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Assessing the value of new information 229
Table 8.1 – Calculating the expected value of perfect information
Test indication Prob.
Best course
of action
Payoff
($)
Prob. × payoff
($)
Virus is absent 0.7 Plant potatoes 90 000 63 000
Virus is present 0.3 Plant alternative 30 000 9 000
Expected payoff with perfect information = 72 000
Best expected payoff without perfect information = 57 000
Expected value of perfect information (EVPI) = 15 000
indicate that the virus is absent then the manager would earn $90 000 by
planting potatoes and $30 000 planting the alternative crop so the best
decision would be to plant potatoes.
Alternatively, the test might indicate that the virus is still present.
There is a 0.3 probability that it will give this indication. In this case,
the manager would lose $20 000 if he planted potatoes, so the best
decision would be to plant the alternative crop and earn a net return
of $30 000.
To summarize: there is a 0.7 probability that the test will indicate that
the virus is absent, in which case the manager would earn net returns of
$90 000, and a 0.3 probability that it will indicate that the virus is present,
in which case he will earn $30 000. This means that his expected returns
if he buys the perfect information will be $72 000.
As we saw earlier, without the test the manager should plant potatoes
when he would earn an expected return of $57 000. So the expected
increase in his returns resulting from the perfect information (i.e. the
expected value of perfect information) would be $72 000 − $57 000, which
equals $15 000. Of course, we have not yet considered the fee which
Ceres would charge. However, we now know that if their test is perfectly
accurate it would not be worth paying them more than $15 000. It is likely
that their test will be less than perfect, in which case the information it
yields will be of less value. Nevertheless, the EVPI can be very useful in
giving an upper bound to the value of new information. We emphasize
that our calculations are based on the assumption that the decision
maker is risk neutral. If the manager is risk averse or risk seeking or if
he also has non-monetary objectives then it may be worth him paying
more or less than this amount. We make the same assumption in the next
section where we consider how to calculate the value of information
which is not perfectly reliable.