Mixed Costs Analysis
LEARNING OBJECTIVE 2
Apply the high-low method to determine the components of mixed costs.
For purposes of cost-volume-profit analysis, mixed costs must be classified into their fixed and variable elements. How does management make the classification? One possibility is to determine the variable and fixed components each time a mixed cost is incurred. But because of time and cost constraints, this approach is rarely followed. Instead, the usual approach is to collect data on the behavior of the mixed costs at various levels of activity. Analysts then identify the fixed- and variable-cost components. Companies use various types of analysis. One type of analysis, called the high-low method, is discussed next.
High-Low Method
The high-low method uses the total costs incurred at the high and low levels of activity to classify mixed costs into fixed and variable components. The difference in costs between the high and low levels represents variable costs, since only the variable-cost element can change as activity levels change.
The steps in computing fixed and variable costs under this method are as follows.
1. Determine variable cost per unit from the formula shown in Illustration 18.6. This is the slope of the cost function.
Change in Total Costs at High versus Low Activity Level ÷ High minus Low Activity Level = Variable Cost per Unit
ILLUSTRATION 18.6 Formula for variable cost per unit using high-low method
To illustrate, assume that Metro Transit Company has the maintenance costs and mileage data for its fleet of buses over a 6-month period shown in Illustration 18.7.
Month
Miles
Driven
Total
Cost
January
20,000
$30,000
February
40,000
48,000
March
35,000
49,000
April
50,000
63,000
May
30,000
42,000
June
43,000
61,000
ILLUSTRATION 18.7 Assumed maintenance costs and mileage data
The high and low levels of activity are 50,000 miles in April and 20,000 miles in January. The maintenance costs at these two levels are $63,000 and $30,000, respectively. The difference in maintenance costs is $33,000 ($63,000 − $30,000), and the difference in miles is 30,000 (50,000 − 20,000). Therefore, for Metro Transit, variable cost per unit is $1.10, computed as follows.
$
33,000
÷
30,000
=
$
1.10
2. Determine the total fixed costs by subtracting the total variable costs at either the high or the low activity level from the total cost at that activity level.
Illustration 18.8 shows the computations for Metro Transit.
ILLUSTRATION 18.8 High-low method computation of fixed costs
Maintenance costs are therefore $8,000 per month of fixed costs plus $1.10 per mile of variable costs. This is represented by the following formula, referred to as the total cost equation.
Maintenance costs
=
$
8,000
+
(
$
1.10
×
Miles driven
)
For example, at 45,000 miles, estimated maintenance costs would be $8,000 fixed and $49,500 variable ($1.10 × 45,000) for a total of $57,500.
The graph in Illustration 18.9 plots the 6-month data for Metro Transit Company. The red line drawn in the graph connects the high and low data points (in squares) and therefore represents the equation that we just solved using the high-low method. The red, “high-low” line intersects the y-axis at $8,000 (the fixed-cost level), and it rises by its slope of $1.10 per unit (the variable cost per unit). Note that a completely different line would result if we chose any two of the other data points. That is, by choosing any two other data points, we would end up with a different estimate of fixed costs and a different variable cost per unit. Thus, from this scatter plot, we can see that while the high-low method is simple, the result is rather arbitrary. A better approach, which uses information from all the data points to estimate fixed and variable costs, is called regression analysis. A discussion of regression analysis is provided in Appendix 18A as well as in the Excel video available in WileyPLUS.
ILLUSTRATION 18.9 Scatter plot for Metro Transit Company
Management Insight Kroger Co.
Are Robotic Workers More Humane?
Warehouse distribution centers for large retailers and grocers employ more than 800,000 people in the United States. But many companies, such as grocer Kroger Co., have a hard time finding and retaining warehouse workers. One reason? Studies have shown that some warehouse workers walk up to 20 miles and lift 50,000 pounds during a single day. As a result, as the needs for storage increases and companies are faced with the proposition of building massive new warehouses, some are choosing instead to invest in robotic warehousing systems.
Robots can provide many advantages over their human counterparts. Robots need aisles that are less than 30 inches wide, as opposed to traditional warehouse aisles that are 10 to 12 feet wide. Moving at speeds of up to 25 miles per hour, robots can drop off and retrieve warehouse cases about five times as fast as a human. Robotic systems cut labor costs by about 80%, and they cut warehouse size anywhere from 25% to 40%. However, a fully automated system costs between $40 to $80 million, so the switch to robotic systems is not a trivial decision.
Source: Robbie Whelan, “Fully Autonomous Robots: The Warehouse Workers of the Near Future,” Wall Street Journal (September 20, 2016).
How would a company’s variable and fixed costs change if it adopts a robotic system? (Go to WileyPLUS for this answer and additional questions).
Importance of Identifying Variable and Fixed Costs
Why is it important to segregate mixed costs into variable and fixed elements? The answer may become apparent if we look at the following four business decisions.
1. If American Airlines is to make a profit when it reduces all domestic fares by 30%, what reduction in costs or increase in passengers will be required?
Answer: To make a profit when it cuts domestic fares by 30%, American Airlines will have to increase the number of passengers or cut its variable costs for those flights. Its fixed costs will not change.
2. If Ford Motor Company meets workers’ demands for higher wages, what increase in sales revenue will be needed to maintain current profit levels?
Answer: Higher wages at Ford Motor Company will increase the variable costs of manufacturing automobiles. To maintain present profit levels, Ford will have to cut other variable or fixed costs, sell more automobiles, or increase the price of its automobiles.
3. If United States Steel Corp.’s program to modernize plant facilities through significant equipment purchases reduces the work force by 50%, what will be the effect on the cost of producing one ton of steel?
Answer: The modernizing of plant facilities at United States Steel Corp. changes the proportion of fixed and variable costs of producing one ton of steel. Fixed costs increase because of higher depreciation charges, whereas variable costs decrease due to the reduction in the number of steelworkers.
4. What happens if Kellogg’s increases its advertising expenses but cannot increase prices because of competitive pressure?
Answer: Sales volume must be increased to cover the increase in fixed advertising costs.
DO IT! 2 | High-Low Method
Byrnes Company accumulates the following data concerning a mixed cost, using units produced as the activity level.
Units Produced
Total Cost
March
9,800
$14,740
April
8,500
13,250
May
7,000
11,100
June
7,600
12,000
July
8,100
12,460
a. Compute the variable-cost and fixed-cost elements using the high-low method.
b. Using the information from your answer to part (a), write the cost formula.
c. Estimate the total cost if the company produces 8,000 units.
ACTION PLAN
Determine the highest and lowest levels of activity.
Compute variable cost per unit as Change in total costs ÷ (High − low activity level) = Variable cost per unit.
Compute fixed cost as Total cost − (Variable cost per unit × Units produced) = Total fixed cost.
Solution
a. Variable cost: ($14,740 − $11,100) ÷ (9,800 − 7,000) = $1.30 per unit
Fixed cost: $14,740 − ($1.30 × 9,800 units) = $2,000 or $11,100 − ($1.30 × 7,000 units) = $2,000
b. Cost = $2,000 + ($1.30 × units produced)
c. Total cost to produce 8,000 units: $2,000 + $10,400 ($1.30 × 8,000 units) = $12,400
Related exercise material: BE18.4, BE18.5, DO IT! 18.2, E18.3, and E18.5.
Cost-Volume-Profit Analysis
LEARNING OBJECTIVE 3
Prepare a CVP income statement to determine contribution margin.
Cost-volume-profit (CVP) analysis is the study of the effects of changes in costs and volume on a company’s profits. CVP analysis is important in profit planning. It also is a critical factor in such management decisions as setting selling prices, determining product mix, and maximizing use of production facilities.
Basic Components
CVP analysis considers the interrelationships among the components shown in Illustration 18.10.
ILLUSTRATION 18.10 Components of CVP analysis
The following assumptions underlie each CVP analysis.
1. The behavior of both costs and revenues is linear throughout the relevant range of the activity index.
2. Costs can be classified accurately as either variable or fixed.
3. Changes in activity are the only factors that affect costs.
4. All units produced are sold.
5. When more than one type of product is sold, the sales mix will remain constant. That is, the percentage that each product represents of total sales will stay the same. Sales mix complicates CVP analysis because different products will have different cost relationships. In this chapter, we assume a single product. In Chapter 19, however, we examine the sales mix more closely.
When these assumptions are not valid, the CVP analysis may be inaccurate.
CVP Income Statement
Because CVP is so important for decision-making, management often wants this information reported in a cost-volume-profit (CVP) income statement format for internal use. The CVP income statement classifies costs as variable or fixed and computes a contribution margin. Contribution margin (CM) is the amount of revenue remaining after deducting variable costs. It is often stated both as a total amount and on a per unit basis.
We use Vargo Electronics Company to illustrate a CVP income statement. Vargo Electronics produces cell phones. Illustration 18.11 presents relevant data for the cell phones sold by this company in June 2022.
Unit selling price of cell phone $500
Unit variable costs* $300
Total monthly fixed costs** $200,000
Units sold 1,600
*Includes variable manufacturing costs and variable selling and administrative expenses.
**Includes fixed manufacturing costs and fixed selling and administrative expenses.
ILLUSTRATION 18.11 Assumed selling and cost data for Vargo Electronics
Note that in Illustration 18.11, as well as in the applications and assignment material of CVP analysis that follow, we assume that the term “cost” includes all costs and expenses related to production and sale of the product. That is, cost includes manufacturing costs plus selling and administrative expenses.
The CVP income statement for Vargo would therefore be reported as shown in Illustration 18.12.
Vargo Electronics Company
CVP Income Statement
For the Month Ended June 30, 2022
Total
Sales (1,600 × $500) $800,000
Variable costs (1,600 × $300) 480,000
Contribution margin 320,000
Fixed costs 200,000
Net income $120,000
ILLUSTRATION 18.12 CVP income statement, with net income
A traditional income statement and a CVP income statement both report the same net income of $120,000. However, a traditional income statement does not classify costs as variable or fixed, and therefore it does not report a contribution margin. In addition, sometimes per unit amounts and percentage of sales amounts are shown in separate columns on a CVP income statement to facilitate CVP analysis. Homework assignments specify which columns to present.
Unit Contribution Margin
Illustration 18.13 shows the formula for unit contribution margin margin and the computation for Vargo Electronics.
Unit Selling Price − Unit Variable Costs = Unit Contribution Margin $500 − $300 = $200
ILLUSTRATION 18.13 Formula for unit contribution margin
Unit contribution margin indicates that for every cell phone sold, the selling price exceeds the variable costs by $200 (see Decision Tools). Vargo generates $200 per unit sold to cover fixed costs and contribute to net income. Because Vargo has fixed costs of $200,000, it must sell 1,000 cell phones ($200,000 ÷ $200) to cover its fixed costs.
Decision Tools
The unit contribution margin indicates the increase in income that results from every additional unit sold after the break-even point.
At the point where total contribution margin exactly equals fixed costs, Vargo will report net income of zero. At this point, referred to as the break-even point, total costs (variable plus fixed) exactly equal total revenue. Illustration 18.14 shows Vargo’s CVP income statement at the point where net income equals zero. It shows a contribution margin of $200,000, and a unit contribution margin of $200 ($500 − $300).
Vargo Electronics Company
CVP Income Statement
For the Month Ended June 30, 2022
Total
Per Unit
Sales (1,000 × $500)
$500,000
$500
Variable costs (1,000 × $300)
300,000
300
Contribution margin
200,000
$200
Fixed costs
200,000
Net income
$ –0–
ILLUSTRATION 18.14 CVP income statement, with zero net income
It follows that for every cell phone sold above the break-even point of 1,000 units, net income increases by the amount of the unit contribution margin, $200. For example, assume that Vargo sold one more cell phone, for a total of 1,001 cell phones sold. In this case, Vargo reports net income of $200, as shown in Illustration 18.15.
Vargo Electronics Company
CVP Income Statement
For the Month Ended June 30, 2022
Total
Per Unit
Sales (1,001 × $500)
$500,500
$500
Variable costs (1,001 × $300)
300,300
300
Contribution margin
200,200
$200
Fixed costs 200,000
Net income $ 200
ILLUSTRATION 18.15 CVP income statement, with net income and per unit data
Contribution Margin Ratio
Some managers prefer to use a contribution margin ratio in CVP analysis. The contribution margin ratio is the contribution margin expressed as a percentage of sales. Vargo Electronics has a contribution margin ratio of 40% (contribution margin of $200,200 divided by sales of $500,500), as shown in the percent of sales column in Illustration 18.16.
Vargo Electronics Company
CVP Income Statement
For the Month Ended June 30, 2022
Total
Percent of Sales
Sales (1,001 × $500)
$500,500
100%
Variable costs (1,001 × $300) 300,300
60
Contribution margin 200,200
40%
Fixed costs 200,000
Net income $ 200
ILLUSTRATION 18.16 CVP income statement, with net income and percent of sales data
Alternatively, the contribution margin ratio can be determined by dividing the unit contribution margin by the unit selling price. Illustration 18.17 shows the ratio for Vargo Electronics.
Unit Contribution Margin ÷ Unit Selling Price = Contribution Margin Ratio $200 ÷ $500 = 40%
ILLUSTRATION 18.17 Formula for contribution margin ratio
The contribution margin ratio of 40% means that Vargo generates 40 cents of contribution margin with each dollar of sales. That is, $0.40 of each sales dollar (40% × $1) is available to apply to fixed costs and to contribute to net income (see Decision Tools).
Decision Tools
The contribution margin ratio indicates by how much every dollar of sales will increase income after the break-even point.
This expression of contribution margin is very helpful in determining the effect of changes in sales on net income. For example, if Vargo’s sales increase $100,000, net income will increase $40,000 (40% × $100,000). Thus, by using the contribution margin ratio, managers can quickly determine increases in net income from any change in sales.
We can also see this effect through a CVP income statement. Assume that Vargo’s current sales are $500,000 and it wants to know the effect of a $100,000 (200-unit) increase in sales. Vargo prepares the comparative CVP income statement analysis shown in Illustration 18.18.
Vargo Electronics Company
CVP Income Statement
For the Month Ended June 30, 2022
No Change
With $100,000 Increase in Sales
Total
Per Unit
Percent of
Sales
Total
Per Unit
Percent of
Sales
Sales
$500,000
$500
100%
$600,000
$500
100%
Variable costs
300,000
300
60
360,000
300
60
Contribution margin
200,000
$200
40%
240,000
$200
40%
Fixed costs
200,000
200,000
Net income
$ –0–
$ 40,000
ILLUSTRATION 18.18 Comparative CVP income statements
The $40,000 increase in net income can be calculated on either a unit contribution margin basis (200 units × $200 per unit) or using the contribution margin ratio times the increase in sales dollars (40% × $100,000). Note that the unit contribution margin and contribution margin as a percentage of sales (that is, the contribution margin ratio) remain unchanged by the increase in sales.
Study these CVP income statements carefully. The concepts presented in these statements are used extensively in this and later chapters.
DO IT! 3 | CVP Income Statement
Ampco Industries produces and sells a cell phone-operated thermostat. Information regarding the costs and sales of thermostats during September 2022 are provided below.
Unit selling price of thermostat $85
Unit variable costs $32
Total monthly fixed costs $190,000
Units sold 4,000
Prepare a CVP income statement for Ampco Industries for the month of September. Provide per unit values and total values.
ACTION PLAN
Provide a heading with the name of the company, name of statement, and period covered.
Subtract variable costs from sales to determine contribution margin. Subtract fixed costs from contribution margin to determine net income.
Express sales, variable costs and contribution margin on a per unit basis.
Solution
Ampco Industries
CVP Income Statement
For the Month Ended September 30, 2022
Total
Per Unit
Sales
$340,000
$85
Variable costs
128,000
32
Contribution margin
212,000
$53
Fixed costs
190,000
Net income
$ 22,000
Related exercise material: BE18.6, BE18.7, DO IT! 18.3, and E18.7.