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CAPM and types of leverages

CAPM, Leverage, and Risk: A Practical Guide

Let's break down these financial concepts in a simple and clear way.

1. Capital Asset Pricing Model (CAPM) - Practical Problems

As we discussed before, CAPM is a model used to calculate the expected return on an investment, considering its risk. The formula is:

Ke = Rf + Beta * (Rm - Rf)

Where:

  • Ke = Cost of Equity (or Expected Return)
  • Rf = Risk-free rate of return (e.g., yield on a government bond)
  • Beta = Measure of a stock's volatility relative to the market.
  • Rm = Expected return on the market portfolio (e.g., a broad stock market index).
  • (Rm - Rf) = Market risk premium (the extra return investors expect for taking market risk).

Practical Problems & Considerations:

  1. Estimating Beta:

    • Historical Data: Beta is often estimated using historical stock price data, comparing a stock's price movements to the market's movements.
    • Time Period: The choice of the time period (e.g., 1 year, 5 years) for historical data can influence the estimated beta.
    • Industry Beta: Sometimes, an average beta of companies in the same industry is used if the stock's historical data is not reliable or does not seem representative.
    • Adjusted Beta: Some analysts adjust historical beta because beta tends to revert to 1 over time.

  2. Selecting the Risk-Free Rate (Rf):

    • Government Bonds: The yield on long-term government bonds (e.g., 10-year bonds) is typically used as a proxy for the risk-free rate.
    • Maturity Matching: It's ideal to match the maturity of the risk-free rate to the investment's time horizon.

  3. Estimating Market Return (Rm):

    • Historical Average: Often, historical average returns of a broad market index (like S&P 500) are used as an estimate for the expected market return.
    • Forward-Looking Estimates: Some analysts use economic forecasts or surveys to estimate future market returns, which are often based on a variety of financial factors, historical data, and analysis.

  4. Model Limitations:

    • Simplification: CAPM is a simplified model and does not capture all real-world complexities of investing.
    • Single Factor: It relies on a single risk factor (market risk) and ignores other potential risks.
    • Assumptions: It's based on certain assumptions that may not always hold true in the real world, such as investor rationality and efficient markets.

  5. Practical Example:

    Let's say:

    • Risk-free rate (Rf) = 3%
    • Beta (β) = 1.1
    • Expected market return (Rm) = 10%
    • Cost of Equity (Ke) = 3% + 1.1 * (10% - 3%)
      • Ke = 3% + 1.1 * 7%
      • Ke = 3% + 7.7%
      • Ke = 10.7%
    • Interpretation: The CAPM model suggests that an investor should expect a return of 10.7% from investing in this particular stock given the overall market risk, as reflected by the stock's beta.

Leverage: Understanding How It Amplifies Results

What is Leverage?

In simple terms, leverage is like using a tool to make something happen with less effort, but also with more potential for both gains and losses. It's about using a fixed cost or debt to amplify the impact of changes in revenue on your profits. Think of it as a see-saw - a small push on one side can have a big impact on the other.

Types of Leverage:

There are three main types of leverage used in business:

  1. Operating Leverage:

    • Definition: This refers to the extent to which a company uses fixed operating costs (like rent, salaries) compared to variable operating costs (like raw materials, sales commissions).

    • High Operating Leverage: A company with high operating leverage has a lot of fixed costs and relatively low variable costs. If sales increase, profits increase significantly. However, if sales decrease, losses can also be significant. It's like a roller coaster.

    • Low Operating Leverage: A company with low operating leverage has more variable costs and fewer fixed costs. The impact on profits from a change in sales is less extreme, making it more stable.

    • Formula: Degree of Operating Leverage (DOL) = Percentage Change in EBIT / Percentage Change in Sales

      OR

      DOL = Contribution Margin / Earnings Before Interest and Taxes (EBIT)

      Where Contribution Margin = Sales - Variable Costs

    • Example: A software company has high operating leverage (lots of development costs) while a retail store has lower operating leverage (lots of costs directly tied to the products it sells).

  2. Financial Leverage:

    • Definition: This refers to the extent a company uses borrowed funds (debt) in its capital structure, as opposed to equity (investor money).

    • High Financial Leverage: A company with high financial leverage has a lot of debt. If the company is profitable, it can generate much higher returns for investors. However, it also faces higher risk of bankruptcy if it cannot repay its debt.

    • Low Financial Leverage: A company with low financial leverage uses less debt. It has lower risk, but also potentially lower returns compared to a highly leveraged business.

    • Formula: Degree of Financial Leverage (DFL) = Percentage Change in Earnings Per Share (EPS) / Percentage Change in EBIT

      OR

      DFL = Earnings Before Interest and Taxes (EBIT) / Earnings Before Taxes (EBT)

    • Example: A real estate company buying properties with loans is a good example of high financial leverage.

  3. Combined Leverage:

    • Definition: This is the combination of operating leverage and financial leverage, it looks at how much a company's Net Profit changes when there is a change in sales.

    • Impact: Combined leverage can significantly amplify both gains and losses, making it a powerful, yet risky tool. A company with high operating and financial leverage is incredibly sensitive to changes in sales and profit.

    • Calculation: Degree of Combined Leverage (DCL) = Degree of Operating Leverage (DOL) * Degree of Financial Leverage (DFL)

      OR

      DCL = Percentage Change in EPS / Percentage Change in Sales

      OR

      DCL = Contribution Margin / Earnings Before Taxes (EBT)

Risk and Leverage:

  • Increased Volatility: Leverage amplifies both positive and negative results. This means that the higher the leverage, the more volatile a company's profits are.
  • Higher Risk of Loss: If sales decline, or interest rates rise, a company with high leverage could face significant financial difficulties.
  • Need for Careful Management: High leverage requires careful management of expenses, sales, and debts. Mismanagement of highly leveraged companies can have drastic consequences.

4. Risk and Leverage

  • Leverage Amplifies Risk: As we mentioned earlier, leverage magnifies both profits and losses. Higher leverage means higher risk.
  • Business Risk: This is the risk that a company will be unable to cover its operating costs due to factors like a decline in sales or increase in expenses. Operating leverage can amplify this risk.
  • Financial Risk: This is the risk of not being able to cover debt obligations. Financial leverage increases financial risk.
  • Higher Leverage = Higher Risk: Companies with high operating or financial leverage are more vulnerable to market fluctuations and can face significant losses during downturns.

5. Practical Problems - Leverage

Let's illustrate these concepts with a simple problem:

Company ABC:

  • Fixed operating costs: $100,000
  • Variable cost per unit: $10
  • Selling price per unit: $20
  • Interest expense: $50,000
  • Current Sales: 20,000 units
  • Taxes: 25%

Calculations:

  1. Operating Leverage

    • Sales Revenue = 20,000 * $20 = $400,000
    • Variable Costs = 20,000 * $10 = $200,000
    • EBIT = $400,000 - $200,000 - $100,000 = $100,000
    • Suppose the company increases the sales by 10% i.e to 22,000 units
    • New Sales Revenue = 22,000 * $20 = $440,000
    • New Variable Costs = 22,000 * $10 = $220,000
    • New EBIT = $440,000 - $220,000 - $100,000 = $120,000
    • Percentage Change in Sales = 22000 -20000 / 20000 = 10%
    • Percentage Change in EBIT = 120000-100000 / 100000 = 20%
    • Degree of Operating Leverage = 20% / 10% = 2

    Interpretation: A 1% change in sales will result in a 2% change in EBIT. This is a result of high fixed costs in operations.

  2. Financial Leverage

    • EBT = EBIT - interest = $100,000 - $50,000 = $50,000
    • Taxes = $50,000*25% = $12,500
    • Net Income = $50,000 - $12,500 = $37,500
    • Suppose, EBIT increases by 10% (i.e to 110000)
    • EBT = 110000 - 50000 = 60000
    • Taxes = 60000 * 25% = 15000
    • Net Income = 60000-15000 = 45000
    • Percentage Change in EBIT = 10%
    • Percentage Change in EPS = (45000-37500) / 37500 = 20%
    • Degree of Financial Leverage = 20% / 10% = 2

    Interpretation: A 1% change in EBIT will result in a 2% change in EPS. This shows that the company relies on debt financing which amplifies the profits for the owners.

  3. Combined Leverage

    • Degree of Combined Leverage = DOL * DFL = 2 * 2 = 4

    Interpretation: A 1% change in sales will result in a 4% change in EPS

Key Takeaways

  • CAPM helps estimate expected returns based on risk, but it has limitations.
  • Leverage amplifies both profits and losses, using debt and fixed costs.
  • Operating leverage focuses on the impact of fixed operating costs on profitability.
  • Financial leverage focuses on the impact of debt financing on profitability.
  • Combined leverage assesses the total impact of operating and financial decisions on profitability.
  • Higher leverage = higher risk; it's important to understand the implications for a company's financial health.

Understanding these concepts is crucial for making sound financial decisions, evaluating investments, and assessing risk.

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