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 $79,200
if demand is low and $130,600 if demand is high. The net present
value for one machine and low demand is $99,000. If demand is high,
there are three options. One option is to do nothing, which would
have a net present value of $124,680. A second option is to
subcontract; that would have a net present value of $115,650. The
third option is to purchase a second machine. This option would
have a net present value of $123,540.

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.

Answer #1

a) EMV for one machine = Probability of Low Demand X Net Prsent Value + Probability of High Demand X Net present value

= 0.3 X 99000 + 0.7 X 124680 [out of 3 options with high demand and one machine, the option with highes NPC has been chosen]

=$116076

b) EMV with two machines = Probability of Low Demand X Net Prsent Value + Probability of High Demand X Net present value

= 0.3 X 79200 + 0.7 X 130600 = $115180

c) Since expected value is more with one machine, the manager should purchase one machine initially

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