Final answer:
The stock price for Firm X, in a Modigliani-Miller world with perfect capital markets and identical cash flows as Firm Y with no debt, is $6 per share.
Step-by-step explanation:
The question involves calculating the stock price for Firm X in an M&M world with perfect capital markets. Firm Y being an all-equity firm with shares priced at $24 and Firm X having both equity and debt, we can use the Modigliani-Miller (M&M) Proposition I to find the value of Firm X. According to M&M Proposition I, in the absence of taxes, bankruptcy costs, and asymmetric information, and in an efficient market, the value of a leveraged firm (Firm X) is equal to the value of an unleveraged firm (Firm Y) with identical assets and cash flows.
Given that Firm Y is all-equity, its market value is simply 1 million shares at $24 per share, which totals $24 million. Firm X has identical assets and identical cash flows but with $12 million in debt at an interest rate of 5%. To find the value of Firm X's equity, we subtract the debt value from Firm Y's total value, which gives us $12 million ($24 million - $12 million in debt). Dividing this equity value by the number of shares outstanding for Firm X (2 million), we find the share price for Firm X: $6 per share.