Vail Venture Investors, LLC is trying to decide how much percent equity ownership in Black Hawk Products, Inc. it will need in exchange for a $$5$ million investment. Vail Venture Investors has a target compound rate of return of $20$ percent on venture investments Tike Black Hawk Products. Depending on the success of products currently under development, Vail Venture's investment in Black Hawk could turn out to be a complete failure $($black hole$),$ barely surviving $($living dead$),$ or wildly successful $($venture utopia$).$ Vail Venture assigns probabilities of $\mathrm{.}20,\mathrm{.}50,$ and $\mathrm{.}30,$ respectively, to the three possible outcomes. Following are the $3$ cash flow scenarios or outcomes for the Black Hawk Products investment that Vail Venture expects to exit at the end of five years.

$\backslash$table$[[$Outcome$,$Yr$1,$Yr $2,$Yr$3,$Yr$4,$Yr$5],[$Black Hole,$0,0,0,0,0\mathrm{.}00],[$Living Dead,$0,0,0,0,$$$0,000,000\mathrm{.}00$