3. The owner of ABC Corp. wishes to take her stock public for the first time by selling 10 million shares. The underwriter determines that the true value will be $30 with probability .4 and $10 with probability .6. There are a group of uninformed investors who are willing to buy 12 million shares as long as their expected profits from investing are greater than or equal to zero. This group also assesses that the true value of the shares will be $30 with probability .4 and $10 with probability .6. There is a group of informed investors who know whether the true value is $30 or $10. They are willing to order 3 million shares if the offer price is less than the true value. (a) [10 points] Calculate the highest offer price at which the entire issue will always sell. (b) [5 points] If the issue is priced at the level you calculated in part (a), what is the expected percentage change in the share price on the first trading day after the IPO? In other words, on average how much is this issue underpriced? (c) [5 points] Suppose that the hypothesis described in this problem (i.e., the winners curse hypothesis) can fully explain the IPO underpricing. If you, as an uninformed investor, apply for every IPO in Korea for one year, would your expected return be significantly positive, significantly negative, or close to zero? Explain your answer.