1. The owner of a landscaping company is considering what to do with her company
ID: 451981 • Letter: 1
Question
1. The owner of a landscaping company is considering what to do with her company over the next two years. The last couple of years, her business has experienced a substantial increase in demand. Lately, however, there has been talk of a developer planning to build a large industrial park in the county. The landscaping company owner forecasts that potential service contracts with the new industrial park complex will increase her demand. To be prepared for the opportunities if the industrial park is built, the owner sees three options for her company: the first is to undertake a one-time major expansion of her business, the second is to commit to a minor expansion this year and another minor expansion in the second year, the third option is to simply wait and do nothing. The probability that the developer will build the industrial park is estimated at about 0.30. The assumptions and conditions are summarized below.
a. With a major expansion will result in two-year service revenues of $300,000 if the industrial park is built and $100,000 if it is not built.
b. A two-year commitment to two minor expansions will result in two-year service revenues of $250,000 if the industrial park is built and $100,000 if it is not built.
c. Waiting and doing nothing will result in service revenues of $100,000 whether or not the industrial park is built. The owner would like to determine the best alternative action.
d. Develop the appropriate pay off table.
e. Draw the decision tree.
f. Which alternative has the highest expected monetary value (EMV) under risk, and therefore would be the best alternative?
g. What is the expected value with perfect information (EVwPI)?
h. What is the expected value of perfect information (EVPI)?
i. If the cost of a major expansion is $70,000, and the total cost of two minor expansions is $90,000, what would be the EP (expected payoff or profit) for each alternative? Given this new information, which alternative would be the best?
Explanation / Answer
Decision tree has two types of nodes, decision nodes and state nodes. Branches out of the decision nodes are the options and or alternatives out of which the most suitable one needs to be selected. Branches out of the state nodes are the outcomes on which one does not have the control and often given with the probabilities of their occurrences.
In the present case there are three options:1. Major expansion, 2. Minor expansion, 3. Do nothing
There are two possibilities/ states, 1. Industrial park is developed, 2. No Industrial park is developed.
The pay-off matrix is as follows:
Expected Monetary Value = sum of the products of gains with the corresponding probabilities.
Maximum EMV corresponds to Major Expansion.
Expected value of perfect information is caculated by considering the maximum value for each state, which again corresponds to Major expansion, therefore EVwPI=$160,000
EVPI = EVwPI - EMV= 0 in the present case.
i. With this new information, EP for Major Expansion= .3*230,000 + .7*30,000 =$90,000 (160,000-70,000)
Similarly for Minor expansions EP =$55,000 whereas Ep in case of Do not act remains $100,000
Therefore the best option is to wait and do nothing.
S T A T E S ACTIONS Industrial park dev. No industrial park 1Major Expansion $300,000 $100,000 2.Minor Expansion $250,000 $100,000 3.Do not act $100,000 $100,000Related Questions
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