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:

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.

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.

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.

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.

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.

2. Understanding Leverage

Leverage is the use of borrowed capital (debt) to finance an investment or project with the expectation that the profits made will be greater than the cost of borrowing. It's like using a lever to lift something heavy - it magnifies results, both good and bad.

Upside: If the investment performs well, the returns can be boosted significantly.

Downside: If the investment performs poorly, losses can be magnified significantly.

3. Types of Leverage

There are three main types of leverage:

Operating Leverage:
- Definition: This is the extent to which a company uses fixed costs in its operations.
- Fixed Costs: Costs that do not vary with production or sales volume (e.g., rent, salaries, depreciation).
- Variable Costs: Costs that vary directly with production or sales volume (e.g., materials, direct labor).
- High Operating Leverage: Companies with high fixed costs and low variable costs have high operating leverage. This means a small change in sales can lead to a larger change in profits. Think of airline companies that have a high fixed cost of maintaining planes regardless of the number of passengers they transport.
- Low Operating Leverage: Companies with low fixed costs and high variable costs have low operating leverage. Changes in sales will lead to smaller changes in profits. Think of companies that sell handicrafts, where materials and direct labor are a large proportion of their costs.
- Formula (Degree of Operating Leverage):
  - DOL = Percentage Change in EBIT / Percentage Change in Sales
  - EBIT = Earnings Before Interest and Taxes

Financial Leverage:
- Definition: This is the extent to which a company uses debt financing.
- Debt vs. Equity: Companies with more debt and less equity have higher financial leverage.
- Magnification of Earnings per Share (EPS): If a company earns more on its borrowed funds than it pays in interest, shareholders earn more per share. The opposite is also true, where shareholders can be severely affected when a company's interest payments increase, and the company's earnings do not grow.
- Increased Financial Risk: Higher debt levels also increase the company's risk of bankruptcy if it cannot meet its debt obligations.
- Formula (Degree of Financial Leverage):
  - DFL = Percentage Change in EPS / Percentage Change in EBIT

Combined Leverage:
- Definition: This combines both operating and financial leverage to see the overall impact of changes in sales on a company's EPS.
- Formula (Degree of Combined Leverage):
  - DCL = Degree of Operating Leverage * Degree of Financial Leverage
  - DCL = Percentage Change in EPS / Percentage Change in Sales
  - DCL = DOL * DFL

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:

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.

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.

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.