Please answer to all the question (a-d) please.

Question 2 [20 points] There is an economy with three dates {t=0, 1, 2}. Consider the following relationship between a private equity firm and the portfolio company CFA (Cash Free Agency) Inc. The portfolio company has a product that generates the following cash flow. At t=1, the demand can be high or low with equal probability. If demand is high (low) the cash flow is CF 11=600 (CF1=200). At t=2, the demand can also be high or low. If demand is high at t=1, then a high demand at t=2 arises with probability 0.8 and CF2h=800. If demand is low at t=2 then CF2L=400. If demand is low at t=1, then a high demand at t=2 arises with probability 0.3 and CF2=400. If demand is low at t=2 then CF2=200. The interest rate is r=0%. (a) Draw the event and decision tree. (3p) (b) What is the market value (expected value) of CFA Inc. at t=0? [3p] Now suppose at t=0 CFA Inc. can invest in a technology that improves the product of the firm. The investment costs are $240. The improved technology has the following effect. In the low demand state at t=1 and t=2 more consumers are now willing to buy and the demand for the product doubles. In the high demand state it has no effect. (C) Should CFA Inc. invest in the new technology at t=0? What is the market value of CFA? [6] Now suppose the private equity firm advises CFA to split the investment. If CFA invests $120 at t=0, it doubles demand in state L at t=1 but has no effect on demand at t=2. At t=1, if CFA invests $120, this doubles demand in the low state at t=2. (d) What is the optimal investment strategy and the associated market value? [8p] Question 2 [20 points] There is an economy with three dates {t=0, 1, 2}. Consider the following relationship between a private equity firm and the portfolio company CFA (Cash Free Agency) Inc. The portfolio company has a product that generates the following cash flow. At t=1, the demand can be high or low with equal probability. If demand is high (low) the cash flow is CF 11=600 (CF1=200). At t=2, the demand can also be high or low. If demand is high at t=1, then a high demand at t=2 arises with probability 0.8 and CF2h=800. If demand is low at t=2 then CF2L=400. If demand is low at t=1, then a high demand at t=2 arises with probability 0.3 and CF2=400. If demand is low at t=2 then CF2=200. The interest rate is r=0%. (a) Draw the event and decision tree. (3p) (b) What is the market value (expected value) of CFA Inc. at t=0? [3p] Now suppose at t=0 CFA Inc. can invest in a technology that improves the product of the firm. The investment costs are $240. The improved technology has the following effect. In the low demand state at t=1 and t=2 more consumers are now willing to buy and the demand for the product doubles. In the high demand state it has no effect. (C) Should CFA Inc. invest in the new technology at t=0? What is the market value of CFA? [6] Now suppose the private equity firm advises CFA to split the investment. If CFA invests $120 at t=0, it doubles demand in state L at t=1 but has no effect on demand at t=2. At t=1, if CFA invests $120, this doubles demand in the low state at t=2. (d) What is the optimal investment strategy and the associated market value? [8p]