What's the math relation/back of envelope correlation between RoC & IRR/Equity Multiple

Based on the most helpful WSO content, here's what you need to know about the relationship between Return on Capital (RoC) and IRR/Equity Multiple:

1. Return on Capital (RoC):

   • RoC is a measure of the return that an investment generates relative to the capital invested.
   • It is typically calculated as: [ \text{RoC} = \frac{\text{Net Operating Profit After Taxes (NOPAT)}}{\text{Invested Capital}} ]

2. Internal Rate of Return (IRR):

   • IRR is the annual rate of return that generates a Net Present Value (NPV) of zero for a series of cash flows.
   • It is a discount rate that makes the present value of future cash flows equal to the initial investment.

3. Equity Multiple:

   • Equity Multiple is a measure of the total return on an investment relative to the equity invested.
   • It is calculated as: [ \text{Equity Multiple} = \frac{\text{Total Cash Inflows}}{\text{Total Cash Outflows}} ]

Correlation and Back-of-Envelope Calculation:

• RoC and IRR:

  • While RoC is a snapshot metric, IRR considers the timing of cash flows. Both metrics aim to measure the efficiency of capital use but from different perspectives.
  • A rough correlation can be established by understanding that a higher RoC generally indicates a higher IRR, assuming consistent cash flow patterns.

• RoC and Equity Multiple:

  • Equity Multiple is more straightforward as it does not consider the time value of money, unlike IRR.
  • A higher RoC can lead to a higher Equity Multiple if the investment period and cash flow patterns are favorable.

Simplified Equations:

• IRR Approximation:

  • For a quick approximation, if the cash flows are relatively stable, IRR can be roughly estimated using RoC: [ \text{IRR} \approx \text{RoC} ]
  • This is a simplification and should be used with caution as it ignores the timing of cash flows.

• Equity Multiple Approximation:

  • If RoC is known and the investment period is ( n ) years, the Equity Multiple can be approximated as: [ \text{Equity Multiple} \approx 1 + (\text{RoC} \times n) ]
  • This assumes that the returns are reinvested at the same RoC rate.

These approximations provide a quick way to think about the relationships but should be validated with detailed financial models for accuracy.

Sources: Relationship among Cap Rate, IRR, Discount rate and NPV, Rough mental return calculations?, Modeling Question: IRR goes down but CoC goes up over time, Why even use EBITDA?, DCF Modeling Course ~ Pre-training text.pdf