Final answer:
To determine the stock price for Company ZZZ if it chooses share repurchase, calculate the present value of perpetual cash flows without the expansion at $40,000,000 per year with a cost of capital at 4%. The value of the firm with these cash flows is $1,000,000,000. The new stock price is then the total PV of the firm's cash flows divided by the new number of shares outstanding post-repurchase.
Step-by-step explanation:
To calculate the stock price of Company ZZZ should they decide to use the cash for a share repurchase instead of expansion, we must first determine the present value of the perpetual cash flow they expect to generate without the expansion. As given, the expected future free cash flows are $40,000,000 per year. Using the formula for the present value of a perpetuity, which is Cash Flow / Cost of Capital, we calculate the present value (PV) as $40,000,000 / 0.04, which equals $1,000,000,000.
After determining the value of the firm's future cash flows, we consider the effect of a share repurchase. If all cash flow ($520,000,000) is used to repurchase shares, the number of shares outstanding will decrease, increasing the value per share for remaining shareholders. To find out how many shares could be bought back, you divide the cash available for repurchase ($520,000,000) by the stock price. As we don't have the current stock price, we will assume a hypothetical stock price (P) and determine that the number of shares repurchased would be $520,000,000 / P. This reduces the number of outstanding shares from the original 200,000,000 by the repurchased amount.
The new value per share, given that the firm's total value is $1,000,000,000, would be calculated as follows: new stock price = Total PV of firm's cash flows / New number of shares outstanding. Without the current market stock price, we cannot give a numerical answer, but this formula shows how to calculate it. An investor would compare it with the value of the expansion opportunity which was stated to increase cash flows to $70,000,000 per year and use the same perpetuity value calculation, resulting in a higher value due to increased cash flows. However, since the question asks explicitly for the share repurchase scenario, the price calculation stops with the formula presented.