Question

There is a company A, which has a share price of 20 and it has 10 shares outstanding. It also has risk-free debt worth 40 outstanding. The equity beta for company A is 1.2. The assets of company A consist of two parts. Company A owns 50% of the shares of company B. Company A also has an investment in company C, which is an all equity financed firm. Company B's share price is 30 and it has 8 shares outstanding. Company B also has 20 worth of debt outstanding. The debt beta for B is 0.5 and the asset beta is 1. None of the companies mentioned holds any cash. What is the beta of the equity of company C?

Answer 1

Asset beta is computed using the following equation :-

Asset beta = Equity Beta / [ 1 + (1 - Tax Rate) (Debt / Equity) ]

Let us compute the Equity Beta for company B

Total Market Value of Equity = (30*8) = 240

Total Market Value of Debt = 20

Debt / Equity = (20/240) = 0.083

Since, the problem does not specify any tax rates, we are ignoring its impact

Plugging in the values in the equation, we get :-

1 = Equity Beta / [ 1 + (0.083) ]

Equity Beta = 1.083

Hence, Equity Beta for company B = 1.083

Also, Equity Beta for company A = 1.2

Company A has equal amount of exposure to company B & C

Hence,

Equity Beta for company A = (0.5 * Equity Beta for company B) + (0.5 * Equity Beta for company C )

1.2 = (0.5 * 1.083) + (0.5 * Equity Beta for company C )

Equity Beta for company C = 1.317

Hence, Equity Beta for company C = 1.317