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 increase 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 demands is .30, and the estimated
probability of high demand is .70.
The net present value associated with the purchase of two machines
initially is $75,000 if demand is low and $130,000 if demand is
high.
The net present value for one machine and low demand is $90,000 .
If demand is high, there are three options. One option is to do
nothing, which would have a net present value of $90,000 . A second
option is subcontract; that would have a net present value of
$110,000 . The third option is to purchase a second machine. This
option would have a net present value of $100,000.
How many machines should the manager purchase initially ? Use a
decision tree to analyze this problem.
We can look at this problem as follows:
If the decision today is to buy 2, then the expected payoff is the weighted average of 130000 and 75000 weighted by the probabilities of high- and low- demand. This comes to 113500.
If the decision today is to buy 1, then there is a future decision in case of high demand (sub-contract or buy 2nd machine) the average payoff of which is 100000 (average of 90000, 110000 and 100000). In case of low demand there's no decision required in future. The average of this would be 0.7*100000 + 0.3*90000 = 97000.
Since the expected payoff from buying 2 machines today (113500) is higher the manager should buy two machines today.
Do nothing | 90000 | |||||
High demand (0.7) | 100000 (avg of 90000, 110000 and 100000) | Tomorrow | Sub-contract | 110000 | ||
Buy 1 | Buy second machine | 100000 | ||||
97000 (0.7*100000 + 0.3*90000) | Low demand (0.3) | 90000 | ||||
Today | ||||||
High demand (0.7 x 130000) | 91000 | |||||
Buy 2 | ||||||
113500 (91000 + 22500) | Low demand (0.3 x 75000) | 22500 | ||||
A manager must decide how many machines of a certain type to buy. The machines will...
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