# Costing with the Break-Even Analysis

If we start a business or simply want to introduce a new or adapted product or service, it is always a crucial need to know how much the costs are, how much one has to sell to break even, how much one has to sell to make a profit of \$x, or also if one can feasibly sell the amounts of units in a realistic time to break even and make a profit. Here we are in the middle of costing, a “managerial accounting method that describes when all fixed and variable costs, including manufacturing costs, are used to compute the total cost per unit” (Investopedia.com).

One basic and simply to understand method deals with the break-even point (BEP). The BEP is defined as the point at which neither losses nor profits are made. In other words, the losses equal the profits. While this covers all the costs and expenses occurred, one has not earned a dime because all the profits are used to cover the costs.

While there are mathematical ways to calculate the BEP, we will first look at a graphical chart to better understand the interrelations between costs and profits and how they relate to one another at different sales levels.

The chart of the break-even point illustrates the relationship between the level of sales and its associated costs and revenues.

In this chart of the break-even point, we can see the relationship between the level of sales and its associated costs and revenues. The blue line depicts the fixed costs. It is a horizontal line because these costs don’t change with the level of sales. The red line shows the total costs, in other words the sum of the fixed costs and variable costs per unit. As the variable costs add up with each unit sold, it is a increasing linear line. The green line represents the sales revenue. At the point it crosses the red line (total costs) is the break-even point. As stated earlier, here the losses and profits are equal. As you will now realize, the break-even point can both be described in the sales level (number of units sold) and the sales value (revenue). So keep this in mind for now.

While a chart gives us a good approximate of where the break-even point is, thus also telling us on how much we have to sell to start making a profit, it is usually difficult to adequately read the break-even point. It helps us, however, to understand the concept of the break-even point. In order to get specific and exact numbers though, it is better to calculate the BEP. For this we need to know and understand the following:

• Fixed costs: These costs remain the same with all levels of sales.
• Variable costs per unit: These costs vary linearly according to the amounts of units produced.
• Sales revenue per unit
• Contribution per unit: The contribution equals the sales revenue per unit minus the variable costs per unit.
• Selling price per unit

With these terms, we can now calculate the break-even point in units as well as in sales value:

How to calculate the break-even point in units

How to calculate the break-even point in sales value

I assume that the factors given and the two formulas are quite self-explanatory now so that I will not give any exemplary calculations here. There is, however, ways to extend the break-even formulae. Just think about that you will probably not only want to know at what sales level or revenue your business breaks even but that you will likewise be interested in accomplishing specific amounts of profit beyond that. This will be the target to achieve, thus it is called target profit, “the amount of net operating income or profit that management desires to achieve at the end of a business period” (accounting4management.com).

One can rather simply adjust the break-even formula to consider the desired target profit. From here we can also calculate the required sales revenue. Of course, we need to know, or rather decide on, a target profit.

How to calculate target sales in units

How to calculate the target sales in revenue

Last but not least, there is one further basic logical extension, calculating the margin of safety. BusinessDictionary.com defines the margin of safety as “an excess of a company’s actual sales revenue over the breakeven sales revenue, expressed usually as a percentage.” While it can also be calculated through the level of sales or the revenue, both cases will conclude with the same percentage. Thus, I illustrate the formula only once:

How to calculate the margin of safety in percentage

As one of the starting thoughts was if it will be at all feasible to sell the amounts of units in a realistic time to break even and make a profit, we come to the limitations of the break-even analysis. While it gives us theoretical number on, for example, how much we have to sell to reach the break-even point or make a specific profit, it does not take into account the general market. If the required sales levels are too high, we may not have enough customers that will buy our products or services in order to get to the desired and needed sales level. Furthermore, the whole article assumes linear variable costs, meaning the variable cost per unit is the same at all sales levels. This can, of course, be correct for some business and thus be directly applicable. On the other hand, a business that starts out with low productions will purchase their components at higher rates than businesses with larger productions can. While this can still be calculated with the computer, it is beyond the frame of this article.

All in all, the break-even point and its different extensions to calculate the break-even point in units, the break-even points in sales value, the target sales in units, and also the margin of safety is a good starting point to analyze potential level of sales at, for example, different profit margins per unit. Among others, it is then important to keep in mind the external factors such as buying power and whether it is enough to reach desired sales levels.

Sources

The Author: Konstantin von Brocke has graduated in business management with magna cum laude from University of Wisconsin-Stout in December 2012. He is interested and enthusiastic about marketing and sales, finance and risk management, and business development and consulting.