A variable cost varies, in total, in direct proportion to changes in the level of activity. Common examples of variable costs include cost of goods sold for a merchandising company, direct materials, direct labor, variable elements of manufacturing overhead, such as indirect materials, supplies, and power, and variable elements of selling and administrative expenses, such as commissions and shipping costs.2
For a cost to be variable, it must be variable with respect to something. That “something” is its activity base. An activity base is a measure of whatever causes the incurrence of a variable cost. An activity base is sometimes referred to as a cost driver. Some of the most common activity bases are direct labor-hours, machine-hours, units produced, and units sold. Other examples of activity bases (cost drivers) include the number of miles driven by salespersons, the number of pounds of laundry cleaned by a hotel, the number of calls handled by technical support staff at a software company, and the number of beds occupied in a hospital. While there are many activity bases within organizations, throughout this textbook, unless stated otherwise, you should assume that the activity base under consideration is the total volume of goods and services provided by the organization. We will specify the activity base only when it is something other than total output.
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A fixed cost is a cost that remains constant, in total, regardless of changes in the level of activity. Examples of fixed costs include straight-line depreciation, insurance, property taxes, rent, supervisory salaries, administrative salaries, and advertising. Unlike variable costs, fixed costs are not affected by changes in activity. Consequently, as the activity level rises and falls, total fixed costs remain constant unless influenced by some outside force, such as a landlord increasing your monthly rental expense.
The Linearity Assumption and the Relevant Range
Management accountants ordinarily assume that costs are strictly linear; that is, the relation between cost on the one hand and activity on the other can be represented by a straight line. Economists point out that many costs are actually curvilinear; that is, the relation between cost and activity is a curve. Nevertheless, even if a cost is not strictly linear, it can be approximated within a narrow band of activity known as the relevant range by a straight line. The relevant range is the range of activity within which the assumption that cost behavior is strictly linear is reasonably valid.
A mixed cost contains both variable and fixed cost elements. Mixed costs are also known as semivariable costs.
Managers can use a variety of methods to estimate the fixed and variable components of a mixed cost such as account analysis, the engineering approach, the high-low method, and least-squares regression analysis. In account analysis, an account is classified as either variable or fixed based on the analyst’s prior knowledge of how the cost in the account behaves. For example, direct materials would be classified as variable and a building lease cost would be classified as fixed because of the nature of those costs. The engineering approach to cost analysis involves a detailed analysis of what cost behavior should be, based on an industrial engineer’s evaluation of the production methods to be used, the materials specifications, labor requirements, equipment usage, production efficiency, power consumption, and so on.
The first step in applying the high-low method or the least-squares regression method is to diagnose cost behavior with a scattergraph plot.Two things should be noted about this scattergraph:
The total maintenance cost, Y, is plotted on the vertical axis. Cost is known as the dependent variable because the amount of cost incurred during a period depends on the level of activity for the period. (That is, as the level of activity increases, total cost will also ordinarily increase.)
The activity, X (patient-days in this case), is plotted on the horizontal axis. Activity is known as the independent variable because it causes variations in the cost.
From the scattergraph plot, it is evident that maintenance costs do increase with the number of patient-days in an approximately linear fashion. In other words, the points lie more or less along a straight line that slopes upward and to the right. Cost behavior is considered linear whenever a straight line is a reasonable approximation for the relation between cost and activity.