Final answer:
The values of Alpha Corporation and Beta Corporation are both $450,000. The value of Beta's equity is $385,000. Owning 20% of Alpha would cost $90,000 and return $15,000 after one year, while owning 20% of Beta would cost $77,000 and return $13,830.
Step-by-step explanation:
The value of Alpha Corporation with an all-equity structure and 15,000 shares at $30 each is $450,000 (15,000 shares * $30 per share). The value of Beta Corporation, which includes both equity and debt, can be determined using the Modigliani-Miller Proposition I without taxes, which states that leveraged and unleveraged firms should have the same value if there are no taxes. Since the firms are identical except for the capital structure, the value of Beta Corporation is also $450,000.
To find the value of Beta's equity, we subtract the value of Beta's debt ($65,000) from Beta's total firm value ($450,000), obtaining an equity value of $385,000. If we want to purchase 20% of each company's equity, it would cost 20% of $450,000 for Alpha, which is $90,000, and 20% of $385,000 for Beta, which equals $77,000. Assuming each firm meets its earnings before interest of $75,000, the dollar return with 20% equity ownership over the next year for Alpha would be 20% of $75,000, a total of $15,000. For Beta, the earnings after interest payments (9% of $65,000 debt) would be $75,000 - $5,850 (interest), or $69,150. Therefore, 20% of Beta's after-interest earnings would be $13,830.