PLEASE WRITE ALL THE FORMULAS AND CALCULATIONS

Question 3 [12 points] Consider an economy with three states which occur with probabilities (0.2, 0.4, 0.4). Suppose an entrepreneur has $140 and owns a firm that has a single project which generates the state dependent cash flows (100, 100, 300) at t=1. The investment costs are $140 at t=0. The market portfolio generates the payoff (100, 200, 300) and has an expected return of 12%. The risk free rate is 3%. Suppose the CAPM holds. (a) What is the beta of this project? [4p] (b) Explain whether the entrepreneur should conduct the project. [6p] (c) Suppose a private equity company wants to acquire the firm. At what price is the entrepreneur willing to sell the firm? [2p]