A manager is trying to decide whether to buy one machineor two. If only one is purchased and demand proves to beexcessive, the second machine can be purchased later. Somesales will be lost, however, because the lead time for produc-ing this type of machine is six months. In addition, the costper machine will be lower if both are purchased at the sametime. The probability of low demand is estimated to be 0.20.The after-tax net present value of the benefits from purchas-ing the two machines together is $90,000 if demand is lowand $180,000 if demand is high.If one machine is purchased and demand is low, the netpresent value is $120,000. If demand is high, the managerhas three options. Doing nothing has a net present value of$120,000; subcontracting, $160,000; and buying the secondmachine, $140,000.a. Draw a decision tree for this problem.b. How many machines should the company buy initially?What is the expected payoff for this alternative?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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A manager is trying to decide whether to buy one machine
or two. If only one is purchased and demand proves to be
excessive, the second machine can be purchased later. Some
sales will be lost, however, because the lead time for produc-
ing this type of machine is six months. In addition, the cost
per machine will be lower if both are purchased at the same
time. The probability of low demand is estimated to be 0.20.
The after-tax net present value of the benefits from purchas-
ing the two machines together is $90,000 if demand is low
and $180,000 if demand is high.
If one machine is purchased and demand is low, the net
present value is $120,000. If demand is high, the manager
has three options. Doing nothing has a net present value of
$120,000; subcontracting, $160,000; and buying the second
machine, $140,000.
a. Draw a decision tree for this problem.
b. How many machines should the company buy initially?
What is the expected payoff for this alternative?

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