What is IRR (Internal Rate of Return)?

IRR is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero. It represents the annualized return of an investment accounting for the exact timing of each cash flow. A higher IRR means a better return. For example, an IRR of 15% means the investment earns the equivalent of 15% per year compounded, considering when money comes in and goes out.

How is IRR calculated?

IRR is found by solving the equation: 0 = Σ [CF_t / (1 + IRR)^t] for t = 0 to n, where CF_t is the cash flow at time t. There is no closed-form solution, so it's solved numerically using methods like Newton-Raphson iteration — starting with a guess, computing NPV and its derivative, then refining the rate until NPV is effectively zero. This calculator uses Newton-Raphson with multiple starting points.

What is the difference between IRR and ROI?

ROI (Return on Investment) is a simple ratio: (total returns − initial investment) / initial investment. It ignores the timing of cash flows. IRR accounts for when exactly each cash flow occurs — a dollar received in year 1 is worth more than a dollar received in year 5. For uneven or multi-period cash flows, IRR is a far more accurate measure of true return. For a single-period investment with one cash in and one cash out, they're equivalent.

What is a good IRR for an investment?

There's no universal 'good' IRR — it depends on your hurdle rate (cost of capital or minimum acceptable return). In general: IRR above your hurdle rate = value-creating investment. For real estate, 8–12% IRR is often considered acceptable. Private equity typically targets 20–30%. A startup investment might target 30%+ to compensate for risk. The key question is always: does the IRR exceed what you could earn elsewhere at similar risk?

What is NPV and how does it relate to IRR?

NPV (Net Present Value) is the sum of all discounted cash flows: NPV = Σ [CF_t / (1 + r)^t]. It tells you the dollar value an investment adds at a given discount rate r. IRR is the specific discount rate at which NPV = 0. When you plot NPV against different discount rates (the NPV Profile), the curve crosses zero exactly at the IRR. If your cost of capital is below the IRR, NPV is positive and the investment creates value.

IRR Calculator

What's the true return on a series of cash flows? Enter your investment and annual cash flows to calculate IRR, compare it to simple ROI, and visualise the NPV profile.

Currency

All amounts displayed in selected currency

Cash FlowsYear 0 = initial investment (negative)

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

IRR is the discount rate that makes NPV = 0. The higher the IRR, the better the investment relative to its hurdle rate.

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Estimates only. Results are pre-tax. Consult a financial adviser for personalised guidance.

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How to Use This Calculator

Tab "Calculate IRR"

Enter your initial investment as a negative number in Year 0 (e.g. −100,000). Then enter each year's cash flow — positive for inflows, negative for additional outflows. Add or remove periods using the "+ Add period" button (up to 10 periods). The calculator instantly shows your IRR, NPV at common hurdle rates, and net profit.

Tab "IRR vs ROI"

Uses the same cash flows to compare three return metrics side by side: IRR (time-weighted, accounts for cash flow timing), Simple ROI (total return ignoring timing), and Annualized ROI (ROI adjusted for the number of years). This shows why IRR is the superior metric for uneven or multi-period cash flows.

Tab "NPV Profile"

Plots the NPV of your investment at discount rates from −10% to 60%. Green bars show positive NPV (investment creates value at that rate); red bars show negative NPV (investment destroys value). The rate where the chart crosses zero is the IRR. A table also shows NPV at key hurdle rates.

The Formulas

Net Present Value (NPV):
NPV = ∑ [ CF_t / (1 + r)^t ] for t = 0 to n
where CF_t = cash flow at time t, r = discount rate, n = number of periods

Internal Rate of Return (IRR):
Find r such that: 0 = ∑ [ CF_t / (1 + r)^t ]
Solved numerically via Newton-Raphson iteration:
r_new = r − NPV(r) / NPV′(r)
where NPV′(r) = ∑ [ −t × CF_t / (1 + r)^t+1 ]

Simple ROI:
ROI = (Total inflows − |Investment|) / |Investment|

Annualized ROI:
Annualized ROI = (1 + ROI)^1/n − 1
where n = number of years

All calculations use standard financial mathematics. No country-specific tax rates are applied. Results are pre-tax estimates.

Worked Examples

Example 1 — Equal Cash Flows: −$100K, $30K × 5 years → IRR = 15.24%

An investor puts $100,000 into a project and receives $30,000 per year for 5 years.

Year 0 (investment)−$100,000

Years 1–5 (each)+$30,000

Total inflows$150,000

Simple ROI50%

IRR15.24%

NPV @ 10%+$13,724

To verify: solve 0 = −100,000 + 30,000/(1+r) + 30,000/(1+r)² + … + 30,000/(1+r)⁵. At r = 0.1524, NPV ≈ 0. Simple ROI (50%) overstates the annualized return because it ignores that later cash flows are worth less than earlier ones.

Example 2 — Real Estate: −$200K, $5K × 4 yrs, $250K → IRR = 6.46%

A property investor buys for $200,000, earns $5,000/year in net rent for 4 years, then sells for $250,000.

Year 0 (purchase)−$200,000

Years 1–4 (rent)+$5,000 each

Year 5 (sale)+$250,000

Total inflows$270,000

Simple ROI35%

IRR6.46%

Even though simple ROI shows 35%, the IRR is only 6.46% — because most of the return ($250K) arrives in year 5 and must be discounted heavily. This is why timing matters: early cash flows are more valuable.

Example 3 — Startup: −$50K, −$20K, $0, $10K, $40K, $120K → IRR = 22.7%

A startup investment requires capital injections in years 0 and 1, breaks even in year 2, and generates increasing returns from year 3.

Year 0−$50,000

Year 1−$20,000

Year 2$0

Year 3+$10,000

Year 4+$40,000

Year 5+$120,000

Net profit+$100,000

IRR22.7%

With two negative cash flows early on, simple ROI would compute (170K − 70K) / 70K = 143% — which is meaningless for decision-making. IRR's 22.7% correctly reflects the time-adjusted return. If this exceeds your cost of capital (say 12%), the investment creates value.

Understanding IRR: Key Concepts

What IRR Really Means

IRR is the annualized rate of return that makes the present value of all future cash flows equal to the initial investment. Think of it as the "break-even discount rate." If your cost of capital (or required return) is below the IRR, the investment creates value. If it's above the IRR, the investment destroys value relative to alternatives.

IRR vs NPV: Which to Use?

NPV tells you the absolute dollar value created at a specific discount rate — it answers "how much richer does this investment make me?" IRR tells you the percentage return — it answers "what rate of return does this investment deliver?" For most single investment decisions, both metrics lead to the same accept/reject decision. But when comparing two mutually exclusive investments of different sizes, NPV is more reliable because a smaller high-IRR project can create less total value than a larger lower-IRR project.

Limitations of IRR

Multiple IRRs: When cash flow signs change more than once (e.g. negative, positive, negative), there can be multiple rates where NPV = 0. In this case, use Modified IRR (MIRR) or NPV instead.

Reinvestment assumption: IRR implicitly assumes intermediate cash flows are reinvested at the IRR rate itself — which may be unrealistic for high-IRR investments. MIRR addresses this by letting you specify a reinvestment rate.

Scale blindness: A 50% IRR on a $1,000 investment creates less value than a 20% IRR on a $1,000,000 investment. Always pair IRR with the investment size and NPV.

Hurdle Rate

The hurdle rate is the minimum acceptable IRR for an investment — your cost of capital or opportunity cost. If IRR > hurdle rate, the investment creates value. Common hurdle rates: 8–12% for real estate, 15–25% for private equity, 6–10% for large corporations' internal projects. The hurdle rate should reflect both the cost of funding and the riskiness of the specific investment.

Frequently Asked Questions

What is a good IRR?▼

A "good" IRR depends entirely on your hurdle rate and the investment type. For real estate, 8–12% is typically acceptable. Private equity targets 20–30%+. Startup investments need 30%+ to compensate for risk. The key test: does IRR exceed your cost of capital (what you could earn elsewhere at similar risk)? If yes, the investment creates value.

Why must Year 0 be negative?▼

Year 0 represents your initial investment — money you pay out, so it's a negative cash flow. IRR requires at least one sign change in the cash flow series (at least one negative and one positive) to have a mathematical solution. Without a negative Year 0, there's no "investment" to compute a return on.

Can IRR be negative?▼

Yes. A negative IRR means the investment returns less than the original capital — you lose money on a time-adjusted basis. For example, investing $100K and only receiving $80K back over 5 years produces a negative IRR of about −4.3%. Any IRR below your hurdle rate (even if positive) means the investment should be rejected in favour of alternatives.

What if IRR shows "Cannot compute"?▼

This happens when: (1) all cash flows have the same sign — you need at least one inflow and one outflow; (2) the cash flows never produce a positive NPV at any discount rate; or (3) there are multiple sign changes creating multiple IRRs (the solver can't converge on one). In these cases, use NPV at your specific hurdle rate instead of IRR.

How is IRR different from CAGR?▼

CAGR (Compound Annual Growth Rate) measures the growth of a single lump-sum investment from a start value to an end value: CAGR = (End/Start)^(1/n) − 1. It ignores intermediate cash flows. IRR handles multiple cash flows at different times and is the correct measure when you have a series of inflows and outflows — like annual dividends, rental income, or capital calls.

Does this calculator account for taxes?▼

No — this is a universal pre-tax calculator. To model after-tax IRR, enter your after-tax cash flows directly. For example, if Year 1 cash flow is $30,000 and you're in a 25% tax bracket, enter $22,500 as the Year 1 figure. For country-specific tax treatment of investment returns, consult a tax adviser or use a country-specific calculator.

What is the NPV Profile used for?▼

The NPV Profile plots NPV at different discount rates, showing how sensitive the investment's value is to the assumed rate. A steep downward slope means the investment is highly sensitive to the discount rate (common for long-horizon investments). A flat slope means sensitivity is low. The crossover point (NPV = 0) is the IRR. Comparing two investments' NPV profiles shows at what discount rate each is preferred.

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