A Short Guide to Expected Monetary Value (EMV)

By Fahad Usmani

I am writing this blog post on expected monetary value (EMV) upon receiving a request from a visitor of my blog named Mohammad Anjum.
This technique is an important part of risk management, which is usually used in large and complex projects. Expected monetary value is used in the Perform Quantitative Risks Analysis process, and is one of the few techniques in the PMBOK Guide which involves mathematical calculations. Therefore, many aspirants leave this topic and try to avoid the whole concept.
On the surface this technique may look complex to you; however this is a very simple technique, which involves simple mathematical calculations. Once you understand the concept, it will be like a piece of cake for you.
Moreover, this concept is also very important from a PMP, and PMI-RMP exam point of view. In your PMP, and/or PMI-RMP test you are going to see a few questions from the expected monetary value analysis.
By avoiding this concept not only do you miss an important risk management concept, you also leave many questions unattended in the exam.
To understand the concepts I suggest you read this blog post, follow the examples, and you are all set!
Before we start discussing the expected monetary value concept, we will talk about probability and impact in brief, because in the EMV calculation we are going to use them. If you understand probability, you won’t face any difficulty in understanding the expected monetary value properly.

Probability

Probability is the measurement of the likelihood of the occurrence of any event.
For example, if you toss a coin, it will either show heads or the tails. There is a 50% chance of showing heads, and a 50% chance of showing tails. So in this case you will say that the probability of showing heads (or tails) is 50% (or 1/2).
Let’s discuss it mathematically.
The formula to calculate the probability is:
Probability of an event happening = (Number of favorable events that can occur)/(Total number of events)
Now let’s see how the above formula fits into tossing the coin.
Total number of events = 2 (because the coin can either show heads or the tails)
Total number of favorable events = 1
Therefore, the probability of showing heads = (Number of favorable events)/(Total number of events)
= ½
= 50%
So if you toss the coin the probability of showing heads is 50%.
Got it?
If not, let me give you another example.
Suppose you are throwing a dice, what is the probability of the number 5 coming up?
If you throw the dice then it will show you either 1, or 2, or 3, or 4, or 5, or 6.
Therefore, the total number of events = 6
Now you want dice to show the number 5.
Total number of favorable events = 1
Therefore the probability of showing the number 5 = (Number of favorable events)/(Total number of events)
= 1/6
= 16.67%
So, if you throw the dice, the probability of the number 5 showing up is 16.67%.
Now let’s find the probability of getting either number 5 or number 3.
In this case, the total number of favorable events = 2
Therefore, the probability of showing either number 5 or number 3 = (Number of favorable events)/(Total number of events)
= 2/6
=1/3
= 33.33%
So, if you throw the dice, the probability of getting either 5 or 3 is 33.33%.
This was a short introduction of probability. Now we come to the “impact”.

Impact

Here you can say that the impact is the amount that you will have to spend if any identified risk occurs.
For example, you have identified that during the peak of your project, some equipment may break down and you may need to buy new equipment that will cost you 2,000 USD.
So the impact of the risk will be 2,000 USD.
This was a short description of impact.
I hope that probability and impact are clear to you. If yes, we can move on to our topic, i.e. expected monetary value (EMV).

Expected Monetary Value (EMV)

Expected monetary value (EMV) is a statistical technique in risk management that is used to convert the risk into a number, which in turn assists the project manager calculate the contingency reserve, and helps compare a risk with other risks.
According to the PMBOK Guide 5th edition, the definition of the expected monetary value is as follows:
“Expected monetary value analysis is a statistical concept that calculates the average outcomes when the future includes the scenarios that may or may not happen.”
Therefore, you can say that:
1. It helps in calculating the amount required to manage all identified risks.
2. It helps in selecting the choice which involves less money to manage the risks.
To calculate the expected monetary value of an event you must have its probability and the impact if it occurs.
Once you get these data, you will multiply the probability with the impact, and the result will be the expected monetary value.
Therefore,
Expected Monetary Value (EMV) = Probability * Impact
If you have multiple risks, you will calculate the EMV of those risks separately and add them all.
Please note that you will calculate the EMV of all risks, regardless of whether they are positive risks or negative risks.
If they are negative risks the EMV will be negative, and if they are positive risks the EMV will be positive. (This will become more clear when I will show you the examples for calculating the EMV.)
Once you calculate the expected monetary value of the project, you will add this amount to your work package costs estimate and get the project baseline.
The amount you added to the work package costs estimate is known as the contingency reserve.
For example, let’s say you have four risks with probabilities and impacts as follows:

From the above table you can say that you may need 4,500 USD to manage all risks, but this is not so.
Why?
Because not all risks are going to happen altogether. Some of them may happen and some of them may not. The risks that will not occur will add their EMV to the pool and the risks that will occur will utilize the money from the pool.
So, in the above case you may need to add 1,100 USD to your budget to cover all identified risks.
The expected monetary value concepts works well to calculate the contingency reserve when you expect a lot of risks, because the more risks you identify, the spread of the contingency reserve will be better among all risks.
If you have identified fewer risks, you will not get enough spread and your reserve may dry up sooner.
Positive risks play an important role in calculating the contingency reserve. You must identify and include the positive risks in expected value calculations.
Expected monetary value also helps you with selecting the best decision.
For example, you have a risk and you have identified two risk response strategies to manage this risk. So how will you select the best strategy?
You will use the expected monetary value to select the best risk response strategy to manage the risk.
How?
You will calculate the expected monetary value for each response and select the one which has the lowest value.
Now it is time to see some examples on expected monetary value analysis.

Example-I

You have identified a risk with a 30% chance of occurring. However, if this risk occurs it may cost you 500 USD. Calculate the expected monetary value (EMV) for this risk event.
Given in the question:
Probability of risk = 30%
Impact of risk = – 500 USD
We know that:
Expected monetary value (EMV) = probability * impact
= 0.3 * -500
= -150
Hence the expected monetary value (EMV) of the risk event is -150 USD.

Example-II

You have identified an opportunity with a 40% chance of happening. However, if this positive risk occurs it may help you gain 2,000 USD. Calculate the expected monetary value (EMV) for this risk event.
Given in the question:
Probability of risk = 40%
Impact of risk = 2,000 USD
We know that:
Expected monetary value (EMV) = probability * impact
= 0.4 * 2,000
= 800
Hence the expected monetary value (EMV) of the risk event is 800 USD.

Example-III

In your project you have identified two risks with a 20% and 15 % chance of occurring. If both of these risks occur they will cost you 1,000 USD and 2,000 USD respectively. What is the expected monetary value of these risk events?
In the above question, you have two negative risks; therefore, the expected monetary value of these two risks will be the sum of the expected monetary value of these risks individually.
Expected monetary value of two risk events = EMV of the first event + EMV of the second event
EMV of the first event = 0.20 * (-1,000)
= -200
EMV of the second event = 0.15 * (-2,000)
= -300
Hence the EMV of these two risks events = (-200) + (-300)
= -500
Therefore, the expected monetary value (EMV) of these two events is -500 USD.

Example-IV

During risk management planning your team has identified three risks with probabilities of 10%, 50%, and 35%. If the first two risks occur, they will cost you 5,000 USD and 8,000 USD; however, if the third risk occurs it will give you benefit of 10,000 USD.
Determine the expected monetary value of these risk events.
Expected monetary value of three events = EMV of the first event + EMV of the second event + EMV of the third event
EMV of the first event = 0.10 * (-5,000)
= -500
EMV of the second event = 0.50 * (-8,000)
= -4,000
EMV of the third event = 0.35 * 10,000
= 3,500
EMV of all three events = EMV of the first event + EMV of the second event + EMV of the third event
= – 500 – 4,000 + 3,500
= -1,000
Hence the expected monetary value (EMV) of all three events is -1,000 USD.
I have selected four of the simplest types of examples on expected monetary value analysis to show you the EMV calculation in different scenarios. In the real PMP exam you will see the question based on these four basic types.
I believe if you understand the above examples, you will not face any problems in solving the questions based on the expected monetary value.

Benefits of Expected Monetary Value (EMV) Analysis

The expected monetary value offers many benefits in risk management planning. A few of them are as follows:

• It gives you average outcome of all uncertain events.
• It helps you select the best decision with a backup of objective data.
• It helps you calculate the contingency reserve.
• It helps you with a make or buy decision during the procurement planning process.
• It helps in decision tree analysis. Decision tree analysis is a graphical diagrammatic technique which helps you understand the problem and solution easily.
• This technique does not require any costly resources, only the experts’ opinion.

Drawbacks of Expected Monetary Value (EMV) Analysis

The following are a few drawbacks of expected monetary analysis:

• This technique is usually not used in small and small-medium sized projects.
• This technique involves experts’ opinion to finalize the probability and impact of the risk. Therefore, personal bias may affect the result.
• This technique works well when you have a large number of risks because it helps spread the impact of the risks.
• Sometimes you may miss the inclusion of positive risks, which may affect the final outcome.
• While doing the expected monetary value your risk attitude should be neutral, otherwise it may affect the calculation.
• The reliability of this analysis is based on the data provided as input to this technique. Therefore the data quality assessment should be thoroughly performed.

Summary

If you have a large project and you want to complete it successfully within your budget and schedule, there is no escape from the expected monetary value analysis. You must perform this risk management technique because it helps you develop the decision tree and the contingency reserve. This helps increase the confidence level in achieving the project objectives.
Here is where this blog post on expected monetary value (EMV) ends. If you have something to say, you can do so through the comments section.
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