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Internal Rate of Return (IRR) Calculator

Calculate the discount rate that makes NPV equal to zero for your investment

IRR Concept

IRR Definition
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NPV at IRR
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Decision Rule
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Cash Flow Year

What is Internal Rate of Return?

The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from an investment equal to zero. In simpler terms, it's the expected compound annual rate of return that an investment will generate. IRR is widely used in capital budgeting to compare and evaluate investment opportunities.

When evaluating a project, you compare the IRR to your required rate of return (hurdle rate). If the IRR exceeds your hurdle rate, the investment is considered acceptable. The higher the IRR above your hurdle rate, the more attractive the investment becomes.

IRR is particularly useful because it provides a single percentage that can be easily compared across different investments, regardless of their size. However, it has limitations that investors should understand, particularly regarding reinvestment assumptions and multiple IRR problems.

IRR vs Other Return Metrics

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IRR

The rate where NPV = 0. Shows effective annual return considering time value of money.

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NPV

Dollar value created. Better for comparing mutually exclusive projects of different sizes.

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ROI

Simple percentage return ignoring timing. (Gain - Cost) / Cost. Quick but less accurate.

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Payback Period

Time to recover investment. Ignores time value of money and cash flows after payback.

IRR Benchmarks by Investment Type

Acceptable IRRs vary significantly by investment type, risk level, and market conditions.

Investment TypeTypical IRR RangeRisk LevelNotes
Treasury Bonds 3-5% Very Low Risk-free baseline
Corporate Bonds 5-8% Low Credit risk premium
Stock Market (Index) 8-12% Medium Long-term average
Real Estate 10-20% Medium-High Location dependent
Private Equity 15-25% High Illiquidity premium
Venture Capital 25-40% Very High Most investments fail
Startup Investment 30-50%+ Extreme Power law returns

Limitations of IRR

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Reinvestment Assumption

IRR assumes intermediate cash flows can be reinvested at the IRR itself. This is often unrealistic for very high IRRs. Modified IRR (MIRR) addresses this issue.

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Multiple IRRs

Projects with alternating positive and negative cash flows can have multiple IRRs or no real IRR at all. Use NPV analysis instead for such projects.

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Scale Ignorance

IRR doesn't account for project size. A 50% return on $1,000 creates less value than 20% on $1 million. Always consider NPV alongside IRR.

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Timing Bias

IRR favors projects with quick returns even if slower projects create more total value. Consider both IRR and NPV in your analysis.

How to use this IRR calculator

  1. Enter the Initial Investment — the upfront cash outflow needed to start the project. Type the positive amount; the calculator records it as the period-0 outflow when running the IRR search.
  2. Enter a Hurdle Rate (%) — your cost of capital or required rate of return. The widget compares IRR to this rate to mark the project Accept, Reject, or Marginal. Leave the default 10% if you don't have a firm benchmark yet.
  3. Fill in Cash Flow Year 1 through Year 5 with the net cash you expect to receive each year. Use positive numbers for inflows and negative numbers for years where the project still consumes cash.
  4. Click + Add Year to extend the projection beyond five years for longer-lived assets, real-estate holds, or any project with a non-standard horizon. Use the × button on any row to remove an extra year.
  5. Click Calculate IRR. The calculator iterates on the discount rate that drives NPV to zero and returns the IRR, total investment, total returns, net gain, and an accept/reject decision against your hurdle rate. Click Reset to start a new scenario.

Examples

Equipment purchase: $100k investment, $30k for 5 years

A small manufacturer is evaluating a CNC machine that costs $100,000 and is expected to produce $30,000 in net annual cash flow for five years, with no salvage value. The firm's cost of capital is 10%.

ResultIRR is about 15.24%. Total investment $100,000, total returns $150,000, net gain $50,000. Decision: Accept because IRR exceeds the 10% hurdle rate.

The calculator searches for the rate r where -100,000 + Σ 30,000 / (1+r)^t (t = 1..5) equals zero. At 10% NPV is positive (~$13,724), at 20% it is negative, and the bisection converges on roughly 15.24%. The 5.24-point cushion over the hurdle gives meaningful margin for assumption error.

Leveraged buyout: 5x return over 5 years

A private-equity sponsor invests $10 million in a buyout and projects a single $50 million exit at the end of year 5 with no interim distributions. This is a classic 5x money-on-money over a five-year hold.

ResultIRR is about 37.97%. Total investment $10,000,000, total returns $50,000,000, net gain $40,000,000. Decision: Accept because IRR is far above the 20% hurdle.

With a single terminal cash flow, IRR collapses to the CAGR formula: (50/10)^(1/5) - 1 = 5^0.2 - 1 ≈ 0.3797, or 37.97%. The headline IRR is dramatic, but note the entire return depends on the year-5 exit; an extra year of hold drops IRR to about 30.8%, illustrating how time-sensitive PE returns are.

Non-conventional flows: the multiple-IRR trap

A mining project requires $4,000 upfront, produces $25,000 in year 1, then requires a $25,000 reclamation outlay in year 2. The cash-flow sign changes twice, so Descartes' rule of signs allows up to two real IRR solutions.

ResultTwo mathematical IRRs satisfy NPV = 0 — roughly 25% and 400%. This widget's bisection returns one root, but neither IRR alone tells you whether to accept. Total investment $4,000, total inflows $25,000, total outflows $29,000, net cash position -$4,000.

Set -4,000 + 25,000/(1+r) - 25,000/(1+r)^2 = 0 and solve the quadratic in x = 1/(1+r). The two roots translate to r ≈ 0.25 and r ≈ 4.00. With non-conventional cash flows, defer to NPV at your actual cost of capital, or compute MIRR with explicit finance and reinvestment rates. At a 10% cost of capital NPV is negative here, so the project should be rejected even though one of the IRRs looks attractive.

How it works

IRR is defined implicitly as the discount rate that satisfies 0=∑t=0nCFt(1+IRR)t0 = \sum_{t=0}^{n} \frac{CF_t}{(1+IRR)^t}, where CF0CF_0 is the negative initial investment and CFtCF_t for t≥1t \geq 1 is the net cash flow in year tt. There is no closed-form solution for n > 4, so calculators find IRR numerically by searching for the rate that drives NPV to zero.

Under the hood this calculator first verifies at least one sign change in the cash-flow series (a necessary condition for a real IRR), then bisects the rate between -99% and +1000%. Each iteration evaluates NPV at the midpoint and narrows the bracket until NPV falls within a 0.0001 tolerance or the bounds converge. Newton-Raphson and the secant method are faster alternatives used in spreadsheet IRR functions, but bisection is robust to discontinuities and avoids divergence.

Once IRR is found, the decision rule is mechanical: accept when IRR > hurdle rate, reject when IRR < hurdle rate, treat as marginal when they are within 0.01%. The hurdle rate should be your weighted average cost of capital plus a risk premium calibrated to the project's volatility — using a hurdle that's too low rubber-stamps value-destroying projects, while a hurdle that's too high rejects acceptable ones.

When to use this calculator

  • Screening a single project with conventional cash flows. When the project has one upfront outflow followed by a stream of positive inflows, IRR is well-defined and intuitive — a percentage you can compare directly against your cost of capital. Use it to make a fast accept/reject call before building a fuller financial model.
  • Benchmarking returns against an industry hurdle. Investment committees often work in IRR rather than NPV because percentages are easier to compare across deal sizes and fund vintages. Use the calculator when you need to translate a forecast cash-flow series into the IRR your LPs, board, or credit committee will recognize.
  • Estimating private-equity, real-estate, or buyout returns. PE, real estate, and infrastructure deals are typically underwritten on a target IRR (commonly 15-25% for buyouts, 10-15% for core real estate). Add multi-year cash flows including the projected exit value in the final year to see whether the deal hits the fund's target.
  • Communicating returns to non-technical stakeholders. A 22% IRR is more concrete to most audiences than "NPV of $4.7 million at a 12% discount rate." Use IRR when explaining results to operators, founders, or business owners — but pair it with NPV in the underlying memo so scale isn't lost.

Common mistakes to avoid

  • MistakeTreating IRR's reinvestment assumption as costless.
    FixStandard IRR assumes interim cash flows are reinvested at the IRR itself. For a project with a 35% IRR this is rarely realistic. Compute MIRR with a finance rate and a separate reinvestment rate equal to your cost of capital to get a more defensible figure.
  • MistakePicking the highest-IRR project among mutually exclusive options.
    FixIRR ignores scale. A 40% IRR on a $50,000 project may create less value than a 20% IRR on a $5 million project. For mutually exclusive choices rank by NPV at your cost of capital, not by IRR.
  • MistakeReporting a single IRR for non-conventional cash flows.
    FixEach sign change in the cash-flow series can introduce another real IRR. If your project has mid-life capex or reclamation outflows, check NPV at multiple discount rates or use MIRR; don't rely on the first root the solver returns.
  • MistakeComparing project IRRs without normalizing horizons.
    FixA 5-year project at 25% IRR and a 10-year project at 18% IRR aren't directly comparable. Either model both over the same horizon (with realistic reinvestment of the shorter project's exit) or rank by NPV, which already handles horizon differences.
  • MistakeMixing nominal cash flows with a real hurdle rate (or vice versa).
    FixPick one convention and stick to it. If cash flows include expected inflation, the hurdle rate must be nominal too. Mismatching nominal and real returns systematically over- or under-states the accept/reject decision over long horizons.
  • MistakeForgetting that IRR doesn't measure risk.
    FixTwo projects with the same 18% IRR can have wildly different risk profiles. Don't treat IRR as a risk-adjusted return — set hurdle rates by project risk class, run sensitivity analysis on the cash flows, and review the dispersion of outcomes, not just the point estimate.

Frequently asked questions

What's the difference between IRR and NPV?

NPV is the present-dollar value a project adds at your specified discount rate; IRR is the discount rate at which NPV would equal zero. NPV requires you to assume a cost of capital and produces a dollar answer that scales with project size; IRR is dimensionless and easier to compare across deals, but it can be misleading on mutually exclusive projects, projects of different scale, and projects with non-conventional cash flows. When the two methods disagree on ranking, follow NPV.

Is a higher IRR always better?

Not for ranking projects. IRR ignores scale, so a 60% return on $20,000 produces less absolute value than a 22% return on $5 million. IRR also implicitly assumes you can reinvest interim cash flows at the IRR itself, which is rarely realistic for double-digit-plus rates. For independent projects "higher IRR > hurdle" is a fine accept/reject signal; for choosing among competing projects, use NPV (or MIRR with a realistic reinvestment rate).

What's MIRR and when should I use it instead?

Modified IRR (MIRR) computes the rate by compounding positive cash flows forward at an explicit reinvestment rate (usually your cost of capital) and discounting negative cash flows back at a finance rate. The result is a single, well-behaved rate even when standard IRR has multiple solutions or assumes implausible reinvestment. Use MIRR for projects with non-conventional cash flows, very high IRRs that obviously won't be available as reinvestment opportunities, or whenever you need an apples-to-apples comparison across long horizons.

Why does my IRR seem too high to be real?

Two common reasons. First, IRR assumes interim cash is reinvested at the IRR; if your modeled IRR is 45%, that compounding is doing a lot of the lifting and likely won't happen in reality. Second, very short-duration projects with quick payback often produce inflated annualized rates that disappear once you model the actual reinvestment opportunities. Recompute MIRR at your real cost of capital before believing a >30% IRR.

Can IRR be negative?

Yes. A negative IRR means the cash inflows don't cover the initial investment even at a zero discount rate — the project loses nominal dollars. The calculator can return rates as low as roughly -99%. If you see a negative IRR, the project destroys value at any positive cost of capital and should be rejected outright unless there is non-financial strategic justification you can quantify separately.

When does a project have multiple IRRs?

Descartes' rule of signs says a cash-flow series with k sign changes can have up to k positive real IRRs. Projects with one upfront outflow and only positive subsequent flows have at most one IRR. Projects with mid-life capex, reclamation costs, or earn-out structures often have two sign changes and can produce two valid IRR solutions. In those cases neither IRR alone tells the full story — switch to NPV at your cost of capital, or use MIRR.

What about projects with no initial outflow?

If every cash flow is positive (e.g., a grant-funded project with no investor outlay), there is no rate at which NPV = 0 and IRR is undefined. The calculator will reject the inputs because it requires at least one sign change in the cash-flow series. For these situations, NPV at your cost of capital is the right metric — the project is value-creating whenever discounted inflows are positive.

How do I choose the hurdle rate?

Start with the weighted average cost of capital (WACC) — the blended after-tax cost of the firm's debt and equity. Add a risk premium of 2-5 percentage points for projects riskier than the firm's average (new geographies, unproven products), and reduce it for low-risk projects like cost-saving capex in core operations. For private investors, benchmark hurdle rates against expected returns on listed peers in the same risk class.

Is IRR the same as CAGR?

Only in the special case where there are exactly two cash flows: one outflow at time 0 and one inflow at time n. Then IRR = CAGR = (Ending / Beginning)^(1/n) - 1. As soon as you add interim cash flows, IRR diverges from CAGR because it weights each flow by its discount factor. CAGR is the right metric for a buy-and-hold position with a single sale; IRR is the right metric for any cash-flow series in between.

Does this calculator handle uneven cash flows?

Yes. Each cash flow input corresponds to a separate year, and you can enter different positive or negative numbers in any cell. Use + Add Year to extend the projection beyond the default five years for longer-lived assets. The IRR returned reflects the exact cash-flow pattern you entered, not an averaged annuity.

How does the calculator solve for IRR?

It uses bisection. Starting with a rate bracket from -99% to +1000%, it evaluates NPV at the midpoint, narrows the bracket toward the side where NPV changes sign, and iterates up to 1000 times until NPV falls within a 0.0001 tolerance. Bisection is slower than Newton-Raphson but robust — it converges as long as a real IRR exists in the bracket, regardless of the shape of the NPV curve.

What's a reasonable IRR by asset class?

Approximate long-run benchmarks: investment-grade bonds 4-6%, public equities 8-12%, core real estate 8-12%, value-add real estate 12-18%, private-equity buyouts 18-25%, venture capital 25-35% gross (with most deals returning zero). These figures are gross of fees and pre-tax; adjust down for your actual fee load and tax position before treating any of them as a personal hurdle.

Sources

Methodology

This calculator solves the implicit IRR equation 0 = Σ CF_t / (1+IRR)^t (t = 0..n) for the discount rate that drives NPV to zero. CF_0 is the negative of the user's Initial Investment; CF_t for t ≥ 1 is the user-entered annual cash flow (positive for inflows, negative for additional outflows). The solver first verifies at least one sign change in the cash-flow series — a necessary condition for a real IRR — then bisects the rate between -99% and +1000% until NPV falls within a 0.0001 tolerance or the bracket converges, capped at 1000 iterations. The Decision field compares the resulting IRR with the user-supplied Hurdle Rate: Accept when IRR exceeds the hurdle, Reject when IRR is below it, and Marginal when the two are within 0.01%. For projects with multiple sign changes, the displayed IRR is one root of an equation that may have more; pair the result with an NPV check at your cost of capital or compute MIRR for a unique, defensible rate.

Learn more about our methodology →

Pro Tips

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