Mixed costs are costs that contain both a variable‐ and a fixed‐cost element. Mixed costs, therefore, change in total but not proportionately with changes in the activity level.
The rental of a U‐Haul truck is a good example of a mixed cost. Assume that local rental terms for a 17‐foot truck, including insurance, are $50 per day plus 50 cents per mile. When determining the cost of a one‐day rental, the per day charge is a fixed cost (with respect to miles driven), whereas the mileage charge is a variable cost. The graphic presentation of the rental cost for a one‐day rental is shown in Illustration 18-5 (page 888).
ILLUSTRATION 18-5 Behavior of a mixed cost
In this case, the fixed‐cost element is the cost of having the service available. The variable‐cost element is the cost of actually using the service. Utility costs such as for electricity are another example of a mixed cost. Each month the electric bill includes a flat service fee plus a usage charge.
DO IT! 1
Types of Costs
Helena Company reports the following total costs at two levels of production.
|10,000 Units||20,000 Units|
Classify each cost as variable, fixed, or mixed.
✓ Recall that a variable cost varies in total directly and proportionately with each change in activity level.
✓ Recall that a fixed cost remains the same in total with each change in activity level.
✓ Recall that a mixed cost changes in total but not proportionately with each change in activity level.
Direct materials, direct labor, and indirect materials are variable costs.
Depreciation and rent are fixed costs.
Maintenance and utilities are mixed costs.
Related exercise material: BE18-1, BE18-2, E18-1, E18-2, E18-4, E18-6, and DO IT! 18-1.
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.
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 following formula.
Change in Total Costs÷High minus Low Activity Level=Variable Cost per UnitChange in Total Costs÷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 following maintenance costs and mileage data for its fleet of buses over a 6‐month period.
|Month||Miles Driven||Total Cost|
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)$33,000 ($63,000−$30,000), and the difference in miles is 30,000 (50,000−20,000)30,000 (50,000−20,000). Therefore, for Metro Transit, variable cost per unit is $1.10, computed as follows.
2. Determine the 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.
For Metro Transit, the computations are shown in Illustration 18-8.
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:
Maintenance costs=$8,000+($1.10×Miles driven)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)($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, 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 $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 a supplement on the book’s companion website.
ILLUSTRATION 18-9 Scatter plot for Metro Transit Company
Tempur Sealy International
Skilled Labor Is Truly Essential
The recent recession had devastating implications for employment. But one surprise was that for some manufacturers, the number of jobs lost was actually lower than in previous recessions. One of the main explanations for this was that in the years preceding the recession, many companies, such as Tempur Sealy International, adopted lean manufacturing practices. This meant that production relied less on large numbers of low‐skilled workers and more on machines and a few highly skilled workers. As a result of this approach, a single employee supports far more dollars in sales. Thus, it requires a larger decline in sales before an employee would need to be laid‐off in order for the company to continue to break even. Also, because the employees are highly skilled, employers are reluctant to lose them. Instead of lay‐offs, many manufacturers now resort to cutting employees’ hours when necessary.
Source: Timothy Aeppel and Justin Lahart, “Lean Factories Find It Hard to Cut Jobs Even in a Slump,” Wall Street Journal Online (March 9, 2009).
Would you characterize labor costs as being a fixed cost, a variable cost, or something else in this situation? (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 costs 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
Byrnes Company accumulates the following data concerning a mixed cost, using units produced as the activity level.
|Units Produced||Total Cost|
(a) Compute the variable‐cost and fixed‐cost elements using the high‐low method.
(b) Estimate the total cost if the company produces 8,000 units.
✓ 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 unitChange in total costs÷(High−low activity level)=Variable cost per unit.
✓ Compute fixed cost as Total cost−(Variable cost per unit×Units produced)=Fixed costTotal cost−(Variable cost per unit×Units produced)=Fixed cost.
(a) Variable cost: ($14,740−$11,100)÷(9,800−7,000)=$1.30 per unit($14,740−$11,100)÷(9,800−7,000)=$1.30 per unit
Fixed cost: $14,740−$12,740*=$2,000$14,740−$12,740*=$2,000 or $11,100−$9,100**=$2,000$11,100−$9,100**=$2,000
* $1.30×9,800 units$1.30×9,800 units
** $1.30×7,000 units$1.30×7,000 units
(b) Total cost to produce 8,000 units: $2,000+$10,400 ($1.30×8,000 units)=$12,400$2,000+$10,400 ($1.30×8,000 units)=$12,400
Related exercise material: BE18-3, BE18-4, BE18-5, E18-3, E18-5, and DO IT! 18-2.
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.
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.