Mathematical Expected Value Worksheet Answer Key

What is Expected Value?

Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values.

Expected Value

Expected value is a commonly used financial concept. In finance, it indicates the anticipated value of an investment in the future. By determining the probabilities of possible scenarios, one can determine the EV of the scenarios. The concept is frequently used with multivariate models and scenario analysis Scenario Analysis Scenario analysis is a process of examining and evaluating possible events or scenarios that could take place in the future and predicting the . It is directly related to the concept of expected return Expected Return The expected return on an investment is the expected value of the probability distribution of possible returns it can provide to investors. The return on the investment is an unknown variable that has different values associated with different probabilities. .

Formula for Expected Value

The first variation of the expected value formula is the EV of one event repeated several times (think about tossing a coin). In such a case, the EV can be found using the following formula:

Expected Value - Formula

Where:

EV – the expected value
P(X) – the probability of the event
n – the number of the repetitions of the event

However, in finance, many problems related to the expected value involve multiple events. In such a scenario, the EV is the probability-weighted average of all possible events. Therefore, the general formula to find the EV for multiple events is:

Expected Value - Formula for Multiple Events

Where:

EV – the expected value
P(X_I) – the probability of the event
X _I– the event

Example of Expected Value (Multiple Events)

You are a financial analyst Financial Analyst Job Description The financial analyst job description below gives a typical example of all the skills, education, and experience required to be hired for an analyst job at a bank, institution, or corporation. Perform financial forecasting, reporting, and operational metrics tracking, analyze financial data, create financial models in a development company. Your manager just asked you to assess the viability of future development projects and select the most promising one. According to estimates, Project A, upon completion, shows a probability of 0.4 to achieve a value of $2 million and a probability of 0.6 to achieve a value of $500,000. Project B shows a probability of 0.3 to be valued at $3 million and a probability of 0.7 to be valued at $200,000 upon completion.

Expected Value - Example

In order to select the right project, you need to calculate the expected value of each project and compare the values with each other. The EV can be calculated in the following way:

EV (Project A) = [0.4 × $2,000,000] + [0.6 × $500,000] = $1,100,000

EV (Project B) = [0.3 × $3,000,000] + [0.7 × $200,000] = $1,040,000

The EV of Project A is greater than the EV of Project B. Therefore, your company should select Project A.

Note that the example above is an oversimplified one. A real-life example will likely assess the Net Present Value (NPV) Net Present Value (NPV) Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present. of the projects instead of their EV. However, NPV calculations also consider the EV of different projects.

More Resources

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