Given the following payoff table with the profits ($m), a firm might expect alternative investments(A, B, C) under different levels of interest rate.payoffs as profits states of nature1(5%)decision2(7%)3(9%)alternativesA14226.B191811121715(a)Which alternative should the firm choose under the maximax criterion?(b)Which option should the firm choose under the maximin criterion?(c)Which option should the firm choose under the LaPlace criterion?(d)Which option should the firm choose with the Hurwicz criterion with a = 0.2?(e)Using a minimax regret approach, what alternative should the firm choose?(f)Economists have assigned probabilities of 0.35, 0.3, and 0.35 to the possible interest levels 1,2, and 3 respectively. Using expected monetary values, what option should be chosen and whatis that optimal expected value?(g)What is the most that the firm should be willing to pay for additional information? UseExpected Regre(h)Use the alternative method to verify EVPI

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 69P

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Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.
In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?
If you want to invest in a project that cost $3.5 million. As we are unsure about the future demand, there is a 40% probability of high demand with a present value for the project $3 million. There is a 25% probability of moderate demand with a present value of $2.5 million. In addition, there is a 35% probability of low demand with a present value is $1.5 million. Draw a decision tree for this problem. What is the expected net present value of the business? Should you invest? Explain. Assume that you can expand the project by investing another $0.6 million after you learn the true future demand state. This would make the present value of the business $3.9 million in the high‐demand state, $3.5 million in the moderate demand state, and $1.80 million in the low demand state. Draw a decision tree to reflect the option to expand. Evaluate the alternatives. What is the net present value of the business if you consider the option to expand? How valuable is the option to expand?
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Given the following payoff table with the profits ($m), a firm might expect alternative investments (A, B, C) under different levels of interest rate. (Attached)(a) Which alternative should the firm choose under the maximax criterion? (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (d) Which option should the firm choose with the Hurwicz criterion with α = 0.2? (e) Using a minimax regret approach, what alternative should the firm choose? (f) Economists have assigned probabilities of 0.35, 0.3, and 0.35 to the possible interest levels 1, 2, and 3 respectively. Using expected monetary values, what option should be chosen and what is that optimal expected value? (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (h) Use the alternative method to verify EVPI Part 2 Assume now that the pay offs are costs answer the following: (a) Using an…
Many decision problems have the following simplestructure. A decision maker has two possible decisions,1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility.
A landlord can either lease for one or two years or sell offices outrightly for K100 million with payoffs as follows: Lease -100 50 150 Sell 100 100 100 The probability of rejecting is 30%, leasing for one year is 50% and for two years 20%. Required: What is the optimal decision strategy if perfect information were available? What is the expected value of perfect information? A decision maker is looking to minimising costs through three alternative decisions a1 , b2 and c3 under two states of nature/events S1 and S2 with S1 having a probability of 30% . For a1 payoffs for s1 K100 million and s2 K540 million For a2 payoff for s1 K150 million and s2 –K50 million For a3 payoff for s1 K350 million and s2 K320 million Required: Find EMV and recommend the course of action Find the…
In the environment of increased competition, a fitness club executive is considering the purchase of additional equipment. His alternatives, outcomes, and payoffs (profits) are shown in the following table: (a). If the executive is an optimistic decision maker, which alternative will he likely choose? (b). if the executive is a pessimistic decision maker, which alternative will he likely choose? (c). Market research suggests the chance of a favorable market for fitness clubs is 76%. If the executive uses this analysis, which alternative will he likely choose? I have provided the data table for the problem.
In the environment of increased competition, a fitness club executive is considering the purchase of additional equipment. His alternatives, outcomes, and payoffs (profits) are shown in the following table: (a). If the executive is an optimistic decision maker, which alternative will he likely choose? (b). if the executive is a pessimistic decision maker, which alternative will he likely choose? (c). Market research suggests the chance of a favorable market for fitness clubs is 76%. If the executive uses this analysis, which alternative will he likely choose? Please provide an excel sheet with calculations as well
The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.
A store owner must decide whether to build a small or a large facility at a new location. Demand at a location can be either small or large, which probabilities estimated to be 0.4 and 0.6, respectively. If small facility is built and demand proves to be high, the manager may choose not to expand (payoff=P235,000) or to expand (payoff=P275,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is P220,000. If a large facility is built and demand proves to be low, the choice is to do nothing (P60,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff grows to P230,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is P900,000.a.) Draw a decision tree.b.) Determine the expected payoff for each decision and event node.c.)…
Which investment should Warren make under each of the following criteria? a. Maximax criterion. b. Maximin criterion. c. Maximum likelihood criterion. d. Bayes’ decision rule. e. The investor decides that Bayes’ decision rule is his most reliable decision criterion. He believes that 0.1 is just about right as the prior probability of an improving economy, but is quite uncertain about how to split the remaining probabilities between a stable economy and a worsening economy. Therefore, he now wishes to do some sort of sensitivity analysis with respect to these latter two prior probabilities. If he still wants to choose the alternative from the Bayes’ decision rule (part d): e1. How much would be the maximum amount of the prior probability of a stable economy? e2. How much would be the minimum amount of the prior probability of a worsening economy?

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