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, and is usually used in medium, 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. Because of this many aspirants leave this topic and try to avoid the whole concept.

On the surface this technique may look complex, however, it is a very simple technique, involving relatively light mathematical calculations. Once you understand the concept, it will be like a piece of cake.

Moreover, this concept is also 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 these concepts I suggest you read this blog post, follow the examples, and ask questions if you have trouble!

Before we start discussing the expected monetary value concept, we will briefly talk about probability and impact, because in the EMV calculation we are going to use them. If you understand probability, you should not have 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 die, what is the probability of the number 5 coming up?

If you throw the die it will show you one of the following: 1, 2, 3, 4, 5, or 6.

Therefore, the total number of events = 6

Now you want die 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 die, the probability of the number 5 showing is 16.67%.

Now let us 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 die, 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**

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 they are, 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 quantify the risks, which in turn assists the project manager to calculate the contingency reserve.

According to the PMBOK Guide 5th edition:

“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:

- It helps in calculating the amount required to manage all identified risks.
- 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 the probability and the impact should it occur.

Once you calculate this data, you will multiply the probability by the impact, and the result will be the expected monetary value.

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 clearer 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 generate 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 that you may need 4,500 USD to manage all risks, but this would not be correct. Not all risks are going to happen, 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 too soon, or may not be large enough to cover a single large risk.

Positive risks also play an important role in calculating the contingency reserve. You should 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

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

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

= -500

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

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

These are four relatively simple types of examples on expected monetary value analysis chosen 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 should 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 identified 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 expert opinions 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 should perform this risk management technique as 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.

Felix says

I like it !

Fahad Usmani says

Thanks Felix.

andres says

Can you please help me… I don’t get this:

Michael Dell, president of Dell Computers, Inc., has two design options for his new high resolution flat screen monitors for CAD workstations. The life cycle sales forecast of the monitors is 100,000 units.

Design option A has a 0.70 probability of yielding 59 good monitors per 100 and 0.3 probability of yielding 64 good monitors per 100. This design cost is $1,000,000.

Design option B has a 0.60 probability of yielding 64 good units per 100 and 0.40 probability of yield 59 good units per 100. This design will cost $1,350,000.

Good or bad, each monitor will cost $75. Each good monitor will sell for $150. Bad monitors are destroyed and have no salvage value. We ignore any disposal cost in this problem.

Which design option should be selected and what is its expected monetary value (EMV)? Note: You must select both parts correctly to get credit for this answer.

A. Design A; EMV=$450,000

B. Design B ; EMV=$450,00

C. Design A; EMV=$575,000

D. Design B; EMV=$575,000

Manuela says

Correct Answer C ( design A / EMV=575.000)

Calculation

Design A EMV= 70%*[ (-1.000.000 cost design A) +(- 7.500.000 cost production ) + (59.000*150=8.850.000 revenue)]+ 30%* [ (-1.000.000 cost design A) +(- 7.500.000 cost production ) + (64.000*150=9.600.000 revenue)= 575

Design B EMV= 60%*[ (-1.350.000 cost design B) +(- 7.500.000 cost production ) + (64.000*150=9.600.000 revenue)]+ 40%* [ (-1.350.000 cost design B) +(- 7.500.000 cost production ) + (59.000*150=8.850.000 revenue)= 450

PMBOK guide fifth edition / Figure 11-16 page339

PK says

But Option B is also correct

Emilio says

Sorry i dont understart why are (64.000*100) or (59.000*100). Where these figures (64000 and 59000) come from?. Them should be 6400 and 5900?

Sorry I am new in this.

Thank you so much

Camilo C says

Hello Emilio

You must produce 100,000, right?

Design A, states that 59/100(0.59) means: (0.59*100000)=59.000.

Design B, states that 64/100 (0.64) means: (0.64*100000)=64.000.

Hello PK

Yes the option B is also correct but the best option to take is Option C.

Regards

Syed Warsi says

This short EMV guide is a great tool for everyone, particularly for those trying to understand and apply this important concept from project risk stand point..

Thanks you very much Fahad..

Fahad Usmani says

Thank you Warsi sahab for your comment.

Expected monetary value is an important concept in risk management which involves the mathematical calculations causing many professionals leave this topic.

I hope this blog post will help them understand this concept better.

raj says

this article is really good for beginners.. it helped me..thank you so much 🙂

Fahad Usmani says

Thanks Raj for your visit and leaving your comment.

Muhammad Anjum says

Jazak Allah Khair for writing this very nice blog post on my request. This helps more to understand the risk management concept.

Here in this blog post, I have a little confusion which is;

Probability tell us the chance of occurring an risk event, e.g. 10% probability means, there is 10 % chance of occurring risk event, but if this risk event occurred, it will consume impact value not expected monitory value. And, if all identified risk events happens at different times then shall we not in loss as we are using expected monitory value (EMV) not impact value which is actually to be consumed on occurring of risk events?

Fahad Usmani says

It is rare that all identified risks will occur.

If this happens, this means that your risk management plan was wrong and you miscalculated the probabilities. EMV provides you the pool and if any risk occurs you will utilize the money (impact money) it to manage the risk, and any risk does not occur it will save the money to this pool.

mike says

Hi Usmani

Thanks for your blog very helpful one query

So based on EMV contingency reserve is applied.

What about the impact amount will it be taken into consideration for any calculation

As I am not clear if 10% probability .. impact is 1000 USD then emv 100 …. CR would be 100 … Wat will happen if risk occurs at the end we need 1000 USD or the impact amount from where we get this

Fahad Usmani says

Contingency reserve is the reserve for all risks. Some of them will happen and rest will not. So if any of your identified risk occurs, you will use money from the pool. The larger the number of risks, the spread of risk impact will be good.

Hope it is clear now.

PD says

This isn’t correct. The reserve is the amount of money set aside for risk mitigation actions, so let’s say the EMV for risk no.1 is 75,000… that means you have 75,000 in which to implement actions designed to mitigate that risk.

The EMV technique isn’t designed so should one of your risks materialise you have the money from the “combined pot” to replace an item of that value, or replace delayed revenue etc., etc.

Fahad Usmani says

Hello PD, what you are saying is not correct.

I suggest you refer some other resources and read them, if you are not satisfied with my explanation.

Or provide me any reference supporting your claim.

awinurdin Alwi says

It is a nice blog to learn project management especially the beginners like me.

Could you please, explain more about “positive risk” due to in my mind the term “risk” means negative impact. If the impact is positive, it does not a risk, it is a benefit, doesn’t it?

Jazakumullah khair

Fahad Usmani says

Please refer the below blog posts on common risks management terms:

https://pmstudycircle.com/2012/02/types-of-risks-and-various-risks-related-terms/

Muhammad Anjum says

Would you please give any example of two risk response strategies for single risk event ?

Fahad Usmani says

Let me give you a real world example.

Suppose you are going to any place by plane and there is a chance that the flight may be cancelled. This is a risk and you identified two options to reach your place. The first option is to use public transport (bus), and the second option is to hire a rental car. The bus will take time but will cost less, and the private car will cost you more but you can reach your place earlier.

Now you have two risk response strategies, and you have to select the one.

Hope it helps.

Muhammad Anjum says

Now its clear.

Jazak Allah Khair

Fahad Usmani says

Great…

Muhammad Anjum says

Now, I would like to raise one more request to you to write blog posts on Decision Tree Method/Analysis and Monte Carlo simulation.

Jazak Allah Khair

Fahad Usmani says

In this month, I’m planning to write on Monte Carlo Simulation.

Muhammad Anjum says

I’ll wait for.

Jazak Allah Khair

Fahad Usmani says

Okay.

Muhammad Anjum says

When are you going to post a blog about decision tree method/analysis?

Fahad Usmani says

I can not give you any time frame for it, but I will write on it in near future.

kalash says

Hi,

I would like to share my experience as i teach to my students… as advise..

1. Never EVER trust on web sites that claims 100% Pass grantee , like actualtests etc. believe me. you will not get a SINGLE question from that site or similar ( Nil support for real exam)

2. Do not cram ITTO, very few question <10Q.

(Etc. Requirement gethering is done now what to do?, Scope is done now whats next?

3. Do practice for calculation receive many question.

4. Conflict management 4Q

5. HR resource leveling, 4Q

6. About Charter 4Q

7. About Scope change, CCB, change management, around 10Q

8. Risk management 7Q

9. Procurment FFP etc 7Q

10. P. Closing 5Q

11. Project selection etc >6Q

12. Leadership style >4Q

13. Free float 3Q

14. Lead Lag 1Q

15. Motivation 1Q

16. S-holder impact selection and identification 3Q

17. Cost 4Q

like buy or rent ???

18. estimation tools and tecn 4Q

19. risk mitigation tech, exp. You made a data center and some natural-disaster occurred, you data center is flooded and stopped working however your company operation is still live from backup site data-center!!!!!!!!!!!!!!!!

20. Many question were too long, with many correct answers

like. CEO given verbal order to initiate project as finance-head requested. you are the project manager what you will do next.?

a. get a signed on project charter and start process

b. start work on the project

c. wait for function manager or sponsor to issue project charter

d. Make a project charter and send to CEO for review and final approval.

21. As i tell you during class ,. PMBOK is the best source. read read and practice.

Fahad Usmani says

Thanks Kalash for sharing your experience.

I see that many students starts their study with the PMBOK Guide, and after reading a few pages, they skip reading it. They find it too dry to read.

That is why I recommend aspirants reading any good PMP exam reference book before reading the PMBOK Guide. It will help them understand the PMBOK Guide better.

You also made a good point here: beware of those who are giving 100% guarantee of passing the exam.

Nevena Taslakova says

Thank you Fahad for all your posts!

I found your website 2 or 3 days before my second attempts for PMP certification and I think that your experience help me very much. I passed the exam and now I come back to your site often to check out your explanation on debatable topics.

Keep good job and thank you once more time!

Fahad Usmani says

Congrates Nevena for passing the PMP exam, and thanks for your comments.

Musa says

Please how can I get hand your book or any useful sample questions? I really enjoy your explanations. I will be having a second attempt in PMP exam shortly.

Fahad Usmani says

Hello Musa,

From below given link, you can have a look on my eBooks:

https://pmstudycircle.com/pmp-products/

Fawzi Mustafa says

20. Many question were too long, with many correct answers

like. CEO given verbal order to initiate project as finance-head requested. you are the project manager what you will do next.?

a. get a signed on project charter and start process

b. start work on the project

c. wait for function manager or sponsor to issue project charter

d. Make a project charter and send to CEO for review and final approval.

What shall we do??

Fahad Usmani says

As per my understading, since the CEO has given you verbal request this means that the charter is not yet ready and you have to help him prepare the project charter and send for review and final approval

Prof Rao says

Very nice article, I like the way of explanation using examples.

Fahad Usmani says

Thanks Professor Rao for your comment.

Nilesh Boradkar says

Thanks for such a good article. Though I am bit confused with EMV explanation in PMBOK 5 page #339 Fig # 11-16.

The decision here is made with higher EMV, but in your article you have mentioned that….. You will calculate the expected monetary value for each response and select the one which has the lowest value.

Could you please clarify.

Fahad Usmani says

In case of opportunities, you will go for the highest choice, which provides you highest value, however, if it is a threat, you will go for the lowest option.

nilesh boradkar says

Thanks Fahad.

Tauseef Qureshey says

Assalam-o-Alaikum

Please make it clear in your notes what happen if only one risk of 10% probability of negative risk occur at an impact of $4000 USD. It will not consume all of the contingency reserve. In that case do we have to get more money for contingency reserve could be from management reserve or from some where else. Please explain. Thanks a lot

Fahad Usmani says

Walaikum assalam Tauseef,

I have already said that “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.”

Anyway, your comment has made it more clear.

Tauseef Qureshey says

Assalam-o-Alaikum

How we can say that EMV is the average of outcomes of scenarios that may or may not be happen in future, it just looks like total of EMVs because average is define as dividing the sum of the values in the set by their number. Please explain to clear.

Thanks you very much

Fahad Usmani says

As per my understanding: Risk management is people oriented process based on subjective evaluation (not the objective process).

Here you are finding the cumulative emv of all risks events and adding them all together. You have already discounted it by multiplying the percentage, so no need to discount it again.

Ahmad Khisal saeed says

Bro,

Can you please help me understand when we actually add the cost in impact value while calculating the path value. I have seen an example, actually that is from Edwel where she is adding the cost in impacted value before he calculates the path value.

Build a house – Cost = 200K – Meet the needs = 85% Does not meet the needs – Impact = 30K

Buy a house – Cost = 85K – Meet the needs = 40% Does not meet the needs – Impact = 300K

Path 1 Build House

So while calculating the path value what he has done is that he has added (200+30)*15%

Second path value on the same path = 200*85%

Path 2 Buy House – Here he also added the cost while calculating the path value like

Now on second path = (300+85)*60%

Second path value on the same path – (300*40%)

Then he added the path values of each path

Path 2 EVM = 265

Path 1 EVM = 204

So i am really confuse, not sure if we can see these type of questions in the exam, but just wondering in which particular scenarios we need to add cost in the impact value before we calculate MV. OR if we solve the question without adding the cost, would end results remains the same. Your help would be much appreciated. Thanks.

Fahad Usmani says

Usually, in question, they will simply give two or three events with chance of happening and the impact. You have to calculate the EMV of these events separately and select the best choice.

Anjali says

I want some examples on decision tree analysis by using emv criteria as I am an MBA student so please help me and send some problems with answers

Fahad Usmani says

I haven’t written any blog post on decision tree yet. If you are member of PMI, you can get some examples on eRead and Reference.

Tauseef Qureshey says

Why we take least EMV, if we have 3 or 4 from the Decision Tree Method.

Please Explain with examples.

Thanks

Fahad Usmani says

You can manage a risk with either spending 100 USD or 200 USD. What option will you select? You will select the option with least value.

Houssam says

First of all, thank you very much for the detailed post and examples.

From the Table where you calculate the EMV you get a contingency reserve of $1,100. However, the fourth risk has a probability of 60% and an impact of $1,500. If that risk occurs, one wouldn’t even be able to cover it. What good is the EMV then ?

Regards,

Fahad Usmani says

The table is just for illustration purpose only. In reality the table will have hundreds of risks so the spread would be better.

virginia says

Just learning about EMV and thought I understood that the probability total for all risks should equal 100. Your table does not reflect this. Can you explain why and any rules for how to establish the probabilities for multiple risks?

Thank you

SALEEM says

if probability not given then how we can find the EMV?

Fahad Usmani says

You can not.

Rachel says

Hi Fahad,

I’m just confused on one thing.

If the EMV is -$500, meaning it is a threat, that would then reflect in the contingency reserve as money we would have to add to the reserve, correct?

Threats are reflected as negative values in EMV but are reflected as positive amounts in the contingency reserve. And vice versa– opportunities are reflected as positive values in EMV but are amounts we would subtract in the contingency reserve?

Thanks in advance,

Rachel

Fahad Usmani says

Correct.

Sharon says

Can you please help me… I don’t know how to solve this :

The product design group of ABC Electric Supplies has determined that it needs to design a new series of switches. It must decide on one of three design strategies. The market forecast is for 200,000 units. The better and more sophisticated the design, DR Berry, has decided that the following costs are a good estimate of the initial and variable costs connected with each of the 3 strategies :

a) Low-tech : a new technology, low-costs process consisting of hiring several new junior engineers. This option has a cost of $45,000 and variable cost probabilities os 0.3 for $0.55 each, 0.5 for $0.5 and 0.3 for $0.45.

b) Subcontract : a medium-cost approach using good outside design staff. This approach would have an initial costs of $65,000 and variable cost probabilities of 0.7 of $0.45, 0.2 of $0.40 and 0.1 of $0.35.

c) High-tech : a high technology approach using the very best if the inside staff and latest computer-aided design technology. This approach has a fixed cost of $75,000 and variable costs probabilities of 0.9 of $0.40 and 0.1 of $35

What is the best decision based on an expected monetary value criterion?

xasan says

It is very valuable resource for me while I am one of project Management to get such questions and answers for simplifications

Fahad Usmani says

Thanks Xasan.

Ayesha Punjani says

There is a 50% chance that the project will miss the schedule. Project worth is 1,000,000 $ and has a penalty of 200,000 $ for late delivery. What is the EMV?

Fahad Usmani says

EMV for this event = 0.5 X (-200,000)

= -100,000 USD.

cera says

please help me,

JD Corporation Sdn.Bhd (JDC) is trying to decide whether to make or buy apart for AIRBUS. Purchasing the part would cost $1.50 each. If they design and produce it themselves, it will result in a per unit cost of $0.75. However, the design investment would be $50,000. Further, they realize that for this type of part, there is a 30% chance that the part will need to be redesigned at an additional cost of $50,000. Regardless of whether they make or buy the part, JDC will need 100,000 of these parts. Using decision trees analysis and EMV, what should JDC do?