You see a fast growing company that is estimated to have dividend growth of $20\%,18\%,16\%$ and $14\%$ over each of the next four years in year $1,18\%$ in year $2,16\%$ in year $3,14\%$ in year $4).$ The company paid a dividend of $$2\mathrm{.}75$ per share over the past twelve months. Dividends are expected to grow at a constant rate of $3\mathrm{.}0\%$ per year beginning in year $5$ to perpetuity. The risk$-$free rate of return is $4\%$ and the market risk premium $($expected return on the S&P $500$ minus the risk$-$free rate of return$)$ is $6\%.$ The stock has a beta of $1\mathrm{.}1$ versus the S&P $500.$ Calculate the intrinsic value of this stock using the two$-$stage dividend discount model.

$$52\mathrm{.}15$

$$59\mathrm{.}59$

$$57\mathrm{.}48$

$$55\mathrm{.}12$