 Expected Monetary Value (EMV) is an integral part of risk management and is used in the perform quantitative risks analysis process.

This technique involves mathematical calculations, which is why many PMP aspirants ignore it. I do not recommend avoiding it. This concept requires only one EMV formula.

EMV is a straightforward concept and involves basic calculations. Once you understand, solving questions will be easy

The EMV calculation involves probability and impact so let’s discuss those first

#### Probability

Probability is the likelihood that any event will occur.

For example, if you toss a coin there is a 50% chance of showing heads and a 50% chance of showing tails. So, you say that the probability of showing heads or tails is 50%.

Now we will discuss it mathematically.

The formula to calculate the probability is:

The probability of an event happening = (Number of favorable events that can occur) / (Total number of events)

Let’s see how the above formula fits with our coin example.

Total number of events = 2 (because the coin can either show heads or tails)

Total number of favorable events = 1 (assuming it’s favorable to show heads)

The probability of showing heads = (Number of favorable events) / (Total number of events)

= 1/2

= 50%

So the probability of showing heads is 50% if you toss the coin.

Let’s look at another example.

Suppose you are throwing a die; what is the probability of rolling a 5?

If you throw the dice, it will show you: 1, 2, 3, 4, 5, or 6.

Therefore, the total number of events = 6

Now, you want the die to show the number 5.

Total number of favorable events = 1

Therefore, the probability of the number 5 showing = (Number of favorable events) / (Total number of events)

= 1 / 6

= 16.67%

So, if you throw the dice, the probability of rolling a 5 is 16.67%.

Now let us find the probability of getting either a 5 or a 3.

Here, the total number of favorable events = 2

Therefore, the probability of getting either 5 or 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 a 5 or a 3 is 33.33%.

This was a short introduction to probability.

#### Impact

The impact is the amount you will spend if a given identified risk occurs.

For example, you have identified that equipment may break during your project, and new equipment will cost you 2,000 USD.

So, the impact of the risk will be 2,000 USD.

This is a description of impact.

I hope that probability and impact are now clearer to you.

## Expected Monetary Value (EMV)

EMV is a statistical technique in risk management used to quantify risks and calculate the contingency reserve

It calculates the average outcome of all future events that may or may not happen.

### Expected Monetary Value (EMV) Formula

You multiply the probability with the impact of the identified risk to get the EMV.

Expected Monetary Value (EMV) = Probability * Impact

If you have multiple risks, you will add the EMVs of all risks. This will be the expected monetary value of the project.

You will calculate the EMV of all risks, regardless of whether they are positive or negative. The EMV will be negative for negative risks and positive for positive risks.

Once you calculate the expected monetary value of the project, you will add it to your work costs estimate and generate the cost baseline. This amount is called the contingency reserve.

The sum of the EMV of all events is the contingency reserve.

For example, let’s say you have four risks with probabilities and impacts as follows:

You might think that you may need 4,500 USD to manage all risks above, but that is incorrect. Among all the identified risks, only a few will occur. The risks that do not occur will add their EMV to the pool, and the risks that do occur will use that money.

So, you will need 1,100 USD to cover all identified risks in this case.

The expected monetary value concept works well to calculate the contingency reserve when you have many risks, because the more you identify, the better your contingency will be to cover them.

If you have identified fewer risks, your reserve may dry up too soon or may not be large enough to cover a high impact.

Positive risks play a crucial role in calculating the contingency reserve. You should identify and include them in expected value calculations.

### Expected Monetary Value Examples

Now let’s have a look at a few EMV examples.

#### Example-I

You have identified risk with a 30% chance of occurring. It may cost you 500 USD. Calculate the expected monetary value for this risk event.

Given in the question:

The probability of risk = 30%

Impact of risk = – 500 USD

We know that:

Expected monetary value (EMV) = probability * impact

= 0.3 * – 500

= – 150

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, 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 of the risk event is 800 USD.

#### Example-III

You have identified two risks with a 20% and a 15% chance of occurring. They will cost you 1,000 USD and 2,000 USD if both happen.

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 their individual EMVs.

The 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

Therefore, the EMV of these two risks events = (–200) + (–300)

= –500

The expected monetary value of these two events is –500 USD.

#### Example-IV

Your team has identified three risks with probabilities of 10%, 50%, and 35% during risk management planning. If the first two risks occur, they will cost you 5,000 USD and 8,000 USD; however, the third risk will give you 10,000 USD if it occurs.

Determine the expected monetary value of these risk events.

The 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

The expected monetary value (EMV) of all three events is –1,000 USD.

These are simple examples of expected monetary value analysis. In the PMP exam, you may see similar questions.

Expected monetary value also helps you with selecting the right choice.

For example, you have a risk, and you have identified two risk response strategies to manage this risk. How will you select the best strategy?

You will use the expected monetary value to select the right risk response strategy to manage the risk.

How?

Calculate the expected monetary value for each response and select the one that is the lowest.

### Benefits of EMV Analysis

• It gives you an average outcome of all identified uncertain events.
• It helps you to calculate the contingency reserve.
• In a decision tree analysis, it helps select the best choice.
• It does not require any costly resources, only experts’ opinions.
• It helps you with a make-or-buy decision during the plan procurement process.

#### Drawbacks of EMV Analysis

• This technique is uncommon in small and small-medium-sized projects.
• This technique involves expert opinions to finalize the probability and impact of the risk; personal bias may affect the result.
• This technique works better when you have many risks.
• If you miss a positive risk, it will affect the outcome.

### Summary

Expected monetary value analysis makes it easier to quantify risks, calculate the contingency reserve and help you select the best choice in a decision tree analysis. Your risk attitude should be neutral during this process; otherwise, your calculation may suffer. Moreover, the reliability of this analysis depends on the input data. A data quality assessment should be thoroughly performed. This technique increases the confidence level in achieving the project objectives