$[$Present Values and Investor Ownership$]$ 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.

PART A

A$.$ Calculate the present value of each scenario or outcome for Black Hawk Products.

B$.$ Calculate the weighted average of the present values for the three scenarios. What is the total equity value for the Black Hawk Products venture?

C$.$ Determine the acquired percentage of final ownership of Black Hawk Products that $\backslash$table$[[$OUTCOME$,$YEAR $1,$YEAR $2,$YEAR $3,$YEAR $4,$YEAR $5],[$Black hole,$0,0,0,0,$$$0$Vail Venture Investors would need for its $$5$ million proposed investment.

PART B

Now assume under the venture Utopia scenario that, in addition to the $$50$ million cash inflow in Year $5,$ there will be an annual $$1$ million preferred dividend $($to be paid to Vail Venture Investors but not other equity investors$).$ Vail Venture expects to receive this $$1$ million dividend under the venture Utopia scenario in each of the five years that the Black Hawk investment will be maintained. No preferred annual cash flows are expected under either the black$-$hole or the living$-$dead scenario.

D$.$ Calculate the acquired percentage of final ownership of Black Hawk Products that Vail Venture Investors would need to earn a $25$ percent compound rate of return on its investment. Use the mean flow method described in the chapter. $($Hint: Use $$goal seek$$ in a spreadsheet software program to find the necessary percentage ownership.$)$

E$.$ Use the expected present value $($PV$)$ method described in the chapter when solving for the acquired percentage of final ownership in Black Hawk that Vail Venture needs to earn its $25$ percent target rate of return.