Question

Given the following sequential decision tree, determine which is the better investment, A or B.

30 N Given the following sequential decision tree, determine which is the optimal investment, A or B: .40 $300,000 (-$20,000) .60 $80,000 $45,000 Investment A .70 $75,000 (-$70,000) 20 $200,000 (-$17,000) .80 $70,000 .15 $60,000 $105,000 (-$9,000) Investment B .55 .65 $40,000 (-$50,000) $55,000 $80,000 5 .35

Read problem description. Compute the expected value (payoff) of each node.

Question 1, the expected value (payoff) of node 7 is___________?

Question 2, the expected value (payoff) of node 4 is___________?

Question 3, the expected value (payoff) of node 5 is___________?

Question 4, the expected value (payoff) of node 6 is___________?

Question 5, the expected value (payoff) of node 3 is___________?

Question 6, the expected value (payoff) of node 1 is___________?

Question 7, based on the calculated expected value, investment option A is the one to choose.

A.True

B.False

Answer 1

Using the given decision tree: ECProbability xpayogy Expected value (E) at o ·E Expected value (E) at o Max { payoff, Payoffs .. - 2 2 41 Now) 1 E17) = 0.41300k) +0.6160k ) = 1566 = $156000 2) E14) Max { 156k-20k, 45k} Max { 136k, 45k} 136K z $136000 3) E18) = 0.2(2006) + 0.8(70K) = 96k E(5) Max { 966 - 17k, Gok? Max {79k, bok} 79K $79000 E(9) = 0.35(105K)+ 0.65 (40) = 62.75K E(6) Max { 62.25k-ak, ssk} Max { 53.75K, 55k} = 55K = $55000 5) El 3) = 0.15(79K) +0:13 (55K) + 0.3(80) 66-1k $ 66100 6) E (2) = 0.3 (136k) + 07(75K) = 83.3k → E (Investment A) 93.3K-70K = El Investment B) 66.1K - SOK = 16.1K s E(I) = Max { 23.3K, 16.1k} = 23.31 $23300 23.3 k v 1) A) True investment A has higher E.