Expected Value

While the concept of expected value might be intuitive and easy to grasp, its application is a standard practice in scenario analysis.

While it has other applications, scenario analysis is the process of calculating the expected value under various assumptions and considerations.

As various scenarios are thought of and analyzed, so too is their probability. The probability of any scenario occurring is also a factor in deriving expected value. 

This is a core concept in statistics and finance and you should attempt to develop a good understanding of this fundamental concept. In this FAQ we will cover what expected value is, why it is important, and how to calculate it.

What Is Expected Value?

Expected Value, in finance and business, is thought to be representative of the probability-weighted average of all possible values. That is to say, it is an expectation of future value that considers different probable outcomes and then weights the outcomes based on how likely they are to happen. 

Much like the name implies, expected value is the future return you expect from an investment. In statistics, it is the anticipated return that is a result of some kind of action.

In investment finance, the concept is typically applied in conjunction with scenario analysis, which is the process of calculating the expected value of an investment pool at some point in the future based on different scenarios. 

In the corporate setting, expected value that is used as part of scenario analysis is a tool that assists business leaders in analyzing the pros and cons of expected outcomes. Therefore, its outputs can be different depending on what is being analyzed. 

For example, if you are calculating the expected value of an investment into your manufacturing process the calculation could be used in various ways. This might include the expected value added to the income statement, expected value of time savings, or cost reduction. 

Why Is It Important

Expected value as a concept is used widely across many different industries and professions. It is common practice in almost every field to make estimations about future outcomes and the expected value represents the outcome of those estimations. 

In investment finance, the concept is heavily relied upon to make predictions about the future value of an asset, or portfolio of assets. It is widely used in valuation practices because it takes into account the likelihood of a variety of outcomes along with the outcome itself. 

In corporate finance, it gives leaders visibility into what products, projects, or decisions might have the best or most desired outcome.

Because of its wide application, broad usefulness, and for its consideration of all possible outcomes and their likelihood, expected value is an important concept in almost any industry. 

How To Calculate Expected Value

The basic formula takes into consideration only one event. Anytime you are attempting to estimate an expected value for a single event, project, decision, etc… you would use this formula. 

EV=PXn

Where:

• EV = expected value
• P(X) = the probability of the outcome
• n = the number of times the event will occur

A simple example would be if you were analyzing a project with a single possible outcome. The outcome would result in $1.0 million in annual savings for three years. In this case, the EV calculation would be: 

EV=PXn 

or,

$3,000,000 = $1,000,000 x 3

Where:

• EV = $3,000,0000
• P(X) = $1.0 million
• n = 3 years

When the concept is applied in the field of corporate or investment finance, the formula has some inadequacies. That is to say, the formula needs to consider the probability of each outcome and weight it based on its likelihood to occur. 

In this way, the formula shifts into a probability-weighted average. Calculations that are considered weighted averages take into account the degree to which a value is relevant to a calculation, giving it its “weight”. 

In this case, the formula would be:

EV= PXiXi

Where:

• EV = expected value
• P(X_i) = the probably of the outcome
• X_i = the outcome 

The formula is the aggregate totals of all of the possible outcomes weighted by their likelihood to occur.

In practice, this can be somewhat subjective because weighting the likelihood of an outcome requires assumptions to be made. In addition, the formula for calculating expected value requires the previous calculation of an outcome. 

An outcome can be anything including dollars, units, and time. A very rudimentary example of the practical application of the formula would be if you were analyzing two different projects and wanted to know which is better to pursue.

Project A has a 50/50 chance of returning either $1.0 million or $500,000. Project B has a 60/40 chance of returning either $900,000 or $600,000. 

The EV of project A is: $1,000,000(.5) + $500,000(.5) = $750,000

The EV of project B is $900,000(.6) + $600,000(.4) = $780,000

In the above example Project B has a higher probability-weighted expected return and is therefore the better project to select. 

Using Datarails to Calculate Expected Value

Every finance department knows how challenging performing spend analytics can be. Regardless of the type of spend analytics you are performing, it requires big data to ensure accuracy, timely execution, and of course, monitoring.

Datarails’ FP&A software can help your team create and monitor financial forecasts faster and more accurately than ever before.

By replacing spreadsheets with real-time data and integrating fragmented workbooks and data sources into one centralized location, you can work in the comfort of excel with the support of a much more sophisticated data management system behind you.

This takes financial forecasting from time-consuming to rewarding.