Patriot Scientific, Inc (PSI), in in the business of converting New Yorks sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce PSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 8% book return on equity. At the end of the year PSI is expected to pay a 5$ dividend. It has been reinvesting 50% of earnings and growing at 5% a year.

a. Suppose PSI continues on this growth trend. What is the expected long-run rate of return from purchasing the stock at 100$? What part of the 100$ price attributable to the present value of growth opportunities (PVGO)?

b. Now the MDC announces a plan for PSI to treat Brooklyn sewage. PSIs plant will, therefore, be expanded gradually over five years. This means that PSI will have to reinvest 75% of its earnings for five years. Starting in year 6, however, it will again be able to pay out 50% of earnings. What will be PSIs stock price once this announcement is made and its consequence for PSI are known ?