Question 2 [20 points] Consider an economy with three dates {t=0, 1, 2}. A startup firm that produces an application for mobile internet access has assets in place that generate an output (profit) of etther $120 1n state L. or 5200 in state H at t=2. Both states are equally likely. At t=1, the firm can implement another project. The investment costs are 5220 and the new project delivers an output of 3X in state L and 5340 1n state H at =2 The firm wants to 1ssue equity to a venture capitalist to finance the new project. Both the entreprenceur of the startup firm and the venture capitalist are risk neutral They maximize their expected payoff. The interest rate 1s r=0%. For questions (a) to (d), assume X=100. (a) What 15 the t=0 value of the firm (1) without and (11) with the project? [2p] (b) What percentage of equity does the entrepreneur need to sell so as to finance the investment cost of $220 for the new project at t=17 [1p] Now suppose prior to selling equity the entrepreneur privately learns the true state of t=2 at t=1. This assumption holds for all subsequent questions. (c) At t=1 does the entrepreneur sell equity in both states? [3p] (d) What 15 the t=1 value of the firm if equity 1s sold at =17 [2p] (e) Determine the set {X} such that there 1s equity 1ssuance in both states at =17 [6p] (f) For the above set of {X}, what 15 the t=1 value of the firm if equity 1s 1ssued 1n both states? [2p] (z) From a welfare and net present value (NPV) perspective, should the entrepreneur who knows the true state raise equity and invest in the project in both (L and H) states? If it 15 not socially efficient, what 1s the rationale for the entrepreneur still to do that? [4p]