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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.

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

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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