Glenn Owens' attractive technology start$-$up requires $$10$ million to launch. Projections show earnings of $$10$ million and sales of $$80$ million in the fifth year. The venture capital firm expects a return of $50$ percent per year for the five$-$year period prior to an IPO. What ownership portion should the venture capitalist expect to receive? Perform a sensitivity analysis on the valuation and rate of return.