You work for an investment bank that underwrites technology IPOs. Firms in this sector can be either good or bad. Good firms are worth $30 per share and bad firms are worth $20 per share. There is an equal proportion of good firms and bad firms in the economy. That is, with 50% probability, an IPO is a good IPO and its opening price is $30 at the start of trading, and with 50% probability, an IPO is a bad IPO and its opening price is $20 at the start of trading. Each type of firm issues 1,000 shares in its IPO.
A proportion of IPO investors are informed and can distinguish between good and bad IPOs. These informed investors only bid on the good IPOs. The remaining investors are uninformed and bid on every IPO. For every uninformed investor, there are three informed investors. Assume that conditional on bidding, each investor bids for all of the shares offered, and bids are filled on a pro-rata basis.
a) What offer price of an IPO in the technology sector would make the uninformed investors indifferent between bidding and not bidding on the IPO? In other words, what offer price for an IPO of unknown type produces zero expected profits for uninformed investors? Explain why your answer implies underpricing of good firms.
b) What are the aggregate expected profits of informed investors in an IPO at the offer price you found in part a?
c) How much money do the good firms leave on the table relative to the case in which all IPO investors are uninformed?