## Accounting Cost-Volume-Profit Analysis

## 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

**+ $10,000,**

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

$5
x ** Q** - $3 x

**= $10,000**

*Q*$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.