# Just how to Calculate the Beta of a Private Company

Such a regression analysis can be performed for listed companies because historical stock-return information is utilized. βu = 1 + (1 − T) × ED βL = 1 +( 1 − 0.35) × 0.341.64 = 1.343

Thus, we obtain the unlevered beta of 1.343. = 1.78

In this example, the beta of the illustratory personal company is greater than the average levered beta due to a higher target debt-to-equity proportion. ΔSi = α + βi × ΔM=+ ewhere: ΔSi = change in price of supply iα = obstruct worth of the regressionβi = beta of the i stock returnΔM = change in the market pricee = recurring mistake term

Such a regression analysis can be performed for detailed companies due to the fact that historic stock-return data is utilized. βu = 1 + (1 − T) × ED βL = 1 +( 1 − 0.35) × 0.341.64 = 1.343

Thus, we obtain the unlevered beta of 1.343. = 1.78

### Calculating Beta From Comparable Public Companies

In this instance, the beta of the illustratory exclusive firm is higher than the typical levered beta due to a higher target debt-to-equity ratio.

Usually, provided firms are huge business that operate in more than one sector, and also consequently, it might be bothersome to find a similar company whose beta would effectively represent the company beta of the private company to be valued.

One approach is to obtain a similar levered beta from a sector standard or from a comparable company (or firms) that ideal mimics the current organisation of the personal firm, unlever this beta, as well as after that locate levered beta for the private business making use of the business’s target debt-to-equity proportion.

For instance, if there is one very large company and three very small companies, then a weighted average method will be biased toward the beta of the large company. In this particular example, however, we can take the weighted average beta as it is close to the arithmetic average, which gives equal weight to each company’s equity.

The next step is unlevering the average beta. For this, we need the average debt-to-equity ratio for these companies. The weighted average debt-to-equity ratio is 0.34.

βu=βL1+(1−T)×DE=1.641+(1−0.35)×0.34=1.343begin{aligned} beta_u &= frac{beta_L}{1 + (1 – T) times frac{D}{E}} \ &= frac{1.64}{1 + (1 – 0.35) times 0.34} \ &= 1.343 \ end{aligned}βu=1+(1T)×EDβL=1+(10.35)×0.341.64=1.343

Thus, we get the unlevered beta of 1.343.

Where D/E is the average debt-to-equity ratio of the comparable companies, T is the tax rate, Bu the unlevered beta, and BL the levered beta.

In the final step, we need to re-lever the equity using the target debt-to-equity ratio of the private company, which equals 0.5.

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βL=βU×[1+(1+T)×DE]=1.343×[1+(1−0.35)×0.5]=1.78begin{aligned} beta_L &= beta_U times [1 + (1 + T) times frac{D}{E}] \ &= 1.343 times [1 + (1 – 0.35) times 0.5]\ &= 1.78 \ end{aligned}βL=βU×[1+(1+T)×ED]=1.343×[1+(10.35)×0.5]=1.78

In this example, the beta of the illustrative private company is higher than the average levered beta due to a higher target debt-to-equity ratio.

This method has certain pitfalls, including the fact that it neglects the difference between the size of the private company and that of the public company. Most of the time, publicly-traded companies are much larger in size compared to private ones.

### Earnings Beta Approach

Usually, listed companies are large companies that operate in more than one segment, and therefore, it may be problematic to find a comparable firm whose beta would adequately represent the business beta of the private company to be valued. For instance, Apple Inc. (AAPL) has a diverse set of operations, including personal computers, smartphones, tablets, etc. This company would likely be poorly comparable to a private company that has a single operation, such as smartphone production.

When it is difficult to obtain reliable comparable beta, a company’s earnings beta can be used as a proxy for the levered beta. In this method, the company’s historical earnings changes are regressed against the market returns. An appropriate market index can be used as a proxy for the market. For instance, if the company is operating in the U.S. market, the S&P 500 can be used as a proxy.

Beta obtained from historical data needs to be adjusted to make sure that it reflects the company’s expected future performance. To reflect the mean-reverting feature of beta (beta tends to revert to one in the long run), we need to estimate adjusted beta using the following equation:

βadj=α+(1+α)×βhwhere:α=smoothing factorβh=historical betaβadj=adjusted betabegin{aligned} &beta_{text{adj}} = alpha + (1 + alpha) times beta_h \ &textbf{where:}\ &alpha=text{smoothing factor}\ &beta_h=text{historical beta}\ &beta_{text{adj}}=text{adjusted beta}\ end{aligned}βadj=α+(1+α)×βhwhere:α=smoothing factorβh=historical betaβadj=adjusted beta

The smooth factor can be derived through complex statistical analysis based on historical data, but as a rule of thumb, the value of 0.33 or (1/3) is used as a proxy.

The earnings beta approach also has some pitfalls. First, private companies do not usually have extensive historical earnings data for reliable regression analysis. Second, accounting earnings are subject to smoothing and accounting policy changes. Therefore, these may not be appropriate for statistical analysis, unless necessary adjustments have been made.

### Bottom Line

The valuation of private companies using CAPM can be problematic because there is no straightforward method for estimating equity beta. To estimate the beta of a private company, there are two primary approaches.

One approach is to obtain a comparable levered beta from an industry average or from a comparable company (or companies) that best mimics the current business of the private company, unlever this beta, and then find levered beta for the private company using the company’s target debt-to-equity ratio. Alternatively, one can find the beta of the company’s earnings and use it as a proxy for the company after appropriate adjustments are made.

Tip: For investors’ reference only, it does not constitute investment advice. Financial investment products have high risks and are not suitable for every investor. If necessary, please consult a professional consultant.