XYZ's revenues this past year were $250,000 and total costs were $150,000; and both costs and revenues have been expected to remain the same in perpetuity. XYZ is an all equity firm (i.e., it has no debt), with a return on assets of 10%, and has 100,000 shares outstanding. XYZ currently pays out all its earnings as dividends (100% payout) and has been expected to do so forever. The dividends on the basis of last year's earnings have just been paid out. Unknown to the market, a team of researchers and the President of XYZ suddenly discover that the firm can introduce a range of new products and start expanding the market and increase earnings. However, this expansion will also increase costs and the company will be unable to pay out all the earnings as dividends. The President and her financial team have come up with two growth alternatives.
(I) Grow earnings at an annual rate of 5% forever, but reduce the payout to 70% forever. No other financing will be necessary apart from this plowback (or reduction in payout).
(II) Grow earnings at an annual rate of 8%, but with a reduction in payout to only 40%. Again no other financing will be necessary apart from this plowback. By how much will the price per share of the firm increase (in dollars) if it adopts the right strategy of growth? (Note that it takes time to implement any growth strategies. So the reinvestment starts at year end, or t = 1.)