Question 3 [12 points] Consider the following economy with three dates (t=0, 1, 2). A rm needs to raise $100 to nance a project at t=0. At t=2, the project is either a failure and pays off nothing or generates $300. Both states are equal likely. At t=1, the rm learns about the outcome of the project. If it is a success it expands the project and raises additional capital by conducting a secondary offering which is observable in the market. If the project is a failure there is no additional capital needed. There is an early consumer who has $100 at t=0 and the utility function uE = CEO + 1.4- min[cEl,100] + max[cE1 100,0] + cm. In addition, there is a late consumer who has W=$3 20 at t=1 and the utility function uL = cl,\"0 + c L] + cm. Suppose the rm issues equity at t=0. If the early consumer buys equity at t=0, he sells his equity holding to the late consumer at 1:]. a) What equity contract does the rm oer the early consumer so as to get $100? What is the fraction of equity the rm is selling? [6 Points] b) What is the price of the equity at t=1 if there is no additional equity issuance? What is the price of the equity at t=1 if there is secondary equity offering? [4 Points] c) What is the expected prot of the rm? [2 Points]