When discussing breakeven (BE), it is useful to know two basic formulas:

contribution margin per unit = sales price - variable cost per unit

contribution margin ratio = contribution margin (sales - variable cost) / sales

Breakeven in Units

Imagine a company, Video Productions, that produces DVDs selling for $20 per unit. Fixed costs per period total $40,000, while variable cost is $12 per unit. We compute the break-even point in units as

BE units = fixed costs / contribution margin per unit

Video Productions’ contribution margin per unit is $8 ($20 selling price per unit – $12 variable cost per unit). The break-even point in units would be calculated as:

BE units = fixed costs / contribution margin per unit = $40,000 / $8 = 5,000 units.

The result tells us that Video Productions breaks even at a volume of 5,000 units per month. We can prove that to be true by computing the revenue and total costs at a volume of 5,000 units. 

revenue = (5,000 units × $20 sales price per unit) $100,000. 

total costs = $100,000 ($40,000 fixed costs + $60,000 variable costs [$12 per unit × 5,000 units]).

Look at the cost-volume-profit chart and note that the revenue and total cost lines cross at 5,000 units—the break-even point. Video Productions has net income at volumes greater than 5,000, but it has losses at volumes less than 5,000 units.

Breakeven in Sales Dollars 

Companies frequently think of volume in sales dollars instead of units. For a company such as GM that makes Cadillacs and certain small components, it makes no sense to think of a break-even point in units. GM breaks even in sales dollars.

The formula to compute the break-even point in sales dollars looks a lot like the formula to compute the break-even in units, except we divide fixed costs by the contribution margin ratio instead of the contribution margin per unit.

The contribution margin ratio expresses the contribution margin as a percentage of sales. To calculate this ratio, divide the contribution margin per unit by the selling price per unit, or total contribution margin by total revenues. Video Production’s contribution margin ratio is

contribution margin ratio = contribution margin / sales = $8 / $20 = 0.4 = 40%.

Or, referring to the income statement in which Video Productions had a total contribution margin of $48,000 on revenues of $120,000, we compute the contribution margin ratio as contribution margin ($48,000) / Revenues ($120,000) = 0.40, or 40 percent.

That is, for each dollar of sales, there is $0.40 left over after variable costs to contribute to covering fixed costs and generating net income.

Using this contribution margin ratio, we calculate Video Production’s break-even point in sales dollars as

BE in sales dollars = fixed costs / contribution margin ratio = $40,000 / .4 = $100,000.

The break-even volume of sales is $100,000 (can also be calculated as break-even point in units 5,000 units × sales price $20 per unit). At this level of sales, fixed costs plus variable costs equal sales revenue, as shown here:

Margin of Safety

If a company’s current sales are more than its break-even point, it has a margin of safety equal to current sales minus break-even sales. The margin of safety is the amount by which sales can decrease before the company incurs a loss. For example, assume Video Productions currently has sales of $120,000 and its break-even sales are $100,000. The margin of safety is $20,000, computed as follows:

margin of safety = current sales – break-even sales

margin of safety = $120,000 – $100,000 = $ 20,000.

Sometimes the margin of safety is expressed as a percentage, called the margin of safety rate or just margin of safety percentage. The margin of safety rate is equal to

margin of safety percent = current sales - break-even sales / current sales.

Using the data just presented, we compute the margin of safety rate as 

$20,000 / 120,000 = 16.67%

This means that sales volume could drop by 16.67 percent before the company would incur a loss.

Targeted Profit or Income

You can also use this same type of analysis to determine how many sales units or sales dollars you would need to make a specific profit. The good news is you have already learned the basic formula—we are just changing it slightly. The formulas we will need are as follows:

units at target profit = fixed costs + target income / contribution margin per unit

sales dollars for target profit = fixed costs + target income / contribution margin ratio.

These are the same formulas we used for break-even analysis, but this time we have added target income. If you think about it, it is actually the same formula because at breakeven our target income is zero.

Let’s look at another example. The management of a major airline wishes to know how many seats must be sold on Flight 529 to make $8,000 in profit. To solve this problem, management must identify and separate costs into fixed and variable categories.

The fixed costs of Flight 529 are the same regardless of the number of seats filled. Fixed costs include the fuel required to fly the plane and crew (with no passengers) to its destination, depreciation on the plane used on the flight, and salaries of required crew members, gate attendants, and maintenance and refueling personnel. Fixed costs are $12,000.

The variable costs vary directly with the number of passengers. Variable costs include snacks and beverages provided to passengers, baggage handling costs, and the cost of the additional fuel required to fly the plane with passengers to its destination. Management would express each variable cost on a per passenger basis. Variable costs are $25 per passenger.

Tickets are sold for $125 each. The contribution margin is $100 ($125 sales – $25 variable) and the contribution margin ratio is 80 percent ($100 contribution margin / $125 sales). We can calculate the units and sales dollars required to make $8,000 in profit as follows:

units at target profit = fixed costs + target income / contribution margin per unit

= $12,000 + $8,000 / $100

= $20,000 / $100

= 200 tickets

The sales dollars required could be calculated as break-even units of 200 tickets × $125 sales price per ticket = $25,000, or by using the following formula:

sales dollars for target profit = fixed costs + target income / contribution margin ratio

= $12,000 + $8,000 / .80

= $20,000 / .80

= $25,000

Management can also use its knowledge of cost-volume-profit relationships to determine whether to increase sales promotion costs in an effort to increase sales volume or to accept an order at a lower-than-usual price. In general, the careful study of cost behavior helps management plan future courses of action.

Breakeven Analysis

Let’s consider another example—forecasting sales of shoes. Selling twelve thousand pair of shoes the first year you run the shoe retail business sounds great, but you still need to find an answer to an important question: are there enough customers willing to buy my jogging shoes at a price that will allow me to make a profit? Is there some way to figure out the level of sales I would need to avoid losing money—to break even? To break even (have no profit or loss), total sales revenue must exactly equal all your expenses (both variable and fixed). To determine the level of sales at which this will occur, you need to work through the following steps:

1. Determine your total fixed costs, (i.e., costs that don’t change as the quantity of goods sold changes
   fixed costs = $210,000 salaries + $60,000 rent + $10,000 advertising + $8,000 insurance + 12,000 other fixed costs = $300,000.
2. Identify your variable costs. These are costs that vary, in total, as the quantity of goods sold changes but that stay constant on a per-unit basis. State variable costs on a per-unit basis:
   Variable cost per unit = $40 (cost of each pair of shoes) + $5 sales commission = $45.
3. Determine your contribution margin per unit (selling price per unit less variable cost per unit):
   Contribution margin per unit = $80 selling price minus $45 variable cost per unit = $35.
4. Calculate your break-even point in units (fixed costs / contribution margin per unit):
   Breakeven in units = $300,000 fixed costs / $35 contribution margin per unit = 8,571 units

 

Your calculation means that if you sell 8,571 pairs of shoes, you will end up with zero profit (or loss) and will exactly break even.

If your sales estimate is realistic (a big if), then you should be optimistic about starting the business. All your fixed costs will be covered once you sell 8,571 pairs of shoes. Any sales above that level will be pure profit. So, if you sell your expected level of twelve thousand pairs of shoes, you’ll make a profit of $120,015 for the first year. Here’s how we calculated that profit:

expected sales level – breakeven sales level

= 12,000 - 8,571

= 3,429 units × $35 contribution margin per unit

= $120,015 first-year profit.

As you can see, breakeven analysis is pretty handy. It allows you to determine the level of sales that you must reach to avoid losing money and the profit you’ll make if you reach a higher sales goal. Such information will help you plan for your business.