A mixed cost contains both variable and fixed cost elements. Mixed costs are also known as semivariable costs.
Mixed costs are very common. For example, the overall cost of providing X-ray services to patients at the Harvard Medical School Hospital is a mixed cost. The costs of equipment depreciation and radiologists’ and technicians’ salaries are fixed, but the costs of X-ray film, power, and supplies are variable. At Southwest Airlines, maintenance costs are a mixed cost. The company incurs fixed costs for renting maintenance facilities and for keeping skilled mechanics on the payroll, but the costs of replacement parts, lubricating oils, tires, and so forth, are variable with respect to how often and how far the company’s aircraft are flown.
The fixed portion of a mixed cost represents the minimum cost of having a service ready and available for use. The variable portion represents the cost incurred for actual consumption of the service, thus it varies in proportion to the amount of service actually consumed.
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 high-low and least-squares regression methods estimate the fixed and variable elements of a mixed cost by analyzing past records of cost and activity data. We will use an example from Brentline Hospital to illustrate the high-low method calculations and to compare the resulting high-low method cost estimates to those obtained using least-squares regression. Appendix 2A demonstrates how to use Microsoft Excel to perform least-squares regression computations.
Diagnosing Cost Behavior with a Scattergraph Plot
Assume that Brentline Hospital is interested in predicting future monthly maintenance costs for budgeting purposes.
The first step in applying the high-low method or the least-squares regression method is to diagnose cost behavior with a scattergraph plot. The scattergraph plot of maintenance costs versus patient-days at Brentline Hospital is shown in Exhibit 2–6. 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.
The High-Low Method
Assuming that the scattergraph plot indicates a linear relation between cost and activity, the fixed and variable cost elements of a mixed cost can be estimated using the high-low method or the least-squares regression method. The high-low method is based on the rise-over-run formula for the slope of a straight line.
The Least-Squares Regression Method
The least-squares regression method, unlike the high-low method, uses all of the data to separate a mixed cost into its fixed and variable components. A regression line of the form Y = a + bX is fitted to the data, where a represents the total fixed cost and b represents the variable cost per unit of activity. The basic idea underlying the least-squares regression method is illustrated in Exhibit 2–8 using hypothetical data points.
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