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CHAPTER 3 Cost behaviour

LEARNING OBJECTIVES 1. Explain the meaning of cost behaviour and define and describe fixed and variable costs 2. Define and describe mixed and step costs. 3. Separate mixed costs into their fixed and variable components using the high-low method, the scattergraph method, and the method of least squares.

LO.1 Explain the meaning of cost behaviour and define and describe fixed and variable costs Basics of Cost Behaviour Cost behaviour is the foundation upon which managerial accounting is built. Describes whether a cost changes when the level of output changes. Costs can be variable, fixed, or mixed. A cost that does not change in total as output changes is a fixed cost. A variable cost, on the other hand, increases in total with an increase in output and decreases in total with a decrease in output. Knowing how costs change as output changes is essential to planning, controlling, and decision making.

Measures of Output and the Relevant Range Fixed and variable costs have meaning only when related to some output measure. A cost driver is a causal factor that measures the output of the activity that leads (or causes) costs to change. Identifying and managing drivers helps managers better predict and control costs. For example: weather is a significant driver in the airline industry. Relevant Range and Cost Relationships Relevant range is the range of output over which the assumed cost relationship is valid for the normal operations of a firm. Limits the cost relationship to the range of operations that the firm normally expects to occur. The following graph shows the relevant range which allows managers to assume a linear cost relationship.

Fixed Costs Fixed costs are costs that in total are constant within the relevant range as the level of output increases or decreases. In this example of Colley Computers, notice while the total fixed cost of supervision remains the same, the unit cost decreases as more computers are produced. Colley computers inc. cost of supervision Number of computers produced

Total cost of supervision

Unit cost

20 000

32 000

1.60

30 000

32 000

1.07

40 000

32 000

0.80

50 000

32 000

0.64

The number of computers produced is called the output measure, or driver. Even though fixed costs may change, this does not make them variable. They are fixed at a new higher (or lower) rate. A graph of Colley’s fixed supervision costs is shown below:

Discretionary Fixed Costs and Committed Fixed Costs Two types of fixed costs: discretionary fixed costs and committed fixed costs. o o

Discretionary fixed costs are fixed costs that can be changed or avoided easily at management discretion. Committed fixed costs, on the other hand, are fixed costs that cannot be easily changed.

Advertising is a discretionary fixed cost, because it depends on a management decision. Lease cost is a committed fixed cost because it involves a long--term contract. Variable Costs Variable costs are costs that vary in direct proportion to changes in output within the relevant range. Variable costs can also be represented by a linear equation. Total variable costs depend on the level of output. This relationship can be described by the following equation or graphs:

The Reasonableness of Straight-line Cost Relationships Caution when applying cost behaviour assumptions to output levels that fall outside of the company’s relevant range of operations. Straight--line cost relationships that are assumed within the relevant range may be semi-variable costs. Example: At extremely low levels of output, workers often use more materials per unit or require more time per unit than they do at higher levels of output. As the level of output increases, workers learn how to use materials and time more efficiently so that the variable cost per unit decreases as more and more output is produced.

LO.2 Define and describe mixed and step costs. Mixed Costs Mixed costs are costs that have both a fixed Anda variable component. Example: Overhead for a company may consist of a fixed supervisor salary plus the cost of supplies that vary with the quantity of output produced.

Step Costs: Narrow Steps Some cost functions may be discontinuous. Known as step costs (or semi-fixed). o

Displays a constant level of cost for a range of output and then jumps to a higher level (or step) of cost at some point, where it remains for a similar range of output.

Step Costs: Wide Steps Step cost with wide steps are more characteristic of fixed costs. Example: A company may have to lease production machinery. o

If the machine can only produce 1,000 units and the company grows, they will have to lease additional machines for each 1,000 units of production needed

Resulting in the wide steps shown in the following graph.

Accounting Records and Need for Cost Separation Only through a formal effort to separate costs canal costs be classified into the appropriate cost behaviour categories. If mixed costs are a very small percentage of total costs, formal cost separation may be more trouble than it’s worth. Mixed costs could be assigned to either the fixed or variable cost category without much concern for the classification error or its effect on decision making. Alternatively, the total mixed cost could be divided between the two cost categories. (This is rarely done and not a good option.) Typically, mixed costs for many firms are large enough to call for separation.

LO.3 Separate mixed costs into their fixed and variable components using the high--low method, the scatter graph method, and the method of least squares.

The scatter graph method is a way to see the cost relationship by plotting the data points on a graph. The first step is to plot the data points so that the relationship between materials handling costs and activity output can be seen. Inspect the scatter graph to see if it reveals one or more points (outliers)that do not seem to fit the pattern of behaviour. This might justify their elimination and perhaps lead to a better estimate of the underlying cost function. Is the line determined by the high and low points is representative of the overall relationship Notice that three points lie above the high--lowline, but five points lie below it.

This does not give us confidence in the high--low results for fixed and variable costs. We wonder if the variable cost (slope) is somewhat higher than it should be and the fixed cost is somewhat lower than it should be. Finally, we can use hectograph to visually fit a line to the datapoints on the graph. The manager or cost analyst will choose the line that appears to fit the points the best. An infinite number of lines might go through the data, but this one goes through the point for January (100,$2,000) and intersects the y-axis at $800.

Our two points are (100, $2,000) and (0, $800). Next, use these two points to compute the variable rate (the slope):

The variable rate is $12 per material move. The fixed cost and variable rate for materials handling cost have now been identified. The cost formula for the materials handling activity can be expressed as: Total Cost = $800 + $12 x Number of Moves Using the Formula from the Scatter graph Method Using this formula, the total cost of materials handling for between 100 and 500 moves can be predicted and then broken down into fixed and variable components. For example, assume that 350 moves are planned for November. Using the cost formula, the predicted cost is: $5,000 = $800 + ($12 x 350) Of this total cost, $800 is fixed, and $4,200 is variable. Unfortunately, the scatter graph method suffers from the lack of any objective criterion for choosing the best--fitting line. The quality of the cost formula depends on the quality of the subjective judgment of the analyst. Separating Mixed Costs into Fixed and Variable Components Three methods of separating a mixed cost into its fixed and variable components: o o o

high-low method scatter graph method method of least squares

Each method requires the simplifying assumption of a linear cost relationship. Expression of cost as an equation for a straight line is: Total cost = Fixed cost + (Variable rate x Output) The dependent variable is a variable whose value depends on the value of another variable. In the previous equation, total cost is the dependent variable; it is the cost we are trying to predict.

The independent variable measures output and explains changes in the cost or other dependent variable. o o

A good independent variable is one that causes or is closely associated with the dependent variable. Many managers refer to an independent variable as a cost driver.

The intercept corresponds to fixed cost. The slope of the cost line corresponds to the variable rate. Creating and Using A Cost Formula Why: The purpose is to provide managers with a quantitative estimate of both total fixed costs and the variable cost per unit of the cost driver(s). After these cost formula components are determined, managers can predict total costs at various levels of output. Information: The art and graphics department of State College decided to equip each faculty office with an inkjet colour printer (computers were already in place). Sufficient colour printers had monthly depreciation of $250. The department purchased paper in boxes of 10,000 sheets (20 reams of 500 sheets each) for $35 per box. Ink cartridges cost $30 and will print, on average, 300 pages. Required: 1. Create a formula for the monthly cost of inkjet printing in the department. 2. If the department expects to print 4,400 pages next month, what is the expected total fixed cost? Total variable cost? Total printing cost? Solution: 1. The cost formula takes the following form: Total Cost = Fixed Cost + (Variable Rate x Number of Pages) The monthly fixed cost is $250 (the cost of printer depreciation), as it does not vary according to the number of pages printed. The variable costs are paper and ink, as both vary with the number of pages printed. Cost of paper per page is $35/10 000 = $ 0.0035 Cost of ink per page is $30/300 = $ 0.10 Variable rate per page is $0.0035 + $ 0.10 = $ 0.1035 The cost formula is: Total Cost of Printing = $ 250 + ($ 0.1035 x Number of Pages) 2. Expected fixed cost for next month is $250. Expected variable cost for next month is $ 0.1035 x 4,400 pages = $ 455.40 Expected total printing cost for next month is $ 250 + $ 455.40 = $ 705.40

The High-low Method Given two points, the slope and the intercept can be determined. The high-low method is method of separating mixed costs into fixed and variable components by using just the high and low data points. To demonstrate, we will use data from materials handling costs at Anderson Company:

Four steps must be taken in the high-low method: Step 1: Find the high point and the low point for a given data set. Step 2: Using the high and low point, calculate the variable rate. Variable rate = (High point cost – Low point cost) ÷ (High point output – Low point output) Step 3: Calculate the fixed cost using the variable rate (from Step 2) and either the high point or low point. Fixed cost = Total cost at high point – (Variable rate x Output at high point) Step 4: Form the cost formula for materials handling based on the high--low method. Using the High-Low Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula Why: The high-low method provides managers with a quick way of estimating cost behaviour. Only two data points are needed (high and low activity/driver points) This method is relatively easy and inexpensive for companies to conduct. Information: BlueDenim Company makes blue jeans. The company controller wants to calculate the fixed and variable costs associated with electricity used in the factory. Data for the past eight months were collected: Month

Electricity Cost

Machine Hours

January

3,255

460

February

3.485

500

March

4,100

600

April

3,300

470

May

3,312

470

June

3,575

350

July

3,910

570

August

4,200

590

Required: Using the high-low method, calculate the fixed cost of electricity, calculate the variable rate per machine hour, and construct the cost formula for total electricity cost. Solution: Step 1: Find the high and low points: The high number of machine hours is in March, and the low number of machine hours is in June. (Hint: Did you notice that the high cost of $4,200 was for August? Yet August is not the high point because its number of machine hours is not the highest activity level. Remember, the high point is associated with the highest activity level; the low point is associated with the lowest activity level.) Variable Rate = (High Cost – Low Cost)/(High Machine Hours – Low Machine Hours) = ($4,100 – $2,575)/(600 – 350) = $1,525/250 = $6.10 per machine hour Step 3: Calculate the fixed cost: Fixed Cost = Total Cost – (Variable Rate x Machine Hours) Let’s choose the high point with cost of $4,100 and machine hours of 600. Fixed Cost = $4,100 – ($6.10 x 600) = $4,100 – $3,660 = $440 (Hint: Check your work by computing fixed cost using the low point.) Step 4: Construct a cost formula: If the variable rate is $6.10 per machine hour and fixed cost is $440 per month, then the formula for monthly electricity cost is: Total Electricity Cost = $440 + ($6.10 x Machine Hours) Using the High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for Budgeted Output Why: After the cost formula is constructed, its components can be used to predict either total variable costs, total fixed costs, or total costs (both variable and fixed). Information: Recall that BlueDenim Company constructed the following formula for monthly electricity cost. (Refer to Cornerstone 3.2 to see how the fixed cost per month and the variable rate were computed.) Total Electricity Cost = $440 + ($6.10 x Machine Hours) Required: Assume that 550 machine hours are budgeted for the month of October. Use the previous cost formula to calculate (1) total variable electricity cost for October and (2) total electricity cost for October.

Solution: 1. Total Variable Electricity Cost = Variable Rate x Machine Hours = $6.10 x 550 = $3,355 2. Total Electricity Cost = Fixed Cost + (Variable Rate x Machine Hours) = $440 + ($6.10 x 550) = $440 + $ 3 355 =$ 3 795 Variable Cost. Total Cost for A Time Period that Differs from the Data Period Using the High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for a Time Period that Differs from the Data Period Why: A cost formula can help managers predict total costs for time periods of varying lengths. This flexibility is important because managers often must predict costs for periods of a week, month, quarter, or year in length. Information: Recall that BlueDenim Company constructed the following formula for monthly electricity cost. (Refer to Cornerstone 3.2 (p. 79) to see how the fixed cost per month and variable rate were computed.) Total Electricity Cost = $440 + ($6.10 x Machine Hours) Required: Assume that 6,500 machine hours are budgeted for the coming year. Use the previous cost formula to calculate (1) total variable electricity cost for the year, (2) total fixed electricity cost for the year, and (3) total electricity cost for the coming year. Solution: 1. Total Variable Electricity Cost = Variable Rate x Machine Hours = $6:10 x 6,500 = $39,650 2. Note: The cost formula is for the month, but we need to budget electricity for the year. Thus, we need to multiply the fixed cost for the month by 12 (the number of months in a year). Total Fixed Electricity Cost = Fixed Cost x 12 Months in a Year = $440 x 12 = $5,280 3. Total Electricity Cost = 12($440) + ($6:10 x 6,500) = $5,280 + $39,650 = $44,930

The Method of Least Squares The method of least squares (regression) is a statistical way to find the best--fitting line through asset of data points. One advantage is that for a given set of data, it will always produce the same cost formula. The best--fitting line is the one in which the datapoints are closer to the line than to any other line. Line Deviations The regression line better describes the pattern of the data than other possible lines. Results because the squared deviations between the regression line and each data point are, in total, smaller than the sum of the squared deviations of the data points and any other line. The least squares statistical formulas can find the one line with the smallest sum of squared deviations or the line which minimizes the cost prediction errors or differences between predicted costs (i.e., on the regression line) and actual costs (i.e., the actual datapoints).

Using the Regression Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula and to Determine Budgeted Cost Why: Regression gives the best estimates of the intercept (total fixed cost) and slope (variable cost per unit) for a set of data points. The regression method can yield a more accurate cost formula than the high-low method, but it also is more expensive and complicated to perform and explain to other managers. Information: BlueDenim Company makes blue jeans. The company controller wanted to calculate the fixed and variable costs associated with electricity used in the factory. Data for the past eight months were collected: Month

Electricity Cost

Machine Hours

January

$3,255

460

February

3,485

500

March

4,100

600

April

3,300

470

May

3,312

470

June

2,575

350

July

3,910

570

August

4,200

590

Coefficients shown by a regression program are: Intercept

321

X Variable 1

6.38

Required: Use the results of regression to perform the following: 1. Calculate the fixed cost of electricity and the variable rate per machine hour. 2. Construct the cost formula for total electricity cost. 3. Calculate the budgeted cost for next month, assuming that 550 machine hours are budgeted. Solution: 1. The fixed cost and the variable rate are given directly by regression. Fixed Cost = $321 Variable Rate = $6.38 2. The cost formula is: Total Electricity Cost = $321 + ($6.38 x Machine Hours) 3. Budgeted Electricity Cost = $321 + ($6.38 x 550) = $3,830 Comparison of Methods Knowing how costs change in relation to changes in output is essential to planning, controlling, and decision making. Each of the methods for separating mixed costs into fixed and variable components help managers understand cost behaviour and consequently make good business decisions. Comparison of Methods for Separating Fixed Costs into Fixed and Variable Components

Managerial Judgment Managerial judgment is critically important in determining cost behaviour and is by far the most widely used method in practice. Many managers simply use their experience and past observation of cost relationships to determine fixed and variable costs.

This method may take several forms. Some managers simply assign some costs to the fixed category and others to the variable category and ignore the possibility of mixed costs. Other managers may identify mixed costs and divide these into fixed and variable components. Management may use experience and judgment to refine statistical estimation results. The exp...