Expected Value
GoSki Industries, Inc., wished to make a decision about whether to build a large or a small plant to produce a newly invented line of snowboards. The small plant will cost $2.8 million to build and put into operation. The large plant will cost $5.6 million to build and put into operation. The company's best estimate of sales over a planning horizon of 10 years is shown in the following table. GoSki's marketing department performed a cost/volume/profit analysis, which is shown in the following table.
|
Demand
|
Probability
|
|
High
|
5
|
|
Moderate
|
3
|
|
Low
|
2
|
GoSki's marketing department performed a cost/volume/profit analysis, which is shown in the following table:
|
Demand
|
Large Plant
|
Small Plant
|
|
High
|
$20,000,000
|
$ 5,000,000
|
|
Moderate
|
$12,000,000
|
$ 9,000,000
|
|
Low
|
$ -4,000,000
|
$11,000,000
|
Including the cost of construction, the payoff table looks like the following:
|
Demand
|
Large Plant
|
Small Plant
|
|
High
|
$14,400,000
|
$2,200,000
|
|
Moderate
|
$ 6,400,000
|
$6.200,000
|
|
Low
|
$ -9,600,000
|
$8,200,000
|
QUESTIONS:
Create a decision tree which represents all of the outcomes. Assume the following:
- There are only two possible plant sizes, and once built the size is fixed.
- Demand is a discrete variable with only three possible values.
- The future consists of a single 10 year period with the time value of money is not a factor.
Calculate the expected value of having built a large plant.
Calculate the expected value of having built the small plant.
Given the results from these two calculations, which plant would you recommend that GoSki Industries build? Provide a rationale.