$2)$ Suppose you are analyzing the stocks of a company. Analysts expect the company to pay dividends of $$10$ per share at the end of the first year, $$12$ per share at the end of the second year, and $$15$ per share at the end of the third year. Afterwards, the dividend will decrease at a regular rate of $3\%.$ If the required rate of return is $12\%,$ what is the stock's value today? Justify your response.