In-Depth Notes on CAPM, Cost of Equity, and WACC

CAPM Betas and Cost of Capital

• Capital Asset Pricing Model (CAPM): Used for estimating the cost of equity.

  • Formula: $R = R<em>f + \beta(R</em>m - R_f)$
  • Where:
  • $R$ = required return on equity
  • $R_f$ = risk-free rate
  • $\beta$ = sensitivity of the asset's return to the market return
  • $R_m$ = expected return of the market

• Beta Estimation:

  • Issues in computing beta from historical data:
  • A) Lack of historical data
  • B) Past data may not reflect future risk accurately

Financial Leverage and Beta

• Operating vs. Financial Leverage:

  • Operating leverage: Sensitivity to fixed production costs.
  • Financial leverage: Sensitivity to fixed financing costs.

• Relationship Between Betas:

  • Financial leverage increases equity beta compared to asset beta.
  • Formula:
  • $\beta<em>{Asset} = \frac{Debt}{Debt + Equity} \times \beta</em>{Debt} + \frac{Equity}{Debt + Equity} \times \beta_{Equity}$

Weighted Average Cost of Capital (WACC)

• Goal of WACC: Find the market’s valuation of future cash flows from projects.

• Steps to Compute WACC:

  1. Estimate Unlevered Cash Flows (UCF):
  • $UCF = EBIT(1 - T) + Depr - CAPEX - \Delta NWC$
  1. Calculate WACC:
  • Formula: $WACC = w<em>E r</em>E + w<em>D r</em>D(1 - T_C)$
    • Where:
      • $w_E$ = weight of equity
      • $r_E$ = cost of equity
      • $w_D$ = weight of debt
      • $r_D$ = cost of debt
      • $T_C$ = corporate tax rate

Estimating Cost of Equity and Debt

• Cost of Equity ($r_E$):

  • Best estimated using CAPM.
  • If historical data is not available, use beta from comparable firms.
  • Be aware of leverage difference as it affects expected returns.

• Cost of Debt ($r_D$):

  • Assume minimal default risk: YTM can estimate $r_D$.
  • Consider the impact of default risk on expected returns:
  • Formula: $r_D = (1 - p)y + p(RR - 1)$
    • Where:
      • $p$ = probability of default
      • $RR$ = recovery ratio

Assessing the Weights for WACC

• Weight Calculation: Reflect market values; use book values for debt when markets are illiquid.
• Forward-looking weights should be used if leverage plans change.

Tax Considerations in WACC

• Expected Marginal Tax Rate ($T_C$): Reflects the tax rate expected on the last dollar of taxable income.

  • Could be an average over previous years.

• Example:

  • If a firm could end up in two tax brackets, an expected marginal tax rate is weighted according to probabilities.

Analyzing CAPM and Betas

• Unleveraging and re-leveraging betas is crucial due to different future leverage policies.
• Needed steps:
  1. Unlever influence of debt on similar firms to find asset beta.
  2. Re-lever based on future debt levels to find the target equity beta.

Practical Applications

• Use historical data, comparable company data, and adjust for different leverage policies to compute betas accurately.
• Be cautious about the differences in operating leverage as that greatly influences required return estimations.