Solution Manual_Chapter 10

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CHAPTER 10

DETERMINING HOW COSTS BEHAVE

10-1 The two assumptions are1. Variations in the level of a single activity (the cost driver) explain the variations in the

related total costs.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 totalcosts versus the level of a single activity forms a straight line.

10-2 Three alternative linear cost functions are1. Variable cost functiona cost function in which total costs change in proportion to the

changes in the level of activity in the relevant range.2. Fixed cost functiona cost function in which total costs do not change with changes in

the level of activity in the relevant range.3. Mixed cost functiona 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 relevantrange.

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

10-4 No. High correlation merely indicates that the two variables move together in the dataexamined. It is essential also to consider economic plausibility before making inferences aboutcause and effect. Without any economic plausibility for a relationship, it is less likely that a highlevel 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 are1. 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 opinionsabout costs and their drivers gathered from various departments of a company (purchasing,process engineering, manufacturing, employee relations, etc.). Advantages of the conferencemethod include1. 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.


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10-7 The account analysis method estimates cost functions by classifying cost accounts in thesubsidiary 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 are1. 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 inthe high-low method.

10-10 Three criteria important when choosing among alternative cost functions are1. 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 ofproduction increase because workers are learning and becoming better at their jobs. Two modelsused to capture different forms of learning are1. 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 lastunit declines by a constant percentage each time the cumulative quantity of unitsproduced doubles.

10-12 Frequently encountered problems when collecting cost data on variables included in acost function are1. 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 variablecost 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.


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10-13 Four key assumptions examined in specification analysis are1. Linearity of relationship 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. Independence of residuals.4. Normal distribution of residuals.

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

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


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Various cost-behavior patterns.

1. K

2. B

3. G4. J Note that A is incorrect because, although the cost per kg eventually equals a constant at Rs 9.20, the total rupees 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

Account analysis method.

1. Variable costs:Car wash labor Rs 24,00,000

Soap cloth and supplies 3,20,000

Water 2,80,000Electric power to move conveyor belt 7,20,000

Total variable costs Rs 37,20,000

Fixed costs:Depreciation Rs 6,40,000

Salaries 4,60,000

Total fixed costs Rs 11,00,000

Costs are classified as variable because the totalcosts in these categories change in proportion to the number of cars washed in

Johnsons operation. Costs are classified as fixed because the totalcosts 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.

2. Variable costs per car =Rs3720000

80000

, ,

,= Rs 46.5 per car

Total costs estimated for 90,000 cars = Rs 11,00,000 + (Rs 46.5 90,000) = Rs 52,85,000

Linear cost approximation.

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

=Rs Rs52 90 0 00 40 0 0 000

7 000 4 000

, , , ,

, ,

= Rs 430

Constant (a) = Rs 52,90,000 (Rs 430 7,000)

= Rs 22,80,000Cost function = Rs 22,80,000 + Rs 430 (professional labor-hours)

The linear cost function is plotted in Solution Exhibit 10-30.

No, the constant component of the cost function does not represent the fixed overhead cost of the Ernst & Young. The relevant range ofprofessional 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 Rs 22,80,000 permonth plus Rs 430 per professional labor-hour.

EXERCISES


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Total overhead cost behavior:

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

Actual total overhead costs Rs 34,00,000 Rs 40,00,000 Rs 43,50,000 Rs 47,70,000 Rs 52,90,000 Rs 58,70,000

Linear approximation 35,70,000 40,00,000 44,30,000 48,60,000 52,90,000 57,20,000

Actual minus linear approximation Rs (1,70,000) Rs 0 Rs (80,000) Rs (90,000) Rs 0 Rs 1,50,000

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

The data are shown in Solution Exhibit 10-30. The linear cost function overstates costs by Rs 80,000 at the 5,000-hour level and under-states costs by Rs 1,50,000 at the 8,000-hour level.

3. Based on Actual Based on Linear Cost Function

Contribution before deducting incremental overhead Rs 3,80,000 Rs 3,80,000

Incremental overhead 3,50,000 4,30,000

Contribution after incremental overhead Rs 30,000 Rs (50,000)

The total contribution margin actually forgone is Rs 30,000.

Solution Exhibit 10-30

Linear Cost Function Plot of Professional Labor-Hourson Total Overhead Costs for Ernst & Young Consulting Group

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

Professional Labor-Hours Billed

TotalOverheadCosts

Rs 7,00,000

6,00,000

5,00,000

4,00,000

3,00,000

2,00,000

1,00,000

Regression analysis, activity-based costing, choosing cost drivers.

1a. Solution Exhibit 10-31A presents the plots and regression line of number of packaged units moved on distribution costs.

SOLUTION EXHIBIT 10-31A

Plots and Regression Line of Number of Packaged Units Moved on Distribution Costs

0 20,000 40,000 60,000 80,000

Number of Packaged Units Moved

0

50 00, 0

1 00 00, , 0

1 50 00, , 0

2 00 00, , 0

2 50 00, , 0

3 00 0, ,0 0

3,50,000

4,00,000

Rs 4,50,000

Distribution

Co

sts


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1b. Solution Exhibit 10-31B presents the plots and regression line of number of shipments made on distribution costs.

SOLUTION EXHIBIT 10-31B

Plots and Regression Line of Number of Shipments Made on Distribution Costs

0 100 200 300 400 500

Number of Shipments Made

0

50,000

1,00,000

1,50,000

2,00,000

2,50,000

3,00,000

3,50,000

4,00,000

Rs 4,50,000

Distribution

Costs

Number of packaged units moved appears to be a better cost driver of distribution costs for the following reasons:

(i) Economic plausibility. Both number of packaged units moved and number of shipments are economically plausible cost drivers. Be-

cause the product is heavy, however, costs of freight are likely to be a sizable component of distribution costs. Thus, number of pack-aged units moved will affect distribution costs significantly because freight costs are largely a function of the number of units

transported.

(ii) Goodness of fit.Compare Solution Exhibits 10-31A and 10-31B. Number of packaged units moved has a better goodness of fit withdistribution costs than do number of shipments made. That is, the vertical differences between actual and predicted distribution costs

are smaller for the number of packaged units moved regression than for the number of shipments made regression.

(iii) Slope of regression line. Again, compare Solution Exhibits 10-31A and 10-31B. The number of packaged units moved regression linehas a relatively steep slope and a small scatter of observations around the regression lines indicating a strong relationship between

number of packaged units moved and distribution costs. On average, distribution costs increase with the number of packaged unitsmoved. The number of shipments made regression line is flatter and has more scatter of observations about the line indicating a weak

relationship between the number of shipments made and distribution costs. On average, the number of shipments made has a smaller

effect on distribution costs.

2. Using the preferred cost function,

Distribution costs = Rs 13,490 + (Rs 4.96 Number of packaged units moved),

Akshita would budget distribution costs of

Rs 13,490 + (Rs 4.96 40,000) = Rs 13,490 + Rs 1,98,400 = Rs 2,11,890

High-low method.

1. Machine-Hours Maintenance Costs

Highest observation of cost driver 125,000 Rs 25,00,000

Lowest observation of cost driver 85,000 17,00,000

Difference 40,000 Rs 8,00,000

Maintenance costs = a + b (Machine-hours)

Slope coefficient (b) =Rs800000

40000

, ,

,= Rs 20

Constant (a) = Rs 25,00,000 (Rs 20 125,000)= Rs 25,00,000 Rs 25,00,000 = Rs 0

or Constant (a) = Rs 17,00,000 (Rs 20 85,000)

= Rs 17,00,000 Rs 17,00,000 = Rs 0Maintenance costs = Rs 20 Machine-hours


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2.

SOLUTION EXHIBIT 10-32

Plot and High-Low Line of Machine-Hours on Maintenance Costs

90,00080,000 100,000 110,000 120,000 130,000

Machine-Hours

10,00,000

12,00,000

14,00,000

16,00,000

18,00,000

20,00,000

22,00,000

24,00,000

Rs 26,00,000

MaintenanceCosts

Solution Exhibit 10-32 presents the high-low line.Economic plausibility. The cost function shows a positive economically plausible relationship between machine-hours and maintenance

costs. There is a clear-cut engineering relationship of higher machine-hours and maintenance costs.

Goodness of fit. The high-low line appears to fit the data well. The vertical differences between the actual and predicted costs appear tobe quite small.

Slope of high-low line.The slope of the line appears to be reasonably steep indicating that, on average, maintenance costs in a quartervaries with machine-hours used.

3. Using the cost function estimated in 1, predicted maintenance costs would be Rs 20 90,000 = Rs 18,00,000.

Faraz should budget Rs 18,00,000 in quarter 13 because the relationship between machine-hours and maintenance costs in SolutionExhibit 10-32 is economically plausible, has an excellent goodness of fit, and indicates that an increase in machine-hours in a quarter

causes maintenance costs to increase in the quarter.

High-low method versus regression analysis.

1. Solution Exhibit 10-30 presents the plots of advertising costs on revenues.

SOLUTION EXHIBIT 10-33

Plot and Regression Line of Advertising Costs on Revenues

Rs 10,000Rs 0 Rs 20,000 Rs 30,000 Rs 40,000 Rs 50,000

Advertising Costs

Rs 9,00,000

8 0,000,0

7 0,000,0

6 0,000,0

5 0,000,0

4 0,000,0

3 0,000,0

2 0,000,0

1 0,000,0

0

Reven

ues


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2. Solution Exhibit 10-33 also shows the regression line of advertising costs on revenues. We evaluate the estimated regression equationusing the criteria of economic plausibility, goodness of fit, and slope of the regression line.

Economic plausibility. Advertising costs appears to be a plausible cost driver of revenues. Restaurants frequently use newspaper adver-

tising to promote their restaurants and increase their patronage.

Goodness of fit. The vertical differences between actual and predicted revenues appears to be reasonably small. This indicates that ad-

vertising costs are related to restaurant revenues.

Slope of regression line.

The slope of the regression line appears to be relatively steep. Given the small scatter of the observations aroundthe line, the steep slope indicates that, on average, restaurant revenues increase with newspaper advertising.

3. The high-low method would estimate the cost function as follows:

Advertising Costs Revenues

Highest observation of cost driver Rs 40,000 Rs 8,00,000

Lowest observation of cost driver 10,000 5,50,000

Difference Rs 30,000 Rs 2,50,000

Revenues = a+ (badvertising costs)

Slope coefficient (b) =Rs

Rs

2 50000

30000

, ,

,= 8.333

Constant (a) = Rs 8,00,000 (Rs 40,0008.333)

= Rs 8,00,000 3,33,320 = Rs 4,66,680or Constant (a) = Rs 5,50,000 (Rs 10,000 8.333)

= Rs 5,50,000 83,330 = Rs 4,66,670Revenues = Rs 4,66,670 + (8.333 Advertising costs)

4. The increase in revenues for each Rs 1,000 spent on advertising within the relevant range is

a. Using the regression equation, 8.723 Rs 1,000 = Rs 8,723

b. Using the high-low equation, 8.333 Rs 1,000 = Rs 8,333

The high-low equation does fairly well in estimating the relationship between advertising costs and revenues. However, Ruha should usethe regression equation. The reason is that the regression equation uses information from all observations whereas the high-low method

relies only on the observations that have the highest and lowest values of the cost driver. These observations are generally not represen-

tative of all the data.

Cost estimation, cumulative average-time learning curve.1. Cost to Produce the Second through the Eighth Troop Deployment Boats:

Direct materials, 7 Rs 3,00,000 Rs 21,00,000Direct manufacturing labor, 39,130* Rs 90 35,21,700

Variable manufacturing overhead, 39,130 Rs 60 23,47,800

Other manufacturing overhead, 25% of Rs 35,21,700 8,80,425

Total costs Rs 88,49,925

*The direct manufacturing labor-hours to produce the second to eighth boats can be calculated in several ways, given the assumption of a cumulative

average-time learning curve of 85%:

a. Use of Table Format:

Cumulative Number of Units Cumulative Average-Time per Unit Cumulative Total Time

1 10,000.00 10,000

2 8,500.00 (10,000 0.85) 17,000

4 7,225.00 (8,500 0.85) 28,900

8 6,141.25 (7,225 0.85) 49,130

The direct labor-hours required to produce the second through the eighth boats is 49,130 10,000 = 39,130 hours.

b. Use of Formula:

y = aXb

where a = 10,000, X = 8, and b= 0.2345

y = 10,000 8 0.2345 = 6,141 hours (rounded)


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The total direct labor-hours for 8 units is 6,141 8 = 49,128 hours

The direct labor-hours required to produce the second through the eighth boats is 49,128 10,000 = 39,128 hours. (By taking the bfactorto 6 decimal digits, an estimate of 49,130 hours would result.)

Note: The question specifies that the tooling cost was assigned to the first boat. Although Bharat Company may well seek to ensure itstotal revenue covers the Rs 21,75,000 cost of the first boat, the concern in this question is only with the cost of producing seven more

PT109s.

2. Cost to Produce the Second through the Eighth Boats Assuming Linear Function for Direct Labor-Hours and Units Produced:

Direct materials, 7 Rs 3,00,000 Rs 21,00,000

Direct manufacturing labor, 7 10,000 hours Rs 90 63,00,000Variable manufacturing overhead, 7 10,000 hours Rs 60 42,00,000

Other manufacturing overhead, 25% of Rs 63,00,000 15,75,000

Total costs Rs 1,41,75,000

The difference in predicted costs is:Predicted cost in requirement 2 (based on linear cost function) Rs 1,41,75,000

Predicted cost in requirement 1 (based on an 85% learning curve) 88,49,925

Difference Rs 53,25,075

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