## What does 'Mutually Exclusive' mean

"Mutually exclusive" is a statistical term describing two or more events that cannot occur simultaneously. For example, it is impossible to roll a five and a three on a single die at the same time. Similarly, someone with $10,000 to invest cannot simultaneously buy $10,000 worth of stocks and invest $10,000 in a mutual fund.

The concept of mutual exclusivity is often applied in capital budgeting.

## BREAKING DOWN 'Mutually Exclusive'

The term "mutually exclusive" is often confused with "independent," but these terms are not interchangeable. Mutually exclusive events cannot occur simultaneously. Independent events have no impact on the viability of other options. For example, in the example above, you cannot roll both a five and three simultaneously on a single die. However, 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.

## Capital Budgeting

Companies often have to choose between a number of different projects that will add value to the company upon completion. Some of these projects are mutually exclusive, while others are independent.

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 afford to also 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.

## 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.

Assume that project A in the above example has a potential return of $100,000, while option 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 (A) minus the profits generated by the selected option (B); that is, $100,000 - $80,000 = $20,000. Since A is the most lucrative option, the opportunity cost of that option is $0.

## Math Is the Answer

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