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Risk-Benefit Analysis

Risk-Benefit Analysis

Tim Toyne Toy Company – Part I

Tim Toyne, president of the Tim Toyne Toy Company (a British firm) is currently trying to decide whether he should bring to market his new model toy truck called the T4 (Tim Toyne’s Toy Truck). Tim is uncertain about both the potential market for this new toy, and the unit cost of producing it. The estimated net profit to be earned by this new toy depends on these two uncertain factors in the following manner (profit is expressed in millions of pounds):

Unit Production Costs (pounds per unit)

1.0 1.5 2.0

Market Large 10.0 6.0 2.0
Small 2.0 -2.0 -4.0

Tim must decide within the next week whether or not he should go into production with the T4. If he decides against the introduction of the T4, he will invest his assets in a diversified mutual fund where the returns are also an uncertainty. Tim has asked you, his chief technical business analyst, to help him analyze this situation. You and your team view the market size and production cost as independent random variables and have assessed the following distributions for them:

Market Production
Size Probability Cost Probability

Large 0.6 1.0 0.2

Small 0.4 1.5 0.3

2.0 0.5

The returns from the mutual fund investment over the same period of time (in millions of pounds) has been assessed using Stuart Varney, a business and financial expert, with the following results:

P(< 4) = 0.99 P(< 1) =0 .75 P(< 0) = 0.50 P(< -1) = 0.25 P(< -2) = 0.01 To assist Tim in his decision, you ask him about his attitude toward risk and he replies, “If you take a big risk you will have a big loss but if you take a small risk you will have only a small loss. Therefore I am neutral toward risk!” He then asks you to have answers for the eight questions listed 1. Structure the influence diagram and decision tree and determine Tim’s optimal strategy, i.e. given the current state of information, what should Tim do 2. Risk Profiles (a) Create a risk profile and cumulative risk profile for Tim’s decision problem. (b) Is there any form of dominance exhibited (deterministic or stochastic) Explain 3. Perform a sensitivity analysis for the market size uncertainty. 4. If before making the decision Tim could obtain perfect information about market size and production cost, what is the most he should be willing to pay for such information 5. What is the most Tim should be willing to pay for perfect information about the market size alone 6. Suppose that Tim’s Director of Manufacturing, Max Factor, is very knowledgeable about manufacturing costs but is not very knowledgeable in probability assessment methods. Thus, you are to assist Max in developing the distribution for the production costs. List the questions you would ask and the corresponding answers that Max could provide. Graph your results and show/explain how this information is used in the decision tree. Note that you have the results in the basic problem; just show how these results were achieved through a probability assessment procedure. 7. After presenting the results of your analysis to Tim, his only comment was “I know I would like to have perfect information about the market, but I also know that is an impossibility. Why don’t you talk to Mike Morris, our Marketing Manager, to see what information he might have You meet with Mike and he says that in the next week he can conduct a QSMS (Quick and Sloppy Market Survey) at only a modest expense. A QSMS is quite crude and results simply in either a positive (looks promising) or negative (doesn’t look promising) result concerning the introduction of a new product such as the T4. Based upon past experience, Mike assesses a probability of 0.70 that the survey result will be positive if the actual potential market is large, and a probability of 0.20 that it will be positive if the market is small. What is the most Tim should pay for the QSMS Tim Toyne Toy Company – Part II After discussing the value of the QSMS with Tim, he accepts your overall approach but has doubts about your recommendations. You replied “But Tim, you said you were risk neutral” to which Tim says “Well, Mr. Chief Analyst, I think you better find out in a hurry.” Being a rather quick thinking sport yourself, you recall your wonderful experiences in class and quickly propose to Tim a series of questions about his attitude towards risk. The dialog goes as follows: You: I know you like to gamble on occasion so I am going to propose some gambling situations to you for your appraisal. Tim: Go right ahead, Mr. Chief Analyst. You: The first gamble is that I toss this fair coin and if it comes up heads you win 10 million pounds, but if it comes up tails you lose 4 million pounds. Tim: Sounds interesting. Should I call heads or tails You: It is interesting, but don’t call anything yet. I would like for you to have another alternative. Tim: Another alternative Why I don’t need another alternative, one is enough!! You: How much would you be just willing to take as a guaranteed amount so you don’t have to take the gamble Tim: 10 million pounds!!! You: Would you take 5 million pounds Tim: Yes, but I prefer 10 million. You: Would you give away your chance at the gamble for nothing Tim: Absolutely not!!! You: What if someone offered you 2 million pounds Would you take it Tim: Now that’s a tough choice. I’m not sure which one I’d take. You: Good, now lets try another. Tim: Another We haven’t finished the first one yet. You: Let’s put it aside for the time being and try the following gamble. Consider the same gamble again except this time if tails comes up you will win 2 million pounds. As before, you win 10 million pounds if its heads. Now how much would it take as a guaranteed amount such that you would be indifferent between the coin toss and the guaranteed amount Tim: I think I’m now getting the idea. I would say 4 million pounds would be about right. You: Now consider the following payoff from the toss of our fair coin. Heads you win 4 million pounds, tails you lose 4 million pounds. What minimum amount would you take for certain to give up the gamble Tim: Now this is the type of gamble that I really like. It would take an offer of at least one million pounds for me to give up the gamble. You: What if the payoffs were 2 million for heads and a loss of 4 million for tails Tim: As you Americans would say, “Not one damn cent.” You: Now let me ask the question a little differently. If I could guarantee you a loss of only one million pounds in lieu of a gamble where you could lose 4 million pounds or win nothing, what would the probability of winning the “ nothing “ have to be to make you indifferent between the gamble and the guaranteed loss Tim: Now that’s a tough question. I sure don’t like the gamble, especially not being able to win anything, but I also don’t like guaranteed losses. You: Would you like to think about it for a few minutes Tim: Yes ….. (two minute pause) ….. Now that I have thoroughly thought about it, I would say that the chances of winning should be close to 40% for me to be indifferent. Why all these hard questions anyway You: Thank you Tim, I’ll have your answers first thing in the morning. 8. Based on your questions and Tim’s answers, (a) what can you say about his attitude towards risk (b) resolve questions 1 and 4 using your new information on risk attitude.


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