MathIsimple
IRR Calculator

IRR Calculator

Calculate internal rate of return (IRR) for capital projects, real estate, and private equity investments. Build a cash flow timeline, compute IRR, and review net present value (NPV) at a 10% discount rate.

100% FreeInvestment AnalysisCash Flow Modeling
Cash Flow Inputs
Enter initial investment (negative) and annual net cash flows.

Use negative values for investments/outflows and positive for returns/inflows.

How to use this IRR calculator

Enter initial investment as a negative number and add projected cash inflows for each year. Click "Calculate IRR" to see internal rate of return and NPV metrics.

Understanding IRR: A Complete Guide

What is Internal Rate of Return (IRR)?

The Internal Rate of Return (IRR) is one of the most widely used metrics in capital budgeting and investment analysis. It represents the annualized effective compounded return rate that can be earned on an invested capital — in other words, the discount rate at which the Net Present Value (NPV) of all future cash flows from a project equals zero.

IRR is deeply connected to NPV. NPV measures the absolute dollar value that an investment creates after discounting all future cash flows back to today at a chosen rate. When you raise that discount rate high enough, NPV eventually reaches zero. That exact rate is the IRR. A project with a positive NPV at a given hurdle rate will always have an IRR greater than that hurdle rate — and vice versa.

The IRR Formula

Mathematically, the IRR (denoted r) is the value that satisfies:

0=t=0nCFt(1+IRR)t0 = \sum_{t=0}^{n} \frac{CF_t}{(1+IRR)^t}

Where CFtCF_t is the cash flow at period tt, nn is the total number of periods, and IRRIRR is the unknown rate we solve for. Because this is a polynomial equation of degree nn, there is no closed-form algebraic solution forn>2n > 2, so numerical methods like bisection or Newton-Raphson iteration are used — exactly as this calculator does.

How to Interpret IRR: The Hurdle Rate Comparison

The most important use of IRR is comparing it to a hurdle rate — the minimum acceptable rate of return set by an organization, also often called the required rate of return or Weighted Average Cost of Capital (WACC).

  • IRR > Hurdle Rate: The project is expected to generate value above the cost of financing it. Accept the project.
  • IRR = Hurdle Rate: The project breaks even in present value terms. Proceed with caution — consider qualitative factors.
  • IRR < Hurdle Rate: The project destroys value relative to the cost of capital. Reject or restructure.

For example, if a real estate investment has an IRR of 14% and your required return (WACC) is 9%, the spread of 5% represents excess return — a strong signal to proceed. Private equity funds typically target IRRs of 20% or higher to compensate for illiquidity and risk.

IRR vs. MIRR vs. NPV: Which Should You Use?

These three metrics answer different questions and work best when used together:

MetricOutputBest For
IRRPercentage return rateComparing projects of similar size/duration
MIRRModified % return rateProjects with non-conventional cash flows or different reinvestment assumptions
NPVAbsolute dollar valueMutually exclusive projects, maximizing total firm value

When two projects have conflicting IRR and NPV rankings — which happens when they differ significantly in scale or timing — always defer to NPV for decision-making, as it directly measures value creation in dollar terms.

Limitations of IRR You Must Know

Despite its popularity, IRR has well-documented limitations that every analyst should understand:

  • Multiple IRR problem: If a project's cash flows change sign more than once (e.g., a large cleanup cost at the end of a mining project), Descartes' Rule of Signs allows for multiple IRR solutions. This makes interpretation ambiguous. The MIRR or NPV profile should be used instead.
  • Reinvestment rate assumption: IRR implicitly assumes that interim cash flows are reinvested at the IRR itself — which is often unrealistically high. MIRR corrects this by using a separate, more realistic reinvestment rate (typically the cost of capital).
  • Scale insensitivity: IRR ignores the absolute size of the investment. A small project with a 30% IRR may create far less value than a large project with a 15% IRR. Always pair IRR with NPV or equity multiple (MoM) when comparing options of different scales.
  • Timing effects: IRR does not account for the duration of an investment in isolation. Two projects with the same IRR but different holding periods have materially different value profiles over time.

Practical Applications of IRR

IRR is used across a wide range of finance and investment contexts:

  • Private equity and venture capital: Funds report IRR as the primary performance metric to limited partners (LPs).
  • Real estate investment: Developers use IRR to evaluate apartment complexes, commercial buildings, and land development projects over multi-year hold periods.
  • Corporate capital budgeting: CFOs use IRR alongside NPV to rank and approve capital expenditure (CapEx) projects.
  • Infrastructure finance: Public-private partnerships evaluate toll roads, airports, and utilities using IRR to justify long-duration commitments.
  • Renewable energy: Solar and wind project developers use IRR to assess the viability of installations given subsidy and tariff structures.

Financial Disclaimer

This IRR calculator is provided for educational and informational purposes only. Results are based solely on the cash flow inputs you provide and mathematical computation. This tool does not constitute financial, investment, tax, or legal advice. IRR is one of many metrics used in investment analysis and should not be used in isolation. Always consult a qualified financial professional before making investment decisions. Past performance and projected returns are not guarantees of future results.

Everyone Nods When Someone Says "22% IRR"

Sit in a real estate pitch. Private equity deck. Any investment meeting. Someone will say the IRR is 22%, or 18%, or 31%. Everyone writes it down.

Ask five of those people afterward what IRR actually measures. You'll get five different answers — and at least two of them will be confidently wrong.

IRR is the most cited metric in finance and one of the least understood. Including by the people citing it.

What It Actually Is

IRR is the discount rate that makes the Net Present Value of all your cash flows equal zero.

That definition is useless until you understand NPV. So: money today is worth more than money later. If you can earn 8% elsewhere, then $1 arriving one year from now is only worth \\frac{\\$1}{1.08} \\approx \\$0.926 in today's terms. NPV applies that logic to every cash flow across the entire investment.

NPV Formula

NPV=t=0nCt(1+r)tNPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}

where CtC_t = cash flow at time t, rr = discount rate

IRR asks: what value of r makes NPV = 0? That rate is your internal rate of return. It's the breakeven discount rate — the return the investment is implicitly earning.

A Concrete Example

You invest $200,000 today. The deal pays you $12,000/year for 4 years, then $252,000 in year 5 (cash flow + principal returned).

YearCash FlowPV at 13.1%
0−$200,000−$200,000
1$12,000$10,609
2$12,000$9,380
3$12,000$8,293
4$12,000$7,332
5$252,000$136,386 (approx)

At a discount rate of ~13.1%, the present values sum to roughly $200,000 — NPV ≈ 0. So IRR = 13.1%.

You can't solve this algebraically. There's no formula that spits out the answer. Every calculator and spreadsheet solves it by iteration — guessing and refining until NPV gets close enough to zero.

Three Ways IRR Can Mislead You

IRR has a few genuine blind spots. Not hypothetical edge cases — things that come up in real deals.

1. It ignores deal size

A 40% IRR on a $10,000 investment makes you $4,000. A 15% IRR on a $10,000,000 investment makes you $1,500,000. IRR says the first deal is better. Your bank account disagrees.

This is why serious investors look at both IRR (efficiency) and NPV (dollars). IRR ranks deals. NPV measures wealth created.

2. Multiple IRRs can exist

If your cash flows change sign more than once — you invest, get some back, invest more, then get paid out — the math can produce two valid IRR solutions. Most spreadsheets just show you one. Which one depends on the starting guess.

Real example: a mining project that requires a large cleanup cost at the end. Cash flows go negative → positive → negative. Can produce two valid IRRs. Neither one is "the" answer.

3. It assumes reinvestment at the same rate

IRR implicitly assumes that every cash flow you receive gets reinvested at the IRR itself. A deal with 25% IRR assumes you can redeploy those interim distributions at 25% too. Usually unrealistic.

MIRR (Modified IRR) fixes this by letting you specify a separate reinvestment rate. Less commonly used, but more honest.

How IRR Compares to the Other Metrics

MetricWhat it measuresWhat it misses
IRRAnnualized return rate, time-weightedDeal size, reinvestment rate
NPVTotal dollars created above your hurdle rateReturn efficiency (a huge NPV could come from a mediocre rate on a giant deal)
ROITotal return as % of costTime — 5% ROI over 1 year is completely different from 5% over 10 years
Cash-on-CashAnnual cash income ÷ cash investedAppreciation, loan paydown — anything that isn't cash in hand

Smart investors use all four. IRR for ranking. NPV for sizing the prize. Cash-on-cash for "does this thing pay my bills while I hold it." ROI for back-of-napkin comparisons.

Common Questions

What's a "good" IRR?

Depends entirely on the asset class and risk. Real estate private equity typically targets 15–25%. Venture capital expects 25%+ because most deals fail. S&P 500 historically returns ~10% annualized. A "good" IRR is one that exceeds your hurdle rate — the minimum return that justifies the risk and illiquidity of not putting money in the index fund instead.

Why can't you calculate IRR by hand?

The IRR equation is a polynomial. For a 5-year investment, it's a 5th-degree polynomial. The Abel-Ruffini theorem proves there's no general algebraic solution for polynomials of degree 5 or higher. So every tool — Excel, calculators, Python — uses numerical methods (Newton-Raphson iteration) to converge on an answer.

IRR vs. CAGR — what's the difference?

CAGR works for a single investment with one entry and one exit — no intermediate cash flows. IRR handles multiple cash flows at different times. For a buy-and-hold with no dividends, they give the same answer. For anything with distributions along the way, use IRR.

Calculate IRR on Your Investment

Enter your initial investment and cash flows by year. The calculator handles the iteration.

*IRR assumes reinvestment at the same rate. Use MIRR for more conservative projections.

Frequently Asked Questions

What is IRR (Internal Rate of Return)?
IRR is the discount rate that makes NPV equal zero. It represents the expected annualized return of an investment over its life. Higher IRR indicates better returns relative to the capital deployed. You compare IRR to your cost of capital or hurdle rate to decide whether to accept or reject a project.
How do I interpret IRR results?
If IRR exceeds your cost of capital (or hurdle rate), the investment adds value and should generally be accepted. If IRR falls below your hurdle rate, the project destroys value relative to your financing cost. For example, if your required return is 10% and the IRR is 15%, the project delivers 5 percentage points of excess return above your threshold.
What's the difference between IRR and NPV?
IRR gives a percentage return rate; NPV gives the absolute dollar value created above your required return. For a single project, both usually agree on accept/reject. For mutually exclusive projects (especially ones of different sizes), NPV is the more reliable metric because it captures the magnitude of value creation, not just the rate.
What are the main limitations of IRR?
IRR has three main limitations: (1) The reinvestment rate assumption — it assumes interim cash flows are reinvested at the IRR itself, which is often unrealistic. (2) Multiple IRR — projects with non-conventional cash flows (more than one sign change) can yield multiple IRRs, making results ambiguous. (3) Scale insensitivity — a small project with 30% IRR may create less total value than a large project with 15% IRR. Use MIRR or NPV to address these limitations.
What is MIRR and when should I use it instead?
Modified Internal Rate of Return (MIRR) corrects two key flaws in IRR: it uses a separate, more realistic reinvestment rate for positive cash flows (typically the cost of capital) and a financing rate for negative cash flows. MIRR always produces a single unique result, making it more reliable for projects with non-conventional cash flows or when the standard reinvestment assumption is inappropriate.
What is considered a 'good' IRR?
A good IRR depends heavily on context and asset class. In private equity, funds typically target 20-25%+ net IRR. Real estate core investments may target 8-12%, while opportunistic deals target 18-25%+. Corporate CapEx projects are usually accepted if IRR exceeds WACC (often 8-12%). Startup venture investments may require 30-40%+ to compensate for high failure rates. Always benchmark against comparable opportunities and the risk profile of the investment.
Advertisement

Disclaimer: This calculator is for general educational purposes only and is not financial, investment, tax, or legal advice. Results are estimates; consult a qualified professional before making financial decisions.