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 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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