Compost Science Incorporated $($CSI$)$ is in the business of converting Boston's sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission $($MDC$)$ has agreed to pay whatever amount is necessary to yield CSI a $13\%$ book return on equity. At the end of the year, CSI is expected to pay a $$3$ dividend. It has been reinvesting $40\%$ of earnings and growing at $3\%$ a year.

a$-1.$ Suppose CSI continues on this growth trend. What is the expected long$-$run rate of return from purchasing the stock at $$100?$

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to the nearest whole number.

a$-2.$ What part of the $$100$ price is attributable to the present value of growth opportunities?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$.$ Now the MDC announces a plan for CSI to treat Cambridge sewage. CSI's plant will, therefore, be expanded gradually over five years. This means that CSI will have to reinvest $80\%$ of its earnings for five years. Starting in year $6,$ however, it will again be able to pay out $60\%$ of earnings. What will be CSI's stock price once this announcement is made and its consequences for CSI are known?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.