C. 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:
1. Create a decision tree which represents all of the outcomes. Assume the following:
a. There are only two possible plant sizes, and once built the size is fixed.
b. Demand is a discrete variable with only three possible values.
c. The future consists of a single 10 year period with the time value of money is not a factor.
2. Calculate the expected value of having built a large plant.
3. Calculate the expected value of having built the small plant.
4. Given the results from these two calculations, which plant would you recommend that GoSki Industries build? Provide a rationale.