IRR Calculator: Internal Rate of Return & Capital Efficiency Model

What is IRR?

• Formula:
  Find r such that

  $$0 = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$$

  where CF_t is cash flow at time t
• Calculation Method:
  Uses Newton-Raphson iterative method to solve for the discount rate numerically
• Key Difference from ROI:
  IRR accounts for timing—a dollar today is worth more than a dollar in 5 years
• Use Cases:
  Private equity, venture capital, real estate flips, project finance, and any investment with multiple cash flows over time

Why IRR Matters for Investment Decisions

• Standardization:
  Allows comparison of investments with different cash flow patterns and time horizons
• Time Value of Money:
  Properly discounts future cash flows, recognizing that money today is worth more than money tomorrow
• Decision Rule:
  If IRR > Hurdle Rate, the investment is value accretive. If IRR < Hurdle Rate, it's sub-optimal.
• Industry Standard:
  IRR is the primary metric used by private equity firms, VCs, and real estate investors for deal evaluation

The IRR Reinvestment Assumption

• The Problem:
  IRR can be "optimistic" because it assumes reinvestment at the same high rate
• Real-World Reality:
  Positive cash flows are typically reinvested at a lower, more realistic rate (e.g., 5% in a savings account or index fund)
• Impact:
  This makes IRR appear higher than the actual return you'll achieve
• Example:
  A 15% IRR might only be a 12% MIRR when using a 5% reinvestment rate

MIRR is the professional's choice for 2026 investment analysis because it uses realistic reinvestment assumptions.

Modified IRR (MIRR) Calculation

• Financing Rate:
  Applied to negative cash flows (outflows). Typically your hurdle rate or cost of capital
• Reinvestment Rate:
  Applied to positive cash flows (inflows). A realistic rate like 5% for savings or 7% for index funds
• Calculation:
  $$\text{MIRR} = \left(\frac{\text{FV of positive flows}}{\text{PV of negative flows}}\right)^{1/n} - 1$$
• Advantage:
  Provides a single, unambiguous answer even when multiple IRRs exist

Understanding Hurdle Rates

• 2026 Risk-Free Rate:
  10-year Treasury yield: ~4.5%. This is the baseline for "risk-free" returns
• Market Benchmark:
  S&P 500 historical average: ~8-10% (inflation-adjusted). This is a common hurdle rate for equity investments
• Risk Premium:
  Add 2-5% for higher-risk investments (venture capital, real estate development, etc.)
• Decision Rule:
  If IRR < Hurdle Rate, the investment is sub-optimal—you could do better with a passive index fund

The Hurdle Rate Spread

• Positive Spread:
  IRR > Hurdle Rate = "Value Accretive." The investment creates value above your minimum threshold
• Negative Spread:
  IRR < Hurdle Rate = "Sub-Optimal Allocation." Consider alternatives like index funds
• Large Positive Spread:
  IRR > 20% = "High-Efficiency Venture." Exceptional returns, but verify assumptions
• Use Case:
  Quickly screen deals: if spread is negative, the deal likely isn't worth your time

Why Timing Matters More Than Total Profit

• Example:
  Receiving $150K in Year 4 vs. Year 5 can increase IRR by 2-3 percentage points, even with the same total profit
• Real Estate Flips:
  Faster flips (6 months vs. 12 months) dramatically boost IRR, even if total profit is slightly lower
• Venture Capital:
  Earlier exits (Year 3 vs. Year 5) significantly improve IRR, making "exit velocity" a key metric
• Strategy:
  Optimize for IRR, not just total return. Faster cash flow realization creates more value

Sensitivity Analysis and Risk Assessment

• Purpose:
  Tests the sensitivity of IRR to exit assumptions, which are often uncertain
• Interpretation:
  If a 10% reduction causes IRR to drop below your hurdle rate, the deal is sensitive to exit value
• Risk Management:
  Use sensitivity analysis to stress-test your assumptions and understand downside scenarios
• Decision Making:
  If IRR is barely above hurdle rate and highly sensitive, consider the deal risky