Homework-2 DECISION ANALYSIS PROBLEMS Problem-1: Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives are shown in the following table: EQUIPMENT FAVORABLE MARKET ($) UNFAVORABLE MARKET ($) Sub 100 300,000 –200,000 Oiler J 250,000 –100,000 Texan 75,000 –18,000 For example, if Ken purchases a Sub 100 and if there is a favorable market, he will realize a profit of $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. But Ken has always been a very optimistic decision maker. • What type of decision is Ken facing? • What decision criterion should he use? • What alternative is best? Problem-2: Although Ken Brown (discussed in previous problem) is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob is vice president of finance. Bob attributes his success to his pessimistic attitude about business and the oil industry. Given the information from previous problem, it is likely that Bob will arrive at a different decision. What decision criterion should Bob use, and what alternative will he select? Problem-3: Allen Young has always been proud of his personal investment strategies and has done very well over the past several years. He invests primarily in the stock market. Over the past several months, however, Allen has become very concerned about the stock market as a good investment. In some cases it would have been better for Allen to have his money in a bank than in the market. During the next year, Allen must decide whether to invest $10,000 in the stock market or in a certificate of deposit (CD) at an interest rate of 9%. If the market is good, Allen believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get no return at all—in other words, the return would be 0%. Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return. • Develop a decision table for this problem. • What is the best decision? Homework-2 Problem-4: Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table: SIZE OF FIRST STATION GOOD MARKET ($) FAIR MARKET ($) POOR MARKET ($) Small 50,000 20,000 –10,000 Medium 80,000 30,000 –20,000 Large 100,000 30,000 –40,000 Very large 300,000 25,000 –160,000 For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000. • Develop a decision table for this decision. • What is the maximax decision? • What is the maximin decision? • What is the equally likely decision? • What is the criterion of realism decision? Use an value α of 0.8. • Develop an opportunity loss table. • What is the minimax regret decision? Problem-5: A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i. e., there is a favorable market for the clinic), the physicians could realize a net profit of $100,000. If the market is not favorable, they could lose $40,000. Of course, they don’t have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50–50 chance the clinic will be successful. Construct a decision tree to help analyze this problem. What should the medical professionals do? Problem-6: The physicians in previous problem have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim their experience enables them to use Bayes’ theorem to make the following statements of probability: probability of a favorable market given a favorable study-------------0.82 probability of an unfavorable market given a favorable study--------0.18 probability of a favorable market given an unfavorable study -------0.11 probability of an unfavorable market given anunfavorable study --0.89 probability of a favorable research study ----------------------------------0.55 probability of an unfavorable research study -----------------------------0.45 Homework-2 • Develop a new decision tree for the medical professionals to reflect the options now open with the market study. • Use the EMV approach to recommend a strategy. • What is the expected value of sample information? How much might the physicians be willing to pay for a market study? • Calculate the efficiency of this sample information. Case Study Starting Right Corporation After watching a movie about a young woman who quit a successful corporate career to start her own baby food company, Julia Day decided that she wanted to do the same. In the movie, the baby food company was very successful. Julia knew, however, that it is much easier to make a movie about a successful woman starting her own company than to actually do it. The product had to be of the highest quality, and Julia had to get the best people involved to launch the new company. Julia resigned from her job and launched her new company—StartingRight. Julia decided to target the upper end of the baby food market by producing baby food that contained no preservatives but had a great taste. Although the price would be slightly higher than for existing baby food, Julia believed that parents would be willing to pay more for a highquality baby food. Instead of putting baby food in jars, which would require preservatives to stabilize the food, Julia decided to try a new approach. The baby food would be frozen. This would allow for natural ingredients, no preservatives, and outstanding nutrition. Getting good people to work for the new company was also important. Julia decided to find people with experience in finance, marketing, and production to get involved with Starting Right. With her enthusiasm and charisma, Julia was able to find such a group. Their first step was to develop prototypes of the new frozen baby food and to perform a small pilot test of the new product. The pilot test received rave reviews. The final key to getting the young company off to a good start was to raise funds. Three options were considered: corporate bonds, preferred stock, and common stock. Julia decided that each investment should be in blocks of $30,000. Furthermore, each investor should have an annual income of at least $40,000 and a net worth of $100,000 to be eligible to invest in Starting Right. Corporate bonds would return 13% per year for the next five years. Julia furthermore guaranteed that investors in the corporate bonds would get at least $20,000 back at the end of five years. Investors in preferred stock should see their initial investment increase by a factor of 4 with a good market or see the investment worth only half of the initial investment with an unfavorable market. The common stock had the greatest potential. The initial investment was expected to increase by a factor of 8 with a good market, but investors would lose everything if the market was unfavorable. During the next five years, it was expected that inflation would increase by a factor of 4.5% each year. Homework-2 Questions: • Sue Pansky, a retired elementary school teacher, is considering investing in Starting Right. She is very conservative and is a risk avoider. What do you recommend? • Ray Cahn, who is currently a commodities broker, is also considering an investment, although he believes that there is only an 11% chance of success. What do you recommend? • Lila Battle has decided to invest in Starting Right. While she believes that Julia has a good chance of being successful, Lila is a risk avoider and very conservative. What is your advice to Lila? • George Yates believes that there is an equally likely chance for success. What is your recommendation? • Peter Metarko is extremely optimistic about the market for the new baby food. What is your advice for Pete? • Julia Day has been told that developing the legal documents for each fundraising alternative is expensive. Julia would like to offer alternatives for both risk-averse and risk-seeking investors. Can Julia delete one of the financial alternatives and still offer investment choices for risk seekers and risk avoiders? PROJECT MANAGEMENT PROBLEMS Problem-1: Sid Davidson is the personnel director of Babson and Willcount, a company that specializes in consulting and research. One of the training programs that Sid is considering for the middlelevel managers of Babson and Willcount is leadership training. Sid has listed a number of activities that must be completed before a training program of this nature could be conducted. The activities and immediate predecessors appear in the following table: ACTIVITY IMMEDIATE PREDECESSORS A — B — C — D B E A, D F C G E, F Develop a network for thisproblem. Homework-2 Problem-2: Sid Davidson was able to determine the activity times for the leadership training program. He would like to determine the total project completion time and the critical path. The activity times appear in the following table (see previous problem). ACTIVITY TIME (DAYS) A 2 B 5 C 1 D 10 E 3 F 6 G 8 35 Problem-3: The estimated times (in weeks) and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are ACTIVITY IMMEDIATE PREDECESSOR a m b A — 9 10 11 B — 4 10 16 C A 9 10 11 D B 5 8 11 • Calculate the expected time and variance for each activity. • What is the expected completion time of the critical path? What is the expected completion time of the other path in the network? • What is the variance of the critical path? What is the variance of the other path in the network? • If the time to complete path A–C is normally distributed, what is the probability that this path will be finished in 22 weeks or less? • If the time to complete path B–D is normally distributed, what is the probability that this path will be finished in 22 weeks or less? • Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks orless. Homework-2 Problem-4: The following costs have been estimated for the activities in a project: ACTIVITY IMMEDIATE PREDECESSORS TIME COST ($) • Develop a cost schedule based on earliest start times. • Develop a cost schedule based on latest start times. • Suppose that it has been determined that the $6,000 for activity G is not evenly spread over the three weeks. Instead, the cost for the first week is $4,000, and the cost is $1,000 per week for each of the last two weeks. Modify the cost schedule based on earliest start times to reflect this situation. A — 8 8,000 B — 4 12,000 C A 3 6,000 D B 5 15,000 E C, D 6 9,000 F C, D 5 10,000 G F 3 6,000