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# Consider the economy (above) again where the following set of stocks is traded: />x1=(10,0,30)x2=(0,20,40) x3=(20,20,0) for the prices (p1, p2, p3)=(12, 14, 8).Suppose a start-up company wants to go public. The firm has total costs of \$100,000 at date t=1 and sales of \$120,000 in state 1, \$140,000 in state 2, and \$200,000 in state 3. The firm wants to issue 1,000 IPO shares. (A share is endowed with a cash flow right of 0.1% of the total profits of the firm.) The underwriter suggests an IPO price of \$42 per share. Will this IPO be successful, i.e. will there be a positive demand for the shares? I understand V(Value of the firm) = (120k-100k)(.3) + (140k-100k)(.1) + (200k-100k)(.3) = 46kHow do I solve for payoff per share?Also, how do determine if this IPO will be successful and find out if there will be a positive demand for shares?Please show me the mathematical steps.

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