Question

PU, INC (PUI) has the business of converting sewage sludge into fertilize. The business is not in itself very profitable. However, to induce PUI to remain in business, the Owner has agreed to pay whatever amount is necessary to yield PUI a 10 percent book return on equity. At the end of the year PUI is expected to pay a $4 dividend. It has been reinvesting 40 percent of earning and growing at 4 percent a year.
Suppose PUI continues on this growth trend. What is the expected long-run rate of return (r) from purchasing the stock at $100? What part of the $100 price is attributable to the present value of growth opportunities (PVGO)?
Now the Owner announces a plan for PUI to treat another type of sewage. PUI’s plant will, therefore, be expanded gradually over 5 years. This means that PUI will have to reinvest 80 percent of its earnings for 5 years. Starting in year 6, however, it will again be able to pay out 60 percent of earnings. What will be PUI’s stock price (Po) once this announcement is made and its consequences for PUI are known?
Note to answer the problems above please use formulas: r = DIVI/Po + g ; Po = EPS1/r + PVGO; Pn = DIVn/r-g; Po = DIVI/(1+r) + DIV2/(1+r)2 +…DIVn + Pn/(1+r)n

Answer 1

Part 1: In this case, PUI pays a dividend of $4 at the end of the year. Hence,

Also, the firm is reinvesting 40% of the earnings. Hence, the dividend payout ratio is 60%. Calculating the earnings the coming year, if p represents the payout ratio,

Hence, assuming a constant growth of 4% thereafter, using the formulae,

Using the formulae,

On solving,

Hence, the expected long-term rate is 8% and $16.67 out of $100 is attributable to the present value of growth opportunities.

Part 2: The stock price depends on the present value of future cash flows (in this case, dividends) to the investors. Hence, we can write:

For the first five years, the reinvestment ratio is 80%. Hence, the payout ratio is 20%. From year 6 onwards, the payout ratio is 60%. Given earnings per share in year 1 is $6.67, we've:

Hence,

On solving,

Hence, the required stock price would be $88.53.