Activity Cost Behavior Prepared by Douglas Cloud Pepperdine University

After studying this chapter, you should be able to: Objectives 1. Define and describe fixed, variable, and mixed costs. 2. Explain the use of resources and activities and their relationship to cost behavior. 3. Separate mixed costs into their fixed and variable components using the high-low method, the scatterplot method, and the method of least squares. After studying this chapter, you should be able to:

Objectives 4. Evaluate the reliability of the cost formula. 5. Explain how multiple regression can be used to assess cost behavior. 6. Define the learning curve, and discuss its impact on cost behavior. 7. Discuss the use of managerial judgment in determining cost behavior.

Fixed Costs Fixed costs are costs that in total are constant within the relevant range as the level of the activity driver varies.

Fixed Costs Two production lines can process 10,000 computers per year each. The workers on each line are supervised by a production-line manager who is paid $24,000 per year. For production up to 10,000 units, only one supervisor is needed. When production is between 10,001 and 20,000 computers being produced, two supervisors are required.

Fixed Costs Supervision Computers Processed 24,000 8,000 3.00 Total Fixed Cost Graph $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 Fixed Costs Total Costs F = $24000 4 8 10 12 16 Units Produced (000) Supervision Computers Processed $24,000 4,000 $6.00 24,000 8,000 3.00 24,000 10,000 2.40 48,000 12,000 4.00 48,000 16,000 3.00 48,000 20,000 2.40 Unit Cost

Fixed Costs Supervision Computers Processed 24,000 8,000 3.00 Total Fixed Cost Graph $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 Fixed Costs Total Costs F = $24000 4 8 10 12 16 Units Produced (000) Supervision Computers Processed $24,000 4,000 $6.00 24,000 8,000 3.00 24,000 10,000 2.40 48,000 12,000 4.00 48,000 16,000 3.00 48,000 20,000 2.40 Unit Cost

Fixed Costs Supervision Computers Processed 24,000 8,000 3.00 Total Fixed Cost Graph $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 F = $48,000 Fixed Costs Total Costs 4 8 10 12 16 Units Produced (000) Supervision Computers Processed $24,000 4,000 $6.00 24,000 8,000 3.00 24,000 10,000 2.40 48,000 12,000 4.00 48,000 16,000 3.00 48,000 20,000 2.40 Unit Cost

Fixed Costs Supervision Computers Processed 24,000 8,000 3.00 Total Fixed Cost Graph $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 F = $48,000 Fixed Costs Total Costs 4 8 10 12 16 Units Produced (000) Supervision Computers Processed $24,000 4,000 $6.00 24,000 8,000 3.00 24,000 10,000 2.40 48,000 12,000 4.00 48,000 16,000 3.00 48,000 20,000 2.40 Unit Cost

Variable costs are costs that in total vary in direct proportion to changes in an activity driver.

Variable Cost A 3½-inch disk drive is added to each computer at a cost of $30 per computer. The total cost of disk drives for various levels of production is a follows: Total Cost of Disk Driver Number of Computers Produced Unit Cost of Disk Drives $120,000 4,000 $30 240,000 8,000 30 360,000 12,000 30 480,000 16,000 30 600,000 20,000 30

Variable Cost Y = VX Y = Total variable costs V = Variable cost per unit X = Number of units of the driver v

Number of Computers Processed Variable Cost Cost (in thousands) $600 480 360 240 120 Y = $30X v 4,000 8,000 12,000 16,000 20,000 Number of Computers Processed

Units of Activity Driver Nonlinearity of Variable Cost Cost ($) Relevant Range Units of Activity Driver

Mixed costs are costs that has both a fixed and a variable component.

Mixed Costs Y = Fixed cost + Total variable cost Y = F + VX where Y = Total cost Mixed Costs

Mixed Costs For Days Computer, the selling cost is represented by the following equation: Y = $300,000 + $50X

Variable Cost of Selling Mixed Costs Days Computers, Inc. Fixed Cost of Selling Variable Cost of Selling Total Cost Computers Sold Selling Cost Per Unit $300,000 $ 200,000 $ 500,000 4,000 $125.00 300,000 400,000 700,000 8,000 87.50 300,000 600,000 900,000 12,000 75.00 300,000 800,000 1,100,000 16,000 68.75 300,000 1,000,000 1,300,000 20,000 65.00

Number of Computers Sold Mixed Cost Behavior Cost (in thousands) $1,500 1,300 1,100 900 700 500 300 Variable Costs Fixed Cost 4,000 8,000 12,000 16,000 20,000 Number of Computers Sold

Basic Terms When a firm acquires the resources needed to perform an activity, it is obtaining activity capacity. The amount of activity capacity needed which corresponds to the level where the activity is performed efficiency is called practical capacity.

Flexible Resources Flexible resources are supplied as used and needed. They are acquired from outside sources, where the terms of acquisition do not require any long-term commitment for any given amount of the resource. Example: Materials and energy

Committed Resources Committed resources are supplied in advance of usage. They are acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the amount of the resource available is fully used or not. Committed resources may have unused capacity. Example: Buying or leasing a building or equipment

Committed Resources Committed fixed expenses are costs incurred for the acquisition of long-term capacity. Example: Plant, equipment, warehouses, vehicles, and salaries of top employees Discretionary fixed expenses are shorter-term committed resources. Example: The hiring of new receiving clerks

Step-Cost Behavior A step cost function displays a constant level of cost for a range of output and then jumps to a higher level of cost at some point.

Step-Cost Behavior 20 40 60 80 100 120 $500 400 300 200 100 Cost 20 40 60 80 100 120 Activity Output (units)

Normal Operating Range (Relevant Range) Step-Fixed Costs Cost $150,000 100,000 50,000 Normal Operating Range (Relevant Range) 2,500 5,000 7,500 Activity Usage

Step-Fixed Costs Cost of orders supplied = Cost of orders used + Cost of unused orders 7,500($20) = 6,000($20) + 1, 500($20) $150,000 = $120,000 + $30,000 The $30,000 of excess engineering capacity means that a new product could be introduced without increasing current spending on engineering.

Methods for Separating Mixed Costs The High-Low Method The Scatterplot Method The Method of Least Squares Variable Component Fixed Component

Y = F + VX Methods for Separating Mixed Costs Total activity cost Fixed cost component Variable cost per unit of activity Measure of activity output

Step 1: Solve for variable cost (V) The High-Low Method Month Material Handling Costs No. of Moves January $2,000 100 February 3,090 125 March 2,780 175 April 1,990 200 May 7,500 500 June 5,300 300 July 4,300 250 August 6,300 400 September 5,600 475 October 6,240 425 Step 1: Solve for variable cost (V)

The High-Low Method High Cost – Low Cost High Units – Low Units V = Month Material Handling Costs No. of Moves January $2,000 100 February 3,090 125 March 2,780 175 April 1,990 200 May 7,500 500 June 5,300 300 July 4,300 250 August 6,300 400 September 5,600 475 October 6,240 425 V = High Cost – Low Cost High Units – Low Units

The High-Low Method $7,500 – Low Cost 500 – Low Units V = Month Material Handling Costs No. of Moves January $2,000 100 February 3,090 125 March 2,780 175 April 1,990 200 May 7,500 500 June 5,300 300 July 4,300 250 August 6,300 400 September 5,600 475 October 6,240 425 V = $7,500 – Low Cost 500 – Low Units

The High-Low Method $7,500 – $2,000 500 – 100 V = Month Material Handling Costs No. of Moves January $2,000 100 February 3,090 125 March 2,780 175 April 1,990 200 May 7,500 500 June 5,300 300 July 4,300 250 August 6,300 400 September 5,600 475 October 6,240 425 V = $7,500 – $2,000 500 – 100

The High-Low Method $7,500 – $2,000 500 – 100 V = V = $13.75 $7,500 – $2,000 500 – 100 V = $13.75 Step 2: Using either the high cost or low cost, solve for the total fixed cost (F).

The High-Low Method Y = F + V(X) $7,500 = F + $13.75(500) $625 = F High End $7,500 = F + $13.75(500) $625 = F Y = F + V(X) Low End $2,000 = F + $13.75(100) $625 = F The cost formula using the high-low method is: Total cost = $625 + ($13.75 x # of moves)

The Scatterplot Method Graph A--Anderson Company Material Handling Cost $9,000 – 8,000 – 7,000 – 6,000 – 5,000 – 4,000 – 3,000 – 2,000 – 1,000 – 5 8 10 6 9 7 2 3 4 1 | | | | | 100 200 300 400 500 Number of Moves

The Scatterplot Method Material Handling Cost Graph B--High-Low Line Material Handling Cost $9,000 – 8,000 – 7,000 – 6,000 – 5,000 – 4,000 – 3,000 – 2,000 – 1,000 – 5 8 10 6 9 7 2 3 4 1 | | | | | 100 200 300 400 500 Number of Moves

The Scatterplot Method Material Handling Cost Graph C—One Possible Scattergraph LIne Material Handling Cost $9,000 – 8,000 – 7,000 – 6,000 – 5,000 – 4,000 – 3,000 – 2,000 – 1,000 – 5 8 10 6 9 7 2 3 4 1 | | | | | 100 200 300 400 500 Number of Moves

The Scatterplot Method Graph A--Nonlinear Relationship Activity Cost Activity Output

The Scatterplot Method Graph B--Upward Shift in Cost Relationship Activity Cost Activity Output

The Scatterplot Method Graph C--Presence of Outliers Activity Cost Outlier Outlier Activity Output

The Method of Least Squares Annual Cost Predicted Cost Deviation Deviation Squared $2,000 $2,000 0 0 3,090 2,300 790 624,100 2,780 2,900 -120 14,400 1,990 3,200 -1,10 1,464,100 7,500 6,800 700 490,000 5,300 4,400 900 810,000 4,300 3,800 500 250,000 6,300 5,600 700 490,000 5,600 6,500 -900 810,000 6,240 5,900 340 115,600 Total measure of closeness 5,068,200 $3,090 - 2,300 790 x 790

Material Handling Cost The Method of Least Squares Line Deviations Material Handling Cost $9,000 – 8,000 – 7,000 – 6,000 – 5,000 – 4,000 – 3,000 – 2,000 – 1,000 – 5 8 10 6 9 7 2 3 1 4 | | | | | 100 200 300 400 500 Number of Moves

The Method of Least Squares Spreadsheet Data for Anderson Company

The Method of Least Squares Regression Output for Anderson Company

The Method of Least Squares The results give rise to the following equation: Material handling cost = $854.50 + ($12.39 x number of items)

Coefficient of Correlation Positive Correlation r approaches +1 Machine Hours Utilities Costs Machine Hours Utilities Costs

Coefficient of Correlation Negative Correlation r approaches –1 Hours of Safety Training Industrial Accidents Hours of Safety Training Industrial Accidents

Coefficient of Correlation No Correlation r ~ 0 Hair Length Accounting Grade Hair Length Accounting Grade

Multiple Regression Y = F + V1 X1 + V2 X2 X1 = Number of moves X2 = The total distance

Multiple Regression Material Handling Number Pounds Month Cost of Moves Moved January $2,000 100 6,000 February 3,090 125 15,000 March 2,780 175 7,800 April 1,990 200 600 May 7,500 500 29,000 June 5,300 300 23,000 July 4,300 250 17,000 August 6,300 400 25,000 September 5,600 475 12,000 October 6,240 425 22,400

Multiple Regression Y = $507 + $7.84X + $0.11X 2 = $507 + $7.84(350) + $0.11(17,000) = $507 + $2.744 + $1,870 = $5,121

The Learning Curve and Nonlinear Behavior

Cumulative Cumulative Cumulative Individual Units Number Average Time Total Time: Time for nth of Units per Unit in Hours Labor Hours Unit-Labor Hours (1) (2) (3) = (1) x (2) (4) 1 100 100 100 2 80 (0.8 x 100) 160 60 3 70.21 210.63 50.63 4 64 (0.8 x 80) 256 45.37 5 59.57 297.85 41.85 6 56.17 337.02 39.17 7 53.45 374.15 37.13 8 51.20 (0.8 x 64) 409.60 35.45 16 40.96 655.36 28.06 32 32.77 1,048.64 Data for Cumulative Average Time Learning Curve with 80 Percent Learning Rate

Graph of Cumulative Total Hours Required and the Cumulative Average time per Unit 1,200 – 1,000 – 800 – 600 – 400 – 200 – 0 – Total Hours 1 5 10 15 20 25 30 35 36 Units

Cumulative Individual Unit Cumulative Cumulative Number Time for nth Unit Total Time: Average Time per of Units in Labor Hours Labor Hours Unit-Labor Hours (1) (2) (3) (4) = (3)/(1) 1 100 100 100 2 80 (0.8 x 100) 180 90 3 70.21 259.21 83.40 4 64 (0.8 x 80) 314.21 78.55 5 59.57 373.78 74.76 6 56.17 429.95 71.66 7 53.45 483.40 69.06 8 51.20 (0.8 x 64) 534.60 66.83 16 40.96 892.00 55.75 Data for an Incremental Unit-Time Learning Curve with an 80 Percent Learning Rate

Managerial Judgment Managerial judgment is critically important in determining cost behavior and is by far the most widely used method in practice.

End of Chapter