Suppose after a certain amount of discussion, the contractor is able to subjecti

Question

Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand:P(low) = .3 and P(high) = .7. Determine the expected profit of each alternative. Which alternative is best? Why? Analyze the problem using a decision tree. Show the expected profit of each alternative on the tree. Compute the expected value of perfect information. How could the contractor use this knowledge? Refer to Problems 1 and 2. Construct a graph that will enable you to perform sensitivity analysis on the problem. Over what range of P(high) would the alternative of doing nothing be best? Expand? Subcontract? A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be $400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.

Explanation / Answer

Expected pay-of for each alternative is calculated by using the formula for expected value of a variable with given probabilities of its values.

Expected value of X = x1*p1 + x2*p2 where X takes the value x1 with probability p1 and x2 with probability p2

From the above table, it is recommended that Expand alternative has the maximum expected profit of $62,000.

The decision tree has three branches coming out of decision node and two branches out of each state nodes for each alternative.

Expected value of each alternative is shown in the above table and as per the values of expected profit the alternative of Expand is best as this gives the maximum expected profit.

For calculation of expected value of perfect information we are required to calculate the maximum expected profit under perfect information. In case of low demand the best alternative is Do nothing with figure of 50 and in case of high demand the best figure of 80 correspond to alternative Expand. Thus Expected profit under perfect information is $71,000 (50*.3 + 80*.7)

Therefore answer to the third part of the question is:

Expected value of perfect information = $71,000 - $62,000 = $9,000

EVPI = EPPI - EMV

Profit Demand Alternative Low (P.3) High (P.7) Expected profit Do nothing 50 60 57 Expand 20 80 62 Subcontract 40 70 61

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