$5.$ Suppose that the underlying assumptions of the MM hypothesis about dividends are met. The stock price of firm ABC is $$100$ on May $10,$ and the stock goes ex$-$dividend on May $11$ and pays out dividend of $$10$ per share. You have $100$ shares of ABC$$s stocks.

a$.$ Please assess your wealth before and after the stock goes ex$-$dividend $($e$.$g$.,$ on May $10$ and May $11).$ Is there any change in your wealth related to the investment in ABC? b$.$ Under the MM hypothesis, the dividend policy should be irrelevant to investors as they can $$home$-$make$$ dividends. If you prefer the firm to pay only $$5$ dividend per share, what should you do$?$ Can you achieve the same condition as the firm pays out $$5$ rather than $$10$ dividend per share? c$.$ If you prefer the firm to pay $$20$ dividend per share, what should you do$?$ Can you achieve the same condition as the firm pays out $$20$ rather than $$10$ dividend per share? d$.$ What are the underlying assumptions of the MM hypothesis about dividends?