Professor Marie-­‐Louise Viero Econ 423 Assignment 3 Due Thursday, March 12, 2015 at the beginning of class. Problem 1: Currently Technoswim is owned and managed by its founder. The value of the firm is $1,000. The following perks are available to the manager: Heat up
Office
Garage
Parking lot
Cost
100
200
400
Value to manager
100
150
200
a. What is the optimal decision about perks? b. Suppose now that there is instead 25% outside equity. Which decision will the manager make about perks? c. What is the agency cost of 25% outside equity? Problem 2: Consider the following principal-­‐agent problem: Tuques’R’Us needs a manager to run its operations. The company’s Board of Directors (Bod) can observe the company’s gross earnings π , but not how much effort e the manager puts in. Tuques’R’Us will have gross earnings of either π H =500 or π L =300. The manager can either work hard (W) or shirk (S). His effort determines the probability of high vs. low earnings: If €
4
1
e=W, prob( π H |W)= , while if e=S, prob( π H |S)= . 5
10
€
€
The manager’s utility when he is paid salary C and puts in effort e is u(C,e)=v(C)-­‐g(e), where C and g(W)=10, while g€(S)=5. The manager could find a job giving him net utility u
v(C)=
€
€
€
=5 elsewhere. €
€
When the manager signs his contract with the company, he does not yet know whether €
earnings will be high or low, so he maximizes his expected utility: prob(π H | e)(v(C H ) − g(e)) + (1 − prob(π H | e))(v(CL ) − g(e)) . The BoD maximizes the shareholders’ expected utility, which is given by the expected net profits of Tuques’R’Us: prob(π H | e)(π H − C H ) + (1 − prob(π H | e))(π L − CL ) . The BoD has to choose a compensation scheme ( C H , CL ) and which effort to implement. a. Suppose € first that the BoD could observe the manager’s effort. Write down the constraint the BoD faces when maximizing the shareholders’ expected utility. What € €
Professor Marie-­‐Louise Viero Econ 423 is the optimal compensation scheme if the BoD wants to implement e=W? What is the optimal compensation scheme if the BoD wants to implement e=S? What is the shareholders’ expected utility (i.e. net profits) when e=W and e=S, respectively? Which effort level should the BoD implement and what will the compensation scheme be? b. Suppose now that the manager’s effort is unobservable to the BoD. Write down the constraints the BoD faces if it wants to implement e=W. What is the optimal compensation scheme if the BoD wants to implement e=W? What is the optimal compensation scheme if the BoD wants to implement e=S? What is the shareholders’ expected utility (i.e. net profits) when e=W and e=S, respectively? Which effort level should the BoD implement and what will the compensation scheme be? c. What is the agency cost of not being able to observe the manager’s effort? Problem 3: A firm has two choose between two projects. Project 1 generates a cash flow of $200 in a boom and of $100 in a recession. Project 2 generates cash flows of $250 in a boom and of $0 in a recession. A boom and a recession are equally likely. The firm can only take one of the projects. The interest rate is r=0. a. Suppose first the firm has no debt outstanding. Which project will it choose? Why? b. Suppose now that the firm has debt outstanding with a face value of $60, which matures at the time when the cash flows occur. Calculate the values of equity, debt, and the firm for each of the two projects. Which project will the firm choose? c. What is this phenomenon called? d. What is the agency cost of debt? Problem 4: A firm’s cash flows one year from now will be either $2 million if there is a boom or $.96 million if there is a recession. A boom and a recession are equally likely. A new project is available to the firm: It requires an investment today of $.4 million and will generate a cash flow one year from now of $.68 million for sure. The interest rate is 10%. a. Suppose the firm has no debt. Will the project be taken by the all equity firm? b. Suppose now that the company has debt in the form of zero coupon bonds that expire in one year. The debt has face value F=$1.6 million. i. Calculate the value of the firm, the value of debt and the value of equity under a boom and under a recession with and without the project. ii. Calculate the expected value of equity with and without the project. What is the increase in equity value from taking the project? Is this greater or smaller than the cost of the project? Will the project be taken by the levered firm?