# Expected monetary value

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The **expected monetary value** (EMV) is a risk management tool used to calculate the expected values of different outcomes associated with a given decision or gamble. It is calculated by multiplying the probability of each outcome by its associated monetary value, then summing all the values together. The EMV is the expected outcome of a decision, taking into account the likelihood of each outcome and its associated cost or benefit. It is used to help decision makers decide which course of action is more likely to be profitable.

## Application of expected monetary value

Expected monetary value is used in many different contexts, including:

**Business decisions**: It can be used to determine the expected return of a proposed venture, or to compare different options in order to decide which is the most profitable.**Insurance**: It can be used to calculate the expected cost of a policy, taking into account the probabilities of different claims being made.**Investment decisions**: EMV can be used to compare different investment options, helping to determine which one is likely to be the most profitable.**Risk management**: EMV can be used to assess the risk of a particular decision or action, helping to determine if it is worth taking.

## Expected monetary value example

For example, consider a business decision to invest in a new product. The possible outcomes are success, failure, and break-even. The probabilities of each outcome are 20%, 60%, and 20%, respectively. The associated monetary values for the outcomes are $10,000, $0, and $2,000, respectively.

Using the expected monetary value formula, we can calculate the EMV as follows:

EMV = (20% x $10,000) + (60% x $0) + (20% x $2,000) = $2,000

Therefore, the expected monetary value of this decision is $2,000. This indicates that, on average, the decision to invest in the new product will generate a return of $2,000.

## Expected monetary value calculation

To calculate the expected monetary value, you will need to do the following:

- Determine the possible outcomes of the decision.
- Assign a monetary value to each outcome.
- Calculate the probability of each outcome.
- Multiply the probability of each outcome by its associated monetary value.
- Sum the results of the multiplications to get the expected monetary value.

\(EMV = \sum_{i=1}^n p_i V_i\)

where p_{i} is the probability of outcome i and V_{i} is the associated monetary value.

## Expected monetary value and decision tree

Expected monetary value (EMV) is closely related to decision trees. A decision tree is a visual tool used to map out the expected outcomes of a decision, taking into account the probabilities of each outcome. The EMV is the sum of all the expected outcomes (discounted for time) and is calculated by multiplying each outcome’s probability by its associated monetary value. By visualizing the different outcomes and calculating the EMV, decision makers can more easily assess the risk of a particular decision and make better-informed decisions

To use expected monetary value (EMV) in a decision tree, first identify all the possible outcomes of the decision. For each outcome, assign a monetary value to it, either positive or negative. Then, calculate the probability of each outcome.

Once the probabilities have been determined, the EMV can be calculated by multiplying the probability of each outcome by its associated monetary value. This can be done by summing the products of the probability and value for each outcome. After all the calculations are done, the EMV can then be compared to the costs associated with the decision.

This comparison can help decision makers assess the risk of a particular decision and make better-informed decisions. By visualizing the decision tree, decision makers can also identify the most important factors influencing the outcome and use this information to further refine their decision making.

## Suggested literature

- Hoverstad, R., Sylvester, R., & Voss, K. E. (2001).
*The expected monetary value of a student: A model and example*. Journal of Marketing for Higher Education, 10(4), 51-62. - Gagnon, M., Thibault, D., & Blain, M. (2020).
*On the expected monetary value of hydroelectric turbine start-up protocol optimisation*. In Engineering Assets and Public Infrastructures in the Age of Digitalization (pp. 209-216). Springer, Cham. - Rexeisen, R. J., & Sathe, R. S. (2005).
*Prudent Fiscal Stewardship: Estimating the Expected Monetary Value of an Educational Program*. International Education Journal, 6(3), 297-307.