Question

Question 1 1 pts Fancy Hats Inc. is about to issue 9 million shares of new equity in an IPO. The offering price will be set to $26, and the underwriter has an overallotment option for 18% more shares. What is this overallotment option worth if there is a 50% chance that the opening price on the first day of trading will be $48, and a 50% chance that the opening price on the first day will be $11?

Answer 1

The facts of the case are:

1 Fancy Hats Inc is about to issue 9 million shares at $26.

2 the underwriter has an overallotment option for 18% more shares i.e. 9 Million * 18% = 1.62 million shares @ $26

Now there are 2 scenarios

a) 50% chance of the opening price being $28

b) 50% chance of the opening price being $11

In the first scenario the profit to the underwriter will be

No of shares * difference in Opening price and IPO price

i.e 1.62 million * ($48 - $26) = $ 35.640 million

In case of an opening of $ 11, it has to be remembered that the underwriter has an option to buy, which in this case he will not exercise and given that the underwriter has not paid any upfront premium for the option the loss to the underwriter is Zero.

Given, the probability of both the scenarios are 50%

The worth of the over allotment = $ 35.640*50% + Zero* 50% = $1.782 million