## EMV Analysis

EMV stands for **Expected Monetary Value** which is a statistical technique used to measure the average outcome for situations under uncertainties including positives (opportunities) and negatives (threats). Specifically, in project risk management, it can help managers or risk specialists to calculate identified risk and analyse the effect of them quantitatively on overall project objectives. This process is named **Quantitative Risk Analysis**. Moreover, EMV calculation is an essential skill for the PMP exam.

EMV of each possible outcome is calculated by multiplying its probability and its impact (as well as the value). According to the fact that scenarios may be comprised of multiple options, EMV equals to the sum of EMVs of options. As mentioned above, **there may be opportunities and threats, so that the EMV of them are expressed as positive and negative values respectively**. There is the equation of EMV as follows.

`EMV = possibility (%) * value (£)`

In regard to risk analysis, EMV can be utilised to calculate the cost used to remove a risk in theory. It should be noticed that there is no risk which can be completely eliminated by spending money in real practice. Then, the value with the highest EMV is selected after the analysis which reflects the lowest risk.

## Decision Tree Analysis

A decision tree is a decision support tool that uses a tree-like decision model and its potential consequences. Using decision tree analysis is helpful to grasp how alternative capital solutions can be determined when the world includes unpredictable elements. In other words, it can help you making decisions accordingly when there are multiple options appeared.

Satya Narayan Dash has concluded the major points of decision tree analysis. There are:

- Decision Tree takes future uncertain events into account. The event names are put inside rectangles, from which option lines are drawn.
- There will be decision points (or “decision nodes”) and multiple chance points (or “chance nodes”) when you draw the decision tree. Each point has different symbols: a filled up small square node is a “decision node”; a small, filled-up circle is a “chance node”; and a reverse triangle is the end of a branch in the decision tree. These are noted in this table:

- Because this format results in a diagram that resembles a tree branching from left to right, the decision tree is an apt name! To analyze a decision tree, move from left to right, starting from the decision node. This is where the branching starts. Each branch can lead to a chance node. From the chance node, there can be further branching. Finally, a branch will end with an end-of-branch symbol.
- The probability value will typically be mentioned on the node or a branch, whereas the cost value (impact) is at the end.
- Next, come the calculations on the branches of the tree. To calculate, move from right to left on the tree. The cost value can be at the end of the branch or on the node. Just follow the branch to do the calculation.
- The best decision is the option that gives the highest positive value or lowest negative value, depending on the scenario.

## Example

### Scenario

Suppose you are the product manager of a video sharing website PiliPili. Stakeholders have shown interest in expanding business opportunities in the new area of online games. There are two solutions that you can take into account:

- Develop an independent website of online games investing £8M
- Implement a new category of online games in PiliPili investing £3M.

- If you build a new online games website, there is a 75% chance of a high demand and the company will realise £15M and 25% of a weak demand and the company will realise £5M in revenues.
- If you produce a category for online games, there is a 60% chance of high demand and the company will realise £10M in revenues and a 40% chance of weak demand and the company will realise £2M in revenues.

How do you make suggestions to the board?

What is the EMV of either option?

### Application

1. Draw a decision tree starting from the left and move from the left to the right. A decision node following by a topic event will lead to two options. And each option will lead to two events or chances branching out from the chance nodes. Do not forget adding a reverse triangle at the end of each branch. Then, assign a probability of occurrence for each option pertaining to that decision. All information showed on the figure is already known from the scenario.

2. Compute the Expected Monetary Value for each decision path. The calculation sequence should be from right to the left. First, compute the profit of each branch by its outcome minus the investment on it. The EMV of each branch can be determined by multiplying its profit by its probability then. Adding them together, that is the EMV of an option of a decision. In regard to the EMV of the overall scenario decision, it should be considered as the maximum value among its options’ EMV.

Also, there is another way to represent this figure by replacing EMV of options with chance nodes, while the calculating process and result are the same.

References