$1.$ Mack Industries just paid a dividend of $$1\mathrm{.}50$ per share $($i$.$e$.,$ Div$0=$ $$1\mathrm{.}50).$ Analysts expect the company's dividend to grow $20$ percent this year $($i$.$e$.,$ Div$1=$ $$1\mathrm{.}80),$ and $15$ percent next year, and $10$ percent the year after. After three years the dividend is expected to grow at a constant rate of $5$ percent. The required rate of return on the company's stock is $12$ percent. Calculate the expected price of the stock $($P$0).$