Chapter 3 introduced cost–volume–profit analysis. If variable costing is used, the breakeven point (that’s where operating income is $0) is computed in the usual manner. There is only one breakeven point in this case, and it depends on (1) fixed (manufacturing and operating) costs and (2) contribution margin per unit.
The formula for computing the breakeven point under variable costing is a special case of the more general target operating income formula from Chapter 3 (page 73):
Breakeven occurs when the target operating income is $0. In our Stassen illustration for 2020 (see Exhibit 9-1, page 326):
We now verify that Stassen will achieve breakeven under variable costing by selling 4,000 units:
The table depicts how Stassen can break even under variable costing. The details of the table are as follows:
Revenues, 1,000 dollars times 4,000 units: 4,000,000 dollars
Variable costs, 385 dollars times 4,000 units: 1,540,000 dollars
Contribution margin, 615 dollars times 4,000 units: 2,460,000 dollars
Fixed costs: 2,460,000 dollars
Operating income: 0 dollars
If absorption costing is used, the required number of units to be sold to earn a specific target operating income is not unique because of the number of variables involved. The following formula shows the factors that will affect the target operating income under absorption costing:
In this formula, the numerator is the sum of three terms (from the perspective of the two “ ” signs), compared with two terms in the numerator of the variable-costing formula stated earlier. The additional term in the numerator under absorption costing is as follows:
This term reduces the fixed costs that need to be recovered when units produced exceed the breakeven sales quantity. When production exceeds the breakeven sales quantity, some of the fixed manufacturing costs that are expensed under variable costing are not expensed under absorption costing; they are instead included in finished-goods inventory. The breakeven sales quantity under absorption costing is correspondingly lower than under variable costing.*
For Stassen Company in 2020, suppose that actual production is 5,280 units. Then one breakeven point, Q, under absorption costing is as follows:
The table depicts how Stassen can break even under absorption costing. The details of the table are as follows:
Revenues, 1,000 dollars times 3,640 units: 3,640,000 dollars
Cost of goods sold at standard cost, 335 dollars times 3,640 units: 1,219,400 dollars
Production-volume variance, 135 dollars times the quantity 8,000 minus 5,280 units: 367,200 dollars U
Total cost of goods sold: 1,586,600 dollars
Gross margin: 2,053,400 dollars
Variable marketing costs, 185 dollars times 3,640 units: 673,400 dollars
Fixed marketing costs: 1,380,000 dollars
Total marketing costs: 2,053,400 dollars
Operating income: 0 dollars
We next verify that production of 5,280 units and sales of 3,640 units will lead Stassen to break even under absorption costing:
The table depicts how Stassen can break even under absorption costing. The details of the table are as follows:
1. Revenues, 1,000 dollars times 3,640 units: 3,640,000 dollars
2. Cost of goods sold at standard cost, 335 dollars times 3,640 units: 1,219,400 dollars
3. Production-volume variance, 135 dollars times the quantity 8,000 minus 5,280 units: 367,200 dollars U
4. Total cost of goods sold: 1,586,600 dollars
5. Gross margin: 2,053,400 dollars
6. Variable marketing costs, 185 dollars times 3,640 units: 673,400 dollars
7. Fixed marketing costs: 1,380,000 dollars
8. Total marketing costs: 2,053,400 dollars
9. Operating income: 0 dollars
The breakeven point under absorption costing depends on (1) fixed manufacturing costs, (2) fixed operating (marketing) costs, (3) contribution margin per unit, (4) unit level of production, and (5) the capacity level chosen as the denominator to set the fixed manufacturing cost rate. For Stassen in 2020, a combination of 3,640 units sold, fixed manufacturing costs of $1,080,000, fixed marketing costs of $1,380,000, contribution margin per unit of $615, an 8,000-unit denominator level, and production of 5,280 units would result in an operating income of $0. Note, however, that there are many combinations of these five factors that would give an operating income of $0. For example, holding all other factors constant, a combination of 6,240 units produced and 3,370 units sold also results in an operating income of $0 under absorption costing. We provide verification of this alternative breakeven point next:
The table depicts verification of an alternative breakeven point. The details of the table are as follows:
1. Revenues, 1,000 dollars times 3,370 units: 3,370,000 dollars
2. Cost of goods sold at standard cost, 335 dollars times 3,370 units: 1,128,950 dollars
3. Production-volume variance, 135 dollars times the quantity 8,000 minus 6,240 units: 237,600 dollars U
4. Total cost of goods sold: 1,366,550 dollars
5. Gross margin: 2,003,450 dollars
6. Variable marketing costs, 185 dollars times 3,370 units: 623,450 dollars
7. Fixed marketing costs: 1,380,000 dollars
8. Total marketing costs: 2,003,450 dollars
9. Operating income: 0 dollars
Suppose actual production in 2020 was equal to the denominator level, 8,000 units, and there were no units sold and no fixed marketing costs. All the units produced would be placed in inventory, so all the fixed manufacturing costs would be included in inventory. There would be no production-volume variance. Under these conditions, the company could break even under absorption costing with no sales whatsoever! In contrast, under variable costing, the operating loss would be equal to the fixed manufacturing costs of $1,080,000.