## What Is Mutually Exclusive?

Mutually exclusive is a statistical term describing two or more events that cannot coincide. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.

#### Mutually Exclusive

## Mutually Exclusive Explained

Mutually exclusive events may also be considered independent events. Independent events have no impact on the viability of other options. For a basic example, consider the rolling of dice. You cannot roll both a five and a three simultaneously on a single die. Furthermore, getting a three on an initial roll has no impact on whether or not a subsequent roll yields a five. All rolls of a die are independent events.

By comparison, the term *mutually inclusive* refers to an interconnected series of events that cannot occur independently; in business, this could refer to several investments that have to be made once the first investment has gone through.

## Opportunity Cost and Mutually Exclusive Options

When faced with a choice between mutually exclusive options, a company must consider the opportunity cost, which is what the company would be giving up to pursue each option. The concepts of opportunity cost and mutual exclusivity are inherently linked because each mutually exclusive option requires the sacrifice of whatever profits could have been generated by choosing the alternate option.

Mutually exclusive events are completely independent of all other events and have no impact on the outcome of the other event.

## Statistics and the Time Value of Money

The time value of money (TVM) and other factors make mutually exclusive analysis a bit more complicated. For a more comprehensive comparison, companies use the net present value (NPV) and internal rate of return (IRR) formulas to mathematically determine which project is most beneficial when choosing between two or more mutually exclusive options.

## Real World Examples

The concept of mutual exclusivity is often applied in capital budgeting. Companies may have to choose between multiple projects that will add value to the company upon completion. Some of these projects are mutually exclusive.

For example, assume a company has a budget of $50,000 for expansion projects. If available Projects A and B each cost $40,000 and Project C costs only $10,000, then Projects A and B are mutually exclusive. If the company pursues A, it cannot also afford to pursue B and vice versa. Project C, however, is independent. Regardless of which other project is pursued, the company can still afford to pursue C as well. The acceptance of either A or B does not impact the viability of C, and the acceptance of C does not impact the viability of either of the other projects.

Moreover, when looking at opportunity costs, consider the analysis of Projects A and B. Assume that Project A has a potential return of $100,000, while Project B will only return $80,000. Since A and B are mutually exclusive, the opportunity cost of choosing B is equal to the profit of the most lucrative option (in this case, A) minus the profits generated by the selected option (B); that is, $100,000 - $80,000 = $20,000. Because option A is the most lucrative option, the opportunity cost of going for option A is $0.

### Key Takeaways

- Events are considered to be mutually exclusive when they cannot happen at the same time.
- Mutually exclusive events are independent and have no bearing on the outcome of any other events.
- The concept often comes up in the business world in the assessment of budgeting and dealmaking.
- If considering mutually exclusive options, a company must weigh the opportunity cost, or what it would be giving up by choosing each option.