Break-even analysis is a managerial (cost) accounting tool used to examine the relationship of price to cost of a product. It also considers various sales volumes and the effect on profit given the different relationships of price to cost. The break-even analysis is an essential tool in maximizing profit with the least amount of resources. It goes much further by defining the minimum production necessary to cover (pay) fixed costs at various sale prices. Naturally the higher the sales price the sooner fixed costs are covered with production. * *

This article explains the sales price to cost relationship. The impact of sales volume and how it affects total profit is expounded upon in Break-Even Analysis – Sales Volume and Profit on this website. To grasp the fundamentals of break-even analysis the reader must first understand some basic terms used in cost accounting including:

1) Fixed Costs

2) Variable Costs

3) Sunk Costs

4) Markup

5) Contribution Margin

Secondly, a break-even point is explained and evaluated at different sale prices (price points) and the corresponding contribution margin is determined. Finally a comprehensive example along with an outcome table is derived with insights in assessing the results. Once the fundamentals are understood the reader can now evaluate simple and basic single item break-even analysis.

Contents

# Break-even Terminology

There are hundreds of terms used in cost accounting but a few terms are synonymous with cost accounting and they include fixed and variable costs along with contribution margin. These three terms plus two others are often used with break-even analysis and are explained below.

**Fixed Costs** – Those cash out costs per accounting period that must be paid no matter what level of production exists. Examples include rent, property taxes, insurance, legal compliance and so forth. Other fixed costs can include:

*** Management salaries** especially those contractually negotiated

*** Labor Force** – Minimum staff in place without serving the first customer; think of a hotel crew, restaurant staff and hospital personnel.

*** Operational Costs** – Utilities, sanitation and maintenance are required no matter how many customers use the facilities. Great examples include swimming pools, resorts, theme parks and government complexes.

*** Capital costs** of debt service

*** Communications** – Landlines, internet and cell phones

**Variable Costs** – Those costs that have a 1:1 correlation or very high dependency on sales are referred to as variable costs. Traditionally, variable costs include materials and labor for products and services rendered. Other variable costs include utilities and manufacturing equipment costs. Variable costs are referred to as prime costs in the food service sector of the economy.

**Sunk Costs** – Some costs are expended and can not be recouped no matter what the company does. A profit can be earned to pay back the investor’s fronted capital used to pay for initial costs; but they can not be directly recovered. As an example, organizational costs to get the company set up cannot be retrieved whereas cash outlays for raw materials for production can be sold as raw materials thus recovering that cash outlay. Typical sunk costs include building construction (some aspects), specialized equipment purchases and engineering. The difference between sunk and fixed costs is the cash outlay involved. Sunk is where cash has already been expended, fixed are required and ongoing. Usually fixed costs are contractually created like a lease agreement.

**Mark-Up** – The percentage increase over costs charged on costs to generate profit. It is often confused with margin which is the percentage of the sales price that is gross profit. For example, a 25% mark-up on costs of $1.00 is 25 cents. So the sales price is $1.25. The margin created is 20%; 25 cents is 1/5 (one-fifth* of $1.25; which equals 20%).

**Contribution Margin** – This is the value each unit of production generates over variable costs. It is always stated in dollars and rarely stated as a percentage. So an item sold for $1.00 having variable costs of 67 cents has a 33 cents per unit contribution margin. For technical purposes it has a 49% mark-up (33 cents as a percentage of 67 cents equals 49%).

In break-even analysis, sunk costs are not considered in the formula. Only fixed and variable costs are used. Variable costs are at the unit of production level and fixed costs are considered in their totality. The goal of the formula is to calculate the number of units that must be sold to cover all fixed costs after subtracting variable costs. In effect break-even analysis determines the contribution margin per unit needed to offset fixed costs over a production run (multiple units).

# Basic Formula For Break-even Analysis

The concept behind the formula is straightforward. Break-even is the number of units that must be sold to cover all cash costs of fixed and variable. Imagine owning a hot dog cart. It costs $700 per month in fixed costs to operate the cart. As a vendor you have to pay the lease payment for the cart, the monthly food license and insurance. You sell your hot dogs for $5.00 each, they’re the foot long all beef kind with any fixings the customer desires. The variable costs of food, condiments and supplies are $2.25 each. How many hot dogs must you sell to cover fixed costs, i.e. break-even?

The formula is:

# of Units for Break-Even = __Fixed Costs
__ Sales Price minus Variable Costs

# of Units = FC

SP – VC

X =

__$700__

$5.00 – $2.25

X =

__$700__

$2.75

X = 255 Units

From the terminology section above, contribution margin is defined as the value each unit of production contributes towards other costs. In effect it is the sales price minus variable costs. Notice in the formula the denominator is stated exactly the same way. Since sales price less variable costs is identical to contribution margin, the formula can now be simplified as:

Break-even Point (# of Units of Production) = __Fixed Costs
__

Contribution Margin

OR

BE = FC

CM

For the hot dog cart it is:

* *BE = __$700__ = 255 Units (Hot Dogs)

$2.75

It is essential to understand that the break-even point does not include any profit which is used to pay for or recapture sunk costs (historical costs). At this point the hot dog cart vendor has calculated the number of hot dogs he must sell to break-even for cash out purposes. Any units sold in excess of 255 contribute $2.75 each towards profit. Again profit is what is necessary to recoup sunk costs. So to take this example further, suppose the vendor wants to earn $2,000 for himself plus $500 to offset his risk (financial outlay at start-up). What is the formula?

The new break-even or production point is the fixed costs of $700 plus $2,500 more or $3,200. This new production point in units is:

Break-even = $3,200 = 1,164 units

$2.75

Now let’s zero in on the contribution margin for a moment and explain the impact it has on the formula. Remember markup is the percentage on COST used to determine sales price. If the cost is $2.25 and the contribution margin is $2.75 then the markup as a percentage is:

Markup = __$2.75__ __ Contribution Margin__

$2.25 Costs of Production

Markup = 122.22%

This makes perfect sense as $2.75 is much greater than the actual cost. If the cost were $2.50, the markup would be $2.50 (sales price is still $5.00); therefore the markup matches cost and would equal 100%. So anytime the contribution margin is greater than costs, markup is at least 100%.

What would happen if the markup was even higher than 122%? To do this, the sales price would have to go higher (we are assuming that we have no control over variable costs of $2.25 and therefore we cannot reduce variable costs).

So if the hot dog vendor goes to a 150% markup, what is the break-even point to cover fixed costs? The markup value is the contribution margin. 150% of variable costs of $2.25 equals ($2.25 X 1.5) which equals $3.38. The new sales price is variable costs plus contribution margin which equals $5.63 per unit. The new break-even point for fixed costs is now:

Break-even = __$700__ = 207 Units

$3.38

Notice that as the markup increases there is greater contribution margin so unit sales can go down and still cover fixed costs. This goes back to the fundamental business principle of sell high. If you really want to cover fixed costs as fast as possible, sell one hot dog (unit) for $702.25. One unit will cover the variable costs of $2.25 plus fixed costs of $700. By the way, what is the markup?

Markup equals contribution margin of $700 divided by variable costs of $2.25.

Markup = __$700__

$2.25

Markup = 31,111%.

**THE KEY TO BREAK-EVEN ANALYSIS IS THAT AS THE PRICE FOR THE SALE OF A UNIT INCREASES, **CONTRIBUTION MARGIN INCREASES THEREFORE THE NUMBER OF UNIT SALES NEEDED DECREASE TO COVER FIXED COSTS. THE LOWER THE SALES PRICE THE MORE UNIT SALES ARE NEEDED TO COVER FIXED COSTS.

To illustrate how the break-even point is analyzed, let’s look at a comprehensive example.

# Break-even Analysis – Comprehensive Example

Dennis wants to open an auto repair shop and decides to specialize in brakes only.

His idea is to replace existing pads and turn the rotors. After discussing with his CPA, he calculates the monthly fixed costs to operate including his salary will run $13,700 per month. The variable costs for a two brake system, single axle is as follows:

Brake Pads – $21.77 (combined for both wheels)

Supplies – 2.49

Labor 38.52 (includes taxes and insurance)

Tools __.41
__Total Variable Costs $63.19

Dennis wants to know how many jobs (customers agreeing to purchase a single axle brake replacement) will it take to cover fixed costs. He has heard his competition mention at least a 50% markup is required. Dennis wants a schedule in 10% increments of markup starting at 50% and ending at 120% to determine how many brake jobs per month must be performed to cover fixed costs of $13,700.

**Step 1** – Determine markup values and final sales price for all eight increments

Incremental Markup Value Sales Price

M__arkup__ __Cost__ __Cost * Markup__ __Cost Plus Markup__ __
__50% $63.19 $31.60 $94.79

60% 63.19 37.91 101.10

70% 63.19 44.23 107.42

80% 63.19 50.55 113.74

90% 63.19 56.87 120.06

100% 63.19 63.19 126.38

110% 63.19 69.51 132.70

120% 63.19 75.83 139.02

**Step 2** – Calculate break-even points for various markups

__Fixed Costs__ __Markup %__ __Contribution Margin__ __Break-even__ __Units
__$13,700 50% $31.60 434

13,700 60% 37.91 361

13,700 70% 44.23 310

13,700 80% 50.55 271

13,700 90% 56.87 241

13,700 100% 63.19 217

13,700 110% 69.51 197

13,700 120% 75.83 181

Notice the number of units for 50% in comparison to 100% is a multiple of two? At 50% Dennis must do 434 brake jobs; at 100% markup the number of brake jobs is half.

The above tables follow the fundamentals of break-even as outlined in prior sections:

1) As the sales price increases, the break-even point decreases.

2) As markup increases contribution margin also increases.

3) Therefore, as markup increases the break-even point decreases.

To help the reader understand more about the break-even analysis some insights are appropriate.

# Insights

A very important business fundamental has to be considered here. Break-even analysis functions perfectly in isolation. That is, it works well when only one product or service is rendered.

Think about Dennis and his brake shop. What is the likelihood that brakes are going to be his ONLY product? Realistically most customers will not know if their brakes are bad, so how will he get customers? Sure he can offer free inspections, but now he has two services (inspections and brake replacements), each with variable costs.

All businesses encounter this complexity complicating the formula. It is nearly impossible to think of any business out there with a single product where the formula will work in isolation. Therefore, the formula must be modified to account for more business variables. The next article in break-even takes into consideration the sales (units sold) curve when discussing the sales price which is a function of markup. This is just the first of many additional variables the entrepreneur must consider in understanding break-even analysis.

# Summary – Break-even Analysis

All businesses need to evaluate the level of production necessary to cover cash out costs (both fixed and variable). This process is called break-even analysis. The formula is simple in isolation, i.e. a single product or service. It is:

Break-even Point = Fixed Costs

. Sales Price Less Variable Costs

The denominator is also referred to as a unit contribution margin which is a function of markup. As markup increases, the sales price increases creating greater contribution margin. As this increases, less units are required to be sold to cover fixed costs.

This relationship of sales price to variable costs and the volume of fixed costs is an important business association that has a significant bearing on profitability. An entrepreneur must understand the core break-even analysis fundamentals in order to succeed in business. **ACT ON KNOWLEDGE**.

**If you have any comments or questions, e-mail me at dave (insert the usual ‘at’ symbol) businessecon.org. I would love to hear from you. **If interested in my help as an accountant or consultant, contact me through the ‘My Services’ page in the footer.