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IRR Calculator —
internal rate of return.
Enter any series of cash flows, initial investment, annual revenues, residual values and instantly see the IRR, NPV at common hurdle rates, payback period, and a full NPV-versus-discount-rate curve showing exactly where your project crosses from profitable to unprofitable.
Inputs
Cash flows
- Total invested
- −$100,000
- Total returned
- +$145,000
- Net cash flow
- $45,000
Internal Rate of Return
5 periods
Project returns 12.33%/yr. NPV positive at a 10% hurdle rate — invest.
Visualization
Cash flow by period
NPV curve
Net present value at each discount rateIRR = 12.33% (NPV = $0)
The curve crosses zero at the IRR. Projects are viable when the required return is below this rate.
Sensitivity
NPV at common discount rates
| Discount rate | NPV |
|---|---|
| 0% | $45,000 |
| 5% | $23,661 |
| 8% | $13,041 |
| 10% | $6,710 |
| 12%≈ IRR | $903 |
| 15% | -$6,940 |
| 20% | -$18,068 |
| 25% | -$27,245 |
Field guide
What IRR is and how to use it.
The Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of a cash-flow stream equals zero. In plain language: it is the annualised return rate that an investment implicitly earns, accounting for the timing of every cash inflow and outflow. A project with an IRR of 18% earns the equivalent of an 18% annual compound return on the capital deployed in it.
IRR is the dominant metric in private equity, venture capital, real estate development, infrastructure, and corporate capital-budgeting decisions. It reduces any investment, regardless of how irregular the cash flows are, to a single percentage that can be compared directly against a required rate of return (called the hurdle rate).
The NPV equation and why IRR has no closed form
Net Present Value sums the time-discounted value of each cash flow:
NPV(r) = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + … + CFₙ/(1+r)ⁿ
IRR = the value of r that makes NPV(r) = 0
For a cash-flow series with n periods, this is a polynomial of degree n in (1 + r). For n ≥ 5 there is no algebraic solution; the IRR must be found numerically. This calculator uses Newton-Raphson iteration (fast convergence near the root) with a bisection fallback (guaranteed convergence when a sign change can be bracketed), matching the algorithm used in Excel's =IRR() function.
Decision rule: IRR vs hurdle rate
The standard rule is simple: invest if IRR > hurdle rate; reject if IRR < hurdle rate. The hurdle rate is typically the project's cost of capital — the weighted-average cost of debt and equity (WACC), adjusted upward for risk.
| Outcome | Condition | NPV |
|---|---|---|
| Invest ✓ | IRR > hurdle rate | Positive |
| Neutral | IRR = hurdle rate | $0 |
| Reject ✗ | IRR < hurdle rate | Negative |
IRR vs NPV: which should you use?
IRR and NPV almost always agree on a single project (accept/reject), but they can conflict when comparing mutually exclusive alternatives of different scale or duration:
- IRR is scale-blind. A $1,000 investment returning $1,200 has an IRR of 20%. A $1,000,000 investment returning $1,050,000 has an IRR of 5%. The first has a higher IRR, but the second creates vastly more absolute value. NPV (at a 4% hurdle) correctly identifies the $1M project as superior.
- IRR assumes reinvestment at IRR. The implicit assumption is that every interim cash inflow can be reinvested at the same rate as the IRR. For very high IRRs (30%+) this is unrealistic. Modified IRR (MIRR) corrects this by specifying separate financing and reinvestment rates.
- NPV is always additively consistent. The NPV of a portfolio equals the sum of individual project NPVs. IRRs cannot be averaged or summed in any meaningful way.
For most capital-budgeting decisions, use NPV as the primary decision metric and IRR as a sanity check and communication tool. IRR is easier to explain to stakeholders who don't want to argue about discount rates; NPV is more mathematically rigorous.
IRR vs CAGR vs ROI
These three metrics are frequently confused:
- IRR accounts for the timing of every cash flow. Receiving $100K in year 1 is worth more than receiving $100K in year 5 and IRR captures that difference.
- CAGR (Compound Annual Growth Rate) measures the annualised growth of a single lump-sum investment from a start value to an end value, with no intermediate cash flows. CAGR = (FV/PV)^(1/n) − 1.
- ROI (Return on Investment) is a simple percentage: (Gain − Cost) / Cost × 100. It ignores time entirely. A 50% ROI over 10 years is far less impressive than a 50% ROI over 1 year.
IRR is the most information-rich of the three: it handles irregular timing, unequal cash flows, and multiple periods, all in a single percentage.
Multiple IRRs and non-conventional cash flows
A conventional cash-flow series has exactly one sign change — typically a negative initial investment followed by positive returns. Descartes' rule guarantees it has exactly one positive real IRR.
A non-conventional series (e.g., a project that requires a large midstream cash injection for a renovation, followed by positive terminal cash flows) has multiple sign changes and may have multiple positive IRRs. In that case the IRR decision rule breaks down, and NPV analysis becomes the only reliable approach. This calculator flags when multiple sign changes are detected and returns the smallest positive root.
What is a good IRR?
“Good” is always relative to the cost of capital and the asset class:
| Asset class | Typical IRR target |
|---|---|
| Infrastructure / core real estate | 7 – 12% |
| Value-add real estate | 12 – 18% |
| Opportunistic real estate | 18 – 25% |
| Private equity (buyout) | 20 – 30% |
| Venture capital | 25 – 40%+ |
| Corporate capital projects | WACC + risk premium |
| S&P 500 historical average | ~10% nominal |