Question $4,(14$ marks$)$

You just bought $200$ shares of common stock issued by Rita Corporation at the price of $$18.$ You plan to keep these shares for $4$ years, and you made predictions on the stock$-$related items for these $4$ years. It is believed that dividend per share will be $$1$ this year, and the share price is expected to be $$20$ at the end of this year. The earnings per share is expected to be $$3$ in the second year, and you predict that the dividend payout ratio will keep constant at $60\%$ in the second year. The share price is expected to be $$12$ at the end of the second year. The dividend payout ratio is expected to be $0\%$ for the third and the fourth year, and the expected price of a share is $$18$ at the end of the third year. At the end of the fourth year, the price is predicted to be $$22,$ and you will see all the shares at $$22$ at that time.

a$)$ Calculate the total dollar returns in these $4$ years.

b$)$ Calculate the geometric average return rate for your investment.

c$)$ Calculate the simple average return rate for your investment.

d$)$ Suppose the standard deviation of the return rate is $0\mathrm{.}336394.$ Your friend, Jason, likes to buy the stock if the coefficient of variation is less than $2\mathrm{.}2,$ and sell the stock if the coefficient of variation is greater than $2\mathrm{.}2.$ What is his investment decision?

$(3$ marks$)$