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I know when we want to calculate project specific discount rates, we use the beta of a proxy company that is in the same line of the business we intend to invest in. There is a question I just came across, which is slightly not straight forward. The proxy company has two lines of business, but the project we want to invest in is just one of the lines of business. The equity beta of the proxy company was given, the asset beta of the other line of business, that we are not interested in, was given; the proportion of the two lines of business was also given. How do we calculate the asset beta of the line of business we are interested in?
When a business has two streams with different betas, then the overall beta of the business is the weighted average of the two individual betas, weighted by the total investment in each of the two streams.
So if we know the individual betas we can calculate the overall beta. Similarly, if we know the total beta and one of the individual betas, then we can work ‘backwards’ to calculate the other individual beta.I explain this in my free lectures on CAPM, together with examples.
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