5. Two all-equity firms, Aegis Industries Inc. and Theta Systems Co., produce the same product. Aegis produces 1,000,000 units every year at a cost of $10 per unit. Theta produces 250,000 units every year at a cost of $7 per unit. Both firms sell their products at a price of $15 per unit. In addition to production costs, Aegis has annual general costs of $800,000, and Theta has annual general costs of $200,000. The tax rate is 20%. Assume that the cash flows described above are expected to be generated every year, starting next year, and that the firms have no other assets, liabilities, or cash flows. The required return is 10%. If both firms merge into one firm, the combined firm will benefit from a greater market power. Thus, it will increase the price per unit to $16. At this price, however, it will have the same annual revenues as the sum of revenues of Aegis and Theta when they were separated. The combined firm will also benefit from economies of scale, and thus the production cost will decrease to $6 per unit, and the general costs will be $900,000 every year. Finally, the combined firm will be able to hold perpetual debt at the amount of its annual revenues. a. Calculate the equity values of Aegis and Theta as standalone firms, and the equity value of the combined firm. Describe the sources of gains from the merger. b. Suppose that Aegis has 500,000 shares and Theta has 4,750,000 shares. Aegis intends to buy Theta in a stock-based acquisition. In particular, Aegis will issue new shares and give them to the shareholders of Theta in exchange for their old shares in Theta. Define the exchange ratio as the number of new shares in the combined firm to be issued for each of Theta's existing shares. Calculate the maximum exchange ratio that Aegis's shareholders will be willing to accept, and the minimum exchange ratio that Theta's shareholders will be willing to accept.

Two all-equity firms, Aegis Industries Inc. and Theta Systems Co., produce the same product. Aegis produces 1,000,000 units every year at a cost of $10 per unit. Theta produces 250,000 units every year at a cost of $7 per unit. Both firms sell their products at a price of $15 per unit. In addition to production costs, Aegis has annual general costs of $800,000, and Theta has annual general costs of $200,000. The tax rate is 20%. Assume that the cash flows described above are expected to be generated every year, starting next year, and that the firms have no other assets, liabilities, or cash flows. The required return is 10%. If both firms merge into one firm, the combined firm will benefit from a greater market power. Thus, it will increase the price per unit to $16. At this price, however, it will have the same annual revenues as the sum of revenues of Aegis and Theta when they were separated. The combined firm will also benefit from economies of scale, and thus the production cost will decrease to $6 per unit, and the general costs will be $900,000 every year. Finally, the combined firm will be able to hold perpetual debt at the amount of its annual revenues. a. Calculate the equity values of Aegis and Theta as standalone firms, and the equity value of the combined firm. Describe the sources of gains from the merger. b. Suppose that Aegis has 500,000 shares and Theta has 4,750,000 shares. Aegis intends to buy Theta in a stock-based acquisition. In particular, Aegis will issue new shares and give them to the shareholders of Theta in exchange for their old shares in Theta. Define the exchange ratio as the number of new shares in the combined firm to be issued for each of Theta's existing shares. Calculate the maximum exchange ratio that Aegis's shareholders will be willing to accept, and