Consider a choice between mutually exclusive projects, both with upfront cost at Year 0 of $100 million. Cash flows in the year following the investment are partially state-contingent. Project 1 has a certain cash flow of $115 million regardless of the state of the world in Year 1, but Project 2 has a cash flow of $142 in the Good state, and a cash flow of $60 million in the Bad state. This means that taking Project 2 subjects the equity holders to cash flow uncertainty in Year 1 that is otherwise absent with Project 1. The risk-neutral probability of the Good state occurring in Year 1 is 1/3. The firms equity holders are considering their ex-ante optimal project choice under two potential interest rate scenarios: Low and High. In the Low scenario, the risk-free rate is 0%. In

the High scenario, the risk-free rate is 10%. The High scenario entails a shift in the entire risk- neutral probability distribution, which means that the risk-neutral probability of the Good state is

unchanged regardless of the interest rate scenario. Assume that the interest rate scenario is determined at Year 0 (e.g., that equity holders are considering the two scenarios in Year -1) and answer the following questions. 1. Assume the interest rate scenario is Low a. Which project maximizes total firm value? b. Assume equity holders wish to finance the entire upfront cost with debt. i. Is it possible for equity holders to issue debt with a face value of $100 million? ii. If it is possible, which project do they choose?

2. Assume now that the interest rate scenario is High a. Show that equity holders would try to issue debt with a face value of $110 million. b. Which project would equity holders take assuming they are able to issue $110 of debt? c. Show that debtholders that rationally anticipate equitys ex-post choice in part (b) would not lend for a face value of $110 ex-ante.

3. Show that the face value of debt equity holders would be required to issue in the High scenario results in neither project being taken.