Corporate Finance Fall 2023 Exercise Set 4
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Corporate Finance
Fall 2023
Exercise Set 4
Due Thursday, 11/2
This problem set consists of four questions. You can obtain a maximum of 40 points.
Question 1 [16 points]
Suppose an entrepreneur owns a firm which has two production opportunities. Technology A generates an output (net profit) of 20 in state 1, an output of 40 in state 2, and an output of 300 in state 3. All states are equally likely. Technology B generates an output of 30, 170, and 220, respectively. Because of technological constraints, the entrepreneur can only implement one
technology. The entrepreneur is risk neutral and maximizes his expected utility. The interest rate is 0%.
(a) Which technology should the entrepreneur implement and what is the value of the firm? [2p]
(b) Suppose the firm has debt with face value 20 outstanding. Which technology does the entrepreneur implement? [2p]
(c) Suppose the firm has debt with face value 140 outstanding. Which technology does the entrepreneur implement? [3p]
(d) Determine the expected utility of the entrepreneur as a function of the face value D for technology A and B, respectively. [4p]
(e) What is the maximal debt level such that the entrepreneur still chooses the efficient technology? [3p]
(f) Suppose the firm only has equity and 80% of shares are owned by retailed investors and the initial entrepreneur owns 20% of the firm. Which technology does theentrepreneur implement? [2p]
Question 2 [8 points]
Suppose an entrepreneur owns a firm with a production technology that generates the following revenue: R(e) = e 2 + 800e where revenue depends on his effort level e. The monetary cost of effort is given by C(e) = 3e2. The entrepreneuer is risk neutral and maximixes his expected utility.
(a) What effort level does the entrepreneur choose? What is the value (gross profit) of the firm? [2p]
(b) Suppose the entrepreneur sells 100% equity for the price equal gross profit. After
selling the firm,what effort level does the entrepreneur choose? What is the value of the firm? [2p]
(c) Suppose the entrepreneur sells β% equity. What effort level does the entrepreneur choose and is it efficient? If β=0.50 (i.e., 50%), what is the value of the firm? [4p]
Question 3 [12 points]
Consider an economy with three dates {t=0, 1, 2}. A firm has assets in place that generate an output (profit) of either 20 in state L or 180 in state H at t=2. Bothe states equally likely. At t=1, the firm can implement another project. The implementation costs are 120 and the new project delivers an output of 130 in state L and 140 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? [2p]
(b) What percentage of equity does the firm sell to raise the investment cost at t=1? [3p]
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? [4p]
(d) What is the value of the firm if equity is issued? [3p]
Question 4 [4 points]
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. [2p]
(b) What are potential solutions? [2p]
2023-11-02