Extended CAPM and Build Up Cost of Equity for Private Company Valuations

I have couple of questions in regards to the extended capm and build up cost of equity.

  1. When solving for the extended CAPM method, we add the risk premiums associated to the size and to the company. How come in none of the problems they include the beta sensitivity for each of factor? Or is it just assumed to be 1? and why?

  2. In the build up cost of equity method, in addition to the size, and company specific factor, we also add the industry factor. But why wasnt the industry factor added to the extended CAPM? Here the beta is assumed to be 1 and again I dont get why?

Is there difference between two formulas just the industry risk factor?

Question 1

Because size premium and company-specific premiums are not factors in the CAPM model, you can take the size premium and company-specific premium as the risk premiums not captured by the market risk premium, i.e. error term (\varepsilon).

E(r) = r_f + \beta [E(r_m) - r_f] + \varepsilon

Question 2

For private companies, equity beta are not available so a convenient point to start off is beta = 1 (i.e. same risk as the stock market):

E(r) = r_f + 1 \times [E(r_m) - r_f] = E(r_m)

Then, from the expected market return, we incrementally add in the risk premiums (i.e. industry risk premium, size premium, company-specific premium) to adjust it until it reflects all the risk of the private company.

The equity beta used in CAPM reflects:

  • the systematic risk arising from the economics of the industry (asset beta or unlevered beta), and
  • which also incorporates the financial leverage of the private company.

Hope it clears things up.