Consider a two-period (t=0 and t=1), two-state economy ("boom" and "recession"). At t=1, the economy can either be in a boom or recession with risk-neutral probabilities of 0.8 and 0.2, respectively. There are two types of firm in the market, Good firm and Bad firm. At t=1, Good firm has assets-in-place, which will generate a single cash flow of $1,100 in both states, while Bad firm's assets-in-place will generate a single cash flow of $1,100 in a booming market or $220 in recession. The manager of each firm knows the types of assets. The investors and the managers know that both firms have an investment opportunity that, with an initial investment I = $600, it will generate a cash flow of $1,100 in the boom state and $0 in the recession state at t=1. Both firms have zero cash. They will need to raise funds from the market if they decide to take the investment project. The risk-free interest rate is 10%. The capital market is so competitive so that the investors can only make zero NPV by accepting the securities offered by both firms.

(a) Suppose the informational environment is perfect. The investors can identify Good firms and Bad firms. Both firms decide to fund their investments. The Good firm will issue debt with a face value of B, and the Bad firm will issue a fraction f of the total equity to the investors. Calculate B and f. Assume now in the imperfect market that the investors do not know which firm has a good type of assets. They are only aware that good and bad firms are equally distributed.

(b) Suppose that the investors believe the firm issuing debt has a good type of assets. Initially, Good firms issue debt with a face value of B, and Bad firms issue a fraction of equity, with the values of B and f found in (a). Under this belief, is there any mispricing for securities offered by the Good and Bad firms initially? Will bad firms mimic Good firms by issuing debt?