A firm's existing assets either have a high value of $345 million (the undervalued firm) or a low value of $135 million (the overvalued firm). The firm's manager knows the value of her firm's assets, but the market does not. The market assesses that there is a 50% chance the firm has high value assets and a 50% chance the firm has low value assets. Regardless of the value of the firm's current assets, the manager and the market are both aware that the firm has the opportunity to invest $30 million in a new project that will generate a cash flow with a present value of $60 million. The firm currently has 900,000 shares outstanding. The firm does not have the internal cash to fund the project, and thus if they want to fund the project they must conduct an equity issue immediately. In the long-run (i.e., next year) the markets will learn whether the firm was the undervalued or overvalued. Assume that managers act to maximize the long-run value of existing shareholder's claims when making the equity issue/investment decision. (a)Show that there is an equilibrium where both undervalued firms and overvalued firms issue equity to invest in the project. In this equilibrium how many shares will be sold? At what price will they be sold? What are the predicted long run stock prices for the undervalued firm and for the overvalued firm in this equilibrium? [Note: By long run I mean after any share sale and after the market learns/realizes the true value of the firm's assets.]