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Compost Science, Inc. $($CSI$),$ is in the business of converting Boston's sewage sludge into

fertilizer. The business is not itself very profitable. Ilowever, to induce CSI to remainn business, the Metropolitan District Commission $($MDC$)$ has agreed to pay whatever

amount is necessary to yield CSI a $10\%$ book return on equity. ${?}^1$ At the end of the year.

CSI is expected to pay a $$4$ dividend. It has been reinvesting $40\%$ of earnings and growing

at $4\%$ a year.

$($a$)$ Suppose CSI 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 is at tributable

to the present value of growth opportunities?

$($b$)$ Now the MDC announces a plan for CSI to treat Cambridge sewage. CSI's plant

will, therefore, be expanded gradually over $5$ years. This means that CSI will have

to reinvest $80\%$ of its earnings for $5$ 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?