$1.)$ Wyat Oil pays a regular dividend of $$2\mathrm{.}50$ per share. Typically, the stock price drops by $$2\mathrm{.}00$ per share when stock goes ex$-$dividend. Suppose the capital gain tax rate is $20\%,$ but investors pay different tax rates on dividends.

$($a$)$ Absent transaction costs, calculate the highest dividend tax rate of an investor who could gain from trading to capture the dividend. $(10$ pts$.)$

$($b$)$ If the investor$$s dividend tax rate is higher than the value calculated in section $($a$),$ advise a trading strategy to the investor around the ex$-$dividend date. $(10$ pts$.)$

$2.)$ Suppose that all capital gains are taxed at a $20\%$ rate, and that the dividend tax rate is $40\%.$ Rearden Metal is currently trading for $$40$ per share, and is about to pay a $$5$ special dividend.

$($a$)$ Absent any other trading frictions or news or arbitrage opportunity, calculate Rearden$$s share price on the ex$-$dividend date. $(7$ pts$.)$

$($b$)$ Calculate the effective dividend tax rate for an investor in Rearden Metal and interpret your number result. $(7$ pts$.)$

$3.)$ Empirical research found that there have been significant increases in stock price on the day a dividend is announced.

$($a$)$ What does this finding imply about the information content of dividend increase? Please name the theory as well.

$($b$)$ What does this finding imply about the dividend increase for a corporation having no investment opportunities? Please name the theory as well.

$4.)$ A stock that you know is held by long$-$term individual investors paid a large one$-$time dividend. You notice that the price drop on the ex$-$dividend date is about the size of the dividend payment. You find this relationship puzzling given the tax disadvantage of dividends. Explain how the dynamic dividend$-$capture theory might account for this behavior.