Chapter 6: Business Analytics_ Data Analysis _ Decision Making

1. Which of the following is true with regard to a good decision? a. It ensures that good outcomes will be obtained b. It accounts for unlucky outcomes c. It should be independent of the sequencing of uncertainties an ...

1. Which of the following is true with regard to a good decision? a. It ensures that good outcomes will be obtained b. It accounts for unlucky outcomes c. It should be independent of the sequencing of uncertainties and decisions d. It should incorporate all information about uncertainties and alternatives e. All of these options ANSWER: d 2. All problems related to decision making under uncertainty have three common elements: a. the mean, median, and mode b. the set of decisions, the cost of each decision and the profit that can be made from each decision c. the set of possible outcomes, the set of decision variables and the constraints d. the set of decisions, the set of possible outcomes, and a value model that prescribes results e. None of these options ANSWER: d 3. The preferred criterion in decision making is. a. maximin b. maximax c. EMV d. None of these options ANSWER: c 4. Expected monetary value (EMV) is: a. the average or expected value of the decision if you knew what would happen ahead of time b. the weighted average of possible monetary values, weighted by their probabilities c. the average or expected value of the information if it was completely accurate d. the amount that you would lose by not picking the best alternative e. a decision criterion that places an equal amount on all states of nature ANSWER: b 5. A payoff table lists the monetary values (profit or loss) for each possible and each possible _______________. a. mean and standard deviation b. decision and utility c. decision and outcome d. risk profile and outcome e. None of these options ANSWER: c Copyright Cengage Learning. Powered by Cognero. Page 1 Name: Class: Date: Chapter 066. There are three types of nodes that are used with the decision trees. They are the: a. mean nodes, variance nodes, and the standard deviation nodes b. probability nodes, risk nodes, and the expected value nodes c. supply nodes, demand nodes, and the expected value nodes d. decision nodes, probability nodes, and end nodes. e. horizontal nodes, vertical nodes, and the diagonal nodes ANSWER: d 7. In decision trees, time: a. is constant b. proceeds from bottom to top c. proceeds from top to bottom d. proceeds from right to left e. proceeds from left to right ANSWER: e 8. In decision trees, probabilities are listed on probability branches. These probabilities may be events that have already been obse a. marginal due to b. conditional on c. averaged with d. increased by e. the same as ANSWER: b 9. If all monetary values in a decision problem are costs, then it is customary to list them as __________ values in a cost table. a. positive b. negative c. either positive or negative d. All of these options ANSWER: a 10. A risk profile lists: a. all possible monetary values and their corresponding probabilities b. all possible outcomes and their corresponding utility c. all options and their possible outcomes d. the nodes and branches for each possible outcome e. None of these options ANSWER: a Copyright Cengage Learning. Powered by Cognero. Page 2 Name: Class: Date: Chapter 0611. In a single-stage decision tree problem, all ___________ are made first and then all ___________ is (are) resolved. a. decisions; uncertainty b. calculations; probabilities c. EMV calculations; posterior probabilities d. likelihoods; posterior probabilities e. prior probabilities; joint probabilities ANSWER: a 12. The solution procedure that was introduced in the book for decision trees is called the: a. folding diagram b. single-stage method c. risk profile method d. precision tree method e. folding back on the tree ANSWER: e 13. In making decisions, we choose the decision with the largest expected monetary value. a. True b. False ANSWER: True 14. In a single-stage decision problem, a single decision is made first, and then all uncertainty is resolved. a. True b. False ANSWER: False 15. In a multistage decision problem, decisions and outcomes alternate. That is, a decision maker makes a decision, then some un resolved, and so on. a. True b. False ANSWER: True 16. Decision trees are composed of nodes (circles, squares, and triangles) and branches (lines). a. True b. False ANSWER: True 17. In decision trees, a decision node (a square) is a time when the result of an uncertain event becomes known. a. True b. False ANSWER: False Copyright Cengage Learning. Powered by Cognero. Page 3 Name: Class: Date: Chapter 0618. In decision trees, a probability node (a circle) is a time when the decision maker makes a decision. a. True b. False ANSWER: False 19. In decision trees, an end node (a triangle) indicates that the problem is completed; that is, all decisions have been made, all unc a. True b. False ANSWER: True 20. In general, the expected monetary values (EMV) represent possible payoffs. a. True b. False ANSWER: True 21. If is the monetary value corresponding to outcome i and is its probability, then the expected monetary value is defined as a. True b. False ANSWER: False 22. For each possible decision and each possible outcome, the payoff table lists the monetary value earned by an organization, wh a. True b. False ANSWER: True 23. The expected monetary value (EMV) criterion is sometimes referred to as “playing the averages” and for that reason should only a. True b. False ANSWER: False 24. A risk profile lists all possible monetary values and their corresponding probabilities. a. True b. False ANSWER: True 25. When you use the expected monetary value (EMV) criterion, you are not using all of the information that is shown in the risk pro a. True b. False ANSWER: True A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future prof land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory Copyright Cengage Learning. Powered by Cognero. Page 4 Name: Class: Date: Chapter 06however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geolo 26. (A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and in (B) What should the landowner do? Why? (C) Suppose the landowner is uncertain about the reliability of her geologist friend’s estimate of the probability that oil will be fou decision? (D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cos variables is the expected value most sensitive? (E) What does the risk profile show about the relative risk levels for the landowner’s two options? (F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn’t feel th with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilitie which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility (G) Apply the risk tolerance given in your answer to the previous question to the landowner’s decision tree in (A). What is the o (H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that informa ANSWER: (A) (B) The decision tree shows the best option is to conduct the exploration on her own. This is option pr (C) Copyright Cengage Learning. Powered by Cognero. Page 5 Name: Class: Date: Chapter 06No, the strategy region chart above shows the best option is to conduct the exploration on her own ov (D) Copyright Cengage Learning. Powered by Cognero. Page 6 Name: Class: Date: Chapter 06The tornado chart above shows that the future profits is the input variable to which the expected value (E) The risk profile above shows that the option of developing the field on her own is much more risky, as (F) R=$1,500,000 (G) Copyright Cengage Learning. Powered by Cognero. Page 7 Name: Class: Date: Chapter 06The decision tree shows the best option in this case is to lease out the prospect. This is option provide (H) Copyright Cengage Learning. Powered by Cognero. Page 8 Name: Class: Date: Chapter 06A construction company has obtained a contract for a highway project and will need to lease an additional road grader for a mo grader: 1) lease an older grader for $8,500, or 2) lease a newer grader for $10,000. The newer grader is still under warranty, so t it leases the older grader. The construction company’s maintenance foreman believes there is a 30% chance that there will be n be needed, and a 25% chance that significant repairs ($5,000) might be required. 27. (A) Construct a decision tree to help the company make its decision. Make sure to label all decision and chance nodes and inc (B) What is the best lease option? Why? (C) Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before th company would pay for the inspection? ANSWER: (A) (B) The decision tree shows the new grader option is better because it provides a slightly lower expected cost ($1 (C) The revised decision tree below shows that if the repair cost for the old grader is determined ahead of time, th should be willing to pay. Copyright Cengage Learning. Powered by Cognero. Page 9 Name: Class: Date: Chapter 06The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC’s alternative million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, r 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below. MKT expands MKT stable MKT contracts Build new plant $1,650,000 $1,000,000 $450,000 Expand plant $1,000,000 $850,000 $450,000 Do nothing $0 $0 $0 28. Formulate a payoff table that specifies WTC’s payoff (in dollars) associated with each possible decision and each market condi ANSWER: MKT expands MKT stable MKT contracts Build new plant $650,000 $0 - $550,000 Expand plant $400,000 $250,000 - $150,000 Do nothing $0 $0 $0 29. Generate a risk profile for each of WTC’s possible decisions in this problem. Characterize the differences in risk for the different ANSWER: There is obviously no risk from doing nothing. The risk profile above shows that the option of constructing a new p negative payoff and the dispersion of the outcomes along the horizontal axis. Copyright Cengage Learning. Powered by Cognero. Page 10 Name: Class: Date: Chapter 06A department store in a small town is in the process of budget planning and will be building a decision tree to select the best op base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 p 30. What is the probability that a randomly selected individual from this population earns less than $50,000 per year? ANSWER: 0.64 A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six mo footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Fur next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footb presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units. Demand (in hundreds) Probability 4 0.30 5 0.50 6 0.20 31. Formulate a payoff table that specifies the contribution to profit (in dollars) from the sales of footballs by this chain for each poss ANSWER: Payoff table D = 400 D = 500 D = 600 Order 400 $18,000 $18,000 $18,000 Order 500 $17,000 $22,500 $22,500 Order 600 $16,000 $24,500 $27,000 Copyright Cengage Learning. Powered by Cognero. Page 11 Name: Class: Date: Chapter 0632. Generate a risk profile for each possible decision in this problem. Would this have any impact on your decision? ANSWER: The risk profile above shows that the option of ordering 500 footballs is less risky, relative to the option of ordering ordering 500 footballs yields only slightly lower EMV, it might be preferable to take that option. A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not app information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loa 33. Construct a decision tree to help the credit union decide whether or not to make the loan. Make sure to label all decision and ch ANSWER: 34. What should the credit union do? What is their expected profit? ANSWER: The tree above shows that the best alternative is not to make the loan, and to invest the funds in bonds earning 6 Copyright Cengage Learning. Powered by Cognero. Page 12 Name: Class: Date: Chapter 06Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amo each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damag Distribution of Accident Types and Corresponding Damage Amounts Type of Accident Conditional Probability Damage to Car Minor 0.60 $200 Moderate 0.20 $1,000 Serious 0.10 $4,000 Catastrophic 0.10 $30,000 35. Formulate a payoff table that specifies the cost (in dollars) associated with each possible decision and type of accident. ANSWER: Input Data Probability of being in an accident 0.05 Collision Insurance Premium $170 Deductible Amount $300 Payoff Table No Minor Moderate Serious Catastrophic Accident Accident Accident Accident Accident Purchase Collision Insurance $170 $370 $470 $470 $470 Do Not Purchase Collision Insurance $0 $200 $1,000 $4,000 $30,000 Probability 0.95 0.03 0.01 0.005 0.005 36. Which of these sensitivity analysis charts is most useful in determining whether the optimal decision changes over the range of a. Strategy region chart b. Tornado chart c. Spider chart d. All of these options e. None of these options ANSWER: a 37. When the lines for two alternatives cross on a strategy region chart, this shows: a. A change in which decision alternative is optimal b. The point at which a decision was made c. The point where the rate of change in expected value is zero d. Resolution of the uncertainty about the input variable e. None of these options ANSWER: a Copyright Cengage Learning. Powered by Cognero. Page 13 Name: Class: Date: Chapter 0638. Which of the following can be obtained with a tornado chart? a. The absolute change in expected value resulting from the change in each input variable b. The percent change in expected value resulting from the change in each input variable c. A ranking of the relative sensitivity of expected value to each input variable d. None of these options e. All of these options ANSWER: e 39. The sensitivity of the expected value to changes in the input variables can be inferred from a spider chart by observing: a. The height of the line above the horizontal axis for each variable b. The length of the line for each variable c. The slope of the line for each variable d. The color of the line for each variable e. None of these options ANSWER: c 40. Tornado charts and spider charts can be used to determine which input variables have the most impact on the expected value in a. True b. False ANSWER: True 41. A strategy region chart is useful for seeing whether the decision changes over the range of the input variable. a. True b. False ANSWER: True 42. The slope of the lines for the input variables on a tornado chart indicates their relative impact on the expected value a. True b. False ANSWER: False 43. A spider chart shows both the range (as a percentage) of the variability of the input variables as well as the resulting changes in a. True b. False ANSWER: True A recent MBA graduate is considering an offer of employment at a biotech company, where she has been offered stock options of stock either one year from now or two years from now at a price of $50, which is the current market price of the stock. If the at the current price, thereby making a risk-free profit. On the other hand, if the price of the stock has dropped below $50, she w market information, she estimates that the stock price in the first year will either go up by 25% from its current price, with proba wait to see what will happen in the second year. If she decides to wait, the in the second year, the stock price will again go up o end of the first year. Copyright Cengage Learning. Powered by Cognero. Page 14 Name: Class: Date: Chapter 0644. (A) Construct a decision tree to help her model her option decision making. Make sure to label all decision and chance nodes a (B) What is the optimal decision making policy regarding the options in all possible scenarios over the next two years? (C) What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs) (D) If her estimates of the increases/decreases or probabilities are inaccurate, could the options have a negative EMV? ANSWER: (A) Copyright Cengage Learning. Powered by Cognero. Page 15 Name: Class: Date: Chapter 06​ (B)The tree above shows that whether the price goes up or down in the first year, she should wait and not exerc whether the price goes up or down. However, if the price has gone down, she will only want to exercise the option expire. (C)The expected value of the option on one share, as shown in the above decision tree, is $10.05. Therefore the (D)No, the ability to make the decision not to exercise the option at every point in time protects the option-holde Copyright Cengage Learning. Powered by Cognero. Page 16 Name: Class: Date: Chapter 0645. Tyson Manufacturing (a maker of industrial products) is interested in marketing a new product. The company must decide whet two tables that represent the information related to the estimated probability distribution of the cost of one unit of this product un Cost under “Make” alternative. Cost under “Buy” alternative. Cost per unit Probability Cost per unit Probability $40 0.20 $40 0.15 $45 0.25 $45 0.30 $50 0.35 $50 0.40 $55 0.20 $55 0.15 Assuming that Tyson seeks to minimize the expected unit cost of manufacturing of buying the new product, should the compan ANSWER: The expected value is the same in either case: Make = (40 0.20) + (45 0.25) + (50 0.35) + (55 0.20) = $47.75 Buy = (40 0.15) + (45 0.30) + (50 0.40) + (55 0.15) = $47.75 Copyright Cengage Learning. Powered by Cognero. Page 17 Name: Class: Date: Chapter 06The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC’s alternative million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, r 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below. MKT expands MKT stable MKT contracts Build new plant $1,650,000 $1,000,000 $450,000 Expand plant $1,000,000 $850,000 $450,000 Do nothing $0 $0 $0 46. Construct a decision tree to identify the course of action that maximizes WTC’s expected profit. Make sure to label all decision ANSWER: 47. What course of action is optimal for WTC? What is the expected profit in that case? ANSWER: The best course of action with the highest expected value is to expand the existing plant. The expected value of t Copyright Cengage Learning. Powered by Cognero. Page 18 Name: Class: Date: Chapter 06The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential domina building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station ow thousands of dollars. Audience Format A1 A2 A3 Rock $ 110 $ 80 $ 70 Country $ 90 $ 120 $ 50 Rap $ 70 $ 60 $ 140 Probability 0.3 0.5 0.2 48. The station is most uncertain about the average monthly revenue associated with the rock format and an A1 audience. Construc optimal decision to select the country format change at any point in this range? ANSWER: Yes, the strategy region chart above shows the optimal format will change from country to rock if the rock format A 49. As the average monthly revenue associated with the rock format and an A1 audience varies between $85,000 to about $140,000 ANSWER: The maximum expected revenue stays constant at $97,000 because country is the optimal format and the rock fo Copyright Cengage Learning. Powered by Cognero. Page 19 Name: Class: Date: Chapter 0650. As the average monthly revenue associated with the rock format and an A1 audience varies between about $142,500 and $200, ANSWER: The maximum expected revenue stays increases linearly from $97,000 because rock becomes the optimal format Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amo each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damag Distribution of Accident Types and Corresponding Damage Amounts Type of Accident Conditional Probability Damage to Car Minor 0.60 $200 Moderate 0.20 $1,000 Serious 0.10 $4,000 Catastrophic 0.10 $30,000 51. Generate a statistical summary and risk profile for each of Mrs. Rich’s possible decisions. Does this information impact her dec ANSWER: The statistical summary above shows much more risk with the “Don’t Buy Insurance” alternative, due to the much purchase insurance, as indicated by greater dispersion of the outcomes. Since the “Buy Insurance” alternative alr Copyright Cengage Learning. Powered by Cognero. Page 20 Name: Class: Date: Chapter 0652. Perform a sensitivity analysis on the optimal decision and summarize your findings. Vary the probability of being in an accident response to which model inputs is the expected total cost value most sensitive? ANSWER: The tornado chart above shows that the probability of being in an accident is the input variable to which the expec band and is positioned at the top of the chart. The spider chart supports this finding, since the P(accident) line ha Copyright Cengage Learning. Powered by Cognero. Page 21 Name: Class: Date: Chapter 0653. What impact, if any, does the probability of being in an accident have on her decision? Briefly explain your answer ANSWER: If the probability of being in an accident were to fall much below 5%, Mrs. Rich would prefer not to purchase the co lower expected cost) the “Buy Insurance” line in that range. She doesn’t need insurance if her accident risk is at s Copyright Cengage Learning. Powered by Cognero. Page 22 Name: Class: Date: Chapter 0654. What impact, if any, does the insurance premium cost have on her decision? Briefly explain your answer ANSWER: If the insurance premium were to increase much above $175, Mrs. Rich would be better off not purchasing the coll lower expected cost) the “Buy Insurance” line in that range. Above $175, the insurance premium is too expensive, Copyright Cengage Learning. Powered by Cognero. Page 23 Name: Class: Date: Chapter 0655. What impact, if any, does the insurance deductible amount have on her decision? Briefly explain your answer ANSWER: If the insurance deductible were to increase to about $500, Mrs. Rich would be better off not purchasing the collisi lower expected cost) the “Buy Insurance” line in that range. Above $500, her out-of-pocket expenses with insuran 56. Why is there a kink in the line for the “Buy Insurance” line in the above strategy region chart? ANSWER: Recall that the minor accident damage amount is $200. Therefore, if she is in a minor accident and the deductible deductible. If the deductible is below $200, the opposite is true. Accordingly, we see differing sensitivity (different l 57. In the nomenclature of Bayes’ Rule, which of the following are probabilities that are conditioned on information that is obtained? a. Prior probabilities b. Posterior probabilities c. Marginal probabilities d. Objective probabilities e. Subjective probabilities ANSWER: b Copyright Cengage Learning. Powered by Cognero. Page 24 Name: Class: Date: Chapter 0658. Bayes’ Rule is useful for? a. Value of Sample Information b. Value of Perfect Information c. Sensitivity Analysis d. All of these options e. None of these options ANSWER: a 59. The expected value of sample information (EVSI) is equal to: a. EMV with posterior information – EMV with prior information b. EMV with free perfect information – EMV free information c. EMV with perfect information – EMV without information d. EMV with free information – EMV without information e. None of these options ANSWER: d 60. The expected value of perfect information (EVPI) is equal to: a. EMV with posterior information – EMV with prior information b. EMV with free perfect information – EMV with information c. EMV with free perfect information – EMV with no information d. EMV with perfect information – EMV with less than perfect information ANSWER: c 61. Bayes’ rule can be used for updating the probability of an uncertain outcome after observing the results of a test or study. a. True b. False ANSWER: True 62. Prior probabilities are sometimes called likelihoods, the probabilities that are influenced by information about the outcome of an a. True b. False ANSWER: False 63. Bayes’ is useful in determining the value of perfect information (EVPI). a. True b. False ANSWER: False Copyright Cengage Learning. Powered by Cognero. Page 25 Name: Class: Date: Chapter 06A department store in a small town is in the process of budget planning and will be building a decision tree to select the best op base of 1500 individuals, 700 of which are women. Data shows that 240 of the women in this population earn at least $50,000 p 64. If a randomly selected individual is observed to earn at least $50,000 per year, what is the probability that this person is a man? ANSWER: 0.5556 65. If a randomly selected individual is observed to earn less than $50,000 per year, what is the probability that this person is a wom ANSWER: 0.4792 A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not app information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loa 66. Suppose that an actual (not perfectly reliable) credit report has the following characteristics based on historical data; in cases wh on the basis of the credit investigation was 80%, while in cases where the customer defaulted on the approved loan, the probab information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions? ANSWER: Copyright Cengage Learning. Powered by Cognero. Page 26 Name: Class: Date: Chapter 06A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each s 25% turn out to be hits and 75% turn out to be flops. 67. Suppose that an actual (not perfectly reliable) market research report has the following characteristics based on historical data program to be a hit, and if the program is actually going to be a flop, there is a 20% chance that the market researchers will pre or a flop, given the market research report? ANSWER: Copyright Cengage Learning. Powered by Cognero. Page 27 Name: Class: Date: Chapter 06Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this transportation costs) of the ore in the future. The metallurgical properties of the ore would be classified as either “high grade” or “low grade”. Southport’s geologists have est Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport’s econ (“high” or “low” net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in mill High Grade metallurgy (p=0.7) Prices Probability Outcome High 0.8 40 Low 0.2 -$20 68. Since the core test can only sample a small part of the mine, Southport’s geologists believe it is somewhat unrealistic to view i metallurgical properties of the ore are actually High Grade, then the probability that this test will return “favorable” results is 0.95 0.25. Otherwise, the test results will be considered “unfavorable”. Given this information, what are the posterior probabilities that ANSWER: Copyright Cengage Learning. Powered by Cognero. Page 28 Name: Class: Date: Chapter 0669. Which of the following statements are true? a. Sensitivity analysis is a process of seeing how optimal decision and EMV vary when one or more inputs vary. b. Multistage decision problem is one where decisions and observations of uncertain outcomes alternate. c. Contingency plan is a strategy in a multistage decision problem that specifies which decision to make for each possible outc d. All of the above e. None of the above ANSWER: d 70. The expected value of perfect information (EVPI) is the difference between the EMV with perfect information and the EMV with n a. True b. False ANSWER: True 71. The expected value of sample information (EVSI) is the difference between the EMV we can obtain with sample information and a. True b. False ANSWER: True 72. The expected value of perfect information (EVPI) is the most the decision maker would be willing to pay for the sample informat a. True b. False ANSWER: False 73. The expected value of perfect information (EVPI) is irrelevant concept since perfect information is almost never available at any a. True b. False ANSWER: False A nuclear power company is deciding whether to build a nuclear plant at Chico Canyon or at Pleasantville. The cost of building t and an earthquake occurs at Chico during the next 5 years, construction will be terminated and the company will lose $14 millio there is a 20% chance that an earthquake will occur at Chico during the next 5 years. 74. (A) Construct a decision tree to help the power company decide what to do. Make sure to label all decision and chance nodes a (B) Where should the power company build the plant? What is the expected cost? (C) Suppose that a geologist (and his team) can be hired to analyze the fault structure at Chico Canyon. He will either predict w should be willing to pay for his services? (D) Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologist’s past re and no earthquake on 85% of the occasions for which an earthquake will not occur. Given this information, what are the posterio (E) Should the company hire the geologist if his fee is $1.5M? ANSWER: (A) Copyright Cengage Learning. Powered by Cognero. Page 29 Name: Class: Date: Chapter 06(B) The plant should be built in Chico Canyon. Even with the earthquake uncertainty, the expected cost is still low (C) The tree above shows that if the geologist predicts an earthquake, the company should locate in Pleasantville, wh $15.2m with the geologist’s information. Thus, the EVPI is $2.8M, which is the most the company should be willin (D) Copyright Cengage Learning. Powered by Cognero. Page 30 Name: Class: Date: Chapter 06(E) The tree above shows that the geologist’s information is still very valuable, even in the imperfect case. The inform would be justified in paying the geologist’s fee. Copyright Cengage Learning. Powered by Cognero. Page 31 Name: Class: Date: Chapter 06A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six mo footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Fur next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footb presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units. Demand (in hundreds) Probability 4 0.30 5 0.50 6 0.20 75. Construct a decision tree to identify the buyer’s course of action that maximizes the expected profit earned by the chain from th ANSWER: 76. What is the optimal strategy for order quantity, and what is the expected profit in that case? ANSWER: The best option in this case is to order 600 footballs. This option has an expected value of $20,950. Copyright Cengage Learning. Powered by Cognero. Page 32 Name: Class: Date: Chapter 06The following is a payoff table giving profits for various situations: States of Nature A B C Alternative 1 160 120 140 Alternative 2 150 140 90 Alternative 3 120 160 80 Do Nothing 0 0 0 The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2 respectively. 77. What are the expected payoffs for the three alternatives? ANSWER: A: 0.3*160+0.5*120+0.2*140=136 B: 0.3*150+0.5*140+0.2*90=133 A: 0.3*120+0.5*160+0.2*80=132 78. What else might one consider in choosing from among these alternatives? ANSWER: Risk should be considered, through an examination of the risk profile of alternatives. Copyright Cengage Learning. Powered by Cognero. Page 33 Name: Class: Date: Chapter 06The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential domina building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station ow thousands of dollars. Audience Format A1 A2 A3 Rock $ 110 $ 80 $ 70 Country $ 90 $ 120 $ 50 Rap $ 70 $ 60 $ 140 Probability 0.3 0.5 0.2 79. Construct a decision tree to help the station identify its optimal format. Make sure to label all decision and chance nodes and in ANSWER: 80. What format is optimal? What is the expected profit in that case? ANSWER: The tree above shows that the best course of action with the highest expected value is to select the country forma Copyright Cengage Learning. Powered by Cognero. Page 34 Name: Class: Date: Chapter 06A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not app information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loa 81. The bank can thoroughly investigate the customer’s credit record and obtain a favorable or unfavorable recommendation. If the ANSWER: The tree above shows that if the credit report is favorable, the credit union should make the loan, and if the report information. Thus, the EVPI is $760, which is the most the credit union should be willing to pay. Copyright Cengage Learning. Powered by Cognero. Page 35 Name: Class: Date: Chapter 0682. Should the credit union purchase the report if it costs $150? ANSWER: The tree above shows that the credit report is still valuable, even in the imperfect case. The information increases justified in purchasing the report for $150. A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each s 25% turn out to be hits and 75% turn out to be flops. 83. Construct a decision tree to help the television network identify the strategy that maximizes its expected profit in responding to a costs, payoffs and probabilities. ANSWER: 84. What should the network do? What is their expected profit? ANSWER: The tree above shows that the best alternative is to air the program. The EMV of this option is $100,000. Copyright Cengage Learning. Powered by Cognero. Page 36 Name: Class: Date: Chapter 0685. The network can conduct market research to determine whether a program will be a hit or a flop. If the market research report is ANSWER: The tree above shows that if the market research report predicts a hit, the network should air the program, but not EVPI is $300,000, which is the most the network should be willing to pay. Copyright Cengage Learning. Powered by Cognero. Page 37 Name: Class: Date: Chapter 0686. Should the network purchase the report if it costs $160,000? ANSWER: The tree above shows that the market report is still fairly valuable, even in the imperfect case. The information incr would be justified in purchasing the report for $160,000. Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this transportation costs) of the ore in the future. The metallurgical properties of the ore would be classified as either “high grade” or “low grade”. Southport’s geologists have est Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport’s econ (“high” or “low” net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in mill High Grade metallurgy (p=0.7) Prices Probability Outcome High 0.8 40 Low 0.2 -$20 87. What should the Southport do? What is their expected profit? ANSWER: The tree above shows that the best alternative is to invest in the mine. The EMV of this option is $18.4m. Copyright Cengage Learning. Powered by Cognero. Page 38 Name: Class: Date: Chapter 0688. Construct a decision tree to help Southport identify the strategy that maximizes its expected profit for this investment. Make su ANSWER: Copyright Cengage Learning. Powered by Cognero. Page 39 Name: Class: Date: Chapter 0689. Suppose that Southport could consider another alternative - postponing the go/no-go decision on the new venture and drilling fo Southport be willing to pay for the core sample? ANSWER: The tree above shows that most Southport should be willing to pay. Copyright Cengage Learning. Powered by Cognero. Page 40 Name: Class: Date: Chapter 0690. Should Southport conduct the imperfect core test if it costs $250,000? ANSWER: The tree ab and Southport is better off proceeding without the test. 91. Mathematically, the utility function for risk adverse individuals is said to be _____________ and/or _______________. a. decreasing, linear b. decreasing, convex c. increasing, linear d. increasing, concave e. increasing, decreasing ANSWER: d Copyright Cengage Learning. Powered by Cognero. Page 41 Name: Class: Date: Chapter 0692. With regard to decision making, most individuals are __________________. a. risk averse b. risk seekers c. risk maximizers d. EMV maximizers e. None of these options ANSWER: a 93. One class of “ready-made” utility functions is called exponential utility. Exponential utility has an adjustable parameter called ris a. how much money the decision maker has to spend b. the decision maker’s attitude toward risk c. how much risk there is in a given decision d. the probability of an unfavorable outcome e. None of these options ANSWER: b 94. If x is a monetary value (a payoff if positive, a cost if negative), U(x) the utility of this value, and R > 0 is an adjustable parameter a. Poisson utility b. exponential utility c. binomial utility d. normal utility ANSWER: b 95. Utility functions are mathematical functions that transform monetary values – payoffs and costs – into ________________. a. expected values b. utility values c. EMV values d. anchor values e. None of the above ANSWER: b 96. Rational decision makers are never willing to violate the expected monetary value (EMV) maximization criterion when large amo a. True b. False ANSWER: False 97. Utility function is a function that encodes a person’s or company’s feelings toward risk. a. True b. False ANSWER: True Copyright Cengage Learning. Powered by Cognero. Page 42 Name: Class: Date: Chapter 0698. The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altoge a. True b. False ANSWER: True 99. For a risk averse decision maker, the certainty equivalent is less than the expected monetary value (EMV). a. True b. False ANSWER: True An investor has $25,000 in assets and faces a difficult choice between two investments. If he invests in the first opportunity the assets by $20,000. If he invests in the second option there is a 40% chance that he will increase his assets by $150,000 and a 100. (A) Construct a decision tree to help the investor make his decision. Make sure to label all decision and chance nodes and inclu (B) What is the best choice for the investor? Why? (C) Suppose that investor has an exponential utility function for final assets with a risk tolerance parameter equal to $60,000. W ANSWER: (A) (B) The decision tree shows the second option is better because it provides a slightly higher EMV ($63,000 vs. $5 (C) The optimal decision would change to the first option, because its certainty equivalent is higher ($52,694 vs. $ Copyright Cengage Learning. Powered by Cognero. Page 43 Name: Class: Date: Chapter 06Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function U(x) = 101. Show that this decision maker is indifferent between gaining nothing and entering a risky situation with a gain of $80,000 (proba ANSWER: The tree above shows the utility values using this utility function. Since the expected utilities for the two alternative situations) 102. If there is a 10% chance that one of the decision maker’s family heirlooms, valued at $5,000, will be stolen during the next year potential loss of her cherished items? ANSWER: The tree above shows the utility values, and we can use it to find the maximum premium to be used in the insuran expected utility for the no insurance branch using the utility function, 0.1*U(-5000)+0.9*U(0)=97.07 and then set th Copyright Cengage Learning. Powered by Cognero. Page 44 Name: Class: Date: Chapter 06Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amo each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damag Distribution of Accident Types and Corresponding Damage Amounts Type of Accident Conditional Probability Damage to Car Minor 0.60 $200 Moderate 0.20 $1,000 Serious 0.10 $4,000 Catastrophic 0.10 $30,000 103. Construct a decision tree to help Mrs. Rich decide whether or not to purchase insurance. Note that the tree should minimize Mr damage payment. In your tree, make sure to label all decision and chance nodes and include appropriate costs, payoffs and pr ANSWER: 104. What should Mrs. Rich do? What is her expected cost in that case? ANSWER: The tree above shows that the best alternative is to purchase the insurance. Her expected cost in that case is $18 Copyright Cengage Learning. Powered by Cognero. Page 45 Name: Class: Date: Chapter 06Suppose that a decision maker’s utility as a function of her wealth, x, is given by U(x) = ln x (the natural logarithm of x). 105. Is this decision maker risk averse? Explain why or why not. ANSWER: Yes, this decision maker is risk averse. The given utility function is increasing and concave. You can verify these p 106. The decision maker now has $10,000 and two possible decisions. For Alternative 1, she loses $500 for certain (x=$9,500). For Which alternative maximizes the expected utility of her net wealth? ANSWER: The tree above, which contains the net wealth levels converted to utility, shows that Alternative 2 maximizes the e 107. The decision maker now has $15,000 and two possible decisions. For decision 1, she loses $1,000 for certain. For decision 2, expected utility of her net wealth? ANSWER: The tree above, which again contains the net wealth levels converted to utility, shows that Alternative 1 maximize Copyright Cengage Learning. Powered by Cognero. Page 46 Name: Class: Date: Chapter 06