Unlevering Betas

Equity Valuation in R

Cliff Ang

Senior Vice President, Compass Lexecon

Unlevering Beta using the Hamada Formula

$$ \beta_U = \beta_L / (1 + (1 - T_c) \times D / E) $$

where

  • $\beta_U$ is the Unlevered Beta (beta without effects of leverage)
  • $\beta_L$ is the Levered or Equity Beta (beta from regression)
  • $T_c$ is the corporate tax rate
  • $D / E$ is the debt-to-equity ratio

Relevering Beta Using Hamada Formula:

$$ \beta_L = \beta_U \times (1 + (1 - T_c) \times D / E) $$

Equity Valuation in R

Unlevering Beta using Fernandez Formula

  $$ \beta_U = [\beta_L + \beta_D (1 - T_c) D / E] / [1 + (1 - T_c) D / E] $$

Same variable definitions as Hamada Formula, except for the addition of $\beta_D$ for the debt beta.

Relevering Beta Using Fernandez Formula:

$$ \beta_L = \beta_U + (\beta_U - \beta_D)(1 - T_c) D / E $$

Hamada Formula = Fernandez Formula if $\beta_D = 0$

Equity Valuation in R

Betas Used in Valuation

Which betas do you use in the CAPM?

  • Use the beta obtained form regressing the stock's return on the market's return
  • Use the relevered beta based on the median or average peer company's unlevered beta
Equity Valuation in R

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Equity Valuation in R

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