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**Analyzing Cost Behavior**

Session Two MBA 502B Managerial Accounting University of Scranton, Dr. Robyn Lawrence

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Classifying Costs In GAAP system, costs are classified according to function Cost of goods sold Selling Administrative Another classification system generally improves internal (management) decisions—according to cost behavior. S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Cost Behavior The manner in which a cost changes**

as a related activity changes Variable Fixed Mixed Activity Base: Cost Driver: causes changes in the behavior of costs. Cost Predictor: accompanied by consistent, observable changes in a cost item (correlated with)--predicts but may not cause the cost to change Activity Base Examples: miles driven – in a trucking company, room occupancy – in a hotel, number of customers called on – by a salesperson, or number of patients—in a hospital. Relevant (Normal or Practical) Range: the range of interest; or the range over which a company expects to operate during a year. S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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Variable Costs Vary in total directly and proportionately with changes in the activity level; Remain the same per unit at every level of activity. Number of Cost per Total Weekday Minutes Minute Cost $10 200 400 600 800 Number of Weekday Minutes Total Cost $20 $80 $60 $40 $100 . S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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Fixed Costs Remain the same in total regardless of changes in the activity level (within the relevant range). Per unit cost varies inversely with the activity level. Number of Cost per Monthly Units Produced Unit Rent $500 200 400 600 800 Number of Units Produced Total Cost $200 $800 $600 $400 $1,000 . 400 600 800 200 Cost Per Unit 1.00 2.00 3.00 . S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Variable versus Fixed Costs**

Total Cost Unit Cost Varies in direct proportion to changes in activity Remains constant throughout the relevant range Variable Cost Varies inversely with changes in activity throughout the relevant range Remains constant throughout the relevant range Fixed Cost S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Mixed Costs . Contain both variable and fixed cost elements.**

Changes in total but not proportionately with changes in the activity level. 200 400 600 800 Number of Miles Driven per Day Cost $100 $800 $600 $400 $1,000 . 50 Example: Assume that local rental terms for a 17-foot moving truck, including insurance, are $50 per day plus $.50 per mile. The per diem charge is a fixed cost with respect to miles driven in a day, while the mileage charge is a variable cost. High-low method, Scattergraph method or OLS Regression can be used to identify/estimate the fixed and variable components. S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Practice Classifying Costs**

Below costs are given for two periods (and two levels of activity). Classify the costs as to variable, fixed, or mixed. January February 1,000 units 1,200 units Classification Rent $ $ 700 Maintenance Utilities Insurance Inspection Supplies Indirect Labor Direct Materials Fixed Variable Mixed S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**High-Low Estimation Method**

Essentially finding the slope (variable cost per activity unit) and then the intercept (total fixed costs) for a line going through two points: EXAMPLE: Production Total cost June 700 units 3,200 July 800 3,800 August 900 4,300 September 500 2,700 October 400 2,050 Find the slope (variable cost per activity): Difference in Total Cost Difference in Activity = Variable Cost per Unit of Activity 4,300 – 2,050 = 2,250 500 = $4.50/unit 900 – 400 Find the intercept (total fixed costs): Using the higher point: 4,300 – (900 x 4.50) = 4,300 – 4,050 = 250 Using the lower point: 2,050 – (400 x 4.50) = 2,050 – 1,800 = 250 Variable costs are $4.50 per unit and fixed costs are $250. Cost formula: Total Costs = $250 + $4.50X S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Graphing Costs . . . Total Variable Costs $5,000 Total Costs $4,000**

$5,000 . (900, 4,300) Total Costs Total Variable Costs $4,000 Total Cost Line $3,000 . (400, 2,050) $2,000 $1,000 250 Fixed Costs . Fixed Costs 100 200 300 400 500 600 700 800 900 Units Produced S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Scattergraph Estimation**

Plot all of the observations Draw the most representative line. Pick two points on the line & use high-low method to determine variable and fixed costs $5,000 . (700, 3,200) (900, 4,300) (800, 3,800) (400, 2,050) (500, 2,700) Total Costs $4,000 $3,000 $2,000 $4,250 - $3,000 = 1,250/300 = variable cost per unit $1,000 $3,000 – x 600 = 3,000 – 2,500 = 500 Total Fixed Costs 100 200 300 400 500 600 700 800 900 Units Produced Total Cost = 4.17X + 500 S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**OLS Regression Method MS Excel Ordinary Least Squares Output:**

For slope (variable cost per unit) use =INDEX(LINEST(known_y's,known_x's)1) For the intercept (total fixed costs) use =INDEX(LINEST(known_y's,known_x's)2) For the full regression output use =LINEST(known_y's,known_x's,const,stats) For Example: m = 4.227 (Variable cost per unit) b = (Total fixed costs) Total Cost = 4.227X S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Comparison of Methods to Calculate Mixed Cost Components**

High-low method Uses the total costs incurred at the high and low levels of activity to calculate the variable cost per unit and the total fixed costs using the line formula. Advantage: easy to calculate. Disadvantages: relies on the representativeness of the high point and the low point. does examine whether a line (linear model) is appropriate. Scattergraph Method Plots observations, draws in the “best” line and calculates the line’s values. Advantage: examines whether there is a linear relationship. Disadvantage: the line drawn might be different from person to person. Ordinary Least Squares Regression Estimates a line that minimizes sum of the squared differences between the actual y-values and the average of the y-values. Advantages: uses all of the points—efficient estimator; provides more information about how much of the variability is explained by the line. harder to use and explain overly affected by outliers. S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Nonlinear Cost Behavior**

Total Mixed costs are fixed over some range then vary over the succeeding range. Total Cost Example: Monthly phone fee plus per call fee if number of calls exceed a preset number. Step-Fixed are fixed for a range, then jump and remain fixed for a range… Example: A salaried supervisor for every ten employees Total Cost Curvilinear (variable) do not have a linear pattern Example: Total cost of direct labor where overtime is sometimes involved. Total Cost S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Linear Estimation of Nonlinear Cost Behavior**

Curvilinear (variable) Total Mixed Step-Fixed Total Cost Total Cost Total Cost Relevant Range is the range over which a company expects to operate during a year. Within this range, a relationship approximating a straight-line might exist. S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Why Does Cost Behavior Matter?**

Determining Cost Behavior: Improves cost forecasts at different levels of activity. Management’s volume response differs for variable versus fixed costs. For example: If fixed costs are $1,000 for the relevant range of 1 to 100 units, then if 10 units are produced, the unit cost is $100; if 100 units are produced, the unit cost is $10. With fixed costs, unit costs change proportionately--there is incentive to produce more units with fixed costs to lower unit costs. If variable costs are $1 per unit, then the unit cost will be $1 per unit whether 1 or 100 are produced. Unit costs will not decline if more units are produced. S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Analyzing Cost Behavior**

This Ends Session 2: Analyzing Cost Behavior S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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**Concluding Activities**

Read Chapter 11: pp Suggested homework: E11-1 [Classify costs] E11-2 [Identify cost graphs] E11-3 [Identify activity bases] E11-6 [Relevant range; calculating variable & fixed costs] E11-7 [High-low method; making an estimate] E11-8 [High-low method] P11-1 [Classify costs] Submit to the Session Two Dropbox your solutions to the following: Required: For each of the different costs given below, indicate whether it is a variable, fixed, or mixed cost. Use the high-low technique to estimate the variable cost per unit and the total fixed costs for each. Cost 400 hours 550 hours A $ $ 875 B C 1, ,980 D 3, ,250 E 1, ,000 F G H S-II: Analyzing Cost Behavior, MBA 502B, Univ. of Scranton, Dr. R. Lawrence

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Cost Behavior: Analysis and Use

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