(solve questions D & E) 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 Ventures 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 0.20, 0.50, and 0.30, 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.

\begin{tabular}{lccccl} OUTCOME & YEAR 1 & YEAR 2 & YEAR 3 & YEAR 4 & YEAR 5 \\ \hline Black hole & 0 & 0 & 0 & 0 & $0 \\ Living dead & 0 & 0 & 0 & 0 & $10 million \\ Venture Utopia & 0 & 0 & 0 & 0 & $50 million \end{tabular} Now assume under the venture Utopia scenario that, in addition to the $50 million cash inflow n Year 5, there will be an annual $1 million preferred dividend (to be paid to Vail Venture nvestors but not other equity investors). Vail Venture expects to receive this $1 million dividend inder the venture Utopia scenario in each of the five years that the Black Hawk investment will e maintained. No preferred annual cash flows are expected under either the black-hole or the iving-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