Analysts predict that earnings for ABC Corp will be $$5\mathrm{.}00$ per share next year and will grow at a rate of $8\%$ indefinity. ABC reinvests $50\%$ of its earnings back into the company each year and intends to keep the plowback ratio constant.

a$)$ If you believe that the company$$s required rate of return is $10\%,$ what is your estimate of the price of the company$$s stock?

b$)$ Suppose you observe that the stock is selling for $$50\mathrm{.}00$ per share, what would you conclude about either your belief of the stock$$s required rate of return or the analyst$$s estimate of the growth rate? $($your answer should include numbers$)$