A manager must decide how many machines of a certain type to buy. The machines w
ID: 361947 • Letter: A
Question
A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the two machines were purchased at the same time. The estimated probability of low demand is .30, and the estimated probability of high demand is .70. The net present value associated with the purchase of two machines initially is $77,000 if demand is low and $132,100 if demand is high. The net present value for one machine and low demand is $95,000. If demand is high, there are three options. One option is to do nothing, which would have a net present value of $105,680. A second option is to subcontract; that would have a net present value of $125,850. The third option is to purchase a second machine. This option would have a net present value of $104,952.
a. What is the EMV (expected monetary value) for alternative buy one machine? The EMV is $.
b. What is the EMV (expected monetary value) for alternative buy two machines? The EMV is $.
c. How many machines should the manager purchase initially? The manager should purchase machine(s) initially.
Explanation / Answer
Expected monetary value is the expected gain/loss calculated as Sigma(i)piXi where pi represents probability of outcome Xi.
a. There are two possibilities, either demand is low or demand is high. Probability (demand low) = .3
and Probability (demand high) = .7
Outcome in case of low demand is $95,000 having probability .3
Outcome in case of high demand is 105,680 (do nothing) having probability .7
Therefore EMV (do nothing) = 95000*.3 + 105680*.7 = $102,476
Details for three options are as follows:
Highest EMV under sub contracting is $116,595
Answer b.
In case of two machines, EMV = .3*77000 + .7*132100 = $115,570
Answer c
Based on the above analysis it is recommended to go for machine 1 with sub contracting with EMV=$116,595
Demand Prob Outcome pi*Xi Low 0.3 95000 28500 High 0.7 105680 73976 Do nothing EMV= 102476 Demand Prob Outcome pi*Xi Low 0.3 95000 28500 High 0.7 125850 88095 Sub-contract EMV= 116595 Demand Prob Outcome pi*Xi Low 0.3 95000 28500 High 0.7 104952 73466.4 Purchase machine2 EMV= 101966.4Related Questions
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