This chapter takes a closer look at cost behavior and how to identify if a cost is fixed, variable, or mixed. When managers are able to predict cost behavior, they can estimate the amount of costs that are expected to be incurred at different levels of activity. Given that planning is one of the primary functions of managerial accounting, estimating costs, is a crucial cornerstone. The key to estimating future costs is to understand the cost behavior. This understanding provides managers the insight needed to accurately forecast operations for the future.

Assumptions

To estimate cost behavior, the following must be assumed:

• The number of units produced is equal to the number of units sold. In other words, there is no change in inventory levels.

• Costs behave in a linear manner.

• The level of activity (sales and production) occurs within the relevant range.

The Relevant Range

A relevant range is a range of activity within which a particular cost behavior holds true. It is the normal range of production or sales that can be expected for a particular product or company. For example, a particular retail store may have normal monthly revenues ranging from \$450,000 to \$580,000. The costs that are identified as fixed, such as manager salaries, are expected to remain the same throughout the entire relevant range. If sales were to increase to \$650,000, the company would likely acquire additional salaried workers, thereby increasing its fixed costs. Conversely, if sales drop to \$320,000, the company would likely lay off a manager to reduce total fixed costs.

Managers expect that within the relevant range, fixed costs will remain the same in total, and variable costs will increase proportionately in total as activity levels increase. Above or below the relevant range, forecasts of cost behavior may not be linear and predictions of future costs will be less accurate.

Variable Cost Behavior

Total variable costs vary in direct proportion to volume. In other words, the more units produced and sold, the higher the total variable cost. The unit variable cost is the same at every level of activity. Total variable cost is zero if no units are produced and sold.

Assume that Bates, Inc. produces beach buckets at a variable production cost of \$0.25 each. Exhibit 4-1 illustrates the total variable costs at each level of activity up to 2,500 buckets. The total variable cost rises to \$625 when the number of buckets sold reaches 2,500 (2,500 x \$0.25). The total variable cost when zero buckets are sold is \$0. As the number of units sold increases, the total cost increases. The mathematical function of this line is shown as:

Y = 0.25x

where Y is the total cost and x represents the 'activity'.

In this case, the activity is the number of buckets sold.

Exhibit 4-1 - Total Variable Costs

Some examples of variable costs include:

• Materials and parts to manufacture products

• Hourly employee labor (wages) to produce or assemble products or to provide services to customers

• Some selling expenses, such as commissions and delivery costs of shipping products to customers

Fixed Cost Behavior

Total fixed costs stay the same amount in total as volume fluctuates. In other words, regardless if more or fewer buckets are sold, total fixed costs are the same total cost.

Assume that Bates, Inc. incurs a monthly rental cost on its retail store totaling \$200, regardless of the number of buckets the company produces and sells. The math function for this cost is:

Y = 200

where Y is the total cost.

The total monthly rent cost is not dependent upon the number of buckets sold.

Exhibit 4-2 -Total Fixed Costs

Unit fixed costs vary inversely when more or fewer units are produced and sold. If total production and sales increase, the unit fixed cost decreases. If total production and sales decrease, the unit fixed cost increases.

Some example of fixed costs are:

• Rent

• Insurance

• Salaries for employees, such as supervisors and janitors

• Depreciation on equipment and buildings

Step Cost Behavior

Step costs are costs that are fixed for a short range of activity, then the total cost jumps up to a new fixed cost level for another short range of activity. Step costs look like stair steps when graphed. There are four 'steps' depicting the total costs at each activity 'step' level in Exhibit 4-3.

Consider the cost of cashier salaries in Daily's Bucket Store. Each cashier is paid \$400 per week. When sales are less than 600 buckets during a month, the store needs only one cashier, resulting in total cashier salaries of \$400 for the month. When production and sales range from 600 buckets up to 1,200 buckets, two salaried workers are necessary costing \$400 a week, for a total fixed salary cost of \$800. The total fixed cost amount 'steps up' (rises) by the cost of one additional cashier at each range of activity.

Exhibit 4-3 - Step Costs

Mixed Cost Behavior

Mixed costs, often called semi-variable costs, contain both a variable cost component and a fixed cost component. When changes in production/sales occur, mixed costs change in total, but not proportionately to the change in activity,

Mixed costs cannot be accurately predicted because only a portion of the total cost is based on a particular activity. In order to use a mixed cost in forecasting, the amount of fixed and variable costs must be known.

Two common examples of mixed costs are a rental car where a flat daily rate must be paid (a fixed cost) in addition to a cost per mile (variable cost), and a cell phone with a monthly fee plus an additional cost per gigabyte of data when data usage exceeds 5 gigabytes.

Assume that Bates, Inc. incurs a basic monthly cell phone cost for its employees totaling \$450. In addition, the cell phone contract requires an additional \$15 cost for each gigabyte of data used beyond the allotted 4 gigabytes. The math function for data usage cost is:

Y = 15.00X + 450

where Y is the total cost and X is the additional gigabytes of data used above 4 gigabytes.

Notice there are two components to the total cell phone cost. The fixed cost portion is \$450, and the variable cost portion is \$15 per gigabyte. Managers must break down all mixed costs into fixed and variable portions. As you will see in the next chapter, there are a number of methods to do this, with some methods more accurate than others.

How to Objectively Determine Cost Behavior Types

When trying to 'guess' the cost behavior of a particular cost for which you have some insight, think about what happens to the total cost when sales and production levels increase proportionately. If an increase in sales/production causes the total cost to increase, the cost is considered variable. If an increase in sales/production has no effect on the amount of the total cost, the cost is considered fixed. Think back to the bucket example used earlier. The production and sale of two more buckets causes no change in the total cost incurred for newspaper advertising, nor does it cause depreciation cost to increase. However, producing and selling two more buckets will cause the total production material cost to increase.

A mathematical two-step process is employed to determine the cost type when costs for two or more data periods are known.

Step 1 - Fixed cost test:

This test involves comparing the total cost at each activity level. If the cost is fixed, the total cost will be the same at all activity levels. If you conclude that the cost is fixed, a second step is not needed and you move on to step 2. For example, assume total costs at 400 units is \$1,200, and total costs at 350 units is \$1,020. Because the total costs differs at the two activity levels, the cost is not fixed.

Step 2 -  Variable cost test:

This test involves comparing the unit cost at all activity levels. Calculate the cost per unit by dividing the total cost by the number of units of activity for each activity period. If the cost is variable, the unit cost will be the same at all activity levels. If you conclude that the cost is variable, you can stop testing and conclude the cost is variable. If the unit cost differs at any two of the activity levels, you can conclude the cost is not variable. By default, the cost is mixed. For example, assume total costs at 400 units is \$1,200, and total costs at 350 units is \$1,020. The unit costs are \$3.00 (\$1,200/400) and \$2.91 (\$1,050/350). Because the unit costs differ at the two activity levels, the cost is not variable. By default since the cost is not fixed or variable, it is a mixed cost.

Walk Through Problem

Two costs at Walco appear below for two months of operations. Determine the type of cost behavior for each cost and briefly justify your choice.

 Cost Month Cost Units Produced Copying costs March \$9,604 9,800 April \$8,064 8,400 Communications costs March \$6,080 800 April \$5,168 680

Solution

Copying Costs

Step 1: Perform the fixed cost test by examining the total copying costs for March and April, \$9,604 and \$8,064. To be considered a fixed cost, the total costs for both activity levels must be the same amount. Since the totals for these two data periods differ at both the 9,800 and 8,400 activity levels, you must conclude that copying costs are not fixed.

Step 2: Perform the variable cost test by calculating and comparing the unit cost at both activity levels.

Unit cost at 9,800 units = \$9,604 / 9,800 = \$0.98 per unit

Unit cost at 8,400 units = \$8,064 / 8,400 = \$0.96 per unit

Because the unit cost differs at the two activity levels, this cost does not meet the definition of a variable cost. Since the cost is neither fixed or variable, you must conclude that copying costs are mixed.

Hint: The calculation of cost per unit is literal, i.e., the 'cost' is the numerator; per means to divide; and number of 'units' is the denominator.

Communications Costs

Step 1: Perform the fixed cost test by examining the total communication costs for March and April, \$6,080 and \$5,168. Costs that have the same total regardless of activity are considered fixed costs. Because the total costs differ at both the 800 and 680 activity levels, communication costs are not considered a fixed cost.

Step 2: Perform the variable cost test by calculating the cost per unit at both activity levels.

Unit cost at 800 units = \$6,080 / 800 = \$7.60 per unit

Unit cost at 680 units = \$5,168 / 680 = \$7.60 per unit

Because the unit cost is the same at the two activity levels, communication costs are variable, as they meet the definition of a variable cost.

This page was last edited on Monday December 29, 2014 01:58 PM
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