Consider an economy with three dates {t=0, 1, 2} and 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=800 (CF1L=240).

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 0.8. If demand was low at t=1, then a high demand at t=2 arises with probability 0.2. If demand is high (low) at t=2 then CF2H=800 (CF2L=240).

The interest rate is r=0%.

(a) Draw the event tree. [3p]

(b) What is the market price (expected value) of CFA Inc. at t=0? [3p]

Now suppose the private equity firm suggests CFA Inc. to invest in marketing at t=0. The marketing costs are K=1000. Marketing has the following effect. In the high demand state more consumers are rich and with marketing the demand for the product doubles at t=1 and t=2. In the low demand state at t=1 and t=2 marketing has no effect.

(c) Should CFA Inc. invest in marketing at t=0? [4p]

Now suppose the firm can invest K/2(=500) at t=0. In that case, marketing doubles demand at t=1 in the high state but has no effect in the low state and no effect on demand at t=2. Only if CFA Inc. invests an additional K/2(=500) at=1, then this doubles demand in the high state at t=2 and has no effect in the low state. The firm can invest at t=1 even if it does not invest at t=0.

(d) What strategy maximizes the value of CFA Inc. and what is the firm value?

Question 2 {20 points] Consider an economy with three dates {t=0, 1, 2}. A startup rm that produces an application for mobile internet access has assets in place that generate an output (prot) of either $120 in state L or $200 in state H at t=2. Both states are equally likely. At t=l, the rm can implement another project. The investment costs are $220 and the new project delivers an output of $X in state L and $340 in state H at 1:2. The rm wants to issue equity to a venture capitalist to nance the new project. Both the entrepreneur of the startup rm and the venture capitalist are risk neutral. They maximize their expected payoff. The interest rate is r=0%. For questions (a) to (d), assume X=100. (a) What is the t=0 value of the rm (i) without and (ii) with the project? [2p] (b) What percentage of equity does the entrepreneur need to sell so as to nance the investment cost of $220 for the new project at t=1? [1p] Now suppose prior to selling equity the entrepreneur privately learns the true state of F2 at 1:1. This assumption holds for all subsequent questions. (c) At t=l does the entrepreneur sell equity in both states? [31)] (d) What is the t=l value of the rm if equity is sold at t=1? [2p] (e) Determine the set {X} such that there is equity issuance in both states at t=1? 161)] (t) For the above set of {X}, what is the t=1 value of the rm if equity is is sued in both states? [2p] (g) 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 is not socially efcient, what is the rationale for the entrepreneur still to do that? [4p]