Activity Cost Behavior CHAPTER Activity Cost Behavior

Objectives 1. Define cost behavior for fixed, variable, and mixed costs. 2. Explain the role of the resource usage model in understanding 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. continued

Objectives 4. Evaluate the reliability of a cost equation. 5. Discuss the role of multiple regression in assessing cost behavior. 6. Describe the use of managerial judgment in determining cost behavior.

A cost that stays the same as output changes is a fixed cost. Fixed Costs A cost that stays the same as output changes is a fixed cost.

Fixed Costs Cutting machines are leased for $60,000 per year and have the capacity to produce up to 240,000 units a year.

Fixed Costs Lease of Machines Number of Units 60,000 60,000 $1.00 Total Fixed Cost Graph Total Costs $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 60 120 180 240 Units Produced (000) F = $60,000 Fixed Costs Lease of Machines Number of Units $60,000 0 N/A 60,000 60,000 $1.00 60,000 120,000 0.50 60,000 180,000 0.33 60,000 240,000 0.25 Units Cost

Fixed Costs Lease of Machines Number of Units 60,000 60,000 $1.00 Unit Fixed Cost Graph Cost per Unit $1.00 $0.50 $0.33 $0.25 60 120 180 240 Units Produced (000) Fixed Costs Lease of Machines Number of Units $60,000 0 N/A 60,000 60,000 $1.00 60,000 120,000 0.50 60,000 180,000 0.33 60,000 240,000 0.25 Units Cost

A variable cost is a cost that, in total, varies in direct proportion to changes in output.

Variable Cost As the cutting machines cut each unit, they use 0.1 kilowatt-hour at $2.00 per kilowatt hour. Thus, the cost of each unit is $0.20 ($2 x 0.1).

Total Variable Cost Graph Total Costs Units Produced (000) $48,000 $36,000 $24,000 $12,000 60 120 180 240 Yv = .20x Variable Cost Cost of Power Number of Units $ 0 0 $ 0 12,000 60,000 0.20 24,000 120,000 0.20 36,000 180,000 0.20 48,000 240,000 0.20 Units Cost

Unit Variable Cost Graph 60 120 180 240 Units Produced (000) $0.40 $0.30 $0.20 $0.10 Cost per Unit Variable Cost Cost of Power Number of Units $ 0 0 $ 0 12,000 60,000 0.20 24,000 120,000 0.20 36,000 180,000 0.20 48,000 240,000 0.20 Units Cost

A mixed cost is a cost that has both a fixed and a variable component. Mixed Costs

Mixed Costs Sales representatives often are paid a salary plus a commission on sales.

Variable Cost of Selling Mixed Cost Behavior $130,000 $110,000 $90,000 $70,000 $50,000 $30,000 Mixed Costs Total Costs 40 80 120 160 180 200 Units Sold (000) Inserts Sold Variable Cost of Selling 40,000 $ 20,000 $30,000 $ 50,000 $1.25 80,000 40,000 30,000 70,000 0.86 120,000 60,000 30,000 90,000 0.75 160,000 80,000 30,000 110,000 0.69 200,000 100,000 30,000 130,000 0.65 Total Selling Cost Fixed Cost of Selling Selling Cost per Unit

Activity Cost Behavior Model Input: Materials Activities Energy Activity Output Labor Cost Behavior Changes in Output Capital Changes in Input Cost

Flexible Resources Flexible resources are resources acquired as used and needed. Materials and energy are examples.

Committed Resources Committed resources are supplied in advance of usage. Buying or leasing a building is an example of this form of advance resource acquisition.

A step cost 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

Step-Cost Behavior 10 20 30 40 50 $500 400 300 200 100 Cost 10 20 30 40 50 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-Cost Behavior Three engineers hired at $50,000 each Each engineer is capable of processing 2,500 change orders $90,000 was spent on supplies for the engineering activity There were 6,000 orders processed The company could process as many as 7,500 orders

Step-Cost Behavior Available orders = Orders used + Orders unused 7,500 orders = 6,000 orders + 1,500 orders Fixed engineering rate = $150,000/7,500 = $20 per change order Variable engineering rate = $90,000/6,000 = $15 per change order

Step-Cost Behavior The relationship between resources supplied and resources used is expressed by the following equation: Resources available = Resources used + Unused capacity

Step-Cost Behavior Cost of orders supplied = Cost of orders used + Cost of unused orders = [($20 + $15) x 6,000] + ($20 x 1,500) = $240,000 The $30,000 of excess engineering capacity means that a new product could be introduced without increasing current spending on engineering. Equal to the $150,000 spent on engineers and the $90,000 spent on supplies.

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

The linearity assumption assumes that variable costs increase in direct proportion to the number of units produced (or activity units used).

Methods for Separating Mixed Costs Y = a + bx Variable Cost per Unit Number of Units Total Fixed Cost Total Cost

Step 1: Solve for variable cost (b) The High-Low Method Month Setup Costs Setup Hours January $1,000 100 February 1,250 200 March 2,250 300 April 2,500 400 May 3,750 500 Step 1: Solve for variable cost (b)

The High-Low Method High Cost – Low Cost High Units – Low Units b = Month Setup Costs Setup Hours January $1,000 100 February 1,250 200 March 2,250 300 April 2,500 400 May 3,750 500 b = High Cost – Low Cost High Units – Low Units

The High-Low Method b = $3,750 – Low Cost 500 – Low Units b = Month Setup Costs Setup Hours January $1,000 100 February 1,250 200 March 2,250 300 April 2,500 400 May 3,750 500 b = $3,750 – Low Cost 500 – Low Units b = High Cost – Low Cost High Units – Low Units

The High-Low Method b = $3,750 – Low Cost 500 – Low Units b = Month Setup Costs Setup Hours January $1,000 100 February 1,250 200 March 2,250 300 April 2,500 400 May 3,750 500 b = $3,750 – Low Cost 500 – Low Units b = $3,750 – $1,000 500 – 100

The High-Low Method $3,750 – $1,000 500 – 100 b = b = $6.875 $3,750 – $1,000 500 – 100 b = $6.875 Step 2: Using either the high cost or low cost, solve for the total fixed cost (a).

The High-Low Method Y = a + b (x) $3,750 = a + $6.875(500) $312.50 = a High End $3,750 = a + $6.875(500) $312.50 = a Y = a + b (x) Low End $1,000 = a + $6.875(100) $312.50 = a The cost formula using the high-low method is: Total cost = $312.50 + ($6.875 x Setup hours)

The Scatterplot Method

The Scatterplot Method Nonlinear Relationship Activity Cost * * * * * Activity Output

The Scatterplot Method Upward Shift in Cost Relationship Activity Cost * * * * * * Activity Output

The Scatterplot Method Presence of Outliers Activity Cost * * * * Estimated regression line * * Estimated fixed cost Activity Output

LEAST SQUARE METHOD Y = a + bX ∑XY = a ∑X + b ∑X^2 (1) ∑Y = na + b ∑X (2) Ekstrapolasi rumus (1) dan (2)

The Method of Least Squares Spreadsheet Data for Larson Company

The Method of Least Squares Regression Output for Larson Company

The Method of Least Squares The results give rise to the following equation: Setup costs = $125 + ($6.75 x Setup hours) R2 = .944, or 94.4 percent of the variation in setup costs is explained by the number of setup hours variable.

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 TC = b0 + ( b1X1) + (b2X2) + . . . b0 = the fixed cost or intercept b1 = the variable rate for the first independent variable X1 = the first independent variable b2 = the variable rate for the second independent variable X2 = the second independent variable

Data for Phoenix Factory Utilities Cost Regression Multiple Regression Data for Phoenix Factory Utilities Cost Regression

Multiple Regression for Phoenix Factory Utilities Cost

Multiple Regression The results gives rise to the following equation: Utilities cost = $243.11 + $1.097(Machine hours) + ($510.49 x Summer) R2 = .967, or 96.7 percent of the variation in utilities cost is explained by the machine hours and summer variables.

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

Chapter Three The End