River Enterprises has $$501$ million in debt and $20$ million shares of equity outstanding. Its excess cash reserves are $$15$ million. They are expected to generate $$209$ million in free cash flows next year with a growth rate of $2\%$ per year in perpetuity. River Enterprises' cost of equity capital is $13\%.$ After analyzing the company, you believe that the growth rate should be $3\%$ instead of $2\%.$ How much higher $($in dollars$)$ would the price per share be if you are right?

$9\mathrm{.}50$

None of the answers mentioned

$8\mathrm{.}50$

$7\mathrm{.}50$