Final answer:
The stock price per share for Firm B, which is otherwise identical to Firm A but with different financing strategies, can be calculated by discounting its future cash flow using the CAPM model and then adjusting for debt to find the equity value. The resulting price per share is $2.50.
Step-by-step explanation:
To calculate the stock price per share for Firm B, we need to factor in the debt and equity structure of the firm in a Modigliani-Miller world, which posits that the valuation of a firm is unaffected by its capital structure under certain conditions, such as no taxes, no transaction costs, and efficient markets. Given that Firm A is an all-equity firm with a CAPM beta of 1.0, we can calculate its expected return using the Capital Asset Pricing Model (CAPM) formula:
Expected return = Risk-free rate + (Beta × Market risk premium) = 10% + (1.0 × 20%) = 30%
Therefore, the total value of the firm can be calculated by discounting its end-of-year cash flow at the expected rate of return:
Total value of Firm A = Cash flow / (1 + Expected return) = $3.9 million / (1 + 30%) = $3 million
Since Firm B is identical to Firm A aside from its financing structure and we are in a Modigliani-Miller world, the value of Firm B will also be $3 million. However, since Firm B has debt, we have to subtract the debt from the total value to get the equity value:
Equity value of Firm B = Total value - Debt = $3 million - $0.5 million = $2.5 million
The stock price per share can be calculated by dividing the equity value by the number of shares outstanding:
Stock price per share = Equity value / Shares outstanding = $2.5 million / 1 million shares = $2.50 per share