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Unformatted text preview: Problem 12-3 Problem 11-3 a) With the entrepreneur making the entire investment, the entrepreneur would want to maximize the NPV of a portfolio of the venture and investment in the market by selecting the size of the investment. Because the entrepreneurs opportunity cost of capital for investing in the venture declines as the fraction of wealth invested in the venture declines, the entrepreneur probably will seek some level of diversification by reducing the scale of the venture. However, at some scale the venture becomes too small to contribute materially to the PV of the entrepreneurs portfolio. Certainly, as the venture becomes inefficient with investment of less than $500,000, this factor will also discourage scale reduction below that size. However, if the inefficiencies are not too great, the entrepreneur may even sacrifices some efficiency for the benefit of greater diversification. b) With proportional sharing, not much is changed. The main thing is that there now is no reason to operate the business at an inefficient scale. If, ignoring inefficiencies of small scale, the entrepreneur would only want to invest, say $400,000 in the venture, an additional investment of $100,000 to $2.1 million from an outside investor would enable the venture to operate in the most efficient zone, and would not affect the value of the entrepreneurs investment. Of course, we are ignoring intangible considerations including the value of retaining a controlling interest. c) If the investor values the venture more highly than does the entrepreneur (and PV is positive to the investor), the investor would want to operate at least at the high end of the efficient scale range ($2.5 million invested in the venture), and might even want a larger scale, as long as incremental NPV due to expanding beyond that level is positive. The entrepreneur should be able to sell the venture for a price approaching the maximum NPV to the investor. Problem 12-4 a Market Information Annual Holding Period Risk-free Rate 4.00% 12.49% Market Rate 9.50% 31.29% Market Risk Premium 5.50% 18.81% Market Variance 1.96% 5.88% Market Standard Deviation 14.00% 24.25% Correlation 0.25 Project Cash Flows Invest Date Harvest Date Years Until Harvest 3 Investment in Project $3,000,000 Expected Project Cash Flow $5,447,544 Based on 22% return Project Standard Deviation of Cash Flows $5,819,691 Selected to make beta = 2.0 Investor Allocation Project beta (based on cost of project) 2.000 Approximate beta Fraction of Investment that is notionally in project 0.781 Outside Investment $1,500,000 True beta Required Percent of Equity 39.07% 1.56 Cash Flow to Investor Expected Cash Flow $2,128,116 Standard Deviation of Cash Flow $2,273,498 Outside Investor Value $1,500,000 Valuation Template 6 Valuation - Investor and Entrepreneur's Partial Commitment Expected project cash flow is found by compounding the investment at 22 percent per year. Standard deviation of cash flows is found by searching for the value that makes the Project beta (based on cost of project) equal to 2.0.cash flows is found by searching for the value that makes the Project beta (based on cost of project) equal to 2....
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- Spring '05