Vic Nguyen, CEO of NewVenture, seeks to raise $$5$ million in a private placement of equity in his early stage venture. Nguyen conservatively projects net income of $$5$ million in year five and knows that comparable companies trade at a price earnings ratio of $20$X$.$ Assume $1$ million shares outstanding.

Maria Garcia of Growing Seeds Capital likes Vic Nguyen$$s business plan, but thinks it na$$ve in one respect: to recruit a senior management team, she believes Vic will have to grant generous stock options in addition to the salaries projected in his business plan. From past experience, she thinks management should have the ability to own at least a $15\%$ share of the company by the end for year $5.$ Given her beliefs, estimate the share of the company Maria should insist on today if her required rate of return is $50\%.$ Then estimate how many shares she would she get. What would be the price per share?

Group of answer choices

$12\mathrm{.}63$

$$4\mathrm{.}23$

$$9\mathrm{.}10$

$$6\mathrm{.}19$