A firm is all-equity financed and operates in a world without taxes or other frictions. It has perpetual earnings of $8 million and currently has 500,000 shareholders. Its cost of equity is 12%.

The firm is considering issuing new equity to finance a special dividend to its current shareholders of $3/share. Would the current shareholders want management to issue this dividend, or are they indifferent? Demonstrate why or why not mathematically. Show what their total wealth will be both when the firm issues the dividend and when it does not. (Extra space for your answer on the next page if you need it)