Consider a firm that distributes the entire annual earnings to its shareholders through dividends once a year. The firm's dividends are expected to grow at a rate of $4\%$ per year for the next $5$ years until the end of $2035.$ From $2036$ on$,$ the firm's growth rate is expected to be $2\%$ per year forever. Assume that investors command $12\%$ return on the investments comparable to the firm's stock. In addition, the firm has just paid an annual dividend of $$10$ per share at the end of $2030.$

Required: If you were considering buying the firm's shares on the first day of $2031,$ at what price would you buy the shares?