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558 CHAPTER 13 DECISION ANALYSIS

decision to construct the small, medium or large complex if the market research
report is unfavourable. Node 5 is a decision node indicating that PDC must make
the decision to construct the small, medium or large complex if the market research is
not undertaken. Nodes 6 to 14 are chance nodes indicating that the strong demand or
weak demand state-of-nature branches will be determined by chance.
We explain in Section Analysis of the decision tree and the choice of an optimal strategy requires that
13.6 how these we know the branch probabilities corresponding to all chance nodes. PDC has
probabilities can be
developed. developed the following branch probabilities.
If the market research study is undertaken:
PðFavourable reportÞ¼ 0:77
PðUnfavourable reportÞ¼ 0:23
If the market research report is favourable:

P(Strong demand given a favourable report) ¼ 0:94
P(Weak demand given a favourable report) ¼ 1:06

If the market research report is unfavourable:
P(Strong demand given an unfavourable report) ¼ 0:35
P(Weak demand given an unfavourable report) ¼ 1:65
If the market research report is not undertaken, the prior probabilities are appli-
cable:
P(Strong demand) ¼ 0:80
P(Weak demand) ¼ 1:20
The branch probabilities are shown on the decision tree in Figure 13.7.

Decision Strategy
A decision strategy is a sequence of decisions and chance outcomes where the
decisions chosen depend on the yet to be determined outcomes of chance events.
The approach used to determine the optimal decision strategy is based on a
backward pass through the decision tree using the following steps:
1 At chance nodes, calculate the expected value by multiplying the payoff at the
end of each branch by the corresponding branch probabilities.
2 At decision nodes, select the decision branch that leads to the best expected
value. This expected value becomes the expected value at the decision node.
Starting the backward pass calculations by calculating the expected values at chance
nodes 6 to 14 provides the following results:

EVðNode6Þ¼ 0:94ð8Þþ 0:06ð7Þ ¼ 7:94
EVðNode7Þ¼ 0:94ð14Þþ 0:06ð5Þ ¼ 13:46
EVðNode8Þ¼ 0:94ð20Þþ 0:06ð 9Þ¼ 18:26
EVðNode9Þ¼ 0:35ð8Þþ 0:65ð7Þ ¼ 7:35
EVðNode10Þ¼ 0:35ð14Þþ 0:65ð5Þ ¼ 8:15
EVðNode11Þ¼ 0:35ð20Þþ 0:65ð 9Þ¼ 1:15
EVðNode12Þ¼ 0:80ð8Þþ 0:20ð7Þ ¼ 7:80
EVðNode13Þ¼ 0:80ð14Þþ 0:20ð5Þ¼ 12:20
EVðNode14Þ¼ 0:80ð20Þþ 0:20ð 9Þ¼ 14:20

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