## 2.1. Equation technique in CVP analysis and break-even point

To use this technique we should recall the basic equation of profit calculation:

Profits = Sales - Costs, where

Costs = Variable Costs + Fixed Costs

If Costs is replaced with Variable Costs + Fixed Costs, we obtain the following equation:

Profits = Sales - Variable Costs - Fixed Costs

Further, if we move Sales to the right side of the equation and Profits to the left side, we obtain the following rearranged equation:

Sales = Variable Costs + Fixed Costs + Profits

The final equation is what we will use in CVP analysis for a single product scenario.

A question we would like to answer now is as follows: What level of sales is necessary to cover all expenses?

The level of sales at which total revenues are equal to total costs (or expenses) is called a break-even point.

A part of CVP analysis which aims to determine the break-even point is called break-even analysis.

A company is "breaking even" when it has zero profit; that is, total costs equal total revenues.

At break-even, Profits = 0; therefore:

Sales = Variable Costs + Fixed Costs + 0 = Variable Costs + Fixed Costs

Knowing the equation above, we can calculate the sales at the break-even point.

Let's take a look at an example. The following data is available for Friends Company:

 Total fixed cost \$10,000 Variable cost per unit \$3 Selling price per unit \$5

If we use the data from the table in the equation, we will obtain the following:

\$5 x Q = \$3 x Q + \$10,000,

where Q is the number of units to be sold to break-even.

\$5 x Q - \$3 x Q = \$10,000

\$2 x Q = \$10,000

Q = 5,000 units

The answer to our question is 5,000 units. If we would like to express the break-even point in dollars, we would multiple the 5,000 units by the selling price per unit: 5,000 units x \$5 = \$25,000.

The company will have neither loss nor gain if it sells 5,000 units (or sales amount to \$25,000). We can check the correctness of our calculation as follows:

Profits = 5,000 x \$5 - 5,000 x \$3 - \$10,000 = 0

This is what we were trying to prove (i.e., zero profits).

If sales fall below that amount, Friends Company will have a loss; if sales increase above that amount, Friends Company will generate a profit. We will see more later about generating a loss or profit.

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