Question

A firm is all-equity financed and operates in a world without taxes or other frictions and that is semi-strong form efficient. 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 issue the dividend and when it does not.) c) Would your answer to part B be different if management were considering issuing debt rather than equity? Why or why not? (Note: no calculations are required for this part)

Answer 1

a. Total dividend to be paid = 300,000 * 2=$600,000

Value of the firm = 2,500,000 / 12% = 20,833,333.33

Price per share = 20,833,333.33/ 300,000 = 69.44

New shares to be issued = 600,000 / 69.44 = 8640 shares

b. Value of the firm will remain same , price per share post dividend = 20,833,333.33/ ( 300,000+ 8640) = 67.50

Total wealth before issue = 20,833,333.33

Total wealth after issue = 300,000* 67.5= 20,250,000

The current shareholders will certainly not want the management to issue this dividend since their wealth has reduced by $583,333.33

c. In case debt is issued to pay the dividend the value of the firm will go up and the shareholders will certainly appreciate the move. Debt has tax benefits and is a cheaper source of capital than equity which will bring down the overall cost of capital. When the cost of capital reduces, the value of the firm increases.