Question $3,(10$ marks$)$

David Corporation has $3,000,000$ outstanding shares, it just paid $$5$ dividend per share, and there are $200$ shares in each lot of stock $($i$.$e$.,1$ lot $=200$ shares$).$ Suppose the risk$-$free rate is $1\%.$ You have estimated that the risk premium for the stock is $6\%,$ and a constant growth rate of $2\%$ is estimated for the dividend per share.

a$)$ Suppose you purchase $5$ lots of shares today, and plan to keep it for a year after receiving the dividend in the coming year. Calculate the expected dividend that you will receive for this investment. $(2$ marks$)$

b$)$ What is your estimated required return rate for this stock? $(4$ marks$)$

c$)$ Suppose you purchase $5$ lots of shares today, calculate the expected price of a share based on the dividend growth model. $(2$ marks$)$

d$)$ Suppose you observe that the current price of the stock is $$300,$ will you invest? Discuss it with at most $40$ words. $(2$ marks$)$