# How do I calculate the beta

## Determination of beta factors as part of the company valuation according to IDW S 1 using the example of a non-listed international automotive supplier

Interesting things from everyday work

Calculating the beta factor is a complex task for the evaluator. Small changes in the beta factor can have a big impact on company value. A change in the unlevered beta from 1.0 to 1.1 can change the company value by around 10 percent or more, depending on the level of debt. Therefore a correct calculation of the beta factor is essential for the determination of a company value according to IDW S1. For this reason, we determine the beta factors for the company to be assessed on a company-by-company basis with the help of data from a financial service provider (Bloomberg).

In the following we want to describe what a beta factor actually is and how we determine it in practice.

### What actually is a beta factor and what do you need it for?

For the valuation of a company, the expected future net inflows to the shareholders must be discounted to the valuation date using a suitable capitalization rate. From an economic point of view, the capitalization interest rate represents the decision alternative of an investor who compares the return on his investment in a certain company with the return on a corresponding alternative investment in company shares.

In particular, observable capital market returns come into consideration as the starting point for determining the alternative returns. In principle, they can be broken down into a risk-free base rate and a risk premium required by the shareholders based on the assumption of the entrepreneurial risk. Capital market models, in particular the Capital Asset Pricing Model (CAPM), can be used to explain the distribution of the risk premiums. A key parameter within this model is the so-called beta factor.

The beta factor is a measure of the company's systematic risk. When determining the beta, one falls back on the share price returns that can be observed on the capital market and compares the fluctuations in the company's share price with the fluctuations in the share price of the overall market. H. the beta reflects the industry and company-specific risk including the capital structure risk of a share in relation to the market risk. The higher the beta factor, the higher the required risk premium. A beta factor greater than one means an above-average risk compared to the overall market of all stocks, a beta factor of less than one means a below-average risk compared to the overall market.

### How do I determine a beta factor?

When we value a listed company, we use the beta data that can be observed on the capital market directly. However, we often rate unlisted companies. Since there are no beta factors of their own observable on the capital market for these companies, we use empirical beta factors from comparable companies and proceed as follows:

1. Analysis and determination of a group of comparable companies (peer group)
2. Identify the peer beta factors and test their quality
3. In and relevant to the beta factors

To 1)
When analyzing and determining a suitable Peer group In the first step, the main value drivers of the business model of the valuation object are identified. Based on this, we use search functions at Bloomberg to determine a group of comparable companies. We do a scoring for these comparison companies and derive the final peer group from this. Their selection is based on the comparability of substantial indicators, such as B. Industry / business area, sales development, investment intensity, research and development expenditure, etc. As a result, the peer group shows a sufficient similarity to the valuation object despite the generally different size in terms of risk.

To 2)
For the Determination and quality check of the beta factors of the peer group, we use capital market data from Bloomberg. For the beta calculation, we make decisions with regard to various questions:

• Do I take the Raw Beta or the Adjusted Beta?
• Which benchmark do I use?
• What period do I take?
• What kind of return interval do I take?
• What day of the week do I take?

As a rule, we use an observation period of two years (with a weekly return interval) or five years (with a monthly return interval) as a basis for determining the beta. With regard to the reference index to be selected, which serves as an approximation for the market return, we usually use the broadest national index (in Germany e.g. the CDAX) of the corresponding benchmark company.

Since stock prices that are rarely traded have price fluctuations that are only related to the low trading volume and not to the risk of the stock, we need to check the beta factors for their usability. We therefore check the quality of the beta factors both with regard to a sufficient trading volume, e.g. using the bid-ask spread, and with regard to statistical significance by performing a t-test and evaluating the regression coefficient.

To 3)
The returns that can be observed on the capital market can only be read after taking into account the company's respective indebtedness, so that the beta factor available on Bloomberg includes the operational risks as well as the financing risks. This beta is called the levered beta factor.

In order to keep the systematic risk in isolation, we have to adjust the levered beta factors for the financing risk; this is called unleverness. In practice, this is done with the help of different calculation formulas. In this context, the evaluator must ask himself what the average debt is: is only the company's debt taken into account, or is the cash on hand subtracted from the debt?

From the mean or median of the unlevered beta of our comparison group, we determine the unlevered beta factor of our valuation object.

In the last step, the non-indebted beta factor is to be adjusted to the individual capital structure of the property being valued (so-called relevant). This results in the indebted beta factor of the valuation object, which multiplied by the market risk premium represents the risk premium within the capitalization interest rate.

### Example: international automotive supplier

In the course of evaluating an international automotive supplier, we calculated the company-specific beta factor in accordance with the procedure described.

In the first step, after an intensive analysis of the business and competitive environment and a scoring of the important value drivers, we determined a peer group.

In the second step, we derived the associated beta factors from this peer group. We used an observation period of two years (with a weekly return interval), the broadest national index and the raw betas. We have also checked all beta factors for their usability and determined that they can be used.

The following beta factors resulted:

In the third step, we unlevered the levered beta factors by eliminating the capital structure risk. We have taken into account both the debt and the cash holdings if, from our point of view, these were not required for the operating business. We used the following formula:

The peer group's unlevered beta factors were as follows:

The smallest beta is 0.985, the other betas are close to each other between 1.241 and 1.291. The median beta is 1.268. The similarity of the beta factors shows us that our comparison companies all have a similar systematic risk and do not differ greatly in terms of risk; For us as evaluators, this underlines the quality of the usability of the beta factors.

The beta above 1 means that the beta of our peer group has a higher systematic risk than the average. We expected this result because an automotive supplier has a higher risk than other companies; therefore the level of the beta factor was also plausible for us as evaluators.

In accordance with the procedure presented, building on this, we have adapted the determined unlevered beta factor to the individual financing structure of the valuation object.

• ### Dipl.-Kfm.Benedikt Kastrup

Auditor, tax advisor, CVA, mediator, partner

+49 521 2993174

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• ### Dipl.-Kffr.Miriam Roll

Auditor, tax advisor, publicly appointed and sworn expert for company valuation, partner

+49 521 2993131

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