Question $3.$ Special Dividends and Repurchases Appel, Inc., has $30$ billion in excess cash and no debt. The firm expects that the current assets in place will generate free cash flows of $50$ billion per year in perpetuity and will pay out these future free cash flows yearly as a regular dividend. Appel$$s cost of capital is $10\%$ and the firm has $1$ billion shares outstanding. Appel$$s board is meeting to decide whether to pay out its $30$ billion of excess cash as a special dividend or to use it to repurchase the firm$$s stock. You own $1,000$ shares of Appel$$s stock. Assume a situation of perfect capital markets with no taxes. IB$9$V$00$: Corporate Finance Page $2$ of $2$ a$.$ If Appel uses the entire $$30$ billion of excess cash to pay a special dividend, what will be Appel's ex$-$dividend price? b$.$ Instead, if Appel uses the entire $$30$ billion for a share repurchase, how many shares will be repurchased? c$.$ Suppose that Appel uses the entire $$30$ billion to repurchase shares, but you would have preferred that Appel used the excess cash to pay a special dividend instead. What is the number of shares that you would have to sell in order to receive the same amount of cash as if Appel paid the special dividend? d$.$ Instead, suppose that Appel uses the entire $$30$ billion to pay a special dividend, but you would have preferred Appel to do the repurchase instead. What is the number of shares that you would have to buy in order to undo for yourself the special cash dividend that Appel paid?