Problem $1$

Micro Inc. $($MI$)$ just paid a dividend of $$2\mathrm{.}00/$share$.$ MI has a new technology that is expected to go on the market this year, and their dividend is expected to grow at $10\%$ per year for the next five years $($i$.$e$.,$ the growth rate applies only to the next five dividend payments$).$ After that, the dividend is not expected to increase for the foreseeable future $($i$.$e$.,$ forever$).$ The next dividend will be paid exactly in one year. Assume investors require a $10\%$ rate of return $($EAR$)$ for MI's stock.

a$)$ What is MI's stock price today?

b$)$ What is MI's stock price in three years from now $($right after the dividend payment$)?$

c$)$ What is MI's stock price in twenty years from now $($right after the dividend payment$)?$