7. A company is considering three different projects (A, B, C) in an attempt to

Question

7. A company is considering three different projects (A, B, C) in an attempt to diversify. The effectiveness of each project (in terms of revenue) are dependent upon the level of the economy There five possible levels (1-5) based on economic projections. The assumed probability of each leve l occurring are listed below Outcome Probability 0.2 0.1 0.4 0.1 The expected payoffs in S100,000's for each alternative under each possible outcome is as follows. Outcome Project $98 $127$133$143$157 $221 $ 57 $173$198$256$297 $156$187 $243 $371 a) Under a MaxiMin policy, which altemative is best? Explain your answer b) Under a MiniMax Regret policy, which alternative is best? Explain your answer c) What is the expected value of each alternative? d) Assume a source of information is available to help predict the level of the economy. What is the expected value of perfect information? e) Assume the probability of outcomes 1 and 2 are not certain. The owner believes that together they do account for 0.3 of the total probability. Determine how much the probabilities of outcomes 1 and 2 could change before Altenative B is better than Alternative A. f) Would a risk seeking decision maker be more likely to use a MaxiMax and MaxiMin decision criteria? Explain your answer

Explanation / Answer

a. Under the MaxiMin policy the best of the worst strategy will be selected. Minimum possible return will be selected for each alternative and the decision that yields the maximum value of the minimum returns will be selected.

From the above table we can see that minimum for project A is 98, for project B is 127 and for C is 57. Maximum of these values is 127. Hence the best alternative is project B.

2. Minimax regret policy: Here regret = opportunity loss. The formula is: regret = best payoff-payoff received.

In this example regret for outcome 1 will be 127-98 = 29 for A. For B = 127-127 = 0 and for C = 127-57 = 70. Similarly other values are computed.

The regret table is shown below:

Next step is to determine maximum regret for each project.

The minimum of the maximum regrets = minimum of (74,150,70) = 70. This pertains to project C.

Hence the best alternative is Project C.

c. Expected value of A = 0.2*98 + 0.1*173 + 0.4*198 + 0.2*256 + 0.1*297 = 197.00

Expected value of B =  0.2*127 + 0.1*133 + 0.4*143 + 0.2*157 + 0.1*221 = 149.40

Expected value of C = 0.2*57 + 0.1*156 + 0.4*187 + 0.2*243 + 0.1*371 = 187.50

d. Expected value of perfect information = expected value under perfect information - expected value of the best action with imperfect information.

Expected value under perfect information = maximum value of maximum of each outcome. Thus for 1 it will be 127 and so on.

Expected return = sum of (probability*value of each outcome)

Thus expected value of perfect information = 210.20 - 197 = 13.20

e. For alternative B to be better than alternative A its expected return should be higher than A. Let 1's probability be x. Thus 2's probability = 0.3-x

Expected return of A = x*98+0.3-x*173+0.4*198+0.2*256+0.1*297

Expected return of B = x*127+0.3-x*133+0.4*143+0.2*157+0.1*221

Now x*127+0.3-x*133+0.4*143+0.2*157+0.1*221>x*98+0.3-x*173+0.4*198+0.2*256+0.1*297

127x+39.90-133x+57.2+31.4+22.1>98x+51.90-173x+79.2+51.2+29.7

or 150.60-6x>212-75x

or 69x>61.40

or x>0.8899

Thus probability of 1 can become 0.89 and for 2 can become 0.3-0.89 = -0.59.

f. A risk seeking decision maker will be more likely to use a maximax decision criteria as such a decision maker would like to have an optimistic point of view and would not like to consider the down side risk. Such a decision maker would like to ignore possible losses from the selected alternative/

Outcome Project 1 2 3 4 5 Min A 98 173 198 256 297 98 B 127 133 143 157 221 127 C 57 156 187 243 371 57

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