#12. The owner of Gator Airlines wishes to take her firm public by selling 6 million shares. The underwriter determines that the true value will be $15 with probability .4 and $8 with probability .6. There are a group of uninformed investors who are willing to buy 6 million shares as long they expect not to lose money on average. They also assess the probability of the true value of the shares being $15 with probability .4 and $8 with probability .6. There is a group of informed investors who always know whether the true value is $15 or $8. They are willing to order 2 million shares if the offer price is less than or equal to what they know the true value of the shares to be. Assume initially that if more shares are ordered than are available for sale, the underwriter allocates the available shares on a pro-rata basis based on the size of each groups order (i.e., the fraction of shares a group gets is equal to: (the group's order)/(total shares ordered).

(a) Calculate the highest offer price at which the entire issue will surely sell.

(b) Could an uninformed investor make money on average by submitting an order to buy some shares of the new issue? Why or why not?

(c) If the stock is sold at the offer price you calculated in (a), what will be the expected change in the stock price on its first day of trading?

(d) Assume now that when an issue is oversubscribed the underwriter follows a rule of allocating 3/4 of the shares to the informed investors and 1/4 of the shares to the uninformed investors. Given this new allocation rule, calculate the highest offer price at which the entire issue will always sell. Has underpricing (i.e., the expected first day change in the stock price) gotten larger or smaller with this new allocation rule?