5.3: Breakeven Point
The breakeven point is the number of units that must be sold to achieve an operating income of zero. At the breakeven point, sales in dollars equals costs. The breakeven calculation answers the question How many units does the company have to sell to pay all its expenses for the month?
This slightly revised information relates to Jonick Company for the month of June and will be used to illustrate the breakeven point.
|
Sales |
1,000 units |
|
Selling price per unit |
$18 |
|
Variable cost per unit |
$10 |
|
Fixed costs |
$8,000 |
The following income statement presents a breakeven situation.
|
Sales |
$18,000 |
|
Variable costs |
10,000 |
|
Contribution margin |
$8,000 |
|
Fixed costs |
8,000 |
|
Operating income |
$0 |
Note that the contribution margin of $8,000, the amount available to cover fixed costs, equals the fixed costs amount of $8,000. Therefore, operating income is zero.
The number of units sold was given in the previous example. In many cases, that is the question that must be answered based on the selling price per unit, the variable cost per unit, and the fixed cost given.
Breakeven analysis is a form of CVP that uses the equation for a line to determine the number of units that must be sold to break even. The equation that follows proves the breakeven point in units is 1,000.
Breakeven point in units $=\frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 8,000}{\$ 18-\$ 10}=1,000$ units per month
The denominator of unit selling price per unit minus the unit variable cost may also be stated as the unit contribution margin.
5.3.1 Interpreting the Breakeven Result
The lower the breakeven point, the better, since it takes relatively fewer units of sales to cover all the fixed and variable costs. Once the volume of sales reaches the number of units needed to break even, all fixed costs have been paid. Every subsequent unit sold yields profit equal to the amount of the unit contribution margin.
The breakeven point is a relative number; it does not have much meaning on its own. It must be compared to another breakeven number, such as the expected or budgeted number of units to break even, an industry average, or the breakeven point for comparable companies. If the breakeven point is higher than a business’s capacity or ability to fulfill, the operation of the business is likely doomed to fail. A breakeven point that is at or below what was expected, easy to accomplish, and/or well beyond the company’s capacity indicates that the business will be successful due to its ability to meet cost obligations and yield profit.
Brian is considering opening a small factory that makes a single product – widgets. Each unit will sell for $80. The variable cost of manufacturing each unit is $30. Fixed factory overhead costs include rent, insurance, maintenance, supervisor salaries, supplies, and depreciation, for a total of $120,000.
The breakeven point in units per month is determined as follows:
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 120,000}{\$ 80-\$ 30}=2,400 \text{ units per month}\)
Proof: 2,400 x ($80 – $30) = $120,000 – $120,000 = 0
The manufacturing capacity is 5,000 units per month. The maximum possible operating income per month is $110,000, determined as follows:
5,000 units capacity - 2,400 units to break even = 2,600 units x $50 contribution margin = $130,000
Brian estimates his monthly sales will be 4,500 per month. The breakeven point of 2,400 per month is encouraging. The first 2,400 units sold would be applied toward paying the $120,000 in fixed costs. When 2,401 units are sold,there will be operating income of $50 since the contribution margin on that one unit above breakeven is pure profit. From that point on, each additional unit sold will generate $50 in operating income as well. Since Brian anticipates that he will sell 1,900 units above the breakeven point of 2,400, he will generate operating income as follows:
1,900 units x $50 contribution margin = $95,000 operating income
The information from Example 1 remains the same, except Brian forecasts he will be able to sell 2,500 units per month. Now the breakeven point of 2,400 is seems a less appealing outcome since anticipated sales are only 100 units more.
100 units x $50 contribution margin = $5,000 operating income
This amount of profit may not be worth the effort of operating the business. Almost all the sales volume must be used to cover fixed and variable costs.
The information from Example 1 remains the same except the manufacturing capacity is 2,500 units per month. Brian may be able to sell 4,000 units if he has them, but he is only able to produce 2,400. Again, the outcome does not seem very lucrative with operating income of only $5,000.
5.3.2 Breakeven Point with Target Profit
One other element that might be included in the breakeven calculation is target profit, which can be built in to the equation as if it were an additional fixed cost. At the breakeven point operating income is zero, which is rarely the goal of a for-profit company. An owner or manager may identify a desired operating income and add that amount to the fixed costs in the numerator. The question then becomes How many units does the company have to sell to pay all its expenses for the month AND earn a profit of $30,000? The resulting number of sales units will generate this desired operating income.
Brian is considering opening a small factory that makes a single product – widgets. Each unit will sell for $80. The variable cost of manufacturing each unit is $30. Fixed factory overhead costs include rent, insurance, maintenance, supervisor salaries, supplies, and depreciation, for a total of $120,000. Brian would also like to generate a target profit of $50,000.
The breakeven point in units per month is determined as follows:
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 120,000+\$ 50,000}{\$ 80-\$ 30}=3,400 \text{ units per month to break even}\)
Proof: 3,400 x ($80 – $30) = $170,000 – $170,000 = 0
Brian must sell an additional 1,000 units to generate enough contribution margin to cover both fixed costs and target profit. The target profit of $50,000 equals the 1,000 additional number of units times the contribution margin per unit of $50.
5.3.3 Relationships in the Breakeven Equation
The breakeven equation uses fixed costs, the unit selling price, and the unit variable cost to determine the number of units. If one of those amounts changes, the breakeven point does as well.
Referring to the previous data for Jonick Corporation, the breakeven point was 1,000 units, computed as follows.
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 8,000}{\$ 18-\$ 10}=1,000\text{ units per month to break even}\)
The following three independent changes would decrease the breakeven point.
-
An increase in the selling price per unit,
which also increases the contribution margin
Change:
Unit selling price increases from $18 to $20
Result:
Breakeven point decreases from 1,000 to 800 units
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 8,000}{\$ 20-\$ 10}=800\text{ units per month to break even}\)
-
A decrease in the variable cost per unit,
which also increases the contribution margin
Change:
Unit variable cost decreases from $10 to $8
Result:
Breakeven point decreases from 1,000 to 800 units
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 8,000}{\$ 18-\$ 8}=800 \text{ units per month to break even}\)
-
A decrease in fixed costs,
in which case the contribution margin is unchanged
Change:
Fixed costs decrease from $8,000 to $6,400
Result:
Breakeven point decreases from 1,000 to 800 units
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 6,400}{\$ 18-\$ 10}=800 \text{ units per month to break even}\)
The breakeven point in units would increase if the direction of any of the previous three changes were reversed.
5.3.4 Breakeven Point with Sales Mix
To this point the breakeven point has been calculated for a company that sells a single product. A sales mix must be considered when calculating the breakeven point for companies that sell two or more products.
A company that sells two different products does not necessarily sell an equal number of each. The first step in calculating the breakeven point in units is to determine the sales mix, which is the percent of overall sales each of the two products represents. Each product has its own unit selling price and unit variable cost. The weighted average of each of the unit amounts is used in the breakeven equation.
Carlie operates a specialty outlet that sells two products – hair dryers and curling irons. Related information is as follows:
|
Unit selling price |
Unit variable cost |
Percent of sales |
|
|
Hair dryer |
$70 |
$30 |
60% |
|
Curling iron |
50 |
20 |
40 |
|
Fixed costs are $25,200 for the month. |
The breakeven point divides the fixed costs by the contribution margin for the sales mix.
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}\)
Only one unit selling price and one unit variable cost may be included in the denominator. Yet there is one of each for each product. Therefore, a weighted average of each will be used to combine them proportionately.
|
Hair dryers |
Curling irons |
||
|
Weighted average unit selling price |
= ($70 x 60%) |
+ ($50 x 40%) |
= $42 + $20 = $62 |
|
Weighted average variable cost |
= ($30 x 60%) |
+ ($20 x 40%) |
= $18 + $ 8 = $26 |
The weighted average contribution margin is $62 - $26, or $36 per unit.
The breakeven calculation can now be performed using these weighted unit amounts.
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 25,200}{\$ 62-\$ 26}=700 \text{ units per month to breakeven}\)
Finally, the sales mix percentages are used to determine how many of each product must be sold to break even. Since it was determined that 60% of sales are hair dryers and 40% are curling irons, the calculations would be as follows.
|
Hair dryers: |
700 units to break even x 60% = 420 hair dryers |
|
Curling irons: |
700 units to break even x 40% = 280 curling irons |
Proof: 420 * ($70 - $30) + 280 * ($50 - $20) = $16,800 + $8,400 = $25,200, which is exactly the amount of the fixed costs!
5.3.5 Breakeven Analysis for a Service Business
A breakeven analysis can be just as useful for a service business as it is for a company that sells product. A simple example of a rental property will be used as an illustration.
Max is considering opening a 10-room upscale boutique hotel. He found a facility suitable for this purpose and would rent the building from its owner for $8,000 per month, which would be one of his fixed costs. Other fixed costs would include monthly payments for salaries, utilities, insurance, maintenance and advertising and would be an additional $10,000 per month. The nightly rate charged to guests would be $110, the going rate in the area. The variable cost perroom night would be $10 for room supplies and breakfast food for the guests.
The monthly capacity is 300 room nights (10 rooms x 30 days). The average occupancy rate for similar properties in the area is 60%, which for this property would be 180 rooms per month.
Based on this information, the breakeven point in number of room nights per month would be as follows:
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 18,000}{\$ 110-\$ 10}=180\text{ room nights per month to break even}\)
Although the property has the capacity for 180 rooms per month, it would have to achieve a 60% occupancy rate – 180 rooms - just to pay its bills. Even this might be challenging for a new start-up since existing properties tend to operate at this rate. A newcomer might need a bit of time to ramp up the business and get the word out to potential guests.
Even at 60%, the property would not produce any operating income. Max would have to be very sure he could exceed the industry average in the area before taking steps to start this business.
However, if Max can justify charging more per room night, the scenario may change. If he can charge guests $190 instead of $110, his breakeven point will decrease to 100 room nights per month.
\(\ \frac{\text { Total fixed costs }}{\text { Unit selling price - unit variable cost }}=\frac{\$ 18,000}{\$ 190-\$ 10}=100 \text{ room nights per month to break even}\)
If he is then able to achieve a 50% occupancy rate, 150 room nights, his venture may be viable. The business would yield operating income of $9,000 for the month.
|
60% occ. |
50% occ. |
|
|
$110 |
$190 |
|
|
Sales |
$19,800 |
$28,500 |
|
Variable costs |
1,800 |
1,500 |
|
Contribution margin |
$18,000 |
$27,000 |
|
Fixed costs |
18,000 |
18,000 |
|
Operating income |
$0 |
$9,000 |
Breakeven analysis is a useful tool for looking at different combinations of costs and selling prices to predict outcomes. It is then up to management or inventors to determine the likelihood of each scenario occurring.