash flows that change sign multiple times can even produce multiple IRRs.
There is no closed-form formula — it is found iteratively. This calculator uses bisection on NPV(r) = 0 with 200 refinement steps.
A 20 percent IRR means the project earns an annualized return of about 20 percent after accounting for the timing of every cash flow. Compare it with your hurdle rate: if your cost of capital is 8 percent, the project clears it by a wide 12-point margin and creates substantial value. If your hurdle rate is 18 percent, the project barely passes and leaves little room for error. Also check the dollar scale, because a 20 percent IRR on a $5,000 project creates far less wealth than a 12 percent IRR on a $500,000 project.
CAGR measures the realized smooth growth rate of a single lump sum between a starting value and an ending value. For example, an investment growing from $10,000 to $16,105 over 5 years has a CAGR of 10 percent. IRR is more general: it handles multiple cash flows going in and out at different times, finding the single discount rate that makes their net present value zero. For a one-time investment with no interim cash flows, IRR and CAGR are identical. When cash moves in and out along the way, only IRR captures the full picture.
The IRR equation discounts every future cash flow back at the IRR and, equivalently, compounds interim cash flows forward at the IRR. Mathematically, this treats each year’s proceeds as if they were reinvested at that same rate for the rest of the project. If you cannot actually reinvest at the IRR, for example a 35 percent IRR when spare cash earns 5 percent, the true realized return will be lower. Cross-check with the modified internal rate of return (MIRR), which lets you specify a realistic reinvestment rate.
Sources: standard corporate finance references, including Brealey, Myers and Allen’s Principles of Corporate Finance and the CFA Institute curriculum.
Also try our Investment Calculator and Payback Period Calculator — or browse all Financial Calculators.