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DECISION MAKING WITH PROBABILITIES 549

Table 13.6 Payoff Table for the PDC Project (R Million)
State of Nature
Decision Alternative Strong Demand s 1 Weak Demand s 2

8 7
Small complex, d 1
14 5
Medium complex, d 2
20 9
Large complex, d 3

To help determine the decision strategy for PDC, we reproduced PDC’s payoff table
as Table 13.6. Note that, if PDC knew for sure that state of nature s 1 would occur, the
best decision alternative would be d 3 , with a payoff of R20 million. Similarly, if PDC
knew for sure that state of nature s 2 would occur, the best decision alternative would
be d 1 , with a payoff of R7 million. Thus, we can state PDC’s optimal decision
strategy when the perfect information becomes available as follows:

If s 1 ; select d 3 and receive a payoff of R20 million:
If s 2 ; select d 1 and receive a payoff of R7 million:

What is the expected value for this decision strategy? To calculate the expected
value with perfect information, we return to the original probabilities for the states
of nature: P(s 1 ) ¼ 0.8, and P(s 2 ) ¼ 0.2. Thus, there is a 0.8 probability that the
perfect information will indicate state of nature s 1 and the resulting decision alter-
native d 3 will provide a R20 million profit. Similarly, with a 0.2 probability for state
of nature s 2 , the optimal decision alternative d 1 will provide a R7 million profit.
Thus, from equation (13.4), the expected value of the decision strategy that uses
perfect information is:
0:8ð20Þþ 0:2ð7Þþ 17:4

We refer to the expected value of R17.4 million as the expected value with perfect
information (EVwPI).
Earlier in this section we showed that the recommended decision using the
expected value approach is decision alternative d 3 , with an expected value of
R14.2 million. Because this decision recommendation and expected value calcula-
tion were made without the benefit of perfect information, R14.2 million is referred
to as the expected value without perfect information (EVwoPI).
The expected value with perfect information is R17.4 million, and the expected
value without perfect information is R14.2; therefore, the expected value of the
perfect information (EVPI) is R17.4 R14.2 ¼ R3.2 million. In other words, R3.2
It would be worth R3.2 million represents the additional expected value that can be obtained if perfect
million for PDC to learn information were available about the states of nature.
the level of market
acceptance before Generally speaking, a market research study will not provide ‘perfect’ informa-
selecting a decision tion; however, if the market research study is a good one, the information gathered
alternative. might be worth a sizeable portion of the R3.2 million. Given the EVPI of R3.2
million, PDC might seriously consider a market survey as a way to obtain more
information about the states of nature.
In general, the expected value of perfect information (EVPI) is calculated as
follows:

EVPI ¼jEVwPI EVwoPIj (13:5)

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