John Thompson, CEO of WVU, Inc., wants to raise $$5$ million in a private equity in his early$-$

stage venture. Thompson projects net income of $$5$ million in year five $($five years from now$)$

and knows that comparable companies trade at a price to earnings ratio of $48.$

Samantha Jones of Gorsuch Capital likes Thompson's plan, but thinks it naive in one respect: to

recruit a senior management team, she believes Thompson will have to grant generous stock

options in addition to the salaries projected in his business plan. From experience, she thinks

management should have the ability to own at least an $17\%$ share of the company at the end of

year $5.$

a$.$ If Ms$.$ Jones now insists that professional managers own $17\%$ of the company at the

end of year $5,$ how much of the company is left for investors to own $($as a dollar value$)?$

b$.$ If Ms$.$ Jones wants her investment in the company to be worth $$30$ million at end of

year $5,$ what percent of the company$$s equity should she insist on owning?