eco204_summer_2009_practice_problem_22_solution

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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 Solutions 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? Answer: EV of company with low risk project = 0.5($100m) + 0.5($200m) = $150m (b) What is the EV of the shareholders if the company adopts this project? 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Answer: EV of shareholders with low risk project = 0.5($0) + 0.5($100m) = $50m Now suppose that another, riskier, project can be substituted for the low risk project: 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? Answer: EV of company with high risk project = 0.5($50m) + 0.5($240m) = $145m (d) What is the EV of the shareholders if the company adopts the high risk project? Answer: EV of shareholders with low risk project = 0.5($0) + 0.5($140m) = $70m (e) Which project maximizes the company's value? Answer: Since the company's EV of the low risk project is greater than the EV of the high risk project, assuming a risk neutral company, the company prefers the low risk project. (f) Which project maximizes shareholder's value? Do you see a conflict of interest between managers and shareholders? Answer: Since the shareholder's EV of the high risk project is greater than the EV of the low risk project, then assuming risk neutrality, shareholders prefer the high risk project. There is a conflict of interest in that the shareholders will press the company to take greater risks, when in fact it's in the company's interests to minimize risk. The conflict occurs because the shareholders are not the only owners of the company. 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain 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? Answer: Answer: Like any decision maker, the risk loving player will choose whichever option gives her greater utility. If she were to split the prize, she would receive $66,000 for sure. But observe that $66,000 is also the EV since: EV = 0.5($100,000 + $32,000) = $66,000 Now, a risk lover is someone for whom the U(EV) < EU. If she plays the match with an uncertain outcome, she'll have the EU while if she splits the prize, her utility is the U(EV). Being a risk lover, this shows that she'll derive greater utility from facing a 5050 gamble between $100,000 and $32,000 than the utility of having a split prize of $66,000. Thus, she will not split the prize. (b) Suppose Patrick Crafter has the following utility function: Utility 19 16 10 10 100 Prize Money ($ `000s) 32 66 (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? Answer: The EV of a 5050 chance of $100,000 and $32,000 is $66,000. Given the utility function above, Patrick's U(EV) > EU, since: 1 The book Freakonomics discusses a similar scandal in Sumo wrestling. 3 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain U(EV) = U($66,000) = 16 > 0.5(U($32,000) + U($100,000)) = 0.5(10 + 19) = 14.5 Thus, Patrick will split the prize (being risk averse, this is to be expected). (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). Answer: If Jen splits the prize, then since her utility is identical to Patrick's, her utility from splitting the prize is 16. Her utility from playing a match in which she receives $100,000 with probability p and $32,000 with probability (1 p) is: EU = p U($100,00) + (1 p) U($32,000) = EU = 19 p + (1 p) 10 EU = 9 p + 10 If Jen rejects splitting the prize, it's because the expected utility from the match is greater than the utility of the split (sure) prize: EU > 16 9p + 10 > 16 9p > 6 p > 6/9 = 2/3 Jen's probability of winning must be at least 2/3 for her to reject splitting the prize. 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. 4 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (a) If you were the consumer who has been hurt, would you accept the out of court settlement before the verdict is announced? Answer: Start by drawing a tree. Both parties need to decide whether to settle of hear the verdict. We don't know the probability of being found guilty: The (allegedly injured) consumer will settle if the settlement is greater than the value of the verdict 0.5 > EV Verdict 0.5 > p 3.5 + (1 p) 0 0.5 > p 3.5 0.5/3.5 > p p < 0.5/3.5 p < 0.14 (approx) That is, if the consumer thinks there is a lower than 14% chance of the jury announcing a guilty verdict, she will settle. Otherwise she will hear the verdict. 5 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (b) If you were the company, would you accept the out of court settlement before the verdict is announced? Answer: By the opposite argument, the company will settle if the cost of settling is lower than the cost from the expected verdict: 0.5 < p 3.5 + (1 p) 0 0.5 < p 3.5 0.5/3.5 < p p > 0.5/3.5 p > 0.14 (approx) That is, if the company thinks there is a greater than 14% chance of the jury announcing a guilty verdict, it will settle. Otherwise it will hear the verdict. 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 (a) Draw the decision tree. Answer: Here is the tree, where "S" denotes strong demand and "W" denotes weak demand: 6 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain (b) Should the studio produce the film? Answer: Assuming the studio is risk neutral, it needs to compute the EV of not making the movie vs. the EV of making the movie: The EV of making the movie is: EV(Movie) = 0.5 EV(Low Cost) + 0.5 EV(High Cost) EV(Movie) = 0.5[0.4 $80 + 0.6 $40] + 0.5[0.4 $0 + 0.6($80m)] 7 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain EV(Movie) = 0.5($56m) + 0.5($48m) EV(Movie) = $28m $24m EV(Movie) = $4m. Since EV(Movie) > EV(Don't Make Movie), Jenn should make the movie. Ajax will be famous. Nice. (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? Answer: This type of contractual clause is common in construction, defense, and projects with uncertainty. In fact, one of the reasons why many cities have "bland" architecture is because there is very little uncertainty in repeating a design. As such, many real estate investment banks, like JP Morgan, do not favor novel architecture because they fear the potential high costs stemming from uncertainty. One way companies protect themselves against uncertainty is through a contractual clause which gives them the right to terminate the project if they think the costs are liable to be high. If the contractor "burns" through funding quickly, then it's plausible to argue that costs are likely to be high. Let's draw a tree with the contractual clause: 8 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Note how after the first $30m is spent the studio has the option to stop and absorb a loss of $30m or the studio can continue and face demand uncertainty. Now, we need to compute the EV of making the movie with the contractual clause. Start from the end of the tree. Say that after the first $30 are spent, the studio knows costs are low (for example, maybe the $30m were spent slowly this of course raises a game theory issue that that Ajax can deliberately spend slowly at first to "fool" the studio that costs are low). If costs are low, the studio can stop and the payoff will be $30m. If it continues, it will expect to make: EV of continuing if cost low = 0.4($80m) + 0.6($40m) = $56m If the studio stops, the studio will make a loss of $30m. Thus, if costs are low, the studio should not exercise the clause and produce the movie. Hence, the EV of low cost is $56m. On the other hand, if costs are high then if the studio makes the movie: EV go if cost high = 0.4($0m) + 0.6 ($80m) = $48m This is worse than exercising the clause and incurring a loss of $30m. Thus, the EV of making the movie is: EV Making Movie = 0.5($56m) + 0.5($30m) = $13m. Thus, the studio should make the movie. Ajax will be famous. Nice. However, this solution so different from the previous question in one respect: the studio has a contingent plan. Produce the movie and watch what happens over the first $30m. If costs are revealed to be low, continue production. But if costs are revealed to be high, cease production. Note how the EV with the clause is $9m higher than the EV without the clause. Hence, inserting this contractual clause is worth $9m for the studio. On the flip side, it implies that legal services for writing this clause should not cost more than $9m. 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. 9 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain 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. Answer: Firstly, that fiend ecowoman shouldn't have charged students for old exams. What a nefarious character. Let's see what her options are. The case can go to trial or attempt a settlement. Note that negotiations over settlement need not be successful and are not binding (this is why many labor disputes have a binding arbitration clause). What you should be careful about is the fact that if a settlement is rejected, the case goes to trial, but you shouldn't "draw" the trial tree again you simply need to know the EV of trial plus settlement expenses if the offer is rejected. The decision tree is: Observe how if Ecowoman rejects any settlement then she has no choice but to go to trial. Observe also how the legal fees have been added to amounts she may have to pay does it matter whether we subtract the legal fees before or after the uncertainty? (Answer: no). 10 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Computing the numbers, we see her optimal decision is: Here's what's happening: if the University asks for a high offer ($0.9m) Ecowoman is better off rejecting that demand as the EV of going to trial is still lower than $0.9m. On the other hand, if the University asks for a low offer ($0.4m) Ecowoman is better off accepting that demand as the EV of going to trial is higher than $0.4m. Thus, the EV of trying to settle is $0.55m which is lower than EV of going to trial. She should swallow her pride and settle. 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. Suppose the profits and probabilities of the competing approaches are: R&D Approach Investment Biochemical 2 Outcome Large Success Gross Profit Probabilities $90m 0.7 $10m No relation to Ecoman. 11 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain Biogenetic $20m Small Success Success Failure $50m $200m $0m 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. Answer: Because the approaches are not mutually exclusive, the options available are: Do not invest at all Only Biochemical Only Biogenetic Biochemical and Biogenetic simultaneously Biochemical first followed by Biogenetic Biogenetic first followed by Biochemical. The decision tree is: 12 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain We need to give a value for each of these branches and choose the highest value. This entails drawing trees for each of these branches. "No R&D" Branch: The value is $0. "Biochemical Only" Branch: I will skip the decision tree for the biochemical branch: EV(Biochemical only) = 0.7($90m) + 0.3($50m) $10m = $68m "Biogenetic Only" Branch: I will skip the decision tree for the biogenetic branch: EV(Biogenetic only) = 0.2($200m) $20m = $20m Biogenetic & Biochemical Simultaneously Branch: There are four uncertain possibilities with simultaneous R&D programs, each of which cost a total of $30m: Biochemical Large Success Small Success Large Success Small Success Biogenetic Success Success Failure Failure Probabilities 0.7*0.2 = 0.14 0.3*0.2 = 0.06 0.7*0.8 = 0.56 0.3*0.8 = 0.24 Here we have used the fact that for two independent events A and B: P(Event A & Event B) = P(A) P(B). These possibilities are drawn in order below: 13 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain The numbers are net profits (gross profits total cost). Here is what's happening branch by branch: Biochemical Large Success & Biogenetic Success: If both programs succeed we have to decide which one to commercialize (recall you can only commercialize one). If we commercialize Biochemical we get $60m and if we commercialize Biogenetic we get $170m. Thus, we choose to commercialize Biogenetic notice how we fill the value of the decision in the decision node. Biochemical Small Success & Biogenetic Success: With two successes, we again face a decision. We choose to commercialize Biogenetics because it has the greater value notice how we fill the value of the decision in the decision node. Biochemical Large Success & Biogenetic Failure: There is no decision here with a failure in Biogenetic R&D (with gross profits $0) and a large success in Biochemical, we commercialize biochemical. The value of this $90m $30m = $60m. Biochemical Small Success & Biogenetic Failure: There is no decision here with a failure in Biogenetic R&D (with gross profits $0) and a small success in Biochemical, we commercialize biochemical. The value of this $50m $30m = $20m. Since these four possibilities are uncertain, the EV of simultaneous development is: EV(Biochemical and Biogenetic R&D) = 0.14($170m) + 0.06($170m) + 0.56($60m) + 0.24($20m) 14 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain EV(Biochemical and Biogenetic R&D) = $72.4m. "Sequential R&D: Biochemical First" Branch: Start with biochemical. If it is a large success, you can go to market and make a net profit of $80m. Or, you can pursue biogenetic (because if it succeeds, you could make $170m!) and see what happens. If so, biogenetic could succeed and you make net profit of $170m ($200 $10 $20), or, biogenetic could fail, in which case you can "go back" to the biochemical large success and net $80 $20 = $60m. Note that even though the outcome of a biogenetic failure is $0m, because you have the option of commercializing biochemical the value of biogenetic failure is not 0. The remainder of the tree follows the same logic. Thus: EV(Biochemical first) = $72.4m Indeed, there is no added value by doing biochemical first versus doing biochemical and biogenetic simultaneously. (Maybe you want to think why this is). 15 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain "Sequential R&D: Biogenetic First" Branch The tree follows the same logic as biochemical first. The big difference is that if you have a biogenetic success, you don't need to explore the option of biochemical R&D because the value of a large success of a biochemical product is always less than value of biogenetic success. Thus: EV(Biogenetic first) = $74.4m In sum: Of all the options, Sequential R&D with biogenetics is the best R&D decision. If it succeeds, take product to market. If it fails, pursue biochemical R&D. 16 ...
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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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