Mutually Exclusive: What It Means, With Examples

What Is Mutually Exclusive?

The concept of mutually exclusive events or factors comes from the field of statistics, where it describes two or more things that cannot happen simultaneously. That is, one must supersede the others, like war and peace or making a left turn and a right turn at the same time.

Mutual exclusivity has been extended into the world of business and finance, where it informs the decision-making processes on opportunities to be pursued or dropped.

Understanding Mutually Exclusive

Mutually exclusive events cannot happen simultaneously, but should not 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 a five and a three simultaneously on a single die. However, you can roll a five and a three on two dice.

The fact that one die cannot roll two different numbers means the outcome is mutually exclusive. Rolling a five on one and a three on the other means they are not mutually exclusive outcomes.

Opportunity Cost

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.

The time value of money (TVM) and other factors make mutually exclusive analysis a bit more complicated. For a more comprehensive comparison, companies use 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.

Example of Mutually Exclusive

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 may be considered 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.

The Bottom Line

Things that are mutually exclusive are not able to occur simultaneously. In business, this is typically concerning the undertaking of projects or allocating a budget. If two things are not mutually exclusive, it means the existence and occurrence of one does not necessarily mean the other cannot coexist.