The following data have been obtained: risk$-$free rate $=4\%$; beta of Green $($Corp$.)=1\mathrm{.}4$ ; and required return on the stock market $=9\%.$

a$.$ If the dividend expected in the coming year is $$2\mathrm{.}4$ and the dividend growth rate is $5\%,$ calculate the fair price of the stock.

b$.$ Now, Green has launched a successful product. The management is confident that the expected dividend growth rate will increase to $6\%.$ Also, due to higher sales and profits, the market risk of Green falls from $1\mathrm{.}4$ to $1\mathrm{.}2.$ If the expected dividend in Year $1,$ the risk$-$free rate, and the required return on the stock market remain unchanged, calculate the new intrinsic value of the stock.