Calculate a Break-Even Point in Units and Dollars

The calculation of the break-even point (BEP) does not account for the cost of capital, interest rates, or projections on a return on this investment. After you read, you should be able to point out how the BEP is used.

Calculate a Break-Even Point in Units and Dollars

Application of Break-Even Concepts for a Service Organization

Because break-even analysis is applicable to any business enterprise, we can apply these same principles to a service organization. For example, Marshall & Hirito is a mid-sized accounting firm that provides a wide range of accounting services to its clients but relies heavily on personal income tax preparation for much of its revenue. They have analyzed the cost to the firm associated with preparing these returns. They have determined the following cost structure for the preparation of a standard 1040A Individual Income Tax Return:

Charge to Client (sales price per return)	$400
Variable Cost per Return	150

They have fixed costs of $14,000 per month associated with the salaries of the accountants who are responsible for preparing the Form 1040A. In order to determine their break-even point, they first determine the contribution margin for the Form 1040A as shown:

Sales Price per Return	$400
Variable Cost per Return	8,500
Contribution Margin per Return	34,000

Now they can calculate their break-even point:

$Break-Even\ Point\ in\ Units = \frac{Total\ fixed\ costs}{Contribution\ margin\ per\ unit}=\frac{$14,000}{$250}=56 returns$

Remember, this is the break-even point in units (the number of tax returns) but they can also find a break-even point expressed in dollars by using the contribution margin ratio. First, they find the contribution margin ratio. Then, they use the ratio to calculate the break-even point in dollars:

$Break-Even\ Point\ in\ Dollars = \frac{Fixed\ costs}{Contribution\ margin\ ratio}=\frac{$14,000}{0.625} = $22,400$

We can confirm these figures by preparing a contribution margin income statement:

MARSHALL & SON, CPAs Contribution Margin Income Statement For Year Ended December 31, 2019
Sales (56 at $400 per return)	$22,400
Variable Costs (56 at $150 per return)	8,400
Contribution Margin	14,000
Fixed Costs	14,000
Operating Income (loss)	$ 0

Therefore, as long as Marshall & Hirito prepares 56 Form 1040 income tax returns, they will earn no profit but also incur no loss. What if Marshall & Hirito has a target monthly profit of $10,000? They can use the break-even analysis process to determine how many returns they will need to prepare in order to cover their fixed expenses and reach their target profit:

$Target\ Profit = \frac{Fixed\ costs + desired\ profit}{Contribution\ margin\ per\ unit} = \frac{$14,000+$10,000}{$250} = 96 returns$

They will need to prepare 96 returns during the month in order to realize a $10,000 profit. Expressing this in dollars instead of units requires that we use the contribution margin ratio as shown:

$Target\ Profit = \frac{Fixed\ costs + desired\ profit}{Contribution\ margin\ per\ unit} = \frac{$14,000+$10,000}{0.625} = $38,400$

Marshall & Hirito now knows that, in order to cover the fixed costs associated with this service, they must generate $38,400 in revenue. Once again, let’s verify this by constructing a contribution margin income statement:

MARSHALL & SON, CPAs Contribution Margin Income Statement For Year Ended December 31, 2019
Sales (90 at $400 per return)	$38,400
Variable Costs (96 at $150 per return)	14,400
Contribution Margin	24,000
Fixed Costs	14,000
Operating Income (loss)	$10,000

As you can see, the $38,400 in revenue will not only cover the $14,000 in fixed costs, but will supply Marshall & Hirito with the $10,000 in profit (net income) they desire.

As you’ve learned, break-even can be calculated using either contribution margin per unit or the contribution margin ratio. Now that you have seen this process, let’s look at an example of these two concepts presented together to illustrate how either method will provide the same financial results.

Suppose that Channing’s Chairs designs, builds, and sells unique ergonomic desk chairs for home and business. Their bestselling chair is the Spine Saver. Figure 3.10 illustrates how Channing could determine the break-even point in sales dollars using either the contribution margin per unit or the contribution margin ratio.

Sales Price per Unit	Cost per Unit	Contribution Margin per Unit	Fixed Costs	Fixed Costs/ Contribution Margin per Unit	Break-Even in Units	Break Even in Dollars
$1,250	$850	$400	$16,800	$16,800/$400	42	42 × $1,250 = $52,500

Contribution Margin per Unit ($1,250 - 850)	Contribution Margin Ratio (CM/Sales or $400 ÷ 1,250)	Break-Even in Sales Dollars (FC ÷ CM or $16,800 ÷ 0.32)	Break-Even in Units (Break Even Sales ÷ Unit Selling Price or $52,500 ÷ $1,250)
$400	32%	$52,500	42 Units

Figure 3.10 Channing’s Break-Even Point.

Note that in either scenario, the break-even point is the same in dollars and units, regardless of approach. Thus, you can always find the break-even point (or a desired profit) in units and then convert it to sales by multiplying by the selling price per unit. Alternatively, you can find the break-even point in sales dollars and then find the number of units by dividing by the selling price per unit.

YOUR TURN

College Creations

College Creations, Inc (CC), builds a loft that is easily adaptable to most dorm rooms or apartments and can be assembled into a variety of configurations. Each loft is sold for $500, and the cost to produce one loft is $300, including all parts and labor. CC has fixed costs of $100,000.

What happens if CC produces nothing?
Now, assume CC produces and sells one unit (loft). What are their financial results?
Now, what do you think would happen if they produced and sold 501 units?
How many units would CC need to sell in order to break even?
How many units would CC need to sell if they wanted to have a pretax profit of $50,000?

Solution

A. If they produce nothing, they will still incur fixed costs of $100,000. They will suffer a net loss of $100,000.

B. If they sell one unit, they will have a net loss of $99,800.

Sales revenue	$500
Variable Costs per unit	300
Contribution Margin	200
Fixed Costs	100,000
Operating Income (loss)	$(99,800)

C. If they produce 501 units, they will have operating income of $200 as shown:

Sales revenue (501 units at $500)	$250,500
Variable Costs per unit (501 units at $500)	150,300
Contribution Margin	100,200
Fixed Costs	100,000
Operating Income (loss)	$ 200

D. Break-even can be determined by FC/CM per unit: $100,000 ÷ $200 = 500. Five hundred lofts must be sold to break even.

E. The desired profit can be treated like a fixed cost, and the target profit would be (FC + Desired Profit)/CM or ($100,000 + $50,000) ÷ $200 = 750. Seven hundred fifty lofts need to be sold to reach a desired income of $50,000. Another way to have found this is to know that, after fixed costs are met, the $200 per unit contribution margin will go toward profit. The desired profit of $50,000 ÷ $200 per unit contribution margin = 250. This means that 250 additional units must be sold. To break even requires 500 units to be sold, and to reach the desired profit of $50,000 requires an additional 250 units, for a total of 750 units.