# Buying a new manufacturing system

Company A faces the decision of buying a new flexible manufacturing system or keeping the current system. Management projections for the cash flows are given below under two demand scenarios: H (high demand) and L (low demand). This information is summarized in the following table.

H(0.5) L(0.5)

Old System $35M $17.5M

FMS $45M $13M

1. To compute the expected value of each alternative and the Expected value under perfect

information.

Old System = 35*0.5 + 17.5*0.5 = 26.25

FMS = 45*0.5 + 13*0.5 = 29

Is this correct?

What is the maximum expected value of additional information?

2. Company A considering the advisability of undertaking a study, which will make a

prediction on demand, at a cost of $2M. Company A's assessment of confidence in the

study is summarized by the conditional probabilities of the prediction, h (high) or l(low),

given the state of nature H or L. These probabilities are: P(h|H) = 0.7, P(h|L) =

0.2, P(l|H) = 0.3 and P(l|L) = 0.8.

Based on this info, how do I compute the posterior probabilities under each prediction, and determine if the study should be undertaken?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

See the attached file.

Company A faces the decision of buying a new flexible manufacturing system or keeping the current system. Management projections for the cash flows are given below under two demand scenarios: H (high demand) and L (low demand). This information is summarized in the following table.

H(0.5) L(0.5)

Old System $35M $17.5M

FMS $45M $13M

1. To compute the expected value of each alternative and the Expected value under perfect

information.

Old System = 35*0.5 + 17.5*0.5 = 26.25

FMS = 45*0.5 + 13*0.5 = 29

Is this correct?This is correct.

EVPI = .5*45 + .5*17.5 = 31.25 ( when u know Demand will be high u will install new system but it will happen only .50 times. When the demand is low you will not install new system).

What is the maximum expected value of additional information?

Max expected value of additional info = EVPI = Expected Info under no info

31.25 - 26.25 = 5M

2. Company A considering the advisability of undertaking a study, which will make a

prediction on demand, at a cost of $2M. Company A's assessment of confidence in the

study is summarized by the conditional probabilities of the prediction, h (high) or l(low),

given the state of nature H or L. These probabilities are: P(h|H) = 0.7, P(h|L) =

0.2, P(l|H) = 0.3 and P(l|L) = 0.8.

Based on this info, how do I compute the posterior probabilities under each prediction, and determine if the study should be undertaken?

It says that the study can tell us more about the Demand.

If the study says High , then probality that demand will be high is .7 , and the probability that actual demand turns out to be low inspite of study saying high , .3.

Demand being high if study says low is .2 and it being low if study says low is .8.

So we will compute expected values for both options ( of installing new/not installing) for both outcomes of the study:

Study says High:

1) Install : Expected Value - .7*45 + .3*13 -2 ( for study cost) = 33.4

2) Do Not install :.7*35 + .3*17.5 - 2 = 27.75

Study says low:

1) Install : .2*45 +.8*13 - 2= 17.4

2) Do Not Install: .2*35 +.8*17.5 - 2 = 19.

Note: One piece of data missing is with what probabilities will the study say the outcome High or Low. I am assuming it to be .5 that the study will say High and .5 that it will say low.

When study says High , Install the new system ( since it has higher value 33.4 against 27.75 for not installing). When the study says low , do not install.

So net expected value = .5*33.4 + .5*19 = 26.2M

Since the value above is lower than 29M ( which is the expected value when you don't do any study and just install the new system) , hence do not undertake the study.

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