SUBDOMAIN 309.3 - QUANTITATIVE ANALYSIS
Competency 309.3.3: Expected Value Decision Analysis - The graduate uses expected value concepts as decision-making tools.
Objective 309.3.3-04: Determine for a given decision tree which decision branch has the most favorable total expected value.
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Introduction:
A company is considering two alternatives for improving profits: develop new products or consolidate existing products. If the company decides to develop new products, it can either develop several products rapidly or take time to develop a few products more thoroughly. If the company chooses to consolidate existing products, it can either strengthen the products to improve profits or simply reap whatever gains are attainable without investing more time and money in the products.
Given:
The “Decision Tree Chart” attachment shows the predicted gains from each decision alternative described above. Gains depend on how the market reacts to the action taken by the company. The probability of each market reaction is shown on the decision tree.
Task:
Develop a response to the attached decision tree chart in which you:
A. Calculate the expected value for each of the four decision branches.

ANSWER: To determine the Expected Value (EV) you multiple the demand probability by the payoff, then add the different states of nature for the decision alternative.
EV= Demand Probability (Payoff) + Demand Probability (Payoff) + Demand Probability (Payoff)

For the first decision alternation, the Develop New Product node has two types of decision alternatives: Develop Thoroughly and Develop Rapidly.

The first EV for the Develop thoroughly nodes are as follows:

DEVELOP THOROUGHLY:
EV = 0.4($500,000) + 0.4($25,000) + 0.2($1000)
EV = $200,000 + $10,000 + $200
EV = $210,200

DEVELOP RAPIDLY:
EV = 0.1($500,000) + 0.2($25,000) +