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3.43 A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation: INVESTMENT Fund A Fund B Probability

GOOD ECONOMY (GE) 10,000 6,000 0.2

STATE OF NATURE FAIR ECONOMY (FE) 2,000 4,000 0.3

POOR ECONOMY (PE) -5,000 0 0.5

a) Draw the decision tree to represent this situation. b) Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value? c) Suppose there is question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (ie., the EMVs would be the same)?

GE 0.2 Invest in Fund A

1

FE PE -

GE

Invest in Fund B

FE 2

Do not invest

PE

b)

10,000

GE 0.2 FE 0.3 1

2,000

Invest in Fund A

PE 0.5 EMV = $100

-5,000

GE 0.2 Invest in Fund B $2400

6,000 FE 0.3

2

EMV = $2400

Do not invest

4,000 PE 0.5

0

0

Calculation: EMV 1 = 0.2*10,000 + 0.3*2,000 + 0.5*-5,000 = $100 EMV 2 = 0.2*6,000 + 0.3*4,000 + 0.5*-0 = $2,400 c) If we compare both funds based on EMV calculation, Fund B yields a higher EMV. Thus, to maximize the expected value, they should choose to invest in Fund B which has an expected value of $2,400. Firstly, the EMV for Fund A would not be the same as the return of Fund A in a good economy could be higher or lower. Thus, the EMV could also result to being higher or lower. However, obviously the economy will rapidly change from time to time. It will not produce the same return the whole time. Thus, relying to only a return figure is risky. The investor should be more versatile as heavily depending on a good economy situation will only make Fund A vulnerable to changes and increasing the investor’s risk. We can carry out a calculation: Let Return of Fund A in a good economy = X Indifferent between A and B: EMV (Fund A) = EMV (Fund B) 0.2*X + 0.3(2,000) + 0.5(-5,000) = 2,400 0.2X = 4,300 X = $21,500 Thus, the return of Fund A in a Good Economy should be $21,500 in order for a person to be indifferent between Fund A and Fund B.

3.44 Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable, he would get a return of $100,000, but if the market for this new type of razor were unfavorable, he would lose $60,000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested that Jim either use a survey or a pilot study to test the market. The survey would be a sophisticated questionnaire administered to a test market. It will cost $5,000. Another alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron Bush has suggested that it would a good idea for Jim to conduct either the survey or the pilot before Jim makes the decision concerning whether to produce the new razor. But Jim is not sure if the value of the survey or the pilot is worth the cost. Jim estimates that the probability of a successful market without performing a surveyor pilot study is 0.5. Furthermore, the probability of a favourable survey result given a favourable market for razors is 0.7, and the probability of a favourable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavourable pilot study given an unfavourable market is 0.9, and the probability of an unsuccessful pilot study result given a favourable market for razors is 0.2. a) Draw the decision tree for this problem without the probability values.

b) Compute the revised probabilities needed to complete the decision, and place these values in the decision tree. P (F. Pilot / F. Market) = 0.80 P(U. Pilot / F. Market) = 0.20 P (F. Pilot / U. Market) = 0.10 P (U. Pilot / U. Market) = 0.90

PILOT FAVOURABLE SN FM UM

P(PF/SN) 0.8 0.1

P(SN) 0.5 0.5 P(PF)

JOINT PROBABILITY 0.4 0.05 0.45

P(SN/PF) 0.89 0.11 1

PILOT UNFAVOURABLE SN FM UM

P(PU/SN) 0.2 0.9

P(SN) 0.5 0.5 P(PU)

JOINT PROBABILITY 0.1 0.45 0.55

P(SN/PU) 0.18 0.82 1

P (F. Survey / F. Market) = 0.70 P (F. Survey / U. Market) = 0.20

P (U. Survey / F. Market) = 0.30 P (U. Survey / U. Market) = 0.80

SURVEY FAVOURABLE SN FM UM

P(SF/SN) 0.7 0.2

P(SN) 0.5 0.5 P(SF)

JOINT PROBABILITY 0.35 0.1 0.45

P(SN/SF) 0.78 0.22 1

SURVEY UNFAVOURABLE SN FM UM

P(SU/SN) 0.3 0.8

P(SN) 0.5 0.5 P(SU)

JOINT PROBABILITY 0.15 0.4 0.55

P(SN/SU) 0.27 0.73 1

c) What is the best decision for Jim? Use EMV as the decision criterion Decision 1: Based on the calculations of EMV in the decision tree, Jim Sellers should conduct a survey in order to determine the new market for his razor because it yields the higher EMV which is $24,160. Decision 2: If the survey is favourable, Jim Sellers should choose to produce the razors. If the survey is unfavourable, Jim Sellers should choose to do nothing. The decision is made on choosing the highest EMV.

3.52 The Jamis Corporation is involved with waste management. During the past 10 years it has become one of the largest waste disposal companies in the Midwest, serving primarily Wisconsin, Illinois, and Michigan. Bob Jamis, president of the company, is considering the possibility of establishing a waste treatment plant in Mississippi. From past experience, Bob believes that a small plant in northern Mississippi would yield a $500,000 profit regardless of the market for the facility. The success of a medium-sized waste treatment plant would depend on the market. With a low demand for waste treatment, Bob expects a $200,000 return. A medium demand would yield a $700,000 return in Bob’s estimation, and a high demand would return $800,000. Although a large facility is much riskier, the potential return is much greater. With a high demand for waste treatment in Mississippi, the large facility should return a million dollars. With a medium demand, the large facility will return only $400,000. Bob estimates that the large facility would be a big loser if there were a low demand for waste treatment. He estimates that he would lose approximately $200,000 with a large treatment facility if demand were indeed low. Looking at the economic conditions for the upper part of the state of Mississippi and using his experience in the field, Bob estimates that the probability of a low demand for treatment plants is 0.15. The probability for a medium-demand facility is approximately 0.40, and the probability of a high demand for a waste treatment facility is 0.45. Because of the large potential investment and the possibility of a loss, Bob has decided to hire a market research team that is based in Jackson, Mississippi. This team will perform a survey to get a better feeling for the probability of a low, medium, or high demand for a waste treatment facility. The cost of the survey is $50,000. To help Bob determine whether to go ahead with the survey, the marketing research firm has provided Bob with the following information:

P(survey results | possible outcomes) POSSIBLE OUTCOME

Low demand Medium demand High demand

LOW SURVEY RESULTS 0.7 0.4 0.1

SURVEY RESULTS HIGH MEDIUM SURVEY SURVEY RESULTS RESULTS 0.2 0.1 0.5 0.1 0.3 0.6

As you see, the survey could result in three possible outcomes. Low survey results mean that a low demand is likely. In a similar fashion, medium survey results or high survey results would mean a medium or a high demand, respectively. What should Bob do?

Probability: P(survey result/possible outcome) to P(possible outcome/survey result) 1) Scenario : Low Survey Result (LSR) SN

P(LSR/SN)

P(SN)

Low Demand Medium Demand High Demand

0.7 0.4 0.1

0.15 0.40 0.45 P(LSR)

JOINT PROBABILITY 0.105 0.16 0.045 0.31

P(SN/LSR) 0.34 0.52 0.14 1

2) Scenario : Medium Survey Result (MSR) SN

P(MSR/SN)

P(SN)

Low Demand Medium Demand High Demand

0.2 0.5 0.3

0.15 0.40 0.45 P(MSR)

JOINT PROBABILITY 0.03 0.20 0.135 0.365

P(SN/MSR) 0.08 0.55 0.37 1

3) Scenario : High Survey Result (HSR) SN

P(HSR/SN)

P(SN)

Low Demand Medium Demand High Demand

0.1 0.1 0.6

0.15 0.40 0.45 P(HSR)

JOINT PROBABILITY 0.015 0.04 0.27 0.325

P(SN/HSR) 0.05 0.12 0.83 1

4) EVSI = (EV with sample information + cost) – (EV without sample information) = (655,145+50,000) – 670,000 = $35,145 CONCLUSION: Decision 1: Bob should choose not to conduct the survey because he will get a larger return of $670,000 without conducting any survey. Decision 2: Bob should choose to invest in the medium facility as it yields the highest EMV compared to the small or and large facility.

3.53 Mary is considering opening a new grocery store in town. She is evaluating three sites: downtown, the mall, and out at the busy traffic circle. Mary calculated the value of successful stores at these locations as follows: downtown, $250,000, the mall, $300,000, $400,000. Mary calculated the losses if unsuccessful to be $100,000 at either downtown or the mall and $200,000 at the circle. Mary figures her chance of success to be 50% downtown, 60% at the mall, and 75% at the traffic circle. (a) Draw a decision tree for Mary and select her best alternative.

Mary should consider to open new grocery at busy traffic circle because the expected monetary value is highest among the rest which is $250,000

(b) Mary has been approached by a marketing firm that offers to study the area to determine if another grocery store is needed. The cost of this study is $30,000. Mary believes there is a 60% chance that the survey result will be positive ( show a need for another grocery store).SRP= survey results positive, SRN = negative, SD= downtown, SM= success at mall, SC = success at circle, SD = don't succeed downtown, and so on. For studies of this nature: P(SRP|success)=0.7; P(SRN|not success)=0.3; P(SRP|not success)=0.2; and P(SRN|not success)=0.8. Calculate the revised probabilities for success (and not success) for each location, depending on survey results.

(c) How much is the marketing research worth to Mary? Calculate the EVSI. EVSI = (EV with sample information + cost) – (EV without sample information) = (224,800 + 30,000) – 250,000 = $4,800 Decision 1: Mary should choose to not conduct the survey as it yields a higher EMV which is $250,000. If Mary conducted a survey, she has to pay additional cost of RM4,800. Marketing research is not worthy as Mary can choose not to conduct a survey to make decision to open her new grocery store as the EMV is higher compared with conduct a survey. Decision 2: Mary should choose to open new grocery at busy traffic circle because the expected monetary value is highest among the rest which is $250,000....