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Vezuvo Technologies has $75 million in excess cash and no debt. The firm expects to generate additional free cash flows of $50 million per year in subsequent years and will pay out these future free cash flows as regular dividends. Vezuvo's unlevered cost of capital is 10% and there are 10 million shares outstanding. Vezuvo's board is meeting to decide whether to pay out its $75 million in excess cash as a special dividend or to use it to repurchase the firm's shares.
-Assume that Vezuvo uses the entire $75 million in excess cash to pay a special dividend. Vezuvo's ex-dividend price is closest to:
A)$75.00.
B)$40.00.
C)$45.00.
D)$50.00.

Question

Quizplus · Accepted Answer

The ex-dividend price can be calculated using the formula for the value of a firm, which is the present value of its future free cash flows plus any excess cash on hand, divided by the number of shares outstanding. Without the excess cash, the firm is worth its future free cash flows discounted at the unlevered cost of capital. The future free cash flows are $50 million per year in perpetuity. Using the formula for a perpetuity, Value = Cash Flow / Discount Rate, the value of the future free cash flows is $50 million / 0.10 = $500 million. Since the firm also has $75 million in excess cash that it will pay out immediately as a special dividend, the total value of the firm just before the dividend is paid is $500 million + $75 million = $575 million. Dividing this by the 10 million shares outstanding gives a per-share value of $57.50. However, once the $75 million is paid out, the value of the firm drops by that amount, leaving the firm worth $500 million. Dividing this by the 10 million shares outstanding gives an ex-dividend price of $50.00 per share.

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