problem: Suppose an entrepreneur owns a firm which has two production opportunities. Technology A produces an output (net profit) of 10 in state 1, an output of 20 in state 2, and an output of 90 in state 3. All states are equally likely. Technology B produces an output of 40, 50, and 60, respectively. Since of technological constraints, the entrepreneur can only implement one technology. The entrepreneur maximizes his expected utility.

a) Which technology must the entrepreneur implement and what is the value of the firm?

b) Assume that the firm has debt with face value 12 outstanding. What project does the entrepreneur implement?

c) Assume that the firm has debt with face value 50 outstanding. What project does the entrepreneur implement?

d) Find out the utility of the entrepreneur as a function of face value D for technology A and B, respectively.

e) What is the maximal debt level such that the entrepreneur still selects the (socially) efficient technology?

f) Assume that the firm only has equity and 98% of shares are owned by retailed investors and the initial entrepreneur owns 2% of the firm. What technology does he implement?

problem: Assume that an entrepreneur owns a firm that has a production technology that produces the following revenue: R(e) = e² +100 e where revenue depends on his effort level e. The monetary cost of effort is given by: C(e) = 2e². The entrepreneur is risk neutral and maximizes his expected utility.

a) What is the maximal value (profit) of the firm?

b) Suppose the entrepreneur sells 100% equity. After selling the firm, what effort level does the entrepreneur choose? What is the value of the firm?

c) Suppose the entrepreneur sells β% equity. What effort level does the entrepreneur choose? Is it efficient?

problem: Consider an economy with three dates {t = 0, 1, 2}. A firm has assets in place that generate an output (profit) of either 40 in state L or 160 in state H at t = 2. Bothe states equally likely. At t = 1, the firm can implement another project. The implementation costs are 110 and the new project delivers an output of 120 in state L and 130 in state H at t = 2. The owner of the firm and investors are risk neutral. They maximize their expected payoff. The risk free rate is r = 0. The firm wants to issue equity to finance the new project.

a) What is the value of the firm (i) without and (ii) with the project at t = 0?

b) What percentage of equity does the firm sell to raise the investment cost at t = 1?

Now suppose prior to issuing equity the firm learns the true state of t = 2 at t = 1.

c) Does the firm issue equity in both states?

d) What is the value of the firm if equity is issued?

problem: Internal finance can avoid the agency costs of debt and equity finance. In practice it is the most important source of funding.

a) Discuss potential problems of internal finance.
b)  What are potential solutions?