Internal Rate of Return (IRR)
$$0 = \sum_{t=0}^{n} \frac{CF_t}{(1+\text{IRR})^t}$$
What is Internal Rate of Return (IRR)?
The Internal Rate of Return (IRR) is the discount rate at which the net present value (NPV) of all cash flows from an investment equals exactly zero. Put simply: it is the implied annual return embedded in a project's cash flow schedule. If you invest $100,000 today and receive $40,000, $40,000, and $40,000 over the next three years, IRR is the single annual rate that makes those future receipts worth exactly $100,000 in present-value terms.
IRR has no closed-form algebraic solution for most real-world cash flow schedules - it must be found by numerical iteration. Spreadsheets (Excel IRR function) and financial calculators do this automatically by guessing a rate, computing NPV, and adjusting until NPV reaches zero. This iterative nature is why IRR cannot easily be back-of-envelope calculated for complex projects.
The decision rule is straightforward: if IRR exceeds the project's hurdle rate (the minimum required return, often the company's weighted average cost of capital), the investment creates value and should be accepted. If IRR falls below the hurdle rate, the project destroys value. When ranking competing projects, higher IRR is generally preferable - but this breaks down when projects differ significantly in scale, duration, or have unusual cash flow patterns.
When to use Internal Rate of Return (IRR)
Use IRR when evaluating a single project against a known hurdle rate, or comparing projects with similar scale and time horizon. It is the standard return language in private equity and venture capital: when a fund reports a "25% net IRR," it means that 25% annually is the rate at which the timing-adjusted value of all capital contributions and distributions break even. Pair IRR with MOIC to capture both the efficiency (IRR) and the magnitude (MOIC) of returns. Do not rely on IRR alone when comparing projects of very different sizes - a 40% IRR on $100K may generate far less value than a 20% IRR on $5M.
Worked examples
| Project | Initial Investment | CF Year 1 | CF Year 2 | CF Year 3 | IRR |
|---|---|---|---|---|---|
| Project A (steady) | -$100,000 | $40,000 | $40,000 | $40,000 | 9.7% |
| Project B (back-loaded) | -$100,000 | $0 | $0 | $150,000 | 14.5% |
| Project C (large) | -$250,000 | $80,000 | $90,000 | $120,000 | 12.8% |
| Project D (loss) | -$100,000 | $20,000 | $20,000 | $20,000 | -22.9% |
Common pitfalls
IRR has two well-known failure modes. First, multiple IRRs: if a project has alternating positive and negative cash flows - for example a mine that generates cash for years, then requires expensive environmental remediation at closure - the underlying polynomial can have multiple solutions, making IRR ambiguous. Second, the reinvestment rate assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR rate itself, which is unrealistic for high-IRR projects. In both cases, Modified IRR (MIRR) or NPV is more reliable.
Frequently asked questions
What is the difference between IRR and NPV?
NPV expresses investment value as an absolute dollar figure at a chosen discount rate. IRR is the specific discount rate at which NPV equals zero - it is a percentage, not a dollar amount. For a standard project (cash out then cash in), the two methods agree: if IRR > hurdle rate, NPV at that hurdle rate is positive. They can disagree when ranking competing projects of different scale or timing - in those cases, NPV is more reliable.
What is a good IRR?
It depends on the asset class and risk. Private equity funds typically target 20-30% gross IRR. Venture capital funds may target 30%+ to compensate for portfolio company failures. Corporate investment projects are often evaluated against the company's WACC, typically 8-15%. Real estate deals commonly target 12-20% IRR depending on risk profile. The only valid benchmark is the opportunity cost: what else can the capital earn at the same risk level?
What is a hurdle rate?
A hurdle rate is the minimum acceptable IRR for an investment. In corporate finance it is typically the company's WACC plus a risk premium. In private equity it is a contractual threshold (commonly 8%) above which the fund manager earns carried interest. Any project with IRR below the hurdle rate is rejected because it earns less than the cost of the capital required to fund it.