Suppose you want to use the CAPM model to estimate the discount rate of a company in order to discount its cash flows but that company does not trade in the stock market. What would be the problem in using the CAPM, What would you do in order to solve the problem?
CAPM model application to private companies becomes difficult because these companies are not traded and one can't find the actual Beta (market vs. individual stock relative risk levels).
In order to overcome this, comparable (similar industry, similar product) beta of public companies needs to be identified and averaged. This then has to be unlevered (as capital structures vary across companies) and then levered with the capital structure of the individual company in question.
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