A common share has just paid $$6$ in annual dividends. It is expected to pay no dividend next year, a $$5$ dividend in $2$ years' time, a decrease $($negative growth$)$ in the dividend of $20\%$ per year for years $3$ and $4,$ growth $($increase$)$ of $30\%$ per year for years $5$ and $6,$ and constant annual growth of $6\%$ per year thereafter.

a$)$ If the required yield is $14\%$ per year today, calculate Po$.$

b$)$ Calculate the effective annual return for an investor who bought the stock at Po and sold it at P$4($in $4$ years$).$

$($Required return in $4$ years $=12\%).$

Show your work for a$)$ and b$)$