1. (IPO underpricing and winner's curse) Dinosaur Cloning Inc., a formerly private company, decides to raise equity capital to fund research of cloning dinosaurs, an extinct species. If dinosaurs can be successfully cloned, the firm can make money by selling cloned dinosaurs to zoos. Everybody knows that the true value of the firm's equity is $120 million with probability 0.4, and $40 million with probability 0.6. Dinosaur Cloning Inc. has hired MS as its lead underwriter. The underwriter decides that the firm ought to offer 4 million shares. The underwriter also needs to set the offer price. Through road shows, MS knows that there is a pool of institutional investors who become fully informed through some costly analyses in the biotechnological business. These informed investors will order 2 million shares due to their budget constraints, if the offer price is lower than the true value, and no shares otherwise. MS also knows that there is a pool of uninformed investors who are willing to order 4 million shares of this IPO as long as their expected profit is not negative. MS allocates shares of the IPO on a pro rata basis.

(a) Compute the equilibrium offer price that MS should set so that uninformed investors are willing to submit bids for the IPO.

(b) Calculate the equilibrium level of underpricing (comparing the equilibrium OP with the expected true value of the firm).

(c) Calculated the expected profit to the informed investors if MS sets the offer price at the value computed in part (a).