eco204_summer_2009_practice_problem_22

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 22 Please help improve the course by sending me an email about typos or suggestions for improvements Question 1 In this question, you will analyze a strategy often practiced by firms near bankruptcy. It has been observed that such companies take greater risks because they feel that they are playing with someone else's money (i.e. the creditor's money). In finance, such a strategy is known as "going for broke". Suppose you're analyzing a leveraged ("indebted") company which has to pay its bondholders $100m or whatever it has if the company has less than $100m. After the bondholders are paid, the company pays the shareholders the difference between the total payoff of the company and the amount the bondholders get. Suppose the company faces two equally likely outcomes: boom or recession. The managers, acting on behest of the shareholders, can choose a low risk project: Low Risk Project Recession Boom Probability 0.5 0.5 Company Value $100m $200m = = = Stocks $0 $100m + + + Bonds $100m $100m (a) What is the EV of the company if it adopts this project? (b) What is the EV of the shareholders if the company adopts this project? Now suppose that another, riskier, project can be substituted for the low risk project: 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain High Risk Project Recession Boom Probability 0.5 0.5 Company Value $50m $240m = = = Stocks $0 $140m + + + Bonds $50m $100m (c) What is the EV of the company if it adopts the high risk project? (d) What is the EV of the shareholders if the company adopts the high risk project? (e) Which project maximizes the company's value? (f) Which project maximizes shareholder's value? Do you see a conflict of interest between managers and shareholders? Question 2 (2007 2008 Final Exam Question) In professional tennis, there is often a large gap between the first and second prize. A few years ago, some tennis players accused certain players of "splitting" the total pot 1 . For example, in a match with first prize $100,000 and second prize $32,000, it was alleged that the winner and loser would split the prize so each would get ($100,000 + $32,000)/2 = $66,000. (a) If a risk loving player believes she has a 5050 chance of winning, will she "split" a first prize of $100,000 and second prize of $32,000? Suppose Patrick Crafter has the following utility function: Utility 19 16 10 10 32 66 100 Prize Money ($ `000s) 1 The book Freakonomics discusses a similar scandal in Sumo wrestling. 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (b) If the first prize is $100,000 and the second prize is $32,000 and Patrick believes that he has a 5050 chance of winning, will he be willing to split the prizes? (c) For an upcoming match with Jen vs. Arthur, some tennis players wonder if Jen will split the prize with Arthur because she has been winning recent matches. What must Jen's probability of winning this match be for her to reject splitting the prize? Assume the prizes are $100,000 and $32,000 and Jen has the same utility function as Patrick Crafter in part (b). Question 3 (In this question you'll see why companies often settle out of court). Your company has been sued for $3.5m by a consumer injured using your product. The case has gone to trial and the jury has announced the verdict. Just before the verdict is announced, both sides' lawyers reach an outofcourt settlement for $0.5m. (a) If you were the consumer who has been hurt, would you accept the out of court settlement before the verdict is announced? (b) If you were the company, would you accept the out of court settlement before the verdict is announced? Question 4 Jenn Studios is thinking of producing a film "Ajax and the Order of Commerce". Analysts predict that the film can be a hit or a flop. Worse, it's hard to predict profits since the director of the movie Ajax Kurosawa is needy, temperamental, egoistical and totally lacking in financial discipline. Based on his previous films, "The Commerce Identity", "Commercinator 2", "Beautiful People with Beautiful Indifference Curves", "The Bald and the Beautiful" and "The EcoWatch Man", analysts estimate that production will have low and high costs with equal probability. The probability of high demand is 0.4. Jenn Studios estimates profits to be: Profits (Low Cost & Strong Demand ) = $80m Profits (Low Cost & Weak Demand ) = $40m Profits (High Cost & Strong Demand ) = $0m Profits (High Cost & Weak Demand ) = $80m 3 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (a) Draw the decision tree. (b) Should the studio produce the film? (c) Due to frivolous demands such as fresh squeezed Durian juice, access to VIP room at Circa, Brr! Yani at all hours of day--Jenn studio fears that Ajax's costs may spiral out of control. The studio now insists on a contractual clause giving it the right to terminate the project after the first $30m has been spent because by this time the studio will know for certain whether the costs are high or low. How much is this contractual clause worth? Question 5 Ecowoman has been sued by University of Tworontoo (UT) for charging students for past exams. The trial legal team for Ecowoman estimates the following judgments against her: ($1m, $0.6m, $0; 0.2, 0.5, 0.3) That is, she will be asked to pay U Tworontoo $1m with probability 0.2, $0.6m with probability 0.5 and $0m with probability 0.3. The trial legal team will charge Ecowoman $0.1m in legal fees. Alternatively, Ecowoman can engage another legal team to negotiate a settlement. The settlement legal team estimates that the University will seek: ($0.9m, $0.4m; 0.5, 0.5) That is, she will settle for $0.9m or $0.4m with equal probability, which Ecowoman can accept or reject. The settlement legal team charges $0.05m. Should Ecowoman go to trial or attempt to settle out of court? Hint: think about what Eco woman must do if she rejects the settlement. Question 6 In this problem you will make a decision under uncertainty where the choices are not mutually exclusive. I hope it makes you think harder about how to setup a problem. You are the CEO of a pharmaceuticals company "EconomicsMan Genetics". It has replicated EconomicsMan's genes 2 . The company must decide whether to commercialize EconomicsMan genes aimed at students studying for Economics tests and the final exam (just like you!) using a Biochemical or Biogenetic R&D approach. 2 No relation to Ecoman. 4 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Suppose the profits and probabilities of the competing approaches are: R&D Approach Investment Biochemical Biogenetic $10m $20m Outcome Large Success Small Success Success Failure Gross Profit Probabilities $90m $50m $200m $0m 0.7 0.3 0.2 0.8 Observe how the Biogenetic approach is more "risky": it has a high upside but also a low downside. In contrast, the Biochemical approach is less risky but also less lucrative. Find the best approach to commercialize the EconomicsMan's genes. In the event that both approaches are successful, assume that you can only take one product to market. Hint: the R&D programs are not mutually exclusive. 5 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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