Unlevered beta

Unlevered beta
See also
Net asset value per share RAROC Profitability index Return on equity (ROE) Beta risk Sum of the parts valuation Risk-return tradeoff Net present value (NPV) Risk measures

Unlevered beta is a measure of the volatility of a company's stock that is independent of its capital structure. It is a measure of the volatility of the stock with respect to the overall market, and can be used to compare the risk of companies with different capital structures. Specifically, it is the beta of a company with no debt in its capital structure.

Example of Unlevered beta

Suppose a company has a levered beta of 1.2 and a capital structure consisting of $50 million in debt and $100 million in equity. If the corporate tax rate is 30%, the unlevered beta of the company can be calculated as follows:

$\beta _{unlevered}={\frac {1.2*(1+(1-0.3)*{\frac {50}{100}})}{1+(1-0.3)*{\frac {50}{100}}-{\frac {50}{150}}}}$

$\beta _{unlevered}={\frac {1.2*(1+0.7)}{1+0.7-0.333}}$

$\beta _{unlevered}=1.04$

Thus, the company has an unlevered beta of 1.04.

Formula of Unlevered beta

Unlevered Beta can be calculated using the following formula:

$\beta _{unlevered}={\frac {\beta _{levered}*(1+(1-t)*{\frac {D}{E}})}{1+(1-t)*{\frac {D}{E}}-{\frac {D}{E}}*{\frac {D}{V}}}}$

where:

• β_levered = the levered beta of the firm
• t = the corporate tax rate
• D = total debt of the firm
• E = total equity of the firm
• V = total value of the firm

The levered beta is used to represent the volatility of a company's stock with respect to the overall market, and the corporate tax rate is used to adjust for the effect of debt on the company’s capital structure. The total debt and total equity of the firm are used to adjust for the effect of debt on the company’s risk. Finally, the total value of the firm is used to represent the company’s overall value.

When to use Unlevered beta

• When performing a comparative analysis of companies with different capital structures - Unlevered beta can be used to compare the risk of companies with different capital structures. It can be used to measure the volatility of a company's stock independent of its capital structure, and can be used to find the best investment opportunities.
• When assessing the risk of a company - Unlevered beta can also be used to assess the risk of a company. By removing the effect of debt from the equation, investors can get a better idea of the true risk of a company.

Types of Unlevered beta

• Beta with respect to the market: This type of unlevered beta measures the volatility of a company's stock with respect to the overall market. It is calculated by taking the levered beta of the company and adjusting it for the effect of debt in the firm's capital structure.
• Beta with respect to the industry: This type of unlevered beta measures the volatility of a company's stock with respect to the overall industry. It is calculated by taking the levered beta of the company and adjusting it for the effect of debt in the firm's capital structure, as well as the industry average beta.

Steps of Unlevered beta

1. Calculate the levered beta of the firm: First, the levered beta must be calculated. This is done by taking the beta of the company's stock, and adjusting it for the effect of the company's debt on the stock.
2. Calculate the corporate tax rate: Next, the corporate tax rate must be calculated. This can be done by taking the company's effective tax rate, and adjusting it for any applicable deductions or credits.
3. Calculate the total debt and equity of the firm: The total debt and equity of the firm must then be calculated. This can be done by taking the total liabilities of the firm, subtracting the total assets, and dividing the result by the total assets.
4. Calculate the total value of the firm: Finally, the total value of the firm must be calculated. This can be done by taking the total assets of the firm and subtracting the total liabilities.

Advantages of Unlevered beta

• Provides an accurate measure of a company's risk: By removing the effect of debt from the equation, unlevered beta provides an accurate measure of a company's risk, and allows investors to compare companies with different capital structures.
• Helps investors make informed decisions: By providing an accurate measure of risk, unlevered beta helps investors make more informed decisions about investments.
• Easy to calculate: Unlevered beta is relatively easy to calculate, using the formula provided above.

Limitations of Unlevered beta

Despite its usefulness, unlevered beta has some limitations. These include the following:

• It assumes that the company is operating at a constant debt level, which may not always be the case.
• It only takes into account the historical volatility of the stock, and does not take into account future volatility.
• It does not account for differences in the risk of debt and the risk of equity.

Other approaches related to Unlevered beta

• Capital Asset Pricing Model (CAPM): This model uses the unlevered beta to determine the cost of equity for a company.
• Comparable Company Analysis: This approach uses the unlevered beta of comparable companies to estimate the beta of the company being analyzed.
• Option Pricing Model: This model uses the unlevered beta to estimate the expected return of a company's stock.

Suggested literature

• Fernandez, P. (2006). Levered and unlevered beta. Available at SSRN 303170.