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 $25$ percent on venture investments like 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 $0\mathrm{.}20,0\mathrm{.}50,$ and $0\mathrm{.}30,$ respectively, to the three possible outcomes. Following are the three 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$,$YEAR $1,$YEAR $2,$YEAR $3,$YEAR $4,$YEAR $5],[$Black hole,$0,0,0,0,$$$0$