A firm is all-equity financed and operates in a world without taxes. It has perpetual earnings of $2.5 million and currently has 300,000 shareholders. Its cost of equity is 12%. The firm is considering issuing new equity to finance a special dividend to its current shareholders of $2/share.

a) How many new shares would the firm need to issue in order to pay this dividend?

b) Would the current shareholders want management to issue this dividend? Demonstrate why or why not mathematically. (Hint - show what their total wealth both when the firm issues the dividend and when it does not.)