1. What is the rationale behind the minimax regret rule? What are some less formal and precise methods of dealing with uncertainty? When are these useful?
2. How does the adverse selection problem arise in the credit- card market? How do credit- card companies reduce the adverse selection problem that they face? To what complaint does this give rise?
3. An individual has to choose between investment A and investment B. The individual estimates that the income and probability of the income from each investment are as given in the following table:
Investment A Investment B
Income Probability Income Probability
4000 0.2 4000 0.3
5000 0.3 6000 0.4
6000 0.3 8000 0.3
7000 0.2
(a) Using Excel's statistical tools, calculate the standard deviation of the distribution of each investment. (b) Which of the two investments is more risky? (c) Which investment should the individual choose?
4. An individual is considering two investment projects. Project A will return a zero profi t if conditions are poor, a profi t of $ 4 if conditions are good, and a profi t of $ 8 if conditions are excellent. Project B will return a profi t of $ 2 if conditions are poor, a profi t of $ 3 if conditions are good, and a profi t of $ 4 if conditions are excellent. The probability distribution of conditions is as follows:
Conditions: Poor Good Excellent
Probability: 40% 50% 10%
(a) Using Excel, calculate the expected value of each project and identify the preferred project according to this criterion. (b) Assume that the individual's utility function for profit is U(X) = X - 0.05X2. Calculate the expected utility of each project and identify the preferred project according to this criterion. (c) Is this individual risk averse, risk neutral, or risk seeking? Why?
5. You're the manager of global opportunities for a U. S. manufacturer, who is considering expanding sales into Europe. Your market research has identified three potential market opportunities: England, France, and Germany. If you enter the English market, you have a 0.5 chance of big success (selling 100,000 units at a per- unit profit of $8), a 0.3 chance of moderate success (selling 60,000 units at a per- unit profit of $6), and a 0.2 chance of failure (selling nothing). If you enter the French market, you have a 0.4 chance of big success (selling 120,000 units at a per- unit profit of $9), a 0.4 chance of moderate success (selling 50,000 units at a per- unit profit of $6), and a 0.2 chance of failure (selling nothing). If you enter the German market, you have a 0.2 chance of huge success (selling 150,000 units at a per- unit profit of $ 10), a 0.5 chance of moderate success (selling 70,000 units at a per- unit profit of $ 6), and a 0.3 chance of failure (selling nothing). If you can enter only one market, and the cost of entering the market (regardless of which market you select) is $250,000, should you enter one of the European markets? If so, which one? If you enter, what is your expected profit?
6. Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for possible future product and estimates that the reservation value is $250,000. Your dealings on the second-hand market lead you to believe that there is a 0.4 chance a random buyer will pay $300,000, a 0.25 chance the buyer will pay $350,000, a 0.1 chance the buyer will pay 400,000, and a 0.25 chance it will not sell. If you must commit to a posted price, what price maximizes profits?
7. Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose you're trying to sell a company a new accounting system that will reduce costs by 10%. Instead of naming a price, you offer to give them the product in exchange for 50% of their cost savings. Describe the information asymmetry, the adverse selection problem, and why soft selling is a successful signal.
8. You need to hire some new employees to staff your start-up venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them:
Employee Value Probability
$50,000 0.25
$60,000 0.25
$70,000 0.25
$80,000 0.25
9. What is the expected value of five employees you hire?
(a) When can the NPV and the IRR methods of evaluating investment projects provide contradictory results? (b) How can this arise? (c) Which method should then be used? Why?
John Piderit, the general manager of the Western Tool Company, is considering introducing some new tools to the company's product line. The top management of the firm has identified three types of tools (referred to as projects A, B, and C). The various divisions of the firm have provided the data given in the following table on these three possible projects. The company has a limited capital budget of $ 2.4 million for the coming year. (a) Which project(s) would the firm undertake if it used the NPV investment criterion? (b) Is this the correct decision? Why?
10. The MacBurger Company, a chain of fast- food restaurants, expects to earn $ 200 million after taxes for the current year. The company has a policy of paying out half of its net after-tax income to the holders of the company's 100 million shares of common stock. A share of the common stock of the company currently sells for eight times current dividends.
Management and outside analysts expect the growth rate of earnings and dividends for the company to be 7.5 percent per year. Calculate the cost of equity capital to this fi rm.
11. The benefits and costs of an investment project (the purchase of a piece of machinery) are those given in the following table. In Excel, calculate net revenue, or the revenue from the investment minus the costs; the present value coefficient for every year; and the present value of the net revenue. Add together column F to get the net present value of the project. Should the firm purchase the machine?