# Unlevering the beta

What does unlevering the beta for a company buy you? If you open any textbook on corporate finance, you will quickly run across the capital asset pricing model or CAPM. Experts use the CAPM in order to figure out business risk. More formally, the model lets you estimate the important discount rate. And that you can use to value the business using the famous discounted cash flow method.

A key element that captures business risk in the CAPM is called beta. This quantity helps you see business risk in comparison to the equities market as a whole. To calculate beta, you need to know historic returns for the business. You then correlate these returns to the equities market index, for example Standard & Poor 500.

But if you are looking to value a privately owned company that does not sell its stock publicly, you have a challenge in beta estimation. Private companies do not sell their stock regularly, so you cannot figure out the returns. What to do?

### Betas from guideline companies

Professional appraisers usually resort to what they call the guideline public companies. Stock prices and returns for such businesses are readily available. As a result, their betas are also well known.  If these businesses resemble your subject company, you can pick their betas as a proxy and use it to estimate your discount rate with the CAPM model.

### Levered betas lump business and financial risk together

Now, a public company beta is determined based on the known historical total returns. Consequently, such an estimate would include both the risk of the business itself and its financial risk. For example, a company with a higher percentage of debt in its capital structure is more risky than its debt-free competitor.  So their betas could differ quite a bit just because of the effect of debt.

### Unlevering the beta

So if your subject business does not use leverage like the guideline public companies, you may want to adjust your beta before using it to figure out the discount rate. In other words, an unlevered beta is what you get if the company uses no debt.

You can get the unlevered beta from a guideline company proxy by this simple calculation:

Beta Unlevered = Beta Levered / (1 + (1 – I) * D / E)

where I is the company’s income tax rate, while D and E are the percentages of debt and equity in the proxy company’s capital structure.

If your subject private company is debt free, you can use the unlevered beta directly in the CAPM model. However, if the company uses debt, you would need to re-lever the beta like this:

Beta Levered = Beta Unlevered * (1 + (1 – I) * D / E)

Here you would use the I, D and E numbers for your company.