Question: 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 CF1H=600 (CF1L=400). At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises with probability 0.3. If demand is high (low) at t=2 then CF2H=600 (CF2L=200). All agents are risk neural. The interest rate is r=0%.Now suppose at t=0 CFA Inc. can invest in a technology that improves the product. The investment costs are $400 which is to be financed by the private equity firm. The improved technology has the following effect. In the high demand state the demand for the product doubles at t=1 and t=2. In the low demand state it has no effect.
Should CFA Inc. invest in the new technology at t=0?