Yad Senapathy, PMP December 21, 2022

Expected Monetary Value (EMV) is a concept used in decision-making to evaluate the potential outcomes of a decision and assign a monetary value to each result. It quantifies the potential risks and rewards associated with a decision and helps individuals and organizations choose the most likely option to lead to the best financial outcome. The monetary value calculation can be used in various contexts, including financial planning, risk management, and project management. It is particularly useful in situations where there is uncertainty or risk involved. By weighing the potential outcomes against their corresponding probabilities and monetary values, individuals and organizations can make more informed decisions and allocate resources more effectively.

To calculate the EMV, you need to consider two factors:

- Probability
- Monetary Value

Probability is essential in calculating a decision's expected monetary value (EMV). Probability represents the likelihood or chance that a particular outcome will occur. It is expressed as a percentage ranging from 0% to 100%. For example, there is a 50% chance that it will rain tomorrow, the probability in this situation will be 50%.

Monetary value is essential in calculating a decision's expected monetary value (EMV). It represents the financial value of each potential outcome of a decision. Monetary value can be positive or negative, depending on whether the outcome is beneficial or detrimental.

For instance, you will receive a certain amount if you win the lottery. In this case, the impact is positive. The effect will be negative if you lose money by making a bad investment.

The formula for calculating the expected monetary value (EMV) is as follows:

For example, consider a company deciding whether to invest in a new product. The company has identified two possible outcomes: the product is successful, with a probability of 20%, and the product is not successful, with a probability of 80%. The company estimates that the product will generate $100,000 in revenue if it is successful and will result in a loss of $50,000 if it is not successful. The EMV for this decision can be calculated as follows:

Successful outcome: 20% x $100,000 = $20,000

Unsuccessful outcome: 80% x -$50,000 = -$40,000

Total EMV: $20,000 + -$40,000 = -$20,000

In this case, the EMV of the decision is -$20,000, indicating that the expected return on investment for this decision is negative, which means the company can expect to lose money if it invests in the new product.

If you want to calculate EMV, you need to do the following.

The first step in calculating EMV is identifying the possible outcomes of the decision or investment. It includes both positive and negative results and their respective probabilities.

Next, you need to determine the value of each outcome. This can be expressed in terms of monetary value, such as dollars or euros, or other units, such as points or satisfaction.

Once you have determined the probability of each outcome and its value, you can multiply these two quantities to obtain the expected value of each result.

Finally, you can sum the expected values of all outcomes to obtain the total predicted value of the decision or investment.

For you to understand EMV analysis, here are some examples of Expected Monetary Analysis.

You have the option to invest $100 in a stock that has a 50% chance of increasing in value by $50 and a 50% chance of decreasing in value by $50. The EMV of this decision is calculated as follows:

Outcome 1: Probability = 50%, Monetary value = $50

Outcome 2: Probability = 50%, Monetary value = -$50

EMV = (0.50 x $50) + (0.50 x -$50) = $25 - $25 = $0

In this example, the EMV is $0, which means you can expect to neither gain nor lose money from this investment.

You have the option to invest $100 in a lottery ticket that has a 1% chance of winning $1 million. The EMV of this decision is calculated as follows:

Outcome 1: Probability = 1%, Monetary value = $1,000,000

Outcome 2: Probability = 99%, Monetary value = -$100

EMV = (0.01 x $1,000,000) + (0.99 x -$100) = $10,000 - $99 = $9,901

In this example, the EMV is $9,901, which means you can expect to make a profit of $9,901 if you buy the lottery ticket. However, it's important to note that the actual outcome could be significantly different from the expected value due to the low probability of winning.

You have the option to invest $100 in a bond that is guaranteed to pay $105 in one year. The EMV of this decision is calculated as follows:

Outcome 1: Probability = 100%, Monetary value = $105

EMV = (1.00 x $105) = $105

In this example, the EMV is $105, which means you can expect to make a profit of $105 if you invest in the bond. Since the probability of this outcome is 100%, you are guaranteed to receive the $105 return on your investment.

You are considering purchasing a car for $20,000. The vehicle has a 50% chance of lasting for ten years without needing any major repairs, in which case it would be worth $10,000 at the end of those ten years. The car also has a 50% chance of needing significant repairs within the first five years, in which case it would be worth $0 at the end of those five years.

Outcome 1: Probability = 50%, Monetary value = $10,000

Outcome 2: Probability = 50%, Monetary value = $0

EMV = (0.50 x $10,000) + (0.50 x $0) = $5,000

In this example, the EMV is $5,000, which means you may lose $5,000 if you purchase the car. This is because the expected value of the vehicle at the end of its lifespan is $5,000, which is less than the cost of purchasing the car.

A homeowner is considering whether to install a home security system. The homeowner estimates that there is a 30% chance of a break-in occurring in the next year and that the security system would cost $1,000 to install. If a break-in were to occur and the security system was not installed, the homeowner estimates that the losses would be $5,000. If the security system was installed, the homeowner estimates that the losses from a break-in would be reduced to $1,000.

Using EMV analysis, the homeowner can calculate the expected monetary value of installing the security system as follows:

No security system: 30% chance x $5,000 loss = $1,500

Security system: 30% chance x $1,000 loss = $300

Expected monetary value: $1,500 - $300 = $1,200

In this example, the expected monetary value of installing the security system is $1,200. This means that, on average, the homeowner can expect to lose $1,200 if they do not install the security system. Based on this analysis, the homeowner may decide that it is worth investing in the security system, as it would reduce their expected losses in the event of a break-in.

It's important to note that the EMV is just one factor to consider when making a decision. Other factors, such as your personal preferences and risk tolerance, may also influence your decision.

Some of the benefits of EMV in decision-making are as follows.

- EMV allows decision-makers to quantify the potential outcomes of a decision in terms of their financial impact. Through EMV, the decision-makers can see which option will likely have the most significant positive or negative effect.
- Another benefit of EMV is that it helps decision-makers to identify and account for potential risks and uncertainties. By assigning probabilities to different outcomes and estimating their potential financial impact, decision-makers can better understand the potential downside of a decision and take steps to mitigate those risks.
- EMV can also be helpful in situations where there are multiple decision points or complex interdependencies between different options. By quantifying the potential outcomes of each decision point, decision-makers can see how other choices at different points in time may impact the overall expected value of a project or decision. This can help them to identify optimal decision paths and make more informed choices.

While EMV can be a valuable tool in decision-making, it is essential to be aware of its limitations. Some of the limitations of EMV analysis are as follows.

- One limitation of EMV is that it assumes that all outcomes are equally likely, which may only sometimes be the case in real-world situations. This can lead to inaccurate estimates of the expected value of a decision, mainly if the likelihood of specific outcomes needs to be properly accounted for.
- Another limitation of EMV is that it only takes into account the financial impact of a decision and does not consider other factors such as the ethical or social implications of a decision. This can lead to financially optimal decisions that may not be socially or ethically responsible.
- The availability and accuracy of data can also limit EMV. In order to calculate the EMV of a decision, decision-makers must have access to reliable data on the likelihood of different outcomes and their potential financial impact. If this data is unavailable or inaccurate, the EMV calculation may be flawed.
- In addition to these limitations, EMV may also be prone to bias if the probabilities and values assigned to different outcomes are not based on objective data. Decision-makers should be careful and ensure that their EMV calculations are based on unbiased, accurate data to avoid making biased decisions.

To sum it up, EMV is a powerful tool for decision-making that can help decision-makers quantify the potential outcomes of a decision and identify the most likely option to maximize their expected financial gain. It is particularly useful in situations with uncertainty or risk involved and can be applied in various contexts to help decision-makers make informed choices.

While there are limitations to EMV, it can still be a valuable tool when used in conjunction with other decision-making techniques and a thorough understanding of the potential risks and uncertainties involved.

Yad is not just the leader of the Project Management Training Institute (PMTI). He helped to write significant portions of the project management standards worldwide. He is helping PMI right now in reviewing, directing, and leading the development of the 7th edition of the PMBOK^{®} Guide to incorporate the most monumental changes to project management standards in 35 years. He shares his wisdom with readers via the PMTI blog.