Question

Consider the economy (above) again where the following set of stocks is traded:

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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) = 46k**

**How 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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