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CHAPTER 10 DETERMINING HOW COSTS BEHAVE

By Keith Bailey,2014-12-25 14:21
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CHAPTER 10 DETERMINING HOW COSTS BEHAVE

    CHAPTER 10

    DETERMINING HOW COSTS BEHAVE

10-1 The two assumptions are:

    1. Variations in total costs are explained by variations in the level of a single activity related

    to those costs (the cost driver).

    2. Cost behavior is approximated by a linear cost function within the relevant range. A linear

    cost function is a cost function where, within the relevant range, the graph of total costs

    versus the level of a single activity forms a straight line.

    10-2 Three alternative linear cost functions are:

    1. Variable cost function––a cost function in which total costs change in proportion to the

    changes in the level of activity in the relevant range.

    2. Fixed cost function––a cost function in which total costs do not change with changes in the

    level of activity in the relevant range.

    3. Mixed cost function––a cost function that has both variable and fixed elements. Total costs

    change but not in proportion to the changes in the level of activity in the relevant range. 10-3 A linear cost function is a cost function where, within the relevant range, the graph of total costs versus the level of a single activity related to that cost is a straight line. An example of a linear cost function is a cost function for use of a telephone line where the terms are a fixed charge of $10,000 per year plus a $2 per minute charge for phone use. A nonlinear cost function is a cost function where, within the relevant range, the graph of total costs versus the level of a single activity related to that cost is not a straight line. Examples include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-function costs, and learning-curve-based costs.

    10-4 No. High correlation merely indicates that the two variables move together in the data examined. It is essential to also consider economic plausibility before making inferences about cause and effect. Without any economic plausibility for a relationship, it is less likely that a high level of correlation observed in one set of data will be similarly found in other sets of data. 10-5 Four approaches to estimating a cost function are:

    1. Industrial engineering method.

    2. Conference method.

    3. Account analysis method.

    4. Quantitative analysis of current or past cost relationships.

    10-6 The conference method estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of a company (purchasing, process engineering, manufacturing, employee relations, etc.). Advantages of the conference method include:

    1. The speed with which cost estimates can be developed.

    2. The pooling of knowledge from experts across functional areas.

    3. The improved credibility of the cost function to all personnel.

     10-1

    10-7 The account analysis method estimates cost functions by classifying cost accounts in the subsidiary ledger as variable, fixed, or mixed with respect to the identified level of activity. Typically, managers use qualitative, rather than quantitative, analysis when making these cost-classification decisions.

    10-8 The six steps are:

    1. Choose the dependent variable (the variable to be predicted, which is some type of cost). 2. Identify the independent variable or cost driver.

    3. Collect data on the dependent variable and the cost driver.

    4. Plot the data.

    5. Estimate the cost function.

    6. Evaluate the cost driver of the estimated cost function.

    Step 3 typically is the most difficult for a cost analyst.

    10-9 Causality in a cost function runs from the cost driver to the dependent variable. Thus, choosing the highest observation and the lowest observation of the cost driver is appropriate in the high-low method.

    10-10 Criteria important when choosing among alternative cost functions are: 1. Economic plausibility.

    2. Goodness of fit.

    3. Slope of the regression line.

    10-11 A learning curve is a function that measures how labor-hours per unit decline as units of production increase because workers are learning and becoming better at their jobs. Two models used to capture different forms of learning are:

    1. Cumulative average-time learning model. The cumulative average time per unit declines

    by a constant percentage each time the cumulative quantity of units produced doubles. 2. Incremental unit-time learning model. The incremental time needed to produce the last

    unit declines by a constant percentage each time the cumulative quantity of units produced

    doubles.

    10-12 Frequently encountered problems when collecting cost data on variables included in a cost function are:

    1. The time period used to measure the dependent variable is not properly matched with the

    time period used to measure the cost driver(s).

    2. Fixed costs are allocated as if they are variable.

    3. Data are either not available for all observations or are not uniformly reliable. 4. Extreme values of observations occur.

    5. A homogeneous relationship between the individual cost items in the dependent variable

    cost pool and the cost driver(s) does not exist.

    6. The relationship between the cost and the cost driver is not stationary. 7. Inflation has occurred in a dependent variable, a cost driver, or both.

     10-2

10-13 Four key assumptions examined in specification analysis are:

    1. Linearity between the dependent variable and the independent variable within the relevant

    range.

    2. Constant variance of residuals for all values of the independent variable. 3. Residuals are independent of each other.

    4. Residuals are normally distributed.

    10-14 No. A cost driver is any factor whose change causes a change in the total cost of a related cost object. A cause-and-effect relationship underlies selection of a cost driver. Some users of regression analysis include numerous independent variables in a regression model in an attempt to maximize goodness of fit, irrespective of the economic plausibility of the independent variables included. Some of the independent variables included may not be cost drivers.

    10-15 No. Multicollinearity exists when two or more independent variables are highly correlated with each other.

10-16 (10 min.) Estimating a cost function

    Difference in costs1. Slope coefficient = Difference in machine-hours

    $3,900 $3,000 = 7,000 4,000

    $900 = = $0.30 per machine-hour 3,000

     Constant = Total cost (Slope coefficient Quantity of cost driver)

     ($0.30 7,000) = $1,800 = $3,900

     = $3,000 ($0.30 4,000) = $1,800

The cost function based on the two observations is:

     Maintenance costs = $1,800 + $0.30 Machine-hours

    2. The cost function in requirement 1 is an estimate of how costs behave within the relevant range, not at cost levels outside the relevant range. If there are no months with zero machine-hours represented in the maintenance account, data in that account cannot be used to estimate the fixed costs at the zero machine-hours level. Rather, the constant component of the cost function provides the best available starting point for a straight line that approximates how a cost behaves within the relevant range.

     10-3

10-17 (15 min.) Identifying variable-, fixed-, and mixed-cost functions.

    1. See Solution Exhibit 10-17.

    2. Contract 1: y = $50

     Contract 2: y = $30 + $0.20X

     Contract 3: y = $1X

     where X is the number of miles traveled in the day.

    3. Contract Cost Function

     1 Fixed

    2 Mixed

    3 Variable SOLUTION EXHIBIT 10-17 $160

    Plots of Car Rental Contracts Offered by Pacific Corp. 140Contract 1: Fixed Costs120

    100

    80

    60

    40

    20al CostsCar Rent

    0501001500Miles Traveled per Day

    $160

    140Contract 2: Mixed Costs120

    100al CostsCar Rent80

    6010050150

    Miles Traveled per Day40

    $16020

    1400

    1200

    100

    80

    60

    40al CostsCar Rent

    20

    Contract 3: Variable Costs

    50100150 Miles Traveled per Day

     10-4

    0

    0

10-18 (20 min.) Various cost-behavior patterns.

    1. K

    2. B

    3. G

    4. J Note that A is incorrect because, although the cost per pound eventually equals a

    constant at $9.20, the total dollars of cost increases linearly from that point

    onward.

    5. I The total costs will be the same regardless of the volume level.

    6. L

    7. F This is a classic step-cost function.

    8. K

    9. C

    10-19 (30 min.) Matching graphs with descriptions of cost and revenue behavior.

a. (1)

    b. (6) A step-cost function.

    c. (9)

    d. (2)

    e. (8)

    f. (10) It is data plotted on a scatter diagram, showing a linear variable cost function with

    constant variance of residuals. The constant variance of residuals implies that there is a

    uniform dispersion of the data points about the regression line. g. (3)

    h. (8)

     10-5

10-20 (15 min.) Account analysis method.

1. Variable costs:

     Car wash labor $240,000

     Soap, cloth, and supplies 32,000

     Water 28,000

     Electric power to move conveyor belt 72,000

     Total variable costs $372,000

     Fixed costs:

     Depreciation $ 64,000

     Salaries 46,000

     Total fixed costs $110,000

Costs are classified as variable because the total costs in these categories change in proportion to

    the number of cars washed in Lorenzo’s operation. Costs are classified as fixed because the total costs in these categories do not vary with the number of cars washed. If the conveyor belt moves

    regardless of the number of cars on it, the electricity costs to power the conveyor belt would be a

    fixed cost.

    $372,0002. Variable costs per car = = $4.65 per car 80,000

     Total costs estimated for 90,000 cars = $110,000 + ($4.65 × 90,000) = $528,500

    10-21 (30 min.) Account analysis method.

    1. Manufacturing cost classification for 2004:

     % of Total Unit

     Total Costs That Is Variable Fixed Variable

     Costs Variable Costs Costs Costs

    Account (1) (2) (4) = (1) (3) (5)=(3) ? 75,000 (3) = (1) (2)

    Direct materials $300,000 100% $300,000 $ 0 $4.00 Direct manufacturing labor 225,000 100 225,000 0 3.00 Power 37,500 100 37,500 0 0.50 Supervision labor 56,250 20 11,250 45,000 0.15 Materials-handling labor 60,000 50 30,000 30,000 0.40 Maintenance labor 75,000 40 30,000 45,000 0.40 Depreciation 95,000 0 0 95,000 0 Rent, property taxes, admin 100,000 0 0 100,000 0 Total $948,750 $633,750 $315,000 $8.45

    Total manufacturing cost for 2004 = $948,750

     10-6

10-21 (Cont’d.)

    Variable costs in 2005:

     Unit Increase in

     Variable Variable

     Cost for Percentage Costs Unit Variable Total Variable

     2004 Increase per Unit Cost for 2005 Costs for 2005

    Account (6) (7) (9) = (6) + (8) (8) = (6) (7) (10) = (9) 80,000

    Direct materials $4.00 5% $0.20 $4.20 $336,000 Direct manufacturing labor 3.00 10 0.30 3.30 264,000 Power 0.50 0 0 0.50 40,000 Supervision labor 0.15 0 0 0.15 12,000 Materials-handling labor 0.40 0 0 0.40 32,000 Maintenance labor 0.40 0 0 0.40 32,000 Depreciation 0 0 0 0 0 Rent, property taxes, admin. 0 0 0 0 0 Total $8.45 $0.50 $8.95 $716,000

    Fixed and total costs in 2005:

     Dollar

     Fixed Increase in Fixed Costs Variable Total

     Costs Percentage Fixed Costs for 2005 Costs for Costs

     for 2004 Increase (13) = (14) = 2005 (16) =

    Account (11) (12) (11) + (13) (15) (14) + (15) (11) (12)

    Direct materials $ 0 0% $ 0 $ 0 $336,000 $ 336,000 Direct manufacturing labor 0 0 0 0 264,000 264,000 Power 0 0 0 0 40,000 40,000 Supervision labor 45,000 0 0 45,000 12,000 57,000 Materials-handling labor 30,000 0 0 30,000 32,000 62,000 Maintenance labor 45,000 0 0 45,000 32,000 77,000 Depreciation 95,000 5 4,750 99,750 0 99,750 Rent, property taxes, admin. 100,000 7 7,000 107,000 0 107,000 Total $315,000 $11,750 $326,750 $716,000 $1,042,750

     Total manufacturing costs for 2005 = $1,042,750

    $948,7502. Total cost per unit, 2004 = = $12.65 75,000

    $1,042,750 Total cost per unit, 2005 = = $13.03 80,000

    3. Cost classification into variable and fixed costs is based on qualitative, rather than

    quantitative, analysis. How good the classifications are depends on the knowledge of individual

    managers who classify the costs. Gower may want to undertake quantitative analysis of costs,

    using regression analysis on time-series or cross-sectional data to better estimate the fixed and

    variable components of costs. Better knowledge of fixed and variable costs will help Gower to

    better price his products, know when he is getting a positive contribution margin, and to better

    manage costs.

     10-7

    10-22 (20 min.) Estimating a cost function, high-low method.

1. See Solution Exhibit 10-22. There is a positive relationship between the number of service

    reports (a cost driver) and the customer-service department costs. This relationship is

    economically plausible.

2. Number of Customer-Service

     Service Reports Department Costs

    Highest observation of cost driver 436 $21,890

     Lowest observation of cost driver 122 12,941

     Difference 314 $ 8,949

     Customer-service department costs = a + b (number of service reports)

    $8,949 Slope coefficient (b) = = $28.50 per service report 314

     Constant (a) = $21,890 $28.50 (436) = $9,464

     = $12,941 $28.50 (122) = $9,464

     Customer-service

     department costs = $9,464 + $28.50 (number of service reports)

    3. Other possible cost drivers of customer-service department costs are:

    a. Number of products replaced with a new product (and the dollar value of the new

    products charged to the customer-service department).

    b. Number of products repaired and the time and cost of repairs.

SOLUTION EXHIBIT 10-22

    Plot of Number of Service Reports versus Customer-Service Dept. Costs for Capitol Products

    $25,000

     20,000

     15,000

     10,000

     5,000

    Customer-Service Department Costs$0

    0100200300400500

    Number of Service Reports

     10-8

10-23 (3040 min.) Linear cost approximation.

    Difference in cost1. Slope coefficient (b) = Difference in labor-hours

    $529,000 -400,000 = = $43.00 7,000-4,000

     Constant (a) = $529,000 ($43.00 × 7,000)

     = $228,000

     Cost function = $228,000 + $43.00 (professional labor-hours)

     The linear cost function is plotted in Solution Exhibit 10-23.

     No, the constant component of the cost function does not represent the fixed overhead cost of the Memphis Group. The relevant range of professional labor-hours is from 3,000 to 8,000. The constant component provides the best available starting point for a straight line that approximates how a cost behaves within the 3,000 to 8,000 relevant range. 2. A comparison at various levels of professional labor-hours follows. The linear cost function is based on the formula of $228,000 per month plus $43.00 per professional labor-hour.

     Total overhead cost behavior:

     Month 1 Month 2 Month 3 Month 4 Month 5 Month 6

Actual total overhead costs $340,000 $400,000 $435,000 $477,000 $529,000 $587,000

    Linear approximation 357,000 400,000 443,000 486,000 529,000 572,000

    Actual minus linear

     approximation $(17,000) $ 0 $ (8,000) $ (9,000) $ 0 $ 15,000

    Professional labor-hours 3,000 4,000 5,000 6,000 7,000 8,000

    The data are shown in Solution Exhibit 10-23. The linear cost function overstates costs by $8,000 at the 5,000-hour level and understates costs by $15,000 at the 8,000-hour level.

3. Based on Based on Linear

     Actual Cost Function

    Contribution before deducting incremental overhead $38,000 $38,000

    Incremental overhead 35,000 43,000

    Contribution after incremental overhead $ 3,000 $ (5,000)

The total contribution margin actually forgone is $3,000.

     10-9

10-23 (Cont’d.)

SOLUTION EXHIBIT 10-23

    Linear Cost Function Plot of Professional Labor-Hours

    on Total Overhead Costs for Memphis Consulting Group

     $7 0 0 , 0 0 0

     60 0 , 0 0 0

    50 0 , 0 0 0

    40 0 , 0 0 0

    30 0 , 0 0 0

    20 0 , 0 0 0 Total Overhead Costs

    10 0 , 0 0 0

    0

    0 0 00 8, 00 0 1, 0 0 0 ,0 0 0 4, 0 0 0 5, 0 0 0 6, 0 0 0 7, 0 0 0 9, 2,000 3

     Professional Labor-Hours Billed

    10-24 (20 min.) Cost-volume-profit and regression analysis.

    Total manufacturing costs1a. Average cost of manufacturing = Number of bicycle frames

    $900,000 = = $30 per frame 30,000

     This cost is greater than the $28.50 per frame that Ryan has quoted.

    1b. Garvin cannot take the average manufacturing cost in 2002 of $30 per frame and multiply it

    by 36,000 bicycle frames to determine the total cost of manufacturing 36,000 bicycle

    frames. The reason is that some of the $900,000 (or equivalently the $30 cost per frame)

    are fixed costs and some are variable costs. Without distinguishing fixed from variable

    costs, Garvin cannot determine the cost of manufacturing 36,000 frames. For example, if

    all costs are fixed, the manufacturing costs of 36,000 frames will continue to be $900,000.

    If, however, all costs are variable, the cost of manufacturing 36,000 frames would be $30

    36,000 = $1,080,000. If some costs are fixed and some are variable, the cost of

    manufacturing 36,000 frames will be somewhere between $900,000 and $1,080,000.

     10-10

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