Assume that a company paid a dividend of $$0\mathrm{.}70$ in $2023.$ Dividends are expected to grow annually by $5\%$ for the next four years $(2024$ to $2027).$ From $2028,$ dividends will grow at a constant rate of $3\%$ per year.

If the cost of equity is $10\%,$ and the market value of the company share was $$15\mathrm{.}65$ after paying the dividend in $2023$:

a$)$ Build a dividend growth model that captures both high growth and constant growth.

b$)$ Should you buy the company share? Explain your answer.