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Estimating Cash Flows in an Uncertain Environment
270 Part IV: Anticipating Surprises: Risk and Uncertainty
This formula indicates that action aj’s expected monetary value equals the summation for all states of nature i = 1 through i = n of the probability of θi occurring, P(θi), multiplied by the payoff associated with action aj and state of nature θi, πij.
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After you calculate the expected monetary value, you choose the action with the best expected payoff.
To use the expected monetary value criterion, Global Airlines must determine the probability associated with each state of nature — what happens to oil prices. Currently, Global believes the probability that the price of oil decreases 10 percent is 0.05, the probability that oil prices stay the same is 0.35, the probability that oil prices increase 10 percent is 0.45, and the probability that oil prices increase 20 percent is 0.15. Note that adding the probabilities for all possible states of nature equals 1.0 (0.05+0.35+0.45+0.15). Thus, Global has considered all possibilities.
To determine the expected monetary value for each action, you take the following steps:
1. Calculate the expected monetary value for reducing fares.
Let reducing fares represent action aj. For each state of nature, multiply the probability of that state of nature by the payoff associated with that state of nature and action aj, reduce fares. Add the resulting values to determine the expected monetary value.
2. Calculate the expected monetary value for keeping the same fares.
Let the same fares represent action aj. For each state of nature, multiply the probability of that state of nature by the payoff associated with that state of nature and action aj, same fares. Add the resulting values to determine the expected monetary value.
3. Calculate the expected monetary value for raising fares.
Let raising fares represent action aj. For each state of nature, multiply the probability of that state of nature by the payoff associated with that state of nature and action aj, raise fares. Add the resulting values to determine the expected monetary value.
