River Enterprises has $$$$498$ million in debt and $18$ million shares of equity outstanding. Its excess cash reserves are $$17$ million. They are expected to generate $$$$198$ million in free cash flows next year with a growth rate of $2\%$ per year in perpetuity. River$$ Enterprises' weighted average cost of capital is $11\%.$ 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?

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Part $1$

If the growth rate is $2\%,$ the price per share is $\_\_\_\_\_$enter your response here. $($Round to the nearest$$ cent.$)$