IRR Calculator

IRR (Internal Rate of Return) is the discount rate that makes the Net Present Value (NPV) of all cash flows from an investment equal to zero. It represents the expected annual compound rate of return on an investment. KEY FORMULA: NPV = Σ [CFt / (1+IRR)^t] = 0 WHERE: • CFt = Cash flow at time t • IRR = Internal Rate of Return (the rate we solve for) • t = Time period (0, 1, 2, ... n) INTERPRETATION: • Higher IRR = More profitable investment • If IRR > Required Rate of Return → Accept project • If IRR < Required Rate of Return → Reject project IRR is widely used in capital budgeting, private equity, real estate, and project finance to evaluate and compare investment opportunities.

A "good" IRR depends on your cost of capital, industry, and risk profile: INDUSTRY BENCHMARKS: | Investment Type | Target IRR | |-----------------|------------| | Venture Capital | 25-30%+ | | Private Equity | 20-25% | | Real Estate Development | 15-20% | | Corporate Projects | 12-15% | | Infrastructure | 8-12% | KEY CONSIDERATIONS: 1. Compare to WACC: IRR should exceed your Weighted Average Cost of Capital 2. Risk-adjusted: Higher risk projects require higher IRR targets 3. Time horizon: Shorter projects may accept lower IRR due to faster capital recovery RULE OF THUMB: • IRR > 20%: Excellent investment • IRR 15-20%: Good investment • IRR 10-15%: Acceptable (depends on risk) • IRR < 10%: Generally weak (unless very low risk)

IRR and ROI measure different things and have important distinctions: ROI (Return on Investment): • Formula: (Gain - Cost) / Cost × 100 • Simple percentage return • Ignores timing of cash flows • Ignores time value of money • Example: $50K profit on $100K = 50% ROI IRR (Internal Rate of Return): • Annualized compound return rate • Considers WHEN cash flows occur • Accounts for time value of money • More accurate for multi-year investments EXAMPLE COMPARISON: Investment A: $100K invested, $150K return in Year 10 • ROI: 50% • IRR: ~4.1% per year Investment B: $100K invested, $130K return in Year 2 • ROI: 30% • IRR: ~14% per year Investment B has lower ROI but higher IRR because returns come much sooner. IRR tells you the actual annual growth rate of your money.

IRR and NPV are complementary investment metrics: NPV (Net Present Value): • Measures absolute dollar value created • Formula: NPV = Σ [CFt / (1+r)^t] • Requires specifying a discount rate (r) • Tells you HOW MUCH money you'll make IRR (Internal Rate of Return): • Measures percentage return rate • Finds the rate where NPV = 0 • No discount rate required as input • Tells you WHAT RATE you'll earn WHEN TO USE EACH: • NPV: Better for mutually exclusive projects (different sizes) • IRR: Better for comparing percentage returns • Use BOTH for comprehensive analysis EXAMPLE: Project A: $1M investment, IRR 25%, NPV $200K Project B: $10M investment, IRR 18%, NPV $1.5M IRR favors Project A (higher %), but NPV shows Project B creates more total value ($1.5M vs $200K).

Yes, IRR can have unusual results in certain situations: NEGATIVE IRR: • Occurs when investment loses money overall • Cash outflows exceed present value of inflows • Example: $100K invested, only $80K total returns = negative IRR • Indicates project destroys value MULTIPLE IRRs: • Can occur with "non-conventional" cash flows • Non-conventional = sign changes more than once • Example: -100, +230, -132 (invest, receive, pay more) • May have 0, 1, 2, or more IRR solutions SOLUTIONS FOR MULTIPLE IRR: 1. Use MIRR (Modified IRR) - always gives single solution 2. Use NPV profile chart to visualize 3. Check NPV at your required rate instead 4. Use incremental IRR for project comparison MIRR ADVANTAGE: MIRR assumes reinvestment at a realistic rate (not at IRR) and always produces a single, meaningful result.

MIRR addresses key limitations of traditional IRR by using realistic reinvestment assumptions. MIRR FORMULA: MIRR = (FV of positive cash flows / PV of negative cash flows)^(1/n) - 1 KEY DIFFERENCES FROM IRR: | Factor | IRR | MIRR | |--------|-----|------| | Reinvestment assumption | At IRR rate | At specified rate | | Multiple solutions | Possible | Never | | Realism | Optimistic | More realistic | | Industry acceptance | Traditional | Growing | WHY MIRR IS BETTER: 1. IRR assumes you reinvest at the IRR rate (often unrealistic for high-IRR projects) 2. MIRR lets you specify a realistic reinvestment rate (often WACC) 3. MIRR always gives one solution, even with non-conventional cash flows EXAMPLE: Project with 40% IRR • IRR assumes all interim cash flows earn 40% (unlikely) • MIRR at 10% reinvestment might show 25% (more realistic) Use MIRR when IRR seems too high or when comparing projects with different timing patterns.

IRR cannot be solved algebraically (except for simple cases) - it requires iteration: STEP-BY-STEP PROCESS: 1. LIST ALL CASH FLOWS: • Year 0: -$100,000 (initial investment) • Year 1: +$25,000 • Year 2: +$30,000 • Year 3: +$35,000 • Year 4: +$40,000 • Year 5: +$45,000 2. SET UP NPV EQUATION: 0 = -100,000 + 25,000/(1+r) + 30,000/(1+r)² + 35,000/(1+r)³ + 40,000/(1+r)⁴ + 45,000/(1+r)⁵ 3. SOLVE ITERATIVELY: • Guess r = 10%: NPV = $33,574 (too high, need higher r) • Guess r = 20%: NPV = $2,897 (still positive, need higher r) • Guess r = 22.9%: NPV ≈ 0 (found it!) 4. RESULT: IRR = 22.9% TOOLS: • Excel: =IRR(range) or =XIRR(values, dates) • Financial calculators: HP 12C, TI BA II Plus • This calculator uses Newton-Raphson method

IRR and NPV are mathematically linked through the NPV equation: THE RELATIONSHIP: • IRR is the discount rate where NPV = 0 • At rates below IRR: NPV is positive • At rates above IRR: NPV is negative • NPV profile crosses zero at the IRR NPV PROFILE INTERPRETATION: Discount Rate | NPV | Decision 0% | $75,000 | Accept (NPV > 0) 10% | $33,574 | Accept 15% | $14,862 | Accept 22.9% (IRR) | $0 | Breakeven 25% | -$6,447 | Reject (NPV < 0) 30% | -$19,288 | Reject DECISION CONSISTENCY: If Required Rate < IRR → NPV > 0 → Accept If Required Rate > IRR → NPV < 0 → Reject Both metrics give the same accept/reject decision for independent projects, but NPV is preferred for ranking mutually exclusive projects.

IRR has several important limitations to understand: 1. REINVESTMENT ASSUMPTION: • IRR assumes cash flows reinvest at the IRR rate • Often unrealistic for high-IRR projects • Solution: Use MIRR instead 2. SCALE BLIND: • IRR ignores project size • $1M at 30% IRR vs $10M at 20% IRR • Higher IRR ≠ more dollars • Solution: Also consider NPV 3. MULTIPLE IRR PROBLEM: • Non-conventional cash flows can have multiple IRRs • Solution: Use MIRR or NPV 4. TIMING BLIND: • Two projects with same IRR may have very different risk profiles • Projects with earlier cash flows are generally safer 5. MUTUALLY EXCLUSIVE RANKING: • IRR can incorrectly rank mutually exclusive projects • Solution: Use incremental IRR or NPV BEST PRACTICE: • Use IRR for quick go/no-go decisions • Use NPV for mutually exclusive project selection • Use MIRR for more realistic returns • Always consider multiple metrics together

IRR is particularly popular in real estate due to the timing of cash flows: TYPICAL REAL ESTATE CASH FLOW PATTERN: • Year 0: -$500,000 (down payment, closing costs) • Years 1-5: +$40,000/year (net rental income) • Year 5: +$600,000 (sale proceeds) IRR CALCULATION: Cash flows: -500,000, 40,000, 40,000, 40,000, 40,000, 640,000 IRR ≈ 18.45% REAL ESTATE IRR BENCHMARKS: | Property Type | Target IRR | |---------------|------------| | Core (low risk) | 8-12% | | Value-Add | 12-18% | | Opportunistic | 18-25%+ | | Development | 20-30%+ | KEY CONSIDERATIONS: • Include ALL costs (maintenance, taxes, insurance) • Account for vacancy and collection loss • Consider refinancing cash-out as positive cash flow • Use realistic exit cap rates for sale projections • Include transaction costs on exit

The hurdle rate is your minimum acceptable return - projects must clear this "hurdle" to be accepted. HURDLE RATE CONCEPT: • Also called: Required Rate of Return, Benchmark Rate, Cutoff Rate • Typically based on WACC (Weighted Average Cost of Capital) • May include risk premium for specific projects IRR DECISION RULE: If IRR ≥ Hurdle Rate → Accept project If IRR < Hurdle Rate → Reject project TYPICAL HURDLE RATES: | Company Type | Hurdle Rate | |--------------|-------------| | Large corporations | 10-15% | | Private equity | 20-25% | | Venture capital | 30-40% | | Pension funds | 7-9% | SETTING YOUR HURDLE RATE: 1. Start with WACC as baseline 2. Add risk premium for specific project uncertainty 3. Consider opportunity cost of capital 4. Factor in strategic value (may accept lower IRR) EXAMPLE: • Your WACC: 10% • Project risk premium: 3% • Hurdle rate: 13% • Project IRR: 15% → ACCEPT (15% > 13%)

Comparing projects of different lengths requires careful consideration: THE PROBLEM: • 3-year project with 25% IRR vs 10-year project with 18% IRR • Which is better? Depends on reinvestment assumptions COMPARISON METHODS: 1. EQUIVALENT ANNUAL VALUE (EAV): Convert NPV to annual equivalent for comparison Better for repeating projects of different lengths 2. CHAIN METHOD (Replacement Chain): Extend shorter project to match longer project duration Assumes identical reinvestment opportunities 3. MIRR WITH COMMON HORIZON: Calculate MIRR for both projects using same time horizon More realistic reinvestment assumption 4. NPV COMPARISON: Compare total value created, adjusted for time PRACTICAL APPROACH: • If projects are repeatable: Use EAV method • If one-time investments: Use NPV at your hurdle rate • Consider capital availability and liquidity needs • Factor in flexibility value of shorter projects SHORT VS LONG PROJECTS: • Short projects: Less risk, faster capital recovery, but reinvestment uncertainty • Long projects: More committed capital, but clearer long-term returns