The owner of Gator Airlines wishes to take her firm public by selling 4 million

Question

The owner of Gator Airlines wishes to take her firm public by selling 4 million shares. The underwriter determines that the true value will be $12 with probability .3 and $8 with probability .7. There are a group of uninformed investors who are willing to buy 4 million shares as long as they expect not to lose money on average. They also assess the probability of the true value of the shares being $12 with probability .3 and $8 with probability .7. There is a group of informed investors who always know whether the true value is $12 or $8. They are willing to order 2 million shares if the offer price is less than the true value. Assume 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 groups order/total shares ordered).

(a) [5 points] Calculate the highest offer price at which the entire issue will surely sell.

(b) [5 points] If the stock is sold at the offer price you calculated in (a), could an uniformed investor make money on average by submitting an order to buy some shares of the new issue? Why or why not?

(c) [5 points] If the stock is sold at the offer price you calculated in (a), what will be the expected stock return on its first day of trading?

Explanation / Answer

Q: a.

The true value of the share = $12 and the probability =0.3

The true value of the share = $8 and the probability =0.7

Expected value of the share = (12×0.3) + (8×0.7)

                                            = 3.6 + 5.6

                                            = 9.2

Therefore the highest offer price of the share is $9.2

Q: b.

The buyer (Uniformed) can make money if the true value of the share will be $12. The average value of the stock is $9.2. So, the investor won’t make money or lose money.

Q: c.

Therefore, Expected Stock Return = (0.3 × 0.3043) + (0.7 × - 0.1304) = 0

Working Notes:

True value is 12 = (12- 9.2) ÷ 9.2 = 30.43%  

True value is 08 = (8 - 9.2) ÷ 9.2 = -13.04%

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