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# Expected Monetary Value (EMV) definition

What is expected monetary value (EVM)? It’s a risk management tool that aims to predict the value of future events.

It’s impossible to accurately predict the exact value of risk or opportunity an event may present to a project because the occurrence and impact of each event is unknown. Statistical concepts rely on historical data and estimations to forecast the value of each risk event.

## EMV mathematical formula

How to calculate expected monetary value? The formula used to estimate EMV is the probability of the event occurring multiplied by the expected impact in the likely occurrence of that event.

If an event is seen as a risk to a project and losses are expected in the occurrence of that event, the impact will be represented by a negative figure. The impact will be a positive figure if the event is seen as an opportunity to profit.

An event and its EMVs is usually mapped out in a decision tree to represent various scenarios and outcomes.

## Expected Monetary Value example: Printer vendor

Let’s say that your printing business recently ordered a printer for \$10,000. You have dealt with the vendor before and you know that they usually deliver late.

You have already promised your clients high-quality photo prints that would be produced by the new printer. Any delay will cost you \$1,000 a day.

Lets say your estimated probability that the vendor delivers your new printer on time is 50% and the likelihood of a five-day delay, which will cost you \$5000 (5 x 1000), is also 50%.

• The EMV of the event with no delay from the vendor is: 50% of \$10,000 = \$5000

• The EMV of the event that includes extra delay charges is 50% of (\$10,000 + \$5000) = 50% of \$10,500 = -\$7500

• Total EMV is: \$5000 + \$7500 = \$12,500

Saying the total cost of using this vendor is \$10,000 does not take into account the risks of late delivery and any potential penalties.

## Decision trees

The use of decision trees allows companies to evaluate the EMVs of multiple options. Let’s go back to the printer example and bring in a second vendor who is less likely to deliver late but charges you \$11,000 for the printer.

Lets say your estimated probability that the new vendor delivers your new printer on time is 95% and the likelihood of a five-day delay is 5%. Once again, late delivery costs you \$1,000 a day.

• The EMV of the no delay event from the second vendor’s end is: 95% x \$11,000 = \$10,450

• The EMV of a delayed event from the second vendor is: 5% x (\$1,100 + \$500) = \$800

• Total EMV is: \$10,450 + \$800 = \$11,250.

It can be concluded that the second vendor is a better option. Their EMV is lower than for the first vendor – \$11,250 versus \$12,500

What does expected monetary value mean in the context of decision trees? It allows companies to compare risk events and allow decision-making based on an organisation's degree of risk aversion.

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