A firm is expected to distribute a dividend of $$6$ per share next year. Its beta is $1\mathrm{.}25,$ the expected market return is $20\%$ and the risk free rate is $8\%.$

$1.$ Price the stock, if dividends are expected to remain constant forever.

$2.$ Price the stock if dividends are expected to grow by $5\%$ every year forever.

$3.$ Price the stock, if dividends are expected to grow by $10\%$ for the first $10$ years and by $5\%$ thereafter.