# Calculate Expected Value: A Comprehensive Guide

## Introduction

As a business owner or investor, it is important to make informed decisions that will maximize profits and minimize losses. One tool that can help in this process is calculating the expected value of an investment or decision. In this article, we will explore what expected value is, how to calculate it, and how it can be used to make better decisions.

## What is Expected Value?

Expected value is the average outcome of a decision or investment, calculated by multiplying the probability of each possible outcome by its respective value and summing the results. It is a way to determine the potential value of a decision or investment, taking into account both the likelihood of success and the potential rewards or losses.

### Calculating Expected Value

To calculate expected value, first, identify all possible outcomes of a decision or investment. Then, assign a probability to each outcome, based on past data or other relevant information. Finally, multiply each outcome by its probability and sum the results. The resulting value is the expected value of the decision or investment.

### Example Calculation

Let’s say you are considering investing in a new product line for your business. You estimate that there is a 60% chance the product line will be successful and generate \$100,000 in revenue, a 30% chance it will break even and generate \$0 in revenue, and a 10% chance it will fail and result in a loss of \$50,000. To calculate the expected value of this investment, you would multiply each outcome by its probability and sum the results: (0.6 x \$100,000) + (0.3 x \$0) + (0.1 x -\$50,000) = \$60,000 The expected value of this investment is \$60,000.

## Using Expected Value to Make Decisions

Expected value can be a powerful tool for making informed decisions. By calculating the expected value of different options, you can compare their potential value and choose the option with the highest expected value. This can help you avoid decisions that may have a high potential reward but an even higher potential loss.

### Risk and Uncertainty

It is important to note that expected value does not take into account the level of risk or uncertainty associated with a decision or investment. While a decision with a high expected value may seem like the obvious choice, it may also come with a higher level of risk or uncertainty. It is important to consider both expected value and risk when making decisions.

## Conclusion

Calculating expected value is a useful tool for making informed decisions in business and investing. By identifying all possible outcomes, assigning probabilities, and multiplying by their respective values, you can determine the potential value of a decision or investment. However, it is important to also consider the level of risk and uncertainty associated with a decision. By using expected value in conjunction with other decision-making tools, you can make more informed and profitable decisions.