# Unlevered Beta

Unlevered beta (also called asset beta) represents the systematic risk of the assets of a company. It is the weighted average of equity beta and debt beta. It is called unlevered beta because it can be estimated by dividing the equity beta by a factor of 1 plus (1 – tax rate) times the debt-to-equity ratio of the company.

Unlevered beta essentially neutralizes the effect of capital structure on a company’s systematic risk exposure. It can be used to assess the ‘true’ systematic risk of a company’s assets (not just equity). It follows from the Modigliani & Miller theories that cost of equity increases with increase in debt to equity ratio. The same applies to a company’s equity beta. Due to higher debt, the risk of the company’s stock return’s varying with reference to the market increases. It is useful to remove the systematic risk that has creeped in due to exposure to debt. Unlevered beta is the measure of systematic risk left after the additional financial risk resulting from debt is removed.

Unlevered beta is an important input in the pure play method. The pure play method is an approach to estimating cost of equity which involves unlevering the publicly-available equity beta value of a comparable company using the comparable company debt-to-equity ratio to get the unlevered (asset) beta which is then relevered using the debt-to-equity ratio of the company under analysis.

## Formula

Unlevered beta can be obtained using the following formula:

$$ Unlevered\ Beta\ (\beta_a)=\frac{Equity\ Beta\ (\beta_e)}{1+(1\ -\ t)\times\frac{D}{E}} $$

Just like the weighted average cost of capital, we can express beta as the weighted average of the debt beta and equity beta:

$$ \beta_a=\beta_d\times\frac{V_d\times(1\ -\ t)}{V_e+V_d\times(1-t)}+\beta_e\times\frac{V_e}{V_e+V_d\times(1-t)} $$

Where β_{a} is the unlevered beta (i.e. asset beta), β_{e} is equity beta (also called levered beta), V_{d} is the market value of debt, V_{e} is the market value of equity and t is the tax rate.

In many cases it is safe to assume that the debt beta is zero. This is because normally debt constitutes a lower percentage of the overall capital structure and the relationship between market risk and debt is inherently low (because debt has fixed charge).

After such simplification, the above equation reduces as follows:

$$ \beta_a=\beta_e\times\frac{V_e}{V_e+V_d\times(1-t)} $$

Dividing the numerator and denominator both by V_{e} and taking V_{e} as a common factor in the denominator give as the equation for unlevered beta:

## Example

Shah works as a financial analyst at Agha Investments. His next assignment is valuation of Bolan Electric Arts (BEA), a company engaged in production of electric vehicles. He is interested in calculating cost of equity for BEA. Since BEA stock is not publically traded, he cannot estimate beta coefficient by regressing stock return on index return. He wants to unlever and relever equity beta of a similar company, Tesla Motors Inc (TSLA), and has requested you to calculate unlevered beta for TSLA.

From a financial database you found that equity beta of Tesla Motors Inc. is 0.7, its debt to equity rate is 2 and applicable tax rate is 35%. Just plug in the figures in the following formula to calculate the unlevered beta.

$$ Unlevered\ Beta \\ = \frac{0.7}{1+2 × (1 − 35\%)} \\ = 0.3 $$

Hidayat must relever this unlevered beta (also called asset beta) in accordance with the capital structure of BEA to find applicable equity beta, which in turn can be used in CAPM to find BEA's cost of equity.