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.