IRR — 内部収益率
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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. In plain terms, it is the annualized rate of return that an investment is expected to generate over its lifetime, accounting for the timing of all cash inflows and outflows. IRR is the single most widely used metric for evaluating and comparing capital investments in corporate finance, private equity, real estate, and project finance. The appeal of IRR is intuitive: it expresses investment performance as a percentage return, comparable to an interest rate or stock market return. A project with an IRR of 20% is expected to return 20% per year on the capital invested, accounting for all cash flows over the life of the project. If this exceeds the company's cost of capital (WACC) or a minimum required return (hurdle rate), the project is worth undertaking. If IRR is below the hurdle rate, the investment destroys value relative to alternatives. IRR has no closed-form algebraic solution — it must be solved iteratively, which is why it was impractical before computers. The Excel IRR() and XIRR() functions, and financial calculators, solve for it using numerical methods. XIRR() is the more powerful version: it handles irregular cash flow timing (actual dates) rather than assuming equal periods between cash flows. Despite its popularity, IRR has important limitations. It implicitly assumes that interim cash flows can be reinvested at the IRR itself — an assumption that is realistic only when IRR is close to the cost of capital, and often unrealistically optimistic for high-IRR projects. It can also produce multiple solutions (multiple IRRs) for non-conventional cash flow patterns (investments with cash outflows after the initial investment). Modified IRR (MIRR) addresses the reinvestment assumption by explicitly specifying a reinvestment rate. Always use IRR alongside NPV — they sometimes give conflicting rankings for mutually exclusive projects, and NPV is the theoretically superior capital budgeting criterion.
NPV = 0 = CF₀ + CF₁/(1+IRR)¹ + CF₂/(1+IRR)² + ... + CFₙ/(1+IRR)ⁿ Solve for IRR iteratively (no closed-form solution). MIRR = [(FV of positive CFs at reinvestment rate) / (PV of negative CFs at finance rate)]^(1/n) − 1
- 1List all cash flows in chronological order: the initial investment (negative) at time 0, followed by each period's net cash inflows or outflows.
- 2Set up the NPV equation: sum of all cash flows discounted at the unknown rate (IRR) must equal zero.
- 3Solve iteratively: start with a guess (e.g., 10%), calculate NPV, then adjust the rate up (if NPV > 0) or down (if NPV < 0), repeating until NPV converges to zero. In practice, use Excel's IRR() or XIRR() function.
- 4Compare IRR to the hurdle rate or WACC. Accept the project if IRR > hurdle rate; reject if IRR < hurdle rate.
- 5For irregular cash flow timing, use XIRR() with actual calendar dates — the standard IRR assumes equal time periods between cash flows.
- 6For non-conventional cash flows or multiple IRR problems, compute MIRR using an explicit reinvestment rate (typically the WACC or cost of capital) for a single, unambiguous answer.
The IRR is the discount rate that makes NPV = 0. At 18.9%: PV of inflows ≈ $25K/1.189 + $30K/1.189² + $35K/1.189³ + $30K/1.189⁴ + $20K/1.189⁵ ≈ $100,000, exactly offsetting the initial investment. If the company's hurdle rate is 15%, this project (IRR 18.9%) should be accepted — it exceeds the minimum required return by nearly 4 percentage points.
Year 0: −$500,000. Years 1–4: +$35,000 each. Year 5: +$35,000 NOI + $650,000 sale = +$685,000. The IRR of 14.2% captures both the income stream and the capital gain from appreciation. Comparing this to a stock market expected return of 9–10% or a WACC of 8%, this real estate investment looks attractive on an IRR basis. Note: the sale price assumption is critical — a $100,000 variance in sale price moves IRR by roughly 1.5–2 percentage points.
Project A IRR (21.9%) > Project B IRR (15.0%). However, Project A NPV at 10% = $13,397. Project B NPV at 10% = $21,869. When projects differ in scale, NPV is the better decision rule — Project B creates $8,472 more value despite a lower IRR. This is the classic IRR vs. NPV conflict for mutually exclusive projects: always defer to NPV when they disagree, as NPV directly measures value creation in dollar terms.
The extreme back-loading of cash flows (no returns for 3 years, then a large exit) produces a very high IRR that reflects venture-capital return expectations. At 49.4% IRR, $2M invested today grows to approximately $2M × 1.494⁵ = $15M over 5 years — consistent with a 7.5× multiple on invested capital (MOIC). VC funds typically target IRRs of 30%+ and 3–5× MOIC to compensate for the high failure rate across the portfolio.
The IRR of 60% assumes the $80K Year 1 cash flow can be reinvested at 60% — clearly unrealistic. MIRR uses an 8% reinvestment rate: FV of positive CFs at 8% = $80K × 1.08 + $80K = $86,400 + $80,000 = $166,400. MIRR = ($166,400/$100,000)^(1/2) − 1 = 29.0%. The large gap between IRR and MIRR signals that the IRR is significantly overstating the realistic return — MIRR is the more honest metric when IRR is very high.
Professionals in finance and lending use Irr Calculator as part of their standard analytical workflow to verify calculations, reduce arithmetic errors, and produce consistent results that can be documented, audited, and shared with colleagues, clients, or regulatory bodies for compliance purposes.
University professors and instructors incorporate Irr Calculator into course materials, homework assignments, and exam preparation resources, allowing students to check manual calculations, build intuition about input-output relationships, and focus on conceptual understanding rather than arithmetic.
Consultants and advisors use Irr Calculator to quickly model different scenarios during client meetings, enabling real-time exploration of what-if questions that would otherwise require returning to the office for detailed spreadsheet-based analysis and reporting.
Individual users rely on Irr Calculator for personal planning decisions — comparing options, verifying quotes received from service providers, checking third-party calculations, and building confidence that the numbers behind an important decision have been computed correctly and consistently.
Terminal value sensitivity: In real estate and PE, a large portion of IRR comes from the exit (terminal value).
A small change in exit cap rate or exit multiple dramatically impacts IRR — always run sensitivity analysis on exit assumptions.
Negative IRR: If total undiscounted cash inflows are less than the initial investment, IRR is negative.
This immediately signals a value-destroying investment.
Zero initial investment: If no upfront capital is required (e.g., carry
Zero initial investment: If no upfront capital is required (e.g., carry interest in a fund), IRR is undefined — use MOIC or total return metrics instead.
GP/LP waterfalls in PE: IRR calculations in PE fund structures must account for
GP/LP waterfalls in PE: IRR calculations in PE fund structures must account for complex distribution waterfalls (preferred returns, carried interest), making the IRR to LPs different from the gross portfolio IRR.
| Investment Type | Typical Target IRR | Notes |
|---|---|---|
| Corporate CapEx (low risk) | 8–15% | Must exceed WACC (typically 7–10%) |
| Corporate CapEx (high risk) | 15–25% | Risk-adjusted hurdle rate |
| Real Estate (core) | 6–9% | Low risk, stabilized assets |
| Real Estate (value-add) | 12–18% | Renovation and repositioning risk |
| Real Estate (opportunistic) | 18–25%+ | Development or distressed assets |
| Private Equity (buyout) | 20–25% | Net of fees to LPs |
| Venture Capital | 30–50%+ | Portfolio average; most investments fail |
| Infrastructure | 8–12% | Long-duration, regulated returns |
What is a good IRR for an investment?
A 'good' IRR depends on the risk profile of the investment and the investor's cost of capital. As a rough benchmark: corporate capital projects typically require IRRs of 15–25% depending on risk. Real estate investors often target 12–20% IRR. Private equity funds target 20–30%+ IRR. Venture capital funds target 30–50%+ IRR to compensate for high failure rates. The key is always whether IRR exceeds the relevant cost of capital or hurdle rate — the excess represents risk-adjusted value creation.
What is the difference between IRR and ROI?
Return on Investment (ROI) is a simple ratio of profit to cost: (Gain − Cost) / Cost. It does not account for the time value of money or the timing of cash flows. A 50% ROI over 1 year is very different from a 50% ROI over 10 years. IRR is a time-weighted, annualized return that properly accounts for when cash flows occur. For multi-year investments with multiple cash flows, IRR is far more meaningful than simple ROI.
Why might IRR give multiple answers?
IRR can produce multiple solutions when cash flows change sign more than once (a 'non-conventional' cash flow pattern). For example: invest $100K (negative), receive $300K in year 2 (positive), pay $200K in year 3 for remediation (negative). This sign change pattern can produce two mathematically valid IRRs. In these cases, rely on NPV instead, or use MIRR which always produces a unique answer by explicitly specifying reinvestment and financing rates.
How is XIRR different from IRR?
IRR assumes cash flows occur at equal intervals (e.g., exactly 12 months apart). XIRR handles cash flows at irregular dates — you provide both the amounts and actual calendar dates. XIRR is more accurate for real-world investments where cash flows occur on specific dates that are not exactly one period apart. For example, a real estate investment where you close on January 15, receive quarterly rent payments, and sell on November 30 three years later — XIRR handles this precisely while IRR would require approximation.
Why does NPV sometimes conflict with IRR in project rankings?
When comparing mutually exclusive projects of different sizes or with different cash flow timing, IRR and NPV can give conflicting rankings. IRR measures the rate of return on capital deployed; NPV measures the total dollar value created. A small project with a very high IRR might create less total value than a larger project with a lower but still positive IRR. The theoretically correct decision rule is to maximize NPV — it directly measures the change in firm value. IRR is useful for communicating returns but should not override NPV when they conflict.
What is the reinvestment rate assumption, and why does it matter?
IRR implicitly assumes that all interim cash flows (cash received before the end of the project) are reinvested at the IRR itself. If the IRR is 30%, the formula assumes you can reinvest every dollar received at 30% — which is usually impossible for high-IRR projects. This makes high IRRs systematically overstate actual returns. MIRR corrects this by using a realistic reinvestment rate (typically WACC or a safe rate like Treasury yields) for interim cash flows. Always compare high IRRs against their MIRR to assess the realistic return.
How do private equity firms calculate IRR?
Private equity IRR calculations use actual investment dates and cash flow dates (like XIRR), not calendar-year approximations. PE firms track IRR from the date each dollar is drawn from limited partners to the date each dollar is returned. This is called the 'money-weighted return' or 'dollar-weighted return.' PE firms also report MOIC (multiple on invested capital) alongside IRR because IRR alone can be gamed — a high IRR on a short hold period with quick capital return may reflect less total value created than a lower IRR on a longer, larger investment.
Can IRR be used for bonds?
Yes. For a fixed-income security, IRR is equivalent to the yield to maturity (YTM) — the discount rate that equates the present value of all coupon payments and principal repayment to the bond's current price. If you buy a $1,000 bond for $950, with $50 annual coupons and maturity in 5 years, the YTM (= IRR of your bond investment cash flows) is approximately 6.1%. This shows that IRR is a universal return metric applicable to any series of cash flows, not just equity investments.
プロのヒント
Always present IRR alongside NPV and MOIC (for equity investments). IRR alone is a percentage that tells you rate but not scale. A project with a 30% IRR on $10,000 creates far less value than a 15% IRR on $10,000,000. Use IRR to pass/fail the hurdle rate test, NPV to compare and rank alternatives, and MOIC to communicate total wealth creation to investors.
ご存知でしたか？
The term 'internal' in Internal Rate of Return refers to the fact that it is determined entirely by the cash flows internal to the investment — it doesn't depend on any external market rate. This distinguishes it from metrics that reference external benchmarks like market returns or risk-free rates.
参考文献
- ›Brealey, Myers & Allen – Principles of Corporate Finance (Chapter on NPV and IRR)
- ›Damodaran – Investment Valuation: IRR and its Alternatives
- ›CFA Institute – Capital Budgeting: NPV and IRR
- ›Investopedia – Internal Rate of Return (IRR)
- ›Harvard Business Review – IRR: Good Guidelines Don't Always Make Good Decisions
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