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What is Mutually Exclusive?

Robinhood LearnJune 19, 2020
Democratize finance for all. Our writers’ work has appeared in The Wall Street Journal, Forbes, the Chicago Tribune, Quartz, the San Francisco Chronicle, and more.
definition

Mutually exclusive refers to the relationship between two or more events that cannot occur at the same time.

🤔 Understanding mutual exclusivity

When two events are mutually exclusive, they cannot happen simultaneously — It’s one or the other. The existence of mutually exclusive events results in an inherent opportunity cost, which is the cost of losing out on one of the events that can’t both happen at the same time. Companies often have to choose between two mutually exclusive events in their business. For example, they might have to choose between two capital projects, only one of which they can afford to do at a time. In some cases, the different options are collectively exhaustive, meaning at least one of the events has to occur. Finally, two events could be independent of one another, in which case the occurrence of one does not affect the other.

example

Imagine that you’re driving down the road, and you’ve arrived at an intersection. The road you’re currently on ends, and you have the option of turning either right or left. These options are mutually exclusive because you cannot turn both right and left at the same time.

Takeaway

Mutually exclusive events are like a coin toss…

When you flip a coin, it’s either going to land with heads or tails facing up — There’s no chance that both sides will be facing up. Other mutually exclusive events work the same way. If two events are mutually exclusive, only one of them can occur.

Tell me more...

What are some mutually exclusive events?
What does mutually exclusive and exhaustive mean?
What is the difference between mutually exclusive and independent?
What is the opportunity cost with mutually exclusive options?

What are some mutually exclusive events?

Two events are mutually exclusive if they cannot both occur at the same time. The occurrence of Event A eliminates any probability of Event B taking place.

Mutually exclusive events also occur regularly in corporate finance. Companies often use capital budgeting to invest in future business growth. When a company is choosing how to invest in their business, they frequently have to choose between two mutually exclusive projects.

For example, let’s say a company has $500,000 to invest in future growth. The business owner is considering two different projects, both of which would cost about half a million dollars. The two projects are mutually exclusive. Because they would both use all of the working capital the company has set aside to invest, it is only possible for them to complete one of the projects.

The concept of mutual exclusivity could also come into play for hiring decisions. If a company is conducting interviews for a new chief executive officer (CEO), they might narrow it down to two different candidates. The two choices are mutually exclusive — The company cannot hire two CEOs.

What does mutually exclusive and exhaustive mean?

When two events are mutually exclusive, it means they cannot both occur at the same time. But it doesn’t necessarily imply that one of the two events has to happen.

When two events are exhaustive, it means that one of them must occur.

Think again of a coin toss. The results are mutually exclusive (it will be either heads or tails; it can’t be both on the same flip). And it will be one of the two options — heads and tails are the only possible options (thus they are exhaustive).

What is the difference between mutually exclusive and independent?

Mutually exclusive events are two events that cannot occur at the same time. The occurrence of one event has a direct impact on the probability of the other. Independent events are the exact opposite — Independent events are those that do not affect the likelihood of each other.

The results of multiple coin flips are independent of one another. We know that when we flip a coin, the chances of flipping either heads or tails are mutually exclusive. We can’t flip both heads and tails at the same time. But what about if you flip a coin three times in a row? The results of the first coin flip and are completely independent of the results of the second and third coin flips. Flipping heads on one of the flips doesn’t make you any more or less likely to flip heads the next time.

The concept of independent events also applies to capital financing. We know that two capital projects are mutually exclusive if the company can only invest in one of them. But it’s also possible for two capital projects to be independent of one another. Let’s say a corporation has a great deal of funding available for capital projects, and they are considering two different options.

In this case, the company could likely invest in both projects if they wanted. Whether they decide to invest in one of the projects has no impact on whether they invest in the other. Suppose a company has $1M set aside for business growth. They are considering two projects, both of which have a price tag of $100,000. If the company invests in Project A, they aren’t necessarily any more or less likely to also invest in Project B.

What is the opportunity cost with mutually exclusive options?

When an individual or company chooses one of two mutually exclusive opportunities, there is always an opportunity cost. The opportunity cost is the potential return on investment of the opportunity they don’t choose.

An example of when an individual might face an opportunity cost when deciding between two mutually exclusive opportunities is when they’re considering what to do after high school. When determining whether or not to attend college, the two options are mutually exclusive.

For someone who chooses to go to college, they have the opportunity cost of the income they could be making if they had entered the workforce right away. And if you only look at the immediate outcome, skipping college might seem more profitable.

But entering the workforce instead of going to college has an opportunity cost as well. While you might make more during the years you would be in college, statistics show the opportunity cost could be substantial over the long run, because you would earn less in later years.

Imagine that a company is investing in a capital project. They’re weighing two options, but they can online invest in one of them. The first option costs $100,000, and the company expects it will bring in an additional $15,000 of annual revenue for 20 years. The second project will cost $200,000, and the company expects it will bring in $18,000 of annual revenue for 20 years.

For the first project, the total revenue would equal $300,000 ($15,000 x 20), with a total profit of $200,000 (ignoring inflation, costs of capital, etc.). The revenue of the second project would come to $360,000 ($18,000 x 20). The revenue is higher, but because the project was more expensive, the profit margin is lower at $160,000.

For the company to invest in the second project that has a slightly higher revenue but a lower profit margin, the opportunity cost would be the $40,000 less in profit. And the implications are even more significant than that. Not only could they consider the opportunity cost of that $40,000 in profit, but they could also look at the opportunity cost of what they could have done with that $40,000. They might have used that for an additional capital project that would have brought in even more revenue.

Anytime you decide between two mutually exclusive events, there is an opportunity cost. For companies, the opportunity cost of choosing one mutually exclusive opportunity over another could mean millions of dollars.

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