Problem:
The Vinson Corporation has earnings of $500,000 with 250,000 shares outstanding. Its P/E ratio is 20. The firm is holding $300,000 of funds to invest or pay out in dividends. If the funds are retained, the after tax return on investment will be 15 percent, and this will add to present earnings. The 15 percent is the normal return anticipated for the corporation, and the P/E ratio would remain unchanged. If the funds are paid out in the form of dividends, the P/E ratio will increase by 10 percent because the stockholders in this corporation have a preference for dividends over retained earnings. Which plan will maximize the market value of the stock?
Please show me the formulas used to work this problem.