#$17$ The Digital Electronic Quotation System $($DEQS$)$ Corporation pays no cash dividends currently and is not expected to for the next five years. Its latest EPS was $$10,$ all of which was reinvested in the company. The firm's expected ROE for the next five years is $20\%$ per year, and during this time it is expected to continue to reinvest all of its earnings. Starting in year $6,$ the firm's ROE on new investments is expected to fall to $15\%,$ and the company is expected to start paying out $40\%$ of its earnings in cash dividends, which it will continue to do forever after. DEQS's market capitalization rate is $15\%$ per year.

a$.$ What is your estimate of DEQS's intrinsic value per share?

b$.$ Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its price over the next year?

c$.$ What do you expect to happen to price in the following year?

d$.$ What effect would it have on your estimate of DEQS's intrinsic value if you expected DEQS to pay out only $20\%$ of earnings starting in year $6?$