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The Internal Rate of Return (IRR) is the annualized rate of return at which the net present value (NPV) of an investment's cash flows equals zero. It's the single number finance professionals, real estate investors, and private equity use most often to compare investments with irregular cash flows.
If you invest $100,000 in a project that returns $25,000 a year for 5 years, the IRR is the discount rate that makes the present value of those five $25k payments equal $100,000. The answer is about 7.93% β the effective compound annual return you're earning on capital that remains in the project.
0 = Ξ£ [CFt / (1 + IRR)t] for t = 0 to n
There's no closed-form solution β IRR is found iteratively. This calculator uses the Newton-Raphson method with bisection fallback, the same approach Excel's IRR() function uses internally.
If your IRR is above your cost of capital (hurdle rate), the project creates value. If below, it destroys value. For most US/UK retail investors, the "cost of capital" is the return they'd get in a low-cost index fund β about 7% real.
US private equity funds routinely target IRRs of 15β25%. Real estate syndicators typically advertise projected IRRs of 14β20% on opportunistic deals and 8β12% on core holdings. Corporate finance uses IRR as one input alongside NPV and payback period for capital-budgeting decisions.
UK property investors use IRR heavily for HMO, buy-to-let, and refurbishment projects where capital goes in and comes back over multiple years. UK PE firms and infrastructure funds report IRRs on all closed-end vehicles. For UK small businesses evaluating equipment purchases, IRR is a standard metric alongside payback period.
| Year | Cash flow |
|---|---|
| 0 | βΒ£50,000 (deposit + fees) |
| 1 | +Β£4,200 net rent |
| 2 | +Β£4,400 |
| 3 | +Β£4,500 |
| 4 | +Β£4,600 |
| 5 | +Β£4,700 + Β£42,000 equity on sale |
IRR β 12.8% β a solid return for a UK buy-to-let at current rates.
Depends on risk. For UK buy-to-let, 10β15% annualized IRR is typical target. For US PE/VC, 20%+ is the expectation. For a simple retail investor comparing to the S&P 500, anything above ~10% nominal beats passive indexing.
No. CAGR is a simple start-to-end compound growth rate, assuming no intermediate cash flows. IRR handles any pattern of inflows and outflows. For a single-purchase-single-exit investment they give identical results.
When cash flows change sign multiple times, when returns are unusually high (>30%), or when you're comparing two mutually exclusive projects of very different sizes. Combine IRR with NPV in those cases.
IRR is computed on nominal cash flows by default. To get real IRR, either input real (inflation-adjusted) cash flows, or subtract the inflation rate from the nominal IRR.
This tool matches Excel's IRR() (equal-period cash flows). For irregular dates, Excel's XIRR() uses actual day counts β a future update will add date-based XIRR here.
This tool provides internal rate of return estimates for informational purposes only and is not financial or investment advice. IRR can be sensitive to timing, sign changes, and irregular cash flows. Always review assumptions, risk, taxes, and alternative measures before making decisions.
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The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows from a project or investment equal to zero. In other words, it is the compound annual growth rate that a project or investment is expected to generate β the "internal" return embedded within the cash flow profile itself. IRR is one of the most widely used metrics in corporate finance, private equity, real estate investment analysis, and capital budgeting in both the United States and United Kingdom.
A positive IRR indicates that the investment generates returns. The decision rule is straightforward: if IRR exceeds the required rate of return (cost of capital or hurdle rate), accept the investment. If IRR falls below the hurdle rate, reject it. For example, a project with an IRR of 18% is attractive to a company whose cost of capital is 10%, because the project generates 8 percentage points of return above the required minimum.
The concept of IRR was widely adopted following its development and popularisation in the mid-20th century by financial economists including Joel Dean. Today it is standard in the financial modelling curriculum of the CFA Institute (US and globally) and in the ICAEW (UK) and CIMA professional accounting qualifications. Excel's IRR function makes the calculation accessible to any analyst.
IRR has no closed-form analytical solution β it requires iterative numerical methods. The mathematical definition is the rate r that satisfies:
NPV = CFβ + CFβ/(1+r) + CFβ/(1+r)Β² + CFβ/(1+r)Β³ + ... + CFβ/(1+r)βΏ = 0
Where CFβ is typically the initial investment (negative cash flow), and CFβ through CFβ are the subsequent period cash flows (often positive inflows from revenues, dividends, or sale proceeds).
Because this equation cannot be solved algebraically for r when n > 2, computers use iterative algorithms to find the rate. The most common is the Newton-Raphson method, which starts with a guess and successively refines it using the formula:
r_new = r_old β NPV(r_old) / NPV'(r_old)
Where NPV'(r) is the first derivative of NPV with respect to r. This is the algorithm used in this calculator and in Excel's IRR function. Convergence is typically achieved within 20-50 iterations to an accuracy of 6 decimal places. The initial guess matters β a poor starting guess can lead to convergence on an incorrect solution if multiple IRRs exist (see limitations below).
The IRR decision framework works as follows: establish the cost of capital (the minimum acceptable return, also called the hurdle rate or required rate of return). Calculate the project's IRR. If IRR > cost of capital, the project creates value and should be accepted. If IRR < cost of capital, the project destroys value relative to the required return and should be rejected.
For a company with a 12% weighted average cost of capital (WACC) evaluating three projects:
| Project | Initial Investment | IRR | Decision |
|---|---|---|---|
| A | Β£500,000 | 22% | Accept β IRR exceeds 12% hurdle |
| B | Β£250,000 | 12% | Indifferent β IRR equals hurdle |
| C | Β£1,000,000 | 8% | Reject β IRR below 12% hurdle |
UK and US property investors commonly use IRR to evaluate buy-to-let or rental property returns, as it captures both the ongoing rental income stream and the eventual sale proceeds in a single, time-value-adjusted return metric. A typical analysis might involve:
Running IRR on these cash flows (initial outflow of βΒ£250,000, annual inflows of Β£12,000, terminal inflow of Β£350,000) gives an IRR that reflects the true compound annual return accounting for both income and capital growth. If the investor's required return is 8%, an IRR of 10-11% on this property would indicate an attractive investment.
IRR is the primary performance metric for UK and US private equity (PE) and venture capital (VC) funds. PE firms typically target gross IRRs of 20-25% on individual investments and aim to deliver net IRRs of 15-20% to limited partners (LPs) after management fees (typically 2%) and carried interest (typically 20% of profits above the hurdle). The British Private Equity and Venture Capital Association (BVCA) publishes annual performance reports using IRR as the primary return metric. Institutional investors (pension funds, endowments) in both the UK and US evaluate PE fund performance against IRR benchmarks and compare net IRR to public market equivalents (PME).
In US corporate finance, the hurdle rate is typically set as the company's Weighted Average Cost of Capital (WACC), which blends the after-tax cost of debt and the cost of equity (estimated using CAPM: Cost of equity = Risk-free rate + Beta Γ Equity risk premium). For S&P 500 companies in 2024, WACC typically ranges from 8-12% depending on capital structure and sector. Capital budgeting decisions at major US corporations (capital expenditure approvals, acquisition decisions, R&D investment) routinely use IRR alongside NPV, payback period, and profitability index to evaluate competing projects.
Modified Internal Rate of Return (MIRR) addresses a key theoretical weakness of standard IRR: the implicit assumption that interim cash flows are reinvested at the IRR itself. For a project with an IRR of 25%, standard IRR assumes all positive cash flows can be reinvested at 25% β which may be unrealistic. MIRR corrects this by using separate rates for financing (negative cash flows discounted at cost of capital) and reinvestment (positive cash flows compounded at the reinvestment rate, typically cost of capital or expected market return):
MIRR = [(FV of positive cash flows at reinvestment rate) / (PV of negative cash flows at financing rate)]^(1/n) β 1
MIRR provides a more conservative and often more realistic estimate of true project returns. It also resolves the multiple IRR problem (discussed below) by producing a unique solution. MIRR is supported in Excel via the MIRR() function and is increasingly required in project finance analysis at major UK and US financial institutions.
Multiple IRRs: Projects with non-conventional cash flows (cash flows that change sign more than once β for example, a project requiring a large decommissioning cost at the end) can have multiple IRRs or no real IRR at all. This is a mathematical consequence of Descartes' Rule of Signs. When multiple IRRs exist, the standard IRR rule breaks down and NPV analysis should be used instead.
Scale problem: IRR ignores the absolute scale of investment. A Β£1,000 investment with 100% IRR creates Β£1,000 of value; a Β£1,000,000 investment with 25% IRR creates Β£250,000 of value. For mutually exclusive projects of different sizes, maximising IRR may not maximise total value created. NPV is the more appropriate metric when comparing projects of different scale. Finance academics (Brealey, Myers, Allen in Principles of Corporate Finance) consistently recommend NPV as the primary decision criterion, with IRR as a useful secondary metric.
XIRR for non-periodic cash flows: Standard IRR assumes cash flows occur at regular intervals (usually annual or monthly). When cash flows occur at irregular dates, Excel's XIRR function (and equivalent in other financial software) calculates the IRR using exact dates, providing more accurate results for real-world investments where payments do not follow a perfectly regular schedule.
The NPV profile is a graph plotting NPV on the y-axis against the discount rate on the x-axis. The curve typically slopes downward from left to right β at low discount rates, NPV is high (future cash flows are barely discounted); at high rates, NPV is low (future cash flows are heavily discounted). The point where the NPV curve crosses zero on the x-axis is the IRR. Visualising the NPV profile helps identify the margin of safety between the IRR and the cost of capital, and reveals whether multiple IRRs might exist (the curve crossing zero more than once).
IRR (Internal Rate of Return) is the discount rate at which the Net Present Value (NPV) of a project's cash flows equals zero. It represents the compound annual return embedded in the cash flows. Because it cannot be solved algebraically, it is calculated by iterative numerical methods (Newton-Raphson or bisection), starting with an initial guess and refining until NPV = 0. Excel's IRR() function uses a similar approach, defaulting to a 10% initial guess.
A good IRR depends on the investment type and required return. For corporate projects, IRR should exceed WACC (typically 8-12% for large US companies). For UK buy-to-let property, many investors target IRR of 8-12% including capital growth. For private equity, gross IRR targets are typically 20-25%. For individual investors comparing alternatives, IRR should exceed the return available on equivalent-risk alternatives. Context is everything β an 8% IRR is excellent for a low-risk property but inadequate for an early-stage startup.
IRR is a percentage rate β the return generated by a project. NPV is an absolute value β the present-value profit in pounds or dollars above the required return. Both use discounted cash flow techniques. IRR is easier to communicate and compare against hurdle rates. NPV is theoretically superior for decision-making because it accounts for project scale. For mutually exclusive projects, NPV maximisation is the correct objective. Academics generally recommend using NPV as the primary criterion and IRR as supplementary. They give the same accept/reject decision for independent, conventional cash flow projects.
MIRR (Modified IRR) corrects a key weakness of IRR: the assumption that interim cash flows are reinvested at the IRR rate itself. MIRR uses a separate reinvestment rate (usually cost of capital or expected market return) for positive cash flows and a financing rate for negative cash flows. MIRR produces a unique value even for non-conventional cash flows and is typically lower than (and more conservative than) IRR. In Excel, use =MIRR(values, financing_rate, reinvestment_rate). MIRR is increasingly preferred in project finance and PE due to its more realistic reinvestment assumption.
Yes. Projects with non-conventional cash flows (cash flows that change sign more than once) can have multiple IRRs, no real IRR, or a single IRR depending on the specific values. This is a mathematical consequence of Descartes' Rule of Signs. When multiple IRRs exist, the standard IRR decision rule breaks down and NPV analysis must be used instead. Real-world examples include mining projects with large initial investment, positive operating cash flows, and a large negative terminal decommissioning cost β creating two sign changes and potentially two IRRs.
XIRR calculates the IRR for a series of cash flows that occur at irregular (non-periodic) dates. Standard IRR assumes equal time intervals between cash flows. XIRR takes actual calendar dates into account. In Excel: =XIRR(values, dates, [guess]). You should use XIRR whenever cash flows occur on specific dates rather than at regular intervals β for example, property investments with monthly rental income, irregular dividend payments, or private equity fund capital calls and distributions that do not follow a fixed schedule. XIRR produces more accurate results in virtually all real-world investment scenarios.
UK private equity firms use IRR as their primary performance metric for both individual investments and fund-level reporting. Fund IRR (net of fees and carried interest) is the key figure disclosed to Limited Partners and benchmarked against peer funds and public market equivalents. The British Private Equity and Venture Capital Association (BVCA) publishes pooled horizon IRRs across all UK PE activity. Typical target gross IRRs are 20-25% for buyout funds and 30%+ for early-stage venture capital. Net IRR to LPs is typically 10-15 percentage points lower after the 2-and-20 fee structure.
In Excel, use =IRR(values, [guess]) where values is the range containing your cash flows (negative initial investment first, then positive inflows) and guess is optional (defaults to 0.1 = 10%). For example: if A1 = -100000, A2 = 30000, A3 = 40000, A4 = 50000, A5 = 20000, then =IRR(A1:A5) returns the IRR. For non-periodic cash flows use =XIRR(values, dates). For modified IRR use =MIRR(values, finance_rate, reinvest_rate). Always verify the result makes intuitive sense given the cash flow profile.