A company just paid an annual dividend of $D_0=$$$3\mathrm{.}00$ for its stock. Company's dividends are expected to grow by $40\%$ in the first year, by $30\%$ in Year $2,$ by $16\%$ in Year $3$ and at a constant rate of $4\%$ in Year $4$ and thereafter. The required return on this stock is $8\%.$

a$.$ What is the stock's price next year?

b$.$ What is the beta of the stock if market risk$-$premium is $4\%,$ the riskfree rate is $2\mathrm{.}1\%.$ Assume that the stock price is $$144\mathrm{.}3$ now and you expect it to increase to the price you found in part b$.$