Question

Interactive Exercise 1: Corporate Raider A corporate raider contemplates the future of a recent acquisition. Three alternatives are being considered in two states of nature: 1. Expand a textile plant and produce for the military 2. Maintain status quo 3. Sell the plant The payoff table is below. Decision Expand Maintain Status Quo Sell now States of Nature Good Foreign Competitive Poor Foreign Competitive Conditions Conditions $ 800,000 $ 500,000 1,300,000 -150,000 320,000 320,000 E.g., Import taxes; Free Trade Agreements Embargo

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Answer:

a)

(part A): Determine Decisions Without Probabilities Maximax: Expand $ 800,000 Status quo 1,300,000 - Maximum Sell 320,000 Decision: Maintain status quo.

Maximin: Expand $ 500,000 Maximum Status quo -150,000 Sell 320,000 Decision: Expand. Minimax regret: Expand $500,000 - Minimum Status quo 650,000 Sell 980,000 Decision: Expand.

Hurwicz (a = .3): Expand $800,000(.3) + 500,000(.7) = $590,000 Status quo $1,300,000(.3) 150,000(.7) = $285,000 Sell $ 320,000(.3) + 320,000(.7) = $ 320,000 Decision: Expand. Equal likelihood: Expand $800,000(.50) + 500,000(.50) = $650,000 Status quo $1,300,000(.50) 150,000(.50) = $575,000 Sell $320,000(.50) + 320,000(.50) = $320,000 Decision: Expand.

b)

(part B): Determine Decisions with EV and EOL Expected value: Expand $800,000(.70) + 500,000(.30) = $710,000 Status quo $1,300,000(.70) 150,000(.30) = $865,000 Sell $320,000(.70) + 320,000(.30) = $320,000 Decision: Maintain status quo. Expected opportunity loss: Expand $500,000(.70) + 01.30) = $350,000 Status quo $0.70) + 650,000(.30) = $195,000 Sell $980,000(.70) + 180,000(.30) = $740,000 Decision: Maintain status quo.

c)

(part C): Compute EVPL expected value given perfect information = 1,300,000(.70) + 500,000(.30) = $1,060,000 [Page 550] expected value without= $1,300,000(.70) 150,000(.30) perfect information = $865,000 EVPI= $1,060,000 865,000 = $195,000

d)

(part D): Develop a Decision Tree $710,000 Good conditions (7) $800,000 Expand $500,000 Poor conditions (3) Good conditions (7) Maintain status quo $1,300,000 $865,000 -$150,000 $865,000 Poor conditions (-3) Good conditions (7) Sell $320,000 Poor conditions (3) $320,000 $320,000

e)

(part E): Determine Posterior Probabilities P(Pg)P(g) P(g|P)= P(Pg)P(g) + P(P|p)P(p) (.70) 0.70) (.70)(.70)+(20)(.30) = .891 P(p|P) = .109 P(N g)P(g) P(g/N) = P(N g)P(g) + P(N|p)P(p) (.30) (.70 (.30) .70) + (.80) (.30) = .467 P(p|N) = .533

f)

(part F): Perform Decision Tree Analysis with Posterior Probabilities Expand $1,141,950 Status quo $767,300 $800,000 Plg P) = .891 P(p|P) = .109 $500,000 P(g|P) = .891 $1,300,000 5 < P(pIP) = .109 $1,141,950 -$150,000 Pag P) = .891 $320,000 PpP) = .109 $320,000 $320,000 Positive report P(P) = .55 Sell 1 $916,117.50 $640,100 $800,000 Expand P(N) = .45 Negative report $640,100 Status quo PagN) = .467 PpN) = .533 $500,000 Plg N) = .467 $1,300,000 Pp N) = .533 $527,150 -$150,000 PagN) = .467 $320,000 P(PN) = .533 $320,000 $320,000 Sell