# Expected Monetary Value – Where’s the Value?

Expected Monetary Value (EMV) is often used in risk analysis to provide an indication of the financial impact of a risk. But, in practical terms, how valuable is this technique?

The answer depends entirely on how the EMV calculation is applied in a risk scenario.

Expected Monetary Value is defined mathematically as: EMV = ∑ (Pi × Ii)

Where:

P = Percentage probability of risk occurrence

I = Impact in monetary terms

When applied to risks that have been qualitatively analysed, and used in isolation, EMV has little real value. The reason being that the probability of risk occurrence, and the impact value of qualitatively analysed risks, are both likely to contain relatively high degrees of uncertainty.

As EMV is calculated as a product of Probability and Impact, the uncertainty of the result is always higher than the uncertainty of the individual components that make up the equation.

Risks that have been quantitatively analysed generally produce more accurate EMV results, but this depends predominantly on the type and accuracy of the quantitative analysis carried out, and whether it has been applied to the probability of risk occurrence, the risk impacts, or both.

In a nutshell, the more uncertainty there is in a risk's probability of occurrence and its impacts, the less accurate the EMV result.

For more information on Qualitative and Quantitative Risk Analysis, see our previous blog post: “Qualitative vs. Quantitative Risk Analysis: What’s the difference?”

### Expected Monetary Value and Risk Reserve

EMV can be used as a relatively simple "first-pass" method to calculate the Contingency Reserve required for a project, where Contingency Reserve is an amount of money included within the overall project budget for use by the Project Manager in response to the occurrence of known risks.

However, in most high value projects, one cannot practically set the project contingency reserve at the total project risk EMV, as this would most likely drain the sponsoring organisation of its financial reserves.

On any one project, there may be several risks that have a very high impact value (ranging upwards from 80% of the project CAPEX budget), albeit with a very low probability (less than 1% chance of occurring). If you therefore identified between ten to fifteen risks that fell into this category, the EMV of these risks alone could equate to up to 10% of the total project budget. If you then add the EMV of all other risks on the project, there is a good chance that the total EMV could approach, or even exceed, the project CAPEX budget.

Using risk EMV may be a good starting point in calculating contingency reserve, but it should by no means be the only defining method.

### Expected Monetary Value and Decision Tree Analysis

Applying the Expected Monetary Value formula is probably most useful when assessing risks in conjunction with Decision Tree Analysis.

When used on its own, Decision Tree Analysis is essentially a qualitative means of deciding the best course of action whenever there are multiple options available, and a level of uncertainty surrounding each option.

However, using “best judgement” in deciding a course of action, without having any empirical data to back up your decision, is generally regarded as a last resort in project decision making. This is especially true where the outcomes of that decision can significantly affect the values and objectives of the project.

Applying the EMV technique to decision trees provides each “chance” (or uncertainty) node with the expected monetary impact of that uncertainty. This, in turn, helps to make a more informed overall decision once the EMVs of each “chance” node along a decision tree branch have been added up and compared against the EMV’s of the other decision tree branches.

By way of example, let us consider a decision that needs to be taken by a commercial property owner who wants to increase their revenue in an existing commercial block. In this particular case, they need to decide whether to:

1. Maintain the block
2. Renovate the block
3. Re-build the block

Each of these options carries both a cost and a level of uncertainty around the impact of each option. Through market research, the property owner has established that there is a potential to increase the revenue of their block by up to \$60 million over the 20-year land lease period that they hold. However, this potential is largely dependent on the quality of the outlets and volume of customers this will generate.

The cheapest option will be to just maintain the block and hope to attract more customers by keeping the block as clean and well maintained as possible. This option would cost \$3 million over the 20-year lease period. However, the best result they could hope for in this case would be an overall increase in revenue of \$20 million and their lowest expectation would be no increase in revenue.

The next option would be to renovate the block to improve its layout, access, and services. This option would cost \$8 million in construction, \$2million in trade disruption and the same \$3 million in maintenance, totalling \$12 million. In this case the maximum expected increase in revenue would be \$45 million and the minimum expected increase would be \$25 million.

Their final option would be to rebuild the entire block to provide more space, better facilities and an overall improvement in the architecture and appeal of the block. This option would cost \$17 million in construction, \$6 million in trade disruption and would reduce their overall maintenance costs to \$2 million, totalling \$25 million.

In this case the maximum expected increase in revenue would be \$60 million and the minimum expected increase would be \$30 million.

Obviously, the owner would like to maximise the increase in their revenue, and doing a complete rebuild of the block would potentially give them this. But what are the chances that they will realise this maximum return?

At this point we have to consider the probability of each outcome. In this example, let us assume the cheapest option of just maintaining the block has a 90% chance of success due to the demographics of the area, leaving a 10% chance that this strategy will fail.

For the renovate and rebuild options, let us assume that each has an equal 70% chance of achieving their respective maximum targets, and a 30% chance of achieving their minimum expectations.

In order to determine the best option for the property owner to take, we now need to map out their decision tree, along with the associated costs, expected returns and probability of achieving these returns. This is shown in the diagram below.

From this decision tree, we can establish that the largest total EMV for the three options (after cost deductions) is \$27 Million, which is our expected average return between the best and worst case scenarios for renovating. This predicts a slightly better outcome than if we chose to rebuild, and choosing to maintain the block gives us the worst predicted return.