The required rate of return on the shares in the companies identified below is $9\%$ pa$.$ Calculate the current share price $($ex$-$dividend$)$ in each case.

$($a$)$ The current earnings per share of Alpha Ltd are $$10\mathrm{.}00.$ Earnings are expected to remain constant for the next three years. For the next $3$ years, Alpha anticipates having to put half of its earnings back into the business to maintain the level of earnings. After this it is expected that all earnings will grow by $3\%$ pa and all earnings will be able to be paid out as dividends.

$($b$)$ Gamma Ltd is planning to reinvest earnings and not pay dividends until year $4,$ when a dividend of $$6$ is expected $($D$4=$ $$6).$ Dividends are expected to remain constant after that.The required rate of return on the shares in the companies identified below is $9\%$ pa$.$ Calculate the current share price $($ex$-$dividend$)$ in each case.GIVE EXCEL SOLUTION WITH FORMULA