Break-even analysis, one of the most popular business tools, is used by companies to determine the level of profitability. It provides companies with targets to cover costs and make a profit. It is a comprehensive guide to help set targets in terms of units or revenue.

In this article, we look at 1) break-even analysis and how it works, 2) application and benefits, and 3) calculations, assumptions, and interpretations.

## BREAK-EVEN ANALYSIS, AND HOW IT WORKS

### Definition

Break-even analysis is a business tool widely used across all industries to evaluate business performance in terms of costs, since this is a supply-side analysis. Break-even analysis is an important aspect of a good business plan, since it helps the business determine the cost structures, and the number of units that need to be sold in order to cover the cost or make a profit. Break-even analysis is usually done as part of a business plan to see the how practical the business idea is, and whether or not it is worth pursuing. Even after a business has been set-up, break-even analysis can be immensely helpful in the pricing and promotion process, along with cost control.

Simply put, break-even point can be determined by calculating the point at which revenue received equals the total costs associated with the production of the goods or services.

Break-even Point = Fixed Costs/ (Unit Selling Price – Variable Costs)

### The Concept Behind the Analysis

Using the above formula, the business can determine how many units it needs to produce in order to break-even. Once the business has reached this point, in sales or units sold, all costs (Fixed and Variable) have been recovered. Beyond this point, every additional unit sold will result in increasing profit for the business. The increase in profit will be by the amount of unit contribution margin, which is the amount of additional revenues that goes towards covering the fixed costs and profit. It can be calculated as follow:

Unit Contribution Margin = Sales Price – Variable Costs

### Costs

There are two distinct nature of costs that a business has to incur in its normal operational activities:

#### Fixed Costs

These costs stay the same regardless of how many units the company is producing. These include start-up costs, and other capital expenses which do not have to be paid periodically. Rent, insurance, utility bills and repairs are also considered fixed costs, since variations are minute and the amount does not directly depend on the number of items produced. For example, if a tire manufacturer rents a building at \$2000 per month, and decides to produce 100 tires, the fixed cost will be \$2000. The amount will stay the same if even there is no activity and zero tires are produced.

#### Variable costs

These costs are directly associated with the number of units produced, and these are recurring in nature, since they have to be paid periodically. As the business produces more and more goods and services, these costs increase proportional. For example, the cost of rubber required to manufacture a tire is \$10. If company produces zero tires, the total variable costs comes down to \$0 (10*0). On the other hand, if the company produces 500 tires, the total variable costs comes down to \$5000 (500*10). These costs usually include material, labor, direct sales and promotion, storage etc.

### Revenue

Revenue is the money that a business actually receives from its customers for the provisions of goods and services during a particular period. Discounts and deductions have already been adjusted, which means it is the gross income from which various costs are later deducted in order to calculate profit or loss. Total revenue can be calculated by multiplying the price at which goods or services are sold by number units sold.

### Contribution Margin

Contribution margin can be calculated by subtracting variable expenses from the revenues. The contribution margin shows how much of the company’s revenues will be contributing towards covering the fixed costs. It can be expressed on per unit basis or for the total amount. It can also be expressed as a percentage of net sales.

### Two Types of Break-Even Calculations – Units and Sales

#### Calculation of Break-even point in units

Break-even point is usually calculated in units, which gives the company the number of units it must produce in order to break-even. It can be calculated by dividing contribution margin by total fixed costs:

Break-even point (Units) = Fixed Costs/Contribution margin per unit

#### Calculation of Break-even point in sales value

In the previous example, the break-even point was calculated in terms of number of units. Break-even point can also be calculated in sales value (Dollars). This can be done by dividing company’s total fixed costs by contribution margin ratio.

Contribution Margin = Contribution Margin per Unit/Sales Price per Unit

OR

Contribution Margin = (Sales Price – Variable Costs) /Sales Price per Unit

Contribution margin, when expressed as percentage of sales is called contribution margin ratio.

Example:

Calculate contribution margin, total contribution margin and contribution margin ratio using the following information:

 Price Per Unit \$20 Units Sold 5000 Variable Cost Per unit \$12

Solution

 Total Sales = 5000 × \$20 = \$100,000 Total Variable Cost = 5000 × \$12 = \$60,000 Total Contribution Margin = \$100,000 – \$60,000= \$40,000 Contribution Margin Per Unit = \$40,000 ÷ 5000 = \$8 CM Ratio = \$8/20 = 40%

Example:

A business has fixed costs of \$100,000 per year, while the variable costs are 60% of total sales value. This would mean the contribution margin is 40%, since 100% – 60%=40%

In order to calculate break-even point in sale:

Break-Even Point in Sales = Fixed Costs/contribution margin ratio

= \$100,000/40%

= \$ 250,000

So, the company needs to sell goods worth \$250,000 in order to break-even. Anything beyond this point will constitute as profit, and if the company falls short of this amount, the difference would be loss incurred.

## APPLICATION AND BENEFITS

### Application of Break-even Analysis

#### Cost Calculation

Break-even analysis is widely used to determine the number of units the business needs to sell in order to avoid losses. This calculation requires the business to determine selling price, variable costs and fixed costs. Once these numbers are determined, it is fairly easy to calculate break-even point in units or sales value.

#### Budgeting and Setting Targets

Break-even charts and calculation be used for budgeting process, since the business know exactly how many units need to be sold in order to break-even. Moreover, the company is also aware of the profits the company will be able to earn at various points, which can be easily illustrated on a simple break-even chart. This can help business set realistic, achievable targets for itself.

#### Motivational Tool

Break-even analysis also helps to motivate the employees, especially the sales staff, since it clearly shows the profits at various points of sales. The chart clearly shows the impact extra sales would have on the profitability of the company.

#### Margin of Safety

Margin of safety is a tool which complements break-even analysis, since these two tool are interrelated. This concept is used when a major proportion of sales are likely to decline or in period of recession or economic turn down. Managers can better make better production and sales decision if they know the margin of safety for a particular product or service. When the margin of safety is large, the business would want to try new pricing, marketing and take risks hoping to further increase sales and revenues. On the other hand, if the margin of safety is meager, managers are likely not to change anything, since any small change could trigger losses. In such a situation managers would want to reduce costs, so that margin of safety can be increased.

The concept of margin of safety might not be useful for businesses with seasonal demand for their products or services, since there will be a lot of variations on monthly basis. The result could be complied for an entire year, so that seasonal fluctuations are removed.

Margin of safety can be calculated by subtracting the current break-even point from current sales, and dividing by current level of sales.

The formula (Version #1) is:

Margin of safety = (Current Sales Level – Break-even Point)/Current Sales Level

There are two ways to calculate margin of safety:

If the company wishes to calculate margin of safety for a budgeted, future period, it can replace the current sales level with budgeted sales level.

If a business wants to calculate margin of safety (Version #2) for number of units sold, then instead of current sales level, selling price per unit in the denominator.

Margin of safety = (Current Sales Level – Break-even Point)/Selling Price per Unit

For example, a business considering expanding its factory. The expansion will increase business’s operating costs by \$50,000. The table below shows how the concept of margin of safety can be employed to assess various situations:

##### Example

Use the following information to calculate margin of safety:

 Before Expansion After Expansion Sales Price per Unit \$50 \$50 Variable Cost per Unit \$30 \$30 Total Fixed Cost \$10,000 \$10,000 Budgeted Sales \$50,000 \$75,000

Solution (Before Expansion)

 Break-even Sales Units = \$10,000 ÷ (\$50 – \$30) = 500 Budgeted Sales Units = \$50,000 ÷ \$50 = 1,000 Margin of Safety = (1000 − 500) ÷ 1,000 = 50%

Solution (After Expansion)

 Break-even Sales Units = \$10,000 ÷ (\$50 – \$30) = 500 Budgeted Sales Units = \$70,000 ÷ \$50 = 1,500 Margin of Safety = (1500 − 500) ÷ 1,000 = 100%

The above example shows how an improvement in actual sales improved margin of safety for the business as the sales improved.

#### Cost Control and Monitoring

Since costs (Fixed and Variable) affect the profitability of the business directly, the managers can easily see these changes through break-even analysis. This would help them control costs, and make sure that they remain within a given range.

#### Helps devise a pricing strategy

Selling price is an important determinant of break-even analysis. If managers have access to break-eve charts, they will be able to see the impact, changes in selling price has on the overall profitability. Hence, this tool provides more information for the mangers to make better pricing decision, considering the supply-side of the production process.

## CALCULATIONS, ASSUMPTIONS AND INTERPRETATION

### Worked Example

For example, if it costs \$50 to produce a tire, and there are fixed costs of \$500, the break-even point for selling the widgets would be:

If selling for \$100: 10 tires (Calculated as 500/ (100-50) =10)

If selling for \$150: 5 tires (Calculated as 500/ (150-50) =5)

As it can be seen from the above example that, higher the selling price of a particular product, the break-even point is lower. One of the major flaws of break-even analysis is that it fails to take into account the demand-side of the business, since looking from a demand-side perceptive it would be easier to sell more units at lower price.

Break-even point calculation is a rather simple calculation that can help businesses with forecasting costs and sales. As mentioned earlier, break-even point there is no profit, no loss. Ideally all business owners would want a lower break-even point, since beyond that point there is profit for the business. The lower limit of profit is the break-even point.

### Key Assumption – Fixed Cost same, Variable Cost and Sales Price are kept constant

Break-even analysis assumes that per unit selling price and variable cost do not change, which is not always the case.

Business in order to sell more goods and services often have to reduce prices. Sometimes prices are not in control of the business, since they depend on market conditions and other factors such as government regulation.

Variable costs also change as material, labor and other indirect variable expenses could increase or decrease as quantity changes. For Example, Labor rates will increase due to overtime if more units are produced. Other variable cost could also vary with number of units. The break-even analysis also assumes that all units produced are also sold, which is not always the case. This tool fails to take into account the demand-side situation, since not all units produced are sold at the assumed price.

### Difficulties And Applicability

Another important aspect of business transaction that is missed in break-even calculation is principal balance of outstanding loans. The interest being paid on all loans should be part of fixed costs, but it is shown as an expense in the profit & loss account.

### Graphical Construction – Break-Even Diagram

Break-even diagram (also known as break-even chart, see above) is a line graph used for break-even analysis to determine the break-even point, the point where business will make a profit or loss. Number of units are plotted on the horizontal (X) axis, and total sales/costs are plotted on vertical (Y) axis. Using the diagrammatical method, break-even point can be determined by pinpointing where the two (revenue and total costs) linear lines intersect. The total revenue and total cost lines are linear (straight lines), since prices and variable costs are assumed to be constant per unit. The Break-even diagram can be modified to reflect different situation with various prices and costs. The diagram clearly shows how a change in cost or selling price can impact the overall profitability of the business.

In the diagram, the line of fixed cost in horizontal with the x-axis, which means it does not change with the quantity, since even if the output is zero, some costs have to be incurred. The total cost line represents the combined sum of both variable and total cost, since both must be taken into account in order to determine profitability.

### Interpretation

It is essential that the results from break-even analysis are interpreted correctly and the information is effectively utilized to make better, informed business decisions. For example, if a break-even analysis of a business reveal that 1000 units need to be produced to break-even. The managers need to assess whether or not they will be able to sell 1000 unit within a reasonable period of time given the market condition. Personal expectations and financial situation of the business must also be taken into consideration. If the managers think that 1000 units can only be sold if price is lowered, break-even point should be re-calculated taking into account the change.