Accounting / Business Excel Problem and Solutions

156 ? Test Item File Chapter Eight ? 155 Excel Problems ABC Inc. must make a decision on its current capacity for next year. Estimated profits (in $000's) based on next year's demand are shown in the table below. Next Year's Demand Alternative Low High Expand $100 $200 Subcontract $50 $120 Do Nothing $40 $50 a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Lapalce criterion? d. Which alternative should be chosen based on criterion of realism with alpha = 0.7? e. Which alternative should be chosen based on the minimax regret criterion? 2. Refer to problem 1. Assume that ABC Inc. has hired a marketing research firm that provided additional information regarding next year's demand. Suppose that the probabilities of low and high demand are assessed as follows: P(Low) = 0.4 and P(High) = 0.6. a. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 3. Refer to problem 2. Develop a decision tree for this problem. b. Analyze the decision tree and determine which alternative should be chosen. c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen? 4. A plant manager is considering buying additional stamping machines to accommodate increasing demand. The alternatives are to buy 1 machine, 2 machines, or 3 machines. The profits realized under each alternative are a function of whether their bid for a recent defense contract is accepted or not. The payoff table below illustrates the profits realized (in $000's) based on the different scenarios faced by the manager. Alternative Bid Accepted Bid Rejected Buy 1 machine $10 $5 Buy 2 machines $30 $4 Buy 3 machines $40 $2 a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Lapalce criterion? d. Which alternative should be chosen based on criterion of realism with alpha = 0.8? e. Which alternative should be chosen based on the minimax regret criterion? 5. Refer to problem 4. Assume that based on historical bids with the defense contractor, the plant manager believes that there is a 65% chance that the bid will be accepted and a 35% chance that the bid will be rejected. a. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 6. Refer to problem 5. a. Develop a decision tree for this problem. b. Analyze the decision tree and determine which alternative should be chosen. c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen? 7. A bakery must decide how many pies to prepare for the upcoming weekend. The bakery has the option to make 50, 100, or 150 pies. Assume that demand for the pies can be 50, 100, or 150. Each pie costs $5 to make and sells for $7. Unsold pies are donated to a nearby charity center. Assume that there is no opportunity cost for lost sales. a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Lapalce criterion? d. Which alternative should be chosen based on criterion of realism with alpha = 0.8? e. Which alternative should be chosen based on the minimax regret criterion? 8. Assume that the bakery (see problem 7) has obtained the following probability information regarding demand for the pies: P(50) = 0.3, P(100) = 0.5, and P(150) = 0.2. a. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 9. Refer to problem 8. a. Develop a decision tree for this problem. b. Analyze the decision tree and determine which alternative should be chosen. c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen? 10. AAA auto supply store sells snow tires which are ordered every Friday to meet next week's demand. The sales price for the most popular size is $50 per tire and its cost for AAA is $35. If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire. If AAA is out of stock, it forgoes the profits from missed sales. AAA has the option to order 100, 150, or 200 tires to meet next week's demand which can be either 100, 150, or 200 tires. a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Lapalce criterion? d. Which alternative should be chosen based on criterion of realism with alpha = 0.7? e. Which alternative should be chosen based on the minimax regret criterion? 11. Refer to problem 10. Based on its historical demand distribution, assume that AAA Inc. has determined the following probability information: P(100) = 0.4, P(150) = 0.3, and P(200) = 0.3. a. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 12. Refer to problem 11. a. Develop a decision tree for this problem. b. Analyze the decision tree and determine which alternative should be chosen. c. Using the expected opportunity loss (EOL) criterion, which alternative should be chosen? 13. A toys store is considering expanding its capacity to meet a growing demand for its products. The options faced by management are to build a new store, expand the existing store, or do nothing. A marketing research firm has projected a 50% probability of a high demand for the toy market, a 30% probability of a low demand, and a 20% probability of an unchanged demand. The following estimates of annual returns (in $000's) are as follows: Demand Alternative High Low Unchanged Build new store $60 $25 $40 Expand existing store $45 $15 $25 Do nothing $10 $4 $6 a. Develop a decision tree for this problem. b. Analyze the decision tree and determine which alternative should be chosen. 14. Limousine Inc. must decide how many new limousines to buy. The owner has narrowed down the decision to two choices: buy one limousine or two limousines. If only one limousine is bought and demand ridership is high, a second limousine can be bought later. The probability of high demand is ridership 0.65, and the probability of low demand ridership is 0.35. The net present value obtained with the purchase of two limousines is $100,000 if demand is high and $65,000 if demand is low. The net present value for one limousine and low demand is $55,000. If demand is high, there are two options. The first option is to buy a second limousine. This option has a net present value of $80,000. The second option is to do nothing, which would have a net present value of $50,000. a. Develop a decision tree for this problem. b. Analyze the decision tree and determine how many limousines should be bought initially.. 15. A company must decide whether to build a small, medium, or large grocery store. Marketing research findings indicate a 0.35 probability that demand will be low and a 0.65 probability that demand will be high. If the company builds a small grocery store and demand is low, the net present value will be $150,000. If demand is high the company can buy its additional grocery needs from a wholesaler and realize a net present value of $100,000 or expand and realize a net present value of $120,000. If the company builds a medium grocery store and demand is low, the net present value will be $175,000; if demand turns to be high the company could do nothing and realize a net present value of $100,000, or expand and realize a net present value of $135,000. If the firm builds a large grocery store and demand is low, the net present value will be $50,000; if demand turns out to be high the net present value will be $250,000. a. Develop a decision tree for this problem. b. Analyze the decision tree and determine which alternative should be chosen? 16. A defense contractor has submitted a bid to make new helmets for the army. The defense contractor believes that the odds of winning the bid stand at 50 - 50 chance. Past history indicates that if the bid is successful, there is a 0.75 probability that the contractor will hear about the status of the bid within one week. There is also a 0.40 probability that the contractor will hear from the army within one week if the bid is unsuccessful. What is the probability that the bid is successful if the contractor hears about the status of the bid within one week? Use Baye's theorem to compute this posterior probability. 17. Strike It Rich is a gold mining company that is attempting to decide whether to invest in a particular site. The probability that the site has gold is 0.50. In order to obtain more information about the potential presence of gold, the company has hired a geologist to analyze the soil. Past history indicates that there is a 60% chance that the geologist’s test is positive given the presence of gold, and 35% chance that the test is positive given the absence of any gold. What is the probability of the presence of gold given that the geologist’s test yielded a positive result? Use Baye’s theorem to compute this posterior probability. 18. Suppose that the utility function for a decision maker is represented as follows: U(x) = . The potential payoffs that are possible are illustrated below. Payoff (x) $100 $200 $300 $400 $500 $600 $700 $800 $900 $1000 Convert these payoffs into utility values using the above function. Plot the utility curve and determine whether the decision maker is a risk avoider, risk indifferent, or risk seeker. 19. Suppose that the utility function for a decision maker is represented as follows: U(x) = x2. The potential payoffs that are possible are illustrated below. Payoff (x) $100 $200 $300 $400 $500 $600 $700 $800 $900 $1000 Convert these payoffs into utility values using the above function. Plot the utility curve and determine whether the decision maker is a risk avoider, risk indifferent, or risk seeker. 20. Suppose that the utility function for a decision maker is represented as follows: U(x) = 2x. The potential payoffs that are possible are illustrated below. Payoff (x) $100 $200 $300 $400 $500 $600 $700 $800 $900 $1000 Convert these payoffs into utility values using the above function. Plot the utility curve and determine whether the decision maker is a risk avoider, risk indifferent, or risk seeker.