1 Cornerstones of Managerial Accounting, 2e Copyright © 2008 Thomson South-Western, a part of the Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Mowen/Hansen Cost Behavior Chapter Three

2 Cost Behavior The way costs change as the related activity changes Fixed Cost A cost that does not change in total as output changes ---

3 Cost Behavior The way costs change as the related activity changes Variable Cost Increases in total with an increase in output and decreases in total with a decrease in output ---

4 Measures of Output “What causes the cost of this particular activity to go up (or down)?” To determine if a cost is fixed or variable, we must first determine the underlying business activity and ask ourselves…. In other words, we are trying to identify its driver.

5 Relevant Range The range of output over which the assumed cost relationship is valid for the normal operations of a firm. Let’s take a closer look at fixed, variable and mixed costs in light of the relevant range. Avoids extremely high levels of activity Avoids extremely low levels of activity

6 Fixed Costs Costs that in total are constant within the relevant range as the level of output increases or decreases.

7 Example It process up to 50,000 computers per year. The production-line manager (supervisor) is paid $32,000 per year. The company was established 5 years ago. Currently the factory produces 40,000 – 50,000 computers per year. Production has never fallen below 20,000 computers in a year. Colley Computers Inc. wants to look at the cost relationship between supervision cost and the number of computers processed. Let’s look at the cost of supervision at several production levels.

8 # of Computers Produced 20,000 30,000 40,000 50,000 Total Cost of Supervision $32,000 We know the total cost of supervision, but what about per computer? Unit Cost Example

9 # of Computers Produced 20,000 30,000 40,000 50,000 Total Cost of Supervision $32,000 Unit Cost Example $ Unit cost changes! As production increases, the per unit amount of a fixed cost decreases.

10 Discretionary Fixed Costs Fixed costs that can be changed relatively easily at management discretion

11 Committed Fixed Costs A fixed cost that cannot be easily changed. Often these involve a long- term contract

12 Variable Costs Costs that in total vary in direct proportion to changes in output within the relevant range

13 Variable Cost Behavior Example Each computer requires one DVD-ROM drive costing $40. The cost of DVD-ROM drives for various levels of production is as follows: Expanding our Colley Computers example…. Let’s look at the cost of DVD-ROM’s at several production levels.

14 # of Computers Produced 20,000 30,000 40,000 50,000 Total Cost of DVD- ROM Drives $800,000 $1,200,000 $1,600,000 $2,000,000 Unit Cost We know the total cost increases as production increases. But what about the cost per computer? Variable Cost Behavior Example

15 # of Computers Produced 20,000 30,000 40,000 50,000 Total Cost of DVD- ROM Drives $800,000 $1,200,000 $1,600,000 $2,000,000 Unit Cost Example: $40 40 Unit Cost stays the same! The per unit variable cost of DVD- ROM drives is always $40 per computer.

16 Total Variable Cost Variable Rate x Amount of Output = Variable Cost Relationship Let’s look at the DVD-ROM costs for 50,000 computers.

17 Total Variable Cost Variable Rate x Amount of Output = 50,000 computers $40 per computer x = $2,000,000 Variable Cost Relationship

18 Mixed Costs Costs that have both a fixed and a variable component. Formula: Total Cost = Total Fixed Cost + Total Variable Cost Let’s look at an example from the Colley Computers

19 Example: Colley Computers has 10 sales representatives. Let’s plug this into our mixed cost formula. Each earns a salary of $30,000 per year. And a commission of $25 per computer sold. Each sales rep sells up to 50,000 computers per year.

20 Mixed Cost Example Formula: Total Cost = Total Fixed Cost + Total Variable Cost ($25 x # of computers sold) $30,000 + = Total Cost

21 Step Costs Displays a constant level of cost for a range of output and then jumps to a higher level of cost at some point, where it remains for a similar range of output

22 Separating Costs Accounting records typically show only the total cost and the associated amount of activity of a mixed cost item. Therefore, it is necessary to separate the total cost into its fixed and variable components. How do we separate the costs?

23 1.High-Low method 2.Scattergraph method 3.Method of Least Squares Separating Costs Three methods:

24 Dependent Variable in the Cost Formula Total Cost = Total Fixed Cost + Total Variable Cost Variable Rate x Output Total Cost = Total Fixed Cost + Variable Rate x Output Dependent Variable

25 Dependent Variable A variable whose value depends on the value of another variable

26 Independent Variable in the Cost Formula Total Cost = Total Fixed Cost + Total Variable Cost Total Cost = Total Fixed Cost + Variable Rate x Output Independent Variable

27 Independent Variable A variable that measures output and explains changes in the cost

28 Intercept Graphically, the intercept is the point at which the cost line intercepts the cost (vertical) axis Intercept

29 Intercept in the Cost Formula Total Cost = Total Fixed Cost + Total Variable Cost Total Cost = Total Fixed Cost + Variable Rate x Output Intercept

30 Slope in the Cost Formula Total Cost = Total Fixed Cost + Total Variable Cost Total Cost = Total Fixed Cost + Variable Rate x Output Slope

31 Slope Corresponds to the variable rate (the variable cost per unit of output). It is the slope of the cost line. Let’s work through an example.

32 High-Low Method A method of separating mixed costs into fixed and variable components by using just the high and low data points Step #1 Find the high point and low point.

33 High-Low Method Step #2 Using the high and low points, calculate the variable rate. Variable rate = High point cost – Low point cost High point output – Low point output

34 High-Low Method Step #3 Calculate the fixed cost using the variable rate and either the high point or the low point. Fixed Cost = Total cost at high point (Variable rate x Output at high point) - Or Low Point

35 High-Low Method Step #4 Form the cost formula based on the high- low method. Cornerstone 3-2 will walk us through an example of the High-Low Method

36 Scattergraph Method Purpose of this method: To see whether or not a straight line reasonably describes the cost relationship To reveal one or more points that do not seem to fit the general pattern of behavior

37 Scattergraph Method Applying the method: Draw a graph with units on the x-axis and cost on the y-axis Plot the data points on the graph Visually fit a line to the data points on the graph. The intercept is the fixed cost. Use the high-low method to determine the variable rate.

38 Scattergraph Method Disadvantage: Lack of any objective criterion for choosing the best-fitting line. We need a method that is objective and produces the best-fitting line.

39 Method of Least Squares A statistical way to find the best-fitting line through a set of data points. What does best-fitting mean? The line is one in which the data points are closer to the line than to any other line.

40 Method of Least Squares ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ Measure distance from points to line. Then square the differences. Add up all the squared differences.

41 Method of Least Squares Spreadsheet programs have packages to calculate the best-fitting line (called regression line).

42 Managerial Judgment Instead of the three methods previously discussed, many managers simply use their experience and past observation of cost relationships to determine fixed and variable costs. The appeal of this method is its simplicity.

43 Managerial Judgment with Estimation Managers may use experience and judgment to refine statistical estimation results. Statistical techniques are highly accurate in depicting the past, but they cannot foresee the future.