$6\mathrm{.}47$ Lewin Skis Inc. $($today$)$ expects to earn $\backslash (\backslash$$ $8\mathrm{.}50\backslash )$ per share for each of the future operating periods $($beginning at time $1)$ if the firm makes no new investments and returns the earnings as dividends to the shareholders. However, Clint Williams, president and CEO, has discovered an opportunity to retain and invest $20$ percent of the earnings beginning three years from today. This opportunity to invest will continue for each period indefinitely. He expects to earn $10$ percent on this new equity investment, with the return beginning one year after each investment is made. The firm's equity discount rate is $12$ percent throughout.

a$.$ What is the price per share of Lewin Skis Inc. stock without making the new investment?

b$.$ If the new investment is expected to be made, per the preceding information, what would the price of the stock be now?

c$.$ Suppose the company could increase the investment in the project by whatever amount it chose. What would the retention ratio need to be to make this project attractive?