Mutually Exclusive

Mutually exclusive is a term used in logic and probability theory. It describes that the occurrence of one of the events excludes the occurrence of other events in one trial. The simplest example of mutually exclusive events is a pair of opposite events, for example, a rat can turn either right or left in a T-maze.

Mutually Exclusive explained

In probability theory, several events are called mutually exclusive if they can’t appear simultaneously in an experiment. Independent events don’t influence the viability of other options. For instance, when flipping a coin, you can’t get two flat faces of coins. These events are called mutually exclusive. Nevertheless, if you roll two dice and get a two and a four on them, such outcomes are non-mutually exclusive.

If an organization chooses between mutually exclusive variants, it should take into consideration the opportunity cost. This is the profit lost when one of the existing alternatives was chosen instead of the other. The amount of lost profit is measured by the value of the best alternative option that was not chosen. Opportunity cost and mutual exclusivity are inextricably linked as opportunity costs occur with every decision made, in other words, when there is a need to choose between the available options. 

The time value of money (TVM) – a phenomenon according to which the value of the amount of money received today differs from the value of the same amount of money received ever in the future – and other parameters make a decision-making process more difficult. Businesses rely on the net present value (NPV) and internal rate of return (IRR) formulas to calculate cost-effectiveness of projects. 

Example

Mutually exclusive analysis is of a high importance in the process of capital budgeting. The project will generate profit only in the future, therefore, when choosing between different projects, the economic attractiveness is evaluated. It is necessary to make an accurate forecast about which project will add value to the business upon completion. Some of them are mutually exclusive. 

For instance, the company seeks to increase sales of existing products in the markets and has a budget of $40,000. If the cost of the first project is $30,000 and the cost of the second project is $30,000, and the third one costs only $5,000, it means that the first and the second projects are mutually exclusive. In other words, if the organization implements the first project, it will not be able to launch the second one, as costs of the projects will exceed the estimated budget. The third project is independent because the organization can afford to start it anyway. 

In addition to this, when evaluating opportunity costs, the company has to pay attention to a potential return of projects. The first project may have a return of $80,000 and the second one – only $60,000. The opportunity cost is equal to the cost of the chosen alternative minus the cost of the next best alternative. Consequently, the opportunity cost of choosing the second project is $20,000. The opportunity cost of picking the first project is $0.