# 3.2.5. Beta

The beta is the measure of systemic risk of the company and records the movements of the company when it is affected by a common factor to the market. A beta above 1 means that variations in the profitability of the company will have an effect greater than that of the market. A beta under 1 means that the company will have a lower volatility than the market.

For non-public companies, it is not possible to calculate the beta. The common practice is to resort to a proxy. Proxys can be:

- Listed companies of the same sector
- Calculation of an industry beta through a weighted average or median of the industry, based on the information of listed companies, by adjusting the level of leverage of the company.
- Use the accounting beta.

#### Leveraged beta

Since the beta is a measure of firm-specific risk and understanding that, from the point of view of equity holders, the risk increases with increasing the leverage of the company it is natural to assume that for two companies exactly alike except in the structure of financing, the company with the higher leverage level will present a greater risk to equity holders. This risk arises from the fact that higher levels of financing implies a greater variability in the results. When using a beta of reference, should take into account the level of leverage of the reference face of the beta leverage of the company itself. For example, consider a beta in sector average ratio between foreign capital and capital of the bearing leading companies of the sector stands at 25%. If the company is evaluating have a ratio between foreign capital and equity capital paid 110%, the specific risk perceived in this company will be superior to the industry. Will not make sense using the same beta. To best suit the beta of the company concerned is required to proceed with the necessary adjustment according to the level of leverage.

The procedure of re-leverage through the following steps:

- Set the reference beta.
- Calculate the beta of an unleveraged firm reference.
- Leverage the beta as a function of the ratio of foreign capital equity blood donation.

To obtain a unlevered beta you can:

- \(\beta_u=\frac{\beta_l}{\left(1+\frac{D}{E}\left(1-t\right)\right)}\)

Where:

- βu: unlevered beta
- D: Debt
- E: Equity
- t: corporate tax rate

Conversely, to lever an unlevered beta you can inverse equation.

- \(\beta_l=\beta_u\left(1+\frac{D}{E}\left(1-t\right)\right)\)

The beta is always higher the greater the indebtedness of the company. There is also an impact from the fiscal effect on the calculation of the beta. Paying attention to the levering is extremely important: if you decide to use as your reference, the beta of a company with significantly different leverage from the company you are analyzing, the estimate of the cost of equity can be quite biased.

#### Accounting beta

The accounting beta is sometimes used in non-listed companies. Estimating the accounting beta is similar to the regular practice: instead of using the variable return arising from stock price movements, the beta uses the accounting net income as the measure of profitability of the company to generate a comparison between the company and the market.

Next Section: 3.2.6. Market risk-premium