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# Chap16 - 704 Chapter 16 Decision Making CHAPTER 16...

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Solutions to End-of-Section and Chapter Review Problems 191 CHAPTER 16 16.1 (a) Opportunity loss table: Profit of Optimum Optimum Alternative Courses of Action Event Action Action A B 1 B 100 100 – 50 = 50 100 – 100 = 0 2 A 200 200 – 200 = 0 200 – 125 = 75 (b) A B 1 2 1 2 50 200 100 125 16.2 (a) Opportunity loss table: Profit of Optimum Optimum Alternative Courses of Action Event Action Action A B 1 A 50 50 – 50 = 0 50 – 10 = 40 2 A 300 300 – 300 = 0 300 – 100 = 200 3 A 500 500 – 500 = 0 500 – 200 = 300 (b) A B 1 2 1 2 3 3 50 300 500 50 300 500 16.3 (a)-(c) Payoff table: Action Event A = Build large factory B = Build small factory 1 10,000•10 – 400,000 10,000•10 – 200,000 = – 300,000 = – 100,000 2 20,000•10 – 400,000 20,000•10 – 200,000 = – 200,000 = 0 3 50,000•10 – 400,000 50,000•10 – 200,000 = 100,000 = 300,000 4 100,000•10 – 400,000 50,000•10 – 200,000 = 600,000 = 300,000

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192 Chapter 16: Decision Making 16.3 (e) Opportunity loss table: cont. Profit of Optimum Optimum Alternative Courses of Action Event Action Action A B 1 B – 100,000 – 100,000 – (– 300,000) = 200,000 – 200,000 – (– 200,000) = 0 2 B 0 0 – (– 200,000) = 200,000 0 – 0 = 0 3 B 300,000 300,000 – (100,000) = 200,000 300,000 – 300,000 = 0 4 A 600,000 600,000 – 600,000 = 0 600,000 – 300,000 = 300,000 16.4 (a)-(b) Payoff table: Action Event Company A Company B 1 \$10,000 + \$2•1,000 = \$12,000 \$2,000 + \$4•1,000 = \$6,000 2 \$10,000 + \$2•2,000 = \$14,000 \$2,000 + \$4•2,000 = \$10,000 3 \$10,000 + \$2•5,000 = \$20,000 \$2,000 + \$4•5,000 = \$22,000 4 \$10,000 + \$2•10,000 = \$30,000 \$2,000 + \$4•10,000 = \$42,000 5 \$10,000 + \$2•50,000 = \$110,000 \$2,000 + \$4•50,000 = \$202,000 (d) Opportunity loss table: Profit of Optimum Optimum Alternative Courses of Action Event Action Action A B 1 A 12,000 0 6,000 2 A 14,000 0 4,000 3 B 22,000 2,000 0 4 B 42,000 12,000 0 5 B 202,000 92,000 0 16.5 (a)-(b) Payoff table: Action A B C D Event Buy 100 Buy 200 Buy 500 Buy 1,000 1: Sell 100 1,000 200 – 2,200 – 6,200 2: Sell 200 1,000 2,000 – 400 – 4,400 3: Sell 500 1,000 2,000 5,000 1,000 4: Sell 1,000 1,000 2,000 5,000 10,000
Solutions to End-of-Section and Chapter Review Problems 193 16.5 (d) Opportunity loss table: cont. Profit of Optimum Optimum Alternative Courses of Action Event Action Action A B C D 1 A 1,000 0 800 3,200 7,200 2 B 2,000 1,000 0 2,400 6,400 3 C 5,000 4,000 3,000 0 4,000 4 D 10,000 9,000 8,000 5,000 0 16.6 (a) EMV A = 50(0.5) + 200(0.5) = 125 EMV B = 100(0.5) + 125(0.5) = 112.50 (b) EOL A = 50(0.5) + 0(0.5) = 25 EOL B = 0(0.5) + 75(0.5) = 37.50 (c) Perfect information would correctly forecast which event, 1 or 2, will occur. The value of perfect information is the increase in the expected value if you knew which of the events 1 or 2 would occur prior to making a decision between actions. It allows us to select the optimum action given a correct forecast. EMV with perfect information = 100 (0.5) + 200 (0.5) = 150 EVPI = EMV with perfect information – EMV A = 150 – 125 = 25 (d) Based on (a) and (b) above, select action A because it has a higher expected monetary value (a) and a lower opportunity loss (b) than action B . (e) σ A 2 = (50 – 125) 2 (0.5) + (200 – 125) 2 (0.5) = 5625 σ A = 75 CV A = 75 125 100% = 60% σ B 2 = (100 – 112.5) 2 (0.5) + (125 – 112.5) 2 (0.5) = 156.25 σ B = 12.5 CV B = 12.5 112.5 100% = 11.11% (f) Return to risk ratio for A = 125 75 = 1.667 Return to risk ratio for B = 112.5 12.5 = 9.0 (g) Based on (e) and (f), select action B because it has a lower coefficient of variation and a higher return to risk ratio. (h) The best decision depends on the decision criteria. In this case, expected monetary value leads to a different decision than the return to risk ratio. 16.7 (a) EMV A = 50(0.8) + 300(0.1) + 500 (0.1) = 120 EMV B = 10(0.8) + 100(0.1) + 200 (0.1) = 38 (b) EOL A = 0(0.8) + 0(0.1) + 0(0.1) = 0 EOL B = 40(0.8) + 200(0.1) + 300(0.1) = 82 (c) EVPI = 0. The expected value of perfect information is zero because the optimum decision is action A across all three event states.

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