IRR Calculator
Internal rate of return: —
Project cash flows
How far apart the cash flows are spaced. This sets how the per-period rate is turned into an annual one.
Period 0 is today — usually your initial investment. Add a row for each later period and mark it money out or money in.
- Period 0 · initial$
- Period 1$
- Period 2$
- Period 3$
- Period 4$
- Period 5$
Advanced options
Add at least one 'money out' cash flow — an investment — so there is a return to measure.
- Capital invested$0
- Net profit$0
Return measures
IRR assumes every interim cash flow is reinvested at the IRR itself — often optimistic. MIRR replaces that with an explicit reinvestment rate, so the two diverge whenever your reinvestment rate differs from the IRR.
NPV profile
Net present value as the discount rate climbs. Wherever the curve crosses zero is an internal rate of return; your hurdle rate is marked for comparison.
Cash-flow timeline
Each period's net cash flow — money out below the line, money in above it.
Cumulative cash flow & payback
The running total of cash, starting negative with the outlay and rising as returns arrive. Where it crosses zero is the payback point; the dashed line discounts each flow, so it crosses later.
Invested vs returned
Total capital put in against total cash taken out, before discounting.
- Total invested$0
- Total returned$0
All results
| Measure | Value |
|---|---|
| Annualized IRR | — |
| Periodic IRR | — |
| Monthly IRR | — |
| Modified IRR (MIRR) | — |
| Net present value | $0 |
| Profitability index | — |
| Payback period | 0.00 periods |
| Discounted payback | 0.00 periods |
| Total invested | $0 |
| Total returned | $0 |
| Net profit | $0 |
Cash-flow tables
| Period | Cash flow | Cumulative |
|---|---|---|
| Period 0 | -$0 | $0 |
| Period 1 | $0 | $0 |
| Period 2 | $0 | $0 |
| Period 3 | $0 | $0 |
| Period 4 | $0 | $0 |
| Period 5 | $0 | $0 |
Present values discount each period's cash flow at your hurdle rate; the cumulative present value of every period equals the project's NPV.
Discount-rate sensitivity
How NPV and the accept-or-reject call shift as your discount rate moves around its current level.
| Discount rate | Net present value | Decision |
|---|---|---|
| 0.00% | $0 | Break-even |
| 0.00% | $0 | Break-even |
| 0.00% | $0 | Break-even |
| 2.50% | $0 | Break-even |
| 5.00% | $0 | Break-even |
How the IRR is found
There is no closed-form formula for the internal rate of return — it is solved numerically. Here is what the calculator does.
- 1
Place each cash flow on its period: period 0 today, period 1 one interval later, and so on, keeping outflows negative and inflows positive.
- 2
Write net present value as a function of an unknown rate r — every cash flow divided by (1 + r) raised to its period number — and look for the rate that makes the total zero.
- 3
Solve for that rate with Newton–Raphson, which follows the slope of the NPV curve to the crossing point, falling back to a bracketing search when the curve is awkward.
- 4
Compound the per-period rate up to an effective annual figure, and scan the whole NPV curve to check whether more than one rate sets it to zero.
- 5
Compare the result with your hurdle rate, and compute NPV, MIRR, payback and the profitability index so the accept-or-reject decision rests on more than one number.
The formula
The internal rate of return r is the discount rate that makes the net present value of every cash flow add up to zero.
Σ CFₜ ÷ (1 + r)ᵗ = 0, for t = 0 … nwhere:
- CFₜ
- the cash flow in period t (negative for money out, positive for money in)
- t
- the period index, counting from 0 at the first cash flow
- n
- the number of the final period
- r
- the internal rate of return — the per-period rate being solved for
MIRR = (FV of inflows at the reinvest rate ÷ PV of outflows at the finance rate)^(1 / n) − 1A worked example
Suppose you invest $50,000 today and the project returns $12,000, $15,000, $18,000, $20,000 and $22,000 over the next five years. The internal rate of return is the single annual rate that, used to discount those five inflows, brings their present value back to exactly $50,000 — about 19.4%.
Your figures
Enter at least one investment (money out) and one return (money in), and the worked example will fill in with your project's internal rate of return.
Key terms
- Outflow (money out)
- Cash you commit to the project — the initial investment and any later top-ups. Entered as money out and treated as negative.
- Inflow (money in)
- Cash the project returns to you — income, distributions or a final sale. Entered as money in and treated as positive.
- Internal rate of return
- The annual return the project earns on the money tied up in it, found as the discount rate that makes NPV zero.
- Net present value
- The value the project adds today, after discounting every cash flow at your hurdle rate. Positive means it beats the hurdle.
- Modified IRR
- A version of IRR that uses explicit finance and reinvestment rates, giving a single rate even when ordinary IRR would have several.
- Profitability index
- Present value of inflows divided by present value of outflows. Above 1.0 the project creates value; below 1.0 it destroys it.
- Payback period
- How long until cumulative cash flow turns positive — when you have recovered your outlay. The discounted version counts the time value of money.
Know what this estimate is based on
- Jurisdiction
- No statute sets these results — they are return, fee and time-value arithmetic that holds in any market. Tools in this category that do turn on U.S. tax law or a contribution limit say so on their own page.
- Scope and limitations
- Scenario model, not a forecast. Returns, volatility, inflation, fees and taxes are assumptions you supply, and actual investment outcomes can be lower or negative. Past performance does not carry forward, and no allocation shown here is a recommendation.
- Source links checked
- Sep 19, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
Primary sources
- Understanding fees and what they cost over timeU.S. Securities and Exchange Commission — Investor.gov
- Beginners' guide to asset allocation, diversification and rebalancingU.S. Securities and Exchange Commission
- Investor.gov's own calculators — cross-check a result hereU.S. Securities and Exchange Commission — Investor.gov
How to use
- 01
Start by entering your period-0 investment as a money-out (negative) figure — the cash you commit today, like a $50,000 outflow on a five-year project — so the stream opens with the capital you are putting at risk.
- 02
Add each following period's net cash flow in sequence, tagging money received as an inflow and any extra spending as an outflow; the worked example uses $12,000, $15,000, $18,000, $20,000 and $22,000 across five periods.
- 03
Pick the period length from the periods-per-year selector (annual, semi-annual, quarterly or monthly) so the solved per-period rate is annualized correctly by effective compounding, and a monthly equivalent is shown too.
- 04
Set your discount or hurdle rate — and, for MIRR, the separate finance and reinvestment rates; leaving the hurdle at 10% reproduces the example's NPV of about $14,150 and MIRR near 15.62%.
- 05
Read the headline IRR (around 19.44% here) next to NPV, MIRR, profitability index and the simple and discounted payback figures, and take seriously any multiple-IRR or no-solution warning when your cash flows switch sign more than once.
Formula
IRR is the periodic rate r that makes net present value equal zero: 0 = Σ CFₜ ÷ (1 + r)ᵗ CFₜ is the signed cash flow at period t: investments are negative and money received is positive. The effective annual IRR is (1 + r)ᵖ − 1, where p is the number of periods per year.
Example
Invest $1,000 now, then receive $600 at the end of year 1 and $600 at the end of year 2. Solving −$1,000 + $600 ÷ (1 + r) + $600 ÷ (1 + r)² = 0 gives an annual IRR of about 13.07%.
Definitions
- Cash flow
- Money entering or leaving the investment at a particular period; outflows are negative and inflows are positive.
- NPV
- Net present value: the sum of every cash flow discounted to period zero at a chosen rate.
- IRR
- The periodic discount rate at which the cash-flow stream's NPV is exactly zero.
- MIRR
- Modified IRR, which uses explicit finance and reinvestment rates to avoid assuming every interim inflow earns the IRR.
- Multiple IRRs
- More than one valid IRR can exist when the cash-flow signs change direction more than once.
Good to know
What the internal rate of return really measures
The IRR is the single per-period rate at which the present value of everything a project pays back exactly offsets the value of everything you commit — the rate that pushes net present value down to zero. Picture it as the break-even discount rate: the steepest interest charge your venture can absorb before it stops being worthwhile. Another lens helps. Imagine the cash you put up is borrowed from a bank, and each inflow first pays interest on the outstanding balance and then chips away at the principal. The IRR is precisely the loan rate at which the final payment leaves that balance at zero — no surplus, no shortfall. It is the yield your money earns while it stays locked inside the venture, weighing both how much arrives and when it arrives. Because this calculator runs on period-indexed flows (period 0, 1, 2, and so on, spaced evenly), the rate it solves is per period; it then annualizes by effective compounding, so a monthly rate r becomes (1+r)^12 − 1 across a year. At the annual setting the periodic and annual figures coincide, matching a spreadsheet's IRR(). A worked example — $50,000 out today, then $12,000, $15,000, $18,000, $20,000 and $22,000 over five years — solves to roughly 19.44%. That number says the project behaves like an account paying about 19.44% a year on the shrinking sum you still have at stake. It is not your total profit ($37,000 here), nor a simple average; it folds timing into one percentage. Crucially, the IRR is a property of the cash-flow shape alone — it knows nothing about your cost of capital or prevailing market rates until you supply those separately to judge it. Solve first, then compare against a benchmark to decide whether the rate is good enough.
Reading your result: the hurdle-rate decision
Once you have an IRR, the standard move is to set it against your hurdle rate — the cost of capital, or the return you could earn elsewhere on money of equal risk. If the project's IRR clears that bar, accept; if it falls short, walk away. On that $50,000 five-year project, 19.44% comfortably tops a 10% hurdle, which is why the calculator also reports a positive NPV near $14,150 at 10%. That pairing is no accident. Because the tool turns your annual hurdle into a per-period rate using the very same effective-compounding rule it applies when annualizing the IRR, net present value comes out positive exactly when the annualized IRR sits above the discount rate, and negative when it dips below. Accept-because-IRR-beats-the-hurdle and accept-because-NPV-is-positive therefore reach the identical verdict — but only for a conventional project, meaning one outlay up front followed by inflows, with a single change of sign in the stream. The instant your cash flows flip sign more than once — an early payout, a mid-life refit, a teardown cost at the close — that tidy equivalence can fracture. A stream may then have several rates that zero NPV, or none at all, and asking whether the IRR exceeds 10% stops being a well-posed question. The profitability index shown alongside (PV of inflows divided by PV of outflows, about 1.283 here) carries the same signal from a different angle: anything above 1.0 means precisely what NPV above zero means. So treat the IRR as a fast, scale-free yardstick when the project is well-behaved, but check the sign pattern first. With exactly one sign change, trust the hurdle comparison outright; with more than one, defer to NPV and MIRR and regard the headline percentage with healthy suspicion rather than acting on it blindly.
IRR versus NPV: why you read them together
NPV and IRR answer the same question in two different languages, and each is weaker alone than the pair is together. NPV speaks in money: discount every cash flow at your chosen rate, add them up, and you have the dollar value the project creates today — $14,150 for that $50,000 five-year project at 10%. IRR speaks in percent: it is the rate that would drag that same NPV down to zero, a gauge of efficiency rather than size. IRR's blind spot is scale. A percentage cannot reveal how much capital it is working on, so a small project flaunting a dazzling rate can outshine a large one carrying a merely solid rate, even though the large one builds far more wealth. Earning 50% on $1,000 hands you $500; earning 20% on $100,000 hands you $20,000 — yet IRR alone would crown the first. This is exactly why the two metrics can rank competing investments differently. They part ways when projects differ in size, in the timing of their payouts, or in how long capital stays committed; front-loaded streams flatter IRR, since early cash is discounted lightly, while NPV's verdict shifts with whatever discount rate you select. The crossover rate — the discount rate at which two projects share an equal NPV — marks where the ranking flips: below it one project leads, above it the other does, even as each keeps its own fixed IRR. The practical resolution is straightforward. When you must pick one among mutually exclusive projects, let NPV settle it, because your real aim is to maximize wealth created rather than the rate per dollar. Keep IRR as the intuitive companion that shows how much cushion you hold above your cost of capital, and as a quick screen — but never let the percentage override the dollars when the two disagree on ranking.
IRR, ROI and CAGR: three different return numbers
IRR, ROI and CAGR all report something called return, yet they treat time so differently that they seldom agree, and picking the wrong one quietly skews your judgment. ROI is the plainest and the most timing-blind: net profit measured against the amount you committed. For that $50,000 five-year project that is $37,000 over $50,000, or 74% — a genuine figure that says nothing about whether the gain took one year or fifty. A 74% ROI across five years is excellent; spread over twenty years it is mediocre, but ROI prints the same number for both. CAGR cures the duration problem, though it only inspects two snapshots — a starting value and an ending value — and smooths everything in between into one constant annual growth rate. It shines when a single sum goes in, sits untouched, and emerges later, yet it ignores any cash added or withdrawn partway through. IRR is the metric that honors each flow's timing: it discounts every payment by exactly how long it stayed outstanding, so a dollar returned in year one outweighs a dollar returned in year five. That makes it the right instrument for staggered, lumpy streams like this one, where money trickles back across several periods. The trade-off is that IRR has no closed form — iteration finds it — and it can misbehave when cash flows switch sign repeatedly. A rough hierarchy keeps you honest: reach for ROI when only total profit on cost matters and timing is irrelevant; reach for CAGR when there is one entry and one exit and you want the annualized rate between them; reach for IRR when contributions and withdrawals scatter across time and their schedule genuinely counts. Here ROI announces 74% in total while IRR announces roughly 19.44% per year — the same project, two honest answers that sound nothing alike.
The reinvestment assumption and MIRR
Every IRR hides one assumption that often escapes scrutiny: it quietly supposes each inflow, once collected, is reinvested at the IRR itself until the project ends. For a venture earning 19.44%, that means every interim payment is presumed to keep compounding at 19.44% — an optimistic wager, since you may only be able to stash returned cash in a money-market account or retire debt at a far humbler rate. When the IRR runs high, this assumption inflates the figure above what you will actually pocket. MIRR — the modified internal rate of return — strips out the guesswork by letting you name two explicit rates: a finance rate at which early outflows are discounted back to today, and a reinvestment rate at which inflows are compounded forward to the final period. It then asks which single rate grows the present value of your outflows into the future value of your inflows over the project's life: MIRR = (FV of inflows ÷ PV of outflows)^(1/n) − 1. Because you fix where interim cash truly lands, MIRR always returns one unambiguous value — no multiple roots, no sign-change traps. On that $50,000 five-year project, setting both the finance and reinvestment rates to 10% pulls the headline from an IRR of 19.44% down to an MIRR near 15.62%. That gap is the price of candor: the 19.44% silently assumed you could redeploy every payout at 19.44%, while 15.62% reflects the more realistic 10% you actually earn on cash as it comes back. Neither figure is wrong — they answer separate questions — but MIRR usually offers the fairer footing for comparing projects, since two ventures judged on the same explicit reinvestment rate are measured on level terms. When IRR and MIRR diverge sharply, read the spread as a flag that the reinvestment assumption is carrying real weight.
When IRR breaks down: multiple and missing solutions
An internal rate of return is dependable only when a project spends money first and earns it back afterwards — a single switch from negative to positive in the cash-flow sequence. Each additional flip of sign can summon another rate at which the discounted flows net to zero, so a stream that dips back into the red mid-life may satisfy the equation at two, three, or more values. The textbook illustration is the series minus $4,000, then plus $25,000, then minus $25,000: feed it to the solver and you find that both 25% and 400% drive net present value to zero, and neither is more 'correct' than the other. A grid scan across candidate rates is the honest way to surface every root, because picking the first one a Newton search lands on can hide the rest. The opposite failure is having no answer at all: if every entry carries the same sign — you only ever pay in, or only ever take out — there is nothing for the rate to balance, and the calculator reports that no IRR exists. When either situation appears, stop treating the percentage as a verdict. Lean on net present value computed at a discount rate you genuinely believe, since NPV gives one unambiguous number for any rate you plug in, and on the modified internal rate of return, which collapses to a single figure by spelling out where interim cash is parked. The profitability index tells the same story as NPV and adds a per-dollar reading. The lesson is that IRR is a convenience that works beautifully for ordinary borrow-then-repay or invest-then-harvest patterns, and quietly misleads the moment the signs zig-zag. Read the warning flags the tool raises, count the sign changes yourself, and let dollar-denominated value rather than a possibly-plural rate make the final call.
Payback period and the profitability index
Payback period answers a blunt question: how long until the money you laid out comes back? In its simplest form you just accumulate the raw inflows until they cover the outlay, which for a project of $50,000 out, then $12,000, $15,000, $18,000, $20,000 and $22,000 in, happens roughly 3.25 years in. That figure is easy to grasp and speaks to liquidity and risk, but it pretends a dollar arriving in year four weighs the same as one in your pocket now. Discounted payback repairs that by shrinking each inflow to its present value before tallying, so recovery takes longer — about 3.96 years here — and the gap between the two numbers widens as the discount rate climbs. Neither version credits anything that lands after the line is crossed, which is why a project can pay back quickly yet still destroy value, or pay back slowly yet be richly worthwhile. The profitability index closes that blind spot. It divides the present value of everything coming in by the present value of everything going out; at a 10% rate that project scores about 1.283, meaning each dollar committed returns $1.28 in today's terms. Because numerator and denominator share the same discounting, the index crosses 1.0 at precisely the moment net present value crosses zero, so PI above 1 and NPV above zero always agree on accept-or-reject. Where PI earns its keep is ranking: when capital is rationed and you cannot fund every worthy idea, value-per-dollar sorts contenders better than total NPV, which favors sheer size. Used together, payback tells you how fast you are made whole, discounted payback tells you the same in honest money, and the profitability index tells you how much value each committed dollar actually buys.
Choosing the discount rate
The discount rate is the hurdle every future dollar must clear, and choosing it is where judgment enters an otherwise mechanical calculation. Conceptually it is your opportunity cost: the yield the same money could fetch in its next-best use at equivalent risk. For a company that often means the weighted average cost of capital, blending what lenders and shareholders each demand; for an individual it might be the yield on an investment you would otherwise hold, or a personal required return that bakes in the riskiness of the venture. The number matters enormously because net present value is acutely sensitive to it. Discount that $50,000 five-year project's inflows at 10% and you get roughly $14,150 of value with a comfortable accept; raise the rate and that surplus shrinks, eventually hitting zero exactly at the internal rate of return of 19.44%, beyond which the same cash flows look value-destroying. So the accept/reject call can flip on an assumption that is rarely known to the decimal. The disciplined response is to treat the rate as a range rather than a point: run the calculation at a pessimistic, central, and optimistic cost of capital and watch how NPV and the verdict move. If the project stays positive across every plausible rate, you can act with confidence; if it only clears the bar under a generously low rate, you have learned that the decision rests on the discounting assumption more than on the cash flows themselves. A wide gap between your hurdle and the IRR is a margin of safety, while a narrow one signals fragility. Pin the rate to something defensible, write down why, and stress-test it — because a value figure is only as trustworthy as the cost of capital you feed the model.
IRR versus XIRR: even periods or real dates
IRR and XIRR answer the same question — what rate makes the discounted flows balance — but they assume different things about timing. The internal rate of return treats your cash flows as a tidy ladder: period 0, period 1, period 2, and so on, each rung an equal interval apart. You tell the tool how many periods make a year — annual, semi-annual, quarterly, or monthly — and it solves a per-period rate, then annualises it by effective compounding, so a periodic rate p becomes (1 + p) raised to the periods-per-year, minus one. That regular-spacing assumption is exactly right for things that genuinely arrive on a fixed cadence: a bond's coupons, a lease, a subscription, or a model where you have lumped activity into clean yearly buckets. XIRR drops the even-spacing requirement and pins every flow to a real calendar date, discounting on an actual-days basis. Reach for it when the timing is irregular — a capital call in March, a distribution the following January, a top-up eleven months after that — because forcing such dates into equal periods would misstate how long money was actually at work. The reassuring part is that the two methods are not rivals but the same engine under different clocks: line your flows up exactly one year apart and feed them to either, and the answers converge, because annual evenly-spaced dates are simply the special case where 'period' and 'year' mean the same thing. Choose by the data you hold. If your cash flows already sit on a uniform grid, period-indexed IRR is simpler and matches a spreadsheet's IRR() function at annual spacing; if they are scattered across the calendar, dated XIRR keeps the arithmetic honest. Picking the wrong one does not break the formula, but it quietly distorts the rate by mis-measuring time.
Practical examples and common mistakes
Picture buying a small rental for $50,000, collecting rising net rents of $12,000 through $22,000 over five years, and the tool reports an IRR near 19.44% with about $14,150 of NPV at a 10% hurdle — a healthy yes. Real decisions go wrong less in the formula than in how people read it. The first trap is confusing rate with size: IRR is a percentage and says nothing about scale, so a tiny project boasting a 40% return can add far less wealth than a large one earning 15%, which is why you check NPV in dollars before crowning a winner. The second is forgetting what IRR quietly assumes — that every interim dollar is reinvested at the IRR itself, often an optimistic stretch; when that bothers you, switch to MIRR and state an explicit, believable reinvestment rate, which for that project pulls the figure down to about 15.62%. The third is comparing projects of different lengths on rate alone: a two-year sprint and a ten-year hold are not interchangeable just because their percentages match, so align horizons or fall back on NPV. A fourth slip is the sign of the opening outlay — period 0 must be entered as a negative, because if you log that initial $50,000 as positive the stream never changes sign and the solver, correctly, refuses to return a rate. Finally, people anchor on payback and ignore everything that happens afterwards, or quote an IRR from a sign-flipping stream that actually has several. Treat the percentage as one witness among many: read it next to net present value, the profitability index, payback in both flavors, and MIRR, sanity-check the cash-flow signs, and remember that even the cleanest single rate still rests on assumptions worth questioning before you commit capital.
Frequently asked questions
What does the internal rate of return actually tell you?
IRR is the single per-period rate that brings the net present value of your whole cash-flow stream to exactly zero. Think of it as the break-even discount rate baked into the project itself: the effective annual return your money earns for as long as it stays invested. Because it is solved straight from the figures you enter, IRR needs no outside guess about what return to expect, which is why a higher IRR signals a steeper effective return.
How do I use IRR to accept or reject a project?
Compare the annualized IRR with your hurdle rate, the minimum return you require. If IRR clears the hurdle the project earns more than your cost of capital and adds value; if it falls short, you pass. There is one important caveat: this clean accept-or-reject shortcut only holds for a conventional project, meaning one initial outflow followed by inflows, so the signs change exactly once. When the cash flows flip sign more than once, lean on NPV and MIRR instead of the IRR rule.
What is the difference between IRR and NPV?
NPV translates a project into a single dollar figure of value created at a rate you choose, while IRR translates the same flows into a single percentage and lets the project pick its own break-even rate. For a normal project they agree on the verdict, since NPV is positive precisely when IRR beats your discount rate, yet they can still rank competing projects differently. The tool shows both at once — on a $50,000 project paying back $12,000 to $22,000 over five years, a 19.44% IRR sits beside an NPV of roughly $14,150 at a 10% hurdle.
IRR vs ROI vs CAGR — which one should I read?
Plain ROI is total profit over money invested with no clock attached, so it cannot distinguish a one-year double from a ten-year one. CAGR pins a single start and end value to one smooth annual rate but assumes nothing happens in between. IRR is the timing-weighted cousin of both: it accounts for exactly when each deposit and withdrawal lands, which is why an uneven, multi-period stream calls for IRR rather than ROI or CAGR.
What is MIRR, and when does it differ from IRR?
MIRR, the modified internal rate of return, swaps out IRR's hidden assumption that every inflow is reinvested at the IRR for an explicit reinvestment rate you set, while discounting outflows at a separate finance rate. Formally it is the future value of inflows compounded at the reinvest rate, divided by the present value of outflows discounted at the finance rate, all raised to the power 1/n, minus one. MIRR is always a single number, and it pulls furthest from IRR when the IRR is high: a $50,000 five-year project shows 19.44% IRR but a 15.62% MIRR with finance and reinvest both set to 10%.
Can a project really have more than one IRR?
Yes. Whenever the cash flows change sign more than once, the NPV equation can cross zero at several rates, so multiple IRRs are all mathematically valid. The classic teaching stream [−$4,000, +$25,000, −$25,000] is solved by both 25% and 400%. This tool scans a grid to surface every root it can find, and when more than one appears you should treat the IRR decision rule as unreliable and judge the project by its NPV at your hurdle rate and by MIRR.