Analysis and use as we shall see in later chapters, the ability to predict how costs respond to changes in activity is critical for making decisions, controlling operations, and evaluating performance. Three major classifications of costs were discussed in this chapter—variable, fixed, and mixed. Mixed costs consist of variable and fixed elements and can be expressed in equation form as Y = a + bX, where X is the activity, Y is the cost, a is the fixed cost element, and b is the variable cost per unit of activity.

Several methods can be used to estimate the fixed and variable cost components of a mixed cost using past records of cost and activity. If the relation between cost and activity appears to be linear based on a scatter graph plot, then the variable and fixed components of the mixed cost can be estimated using the quick-and-dirty method, the high-low method, or the least-squares regression method. The quick-and-dirty method is based on drawing a straight line and then using the slope and the intercept of the straight line to estimate the variable and fixed cost components of the mixed cost.

The high-low method implicitly draws a straight line through the points of lowest activity and highest activity. In most situations, the least-squares regression method is preferred to both the quick-and-dirty and high-low methods. Computer software is widely available for using the least-squares regression method. These software applications provide a variety of useful statistics along with estimates of the intercept (fixed cost) and slope (variable cost per unit).

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Nevertheless, even when least-squares regression is used, the data should be plotted to confirm that the relationship is really a straight line. Managers use costs organized by behavior to help make many decisions. The contribution format income statement can aid decision making because it classifies costs by cost behavior (i. e. , variable versus fixed) rather than by the functions of production, administration, and sales. In this chapter, the following learning objectives will be covered.

In this chapter, the following learning objectives will be covered:

- Understand how fixed and variable costs behave and how to use them to predict costs.
- Use a scattergraph plot to diagnose cost behavior.
- Analyze a mixed cost using the high-low method.
- Prepare an income statement using the contribution format.
- Analyze a mixed cost using the least-squares regression method.

Key terms:

Account analysis - a method for analyzing cost behavior in which an account is classified as either variable or fixed based on the analyst's prior knowledge of how the cost in the account behaves.

Activity base - a measure of whatever causes the incurrence of a variable cost.

For example, the total cost of X-ray film in a hospital will increase as the number of X-rays taken increases. Therefore, the number of X-rays is the activity base that explains the total cost of X-ray film.

Committed fixed costs - investments in facilities, equipment, and basic organizational structure that can't be significantly reduced even for short periods of time without making fundamental changes.

Contribution approach - an income statement format that organizes costs by their behavior.

Costs are separated into variable and fixed categories rather than being separated according to organizational functions.

Contribution margin - the amount remaining from sales revenues after all variable expenses have been deducted.

Cost structure - the relative proportion of fixed, variable, and mixed costs in an organization.

Dependent variable - a variable that responds to some causal factor; total cost is the dependent variable, as represented by the letter Y, in the equation Y = a + bX.

Discretionary fixed costs - those fixed costs that arise from annual decisions by management to spend on certain fixed cost items, such as advertising and research.

Engineering approach - a detailed analysis of cost behavior based on an industrial engineer's evaluation of the inputs that are required to carry out a particular activity and of the prices of those inputs.

High-low method - a method of separating a mixed cost into its fixed and variable elements by analyzing the change in cost between the high and low activity levels.

Independent variable - a variable that acts as a causal factor; activity is the independent variable, as represented by the letter X, in the equation Y = a + bX.

Least-squares regression - a method of separating a mixed cost into its fixed and variable elements by fitting a regression line that minimizes the sum of the squared errors.

Linear cost behavior - cost behavior is said to be linear whenever a straight line is a reasonable approximation for the relation between cost and activity.

Mixed cost - a cost that contains both variable and fixed cost elements.

Multiple regression - an analytical method required when variations in a dependent variable are caused by more than one factor.

Relevant range - the range of activity within which assumptions about variable and fixed cost behavior are reasonably valid.

Step-variable cost - the cost of a resource that is obtainable only in large chunks and that increases and decreases only in response to fairly wide changes in activity.

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