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564 CHAPTER 13 DECISION ANALYSIS

Figure 13.12 Risk Profile for PDC Project with Sample Information Showing Payoffs
Associated with Optimal Decision Strategy

0.8

Probability 0.6

0.4

0.2

–10 0 10 20
Profit (€ millions)

Figure 13.12 provides a graphical representation of the risk profile. Comparing
Figures 13.3 and 13.12, we see that the PDC risk profile is changed by the strategy
to conduct the market research study. In fact, the use of the market research study
has lowered the probability of the R9 million loss from 0.20 to 0.05. PDC’s manage-
ment would most likely view that change as a significant reduction in the risk
associated with the project.

Expected Value of Sample Information
In the PDC problem, the market research study is the sample information used to
The EVSI ¼ R1.73
million suggests PDC determine the optimal decision strategy. The expected value associated with the
should be willing to pay market research study is R15.93 million. In Section 13.3 we showed that the best
up to R1.73 million to
conduct the market expected value if the market research study is not undertaken is R14.20 million.
research study. Thus, we can conclude that the difference, R15.93 million R14.20 million ¼ R1.73
million, is the expected value of sample information (EVSI). In other words, con-
ducting the market research study adds R1.73 million to the PDC expected value. In
general, the expected value of sample information is as follows:

EVSI ¼jEV W SI EV Wo SIj (13:13)

where
EVSI ¼ expected value of sample information
EV W SI ¼ expected value with sample information about the states of nature
EV Wo SI ¼ expected value without sample information about the states of nature
Note the role of the absolute value in Equation (13.13). For minimization problems
the expected value with sample information is always less than or equal to the
expected value without sample information. In this case, EVSI is the magnitude of
the difference between EVwSI and EVwoSI; thus, by taking the absolute value of
the difference as shown in Equation (13.13), we can handle both the maximization
and minimization cases with one equation.

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