Mngt. Acctg. chapter 9

CHAPTER 9

COST BEHAVIOR: ANALYSIS AND USE

I. Questions

1. a. Variable cost: A variable cost is one that remains constant on a per unit basis, but which changes in total in direct relationship to changes in volume.

b. Fixed cost: A fixed cost is one that remains constant in total amount, but which changes, if expressed on a per unit basis, inversely with changes in volume.

c. Mixed cost: A mixed cost is a cost that contains both variable and fixed cost elements.

2. a. Unit fixed costs will decrease as volume increases.

b. Unit variable costs will remain constant as volume increases.

c. Total fixed costs will remain constant as volume increases.

d. Total variable costs will increase as volume increases.

3. a. Cost behavior: Cost behavior can be defined as the way in which costs change or respond to changes in some underlying activity, such as sales volume, production volume, or orders processed.

b. Relevant range: The relevant range can be defined as that range of activity within which assumptions relative to variable and fixed cost behavior are valid.

4. Although the accountant recognizes that many costs are not linear in relationship to volume at some points, he concentrates on their behavior within narrow bands of activity known as the relevant range. The relevant range can be defined as that range of activity within which assumptions as relative to variable and fixed cost behavior are valid. Generally, within this range an assumption of strict linearity can be used with insignificant loss of accuracy.

9-1

Chapter 9 Cost Behavior: Analysis and Use

5. The high-low method, the scattergraph method, and the least-squares regression method are used to analyze mixed costs. The least-squares regression method is generally considered to be most accurate, since it derives the fixed and variable elements of a mixed cost by means of statistical analysis. The scattergraph method derives these elements by visual inspection only, and the high-low method utilizes only two points in doing a cost analysis, making it the least accurate of the three methods.

6. The fixed cost element is represented by the point where the regression line intersects the vertical axis on the graph. The variable cost per unit is represented by the slope of the line.

7. The two assumptions are:

1. A linear cost function usually approximates cost behavior within the relevant range of the cost driver.

2. Changes in the total costs of a cost object are traceable to variations or changes in a single cost driver.

8. No. High correlation merely implies that the two variables move together in the data examined. Without economic plausibility for a relationship, it is less likely that a high level of correlation observed in one set of data will be found similarly in another set of data.

9. Refer to page 312 of the textbook.

10. The relevant range is the range of the cost driver in which a specific relationship between cost and cost driver is valid. This concept enables the use of linear cost functions when examining CVP relationships as long as the volume levels are within that relevant range.

11. A unit cost is computed by dividing some amount of total costs (the numerator) by the related number of units (the denominator). In many cases, the numerator will include a fixed cost that will not change despite changes in the denominator. It is erroneous in those cases to multiply the unit cost by activity or volume change to predict changes in total costs at different activity or volume levels.

9-2

Cost Behavior: Analysis and Use Chapter 9

12. Cost estimation is the process of developing a well-defined relationship between a cost object and its cost driver for the purpose of predicting the cost. The cost predictions are used in each of the management functions:

Strategic Management: Cost estimation is used to predict costs of alternative activities, predict financial impacts of alternative strategic choices, and to predict the costs of alternative implementation strategies.

Planning and Decision Making: Cost estimation is used to predict costs so that management can determine the desirability of alternative options and to budget expenditures, profits, and cash flows.

Management and Operational Control: Cost estimation is used to develop cost standards, as a basis for evaluating performance.

Product and Service Costing: Cost estimation is used to allocate costs to products and services or to charge users for jointly incurred costs.

13. The five methods of cost estimation are:

a. Account Classification. Advantages: simplicity and ease of use. Disadvantages: subjectivity of method and some costs are a mix of both variable and fixed.

b. Visual fit. The visual fit method is easy to use, and requires only that the data is graphed. Disadvantages are that the scale of the graph may limit ability to estimate costs accurately and in both graphical and tabular form, significant perceptual errors are common.

c. High-Low. Because of the precision in the development of the equation, it provides a more consistent estimate than the visual fit and is not difficult to use. Disadvantages: uses only two selected data points and is, therefore, subjective.

d. Work Measurement. The advantage is accurate estimates through detailed study of the different operations in the product process, but like regression, it is more complex.

e. Regression. Quantitative, objective measures of the precision and accuracy and reliability of the model are the advantages of this model; disadvantages are its complexity: the effort, expense, and expertise necessary to utilize this method.

14. Implementation problems with cost estimation include:

a. cost estimates outside of the relevant range may not be reliable.

9-3


b. sufficient and reliable data may not be available.

c. cost drivers may not be matched to dependent variables properly in each observation.

d. the length of the time period for each observation may be too long, so that the underlying relationship between the cost driver and the variable to be estimated is difficult to isolate from the numerous variables and events occurring in that period of time; alternatively the period may be too short, so that the data is likely to be affected by accounting errors in which transactions are not properly posted in the period in which they occurred.

e. dependent variables and cost drivers may be affected by trend or seasonality.

f. when extreme observations (outliers) are used the reliability of the results will be diminished.

g. when there is a shift in the data, as, for example, a new product is introduced or when there is a work stoppage, the data will be unreliable for future estimates.

15. The dependent variable is the cost object of interest in the cost estimation. An important issue in selecting a dependent variable is the level of aggregation in the variable. For example, the company, plant, or department may all be possible levels of data for the cost object. The choice of aggregation level depends on the objectives for the cost estimation, data availability, reliability, and cost/benefit considerations. If a key objective is accuracy, then a detailed level of analysis is often preferred. The detail cost estimates can then be aggregated if desired.

16. Nonlinear cost relationships are cost relationships that are not adequately explained by a single linear relationship for the cost driver(s). In accounting data, a common type of nonlinear relationship is trend and seasonality. For a trend example, if sales increase by 8% each year, the plot of the data for sales with not be linear with the driver, the number of years. Similarly, sales which fluctuate according to a seasonal pattern will have a nonlinear behavior. A different type of nonlinearity is where the cost driver and the dependent variable have an inherently nonlinear relationship. For example, payroll costs as a dependent variable estimated by hours worked and wage rates is nonlinear, since the relationship is multiplicative and therefore not the additive linear model assumed in regression analysis.

9-4


17. The advantages of using regression analysis include that it:

a. provides an estimation model with best fit (least squared error) to the data

b. provides measures of goodness of fit and of the reliability of the model which can be used to assess the usefulness of the specific model, in contrast to the other estimation methods which provide no means of self-evaluation

c. can incorporate multiple independent variables

d. can be adapted to handle non-linear relationships in the data, including trends, shifts and other discontinuities, seasonality, etc.

e. results in a model that is unique for a given set of data

18. High correlation exists when the changes in two variables occur together. It is a measure of the degree of association between the two variables. Because correlation is determined from a sample of values, there is no assurance that it measures or describes a cause and effect relationship between the variables.

II. Exercises

Exercise 1 (Cost Classification)

1. b2. f3. e4. i5. e6. h7. l8. a9. j10. k11. c or d12. g

Exercise 2 (Cost Estimation; High-Low Method)

Requirement (1)

9-5


Cost equation using square fee as the cost driver:

Variable costs:

Fixed costs:

P4,700 = Fixed Cost + P1.134 x 4,050Fixed Cost = P107

Equation One: Total Cost = P107 + P1.134 x square feet

There are two choices for the High-Low points when using openings for the cost driver. At 11 openings there is a cost of P2,800 and at 10 openings there is a cost of P2,875.

Cost equation using 11 openings as the cost driver:

Variable costs:

Fixed costs:

P4,700 = Fixed Cost + P237.50 x 19Fixed Cost = P187.50

Equation Two: Total Cost = P187.50 + P237.50 x openings

Cost equation using 10 openings as the cost driver:

Variable costs:

9-6

P4,700 – P2,8004,050 – 2,375 = P1.134

P4,700 – P2,80019 – 11 = P237.50

P4,700 – P2,87519 – 10 = P202.78


Fixed costs:

P4,700 = Fixed Cost + P202.78 x 19Fixed Cost = P847.18

Equation Three: Total Cost = P847.18 + P202.78 x openings

Predicted total cost for a 3,200 square foot house with 14 openings using equation one:

P107 + P1.134 x 3,200 = P3,735.80

Predicted total cost for a 3,200 square foot house with 14 openings using equation two:

P187.50 + P237.50 x 14 = P3,512.50

Predicted total cost for a 3,200 square foot house with 14 openings using equation three:

P847.18 + P202.78 x 14 = P3,686.10

There is no simple method to determine which prediction is best when using the High-Low method. In contrast, regression provides quantitative measures (R-squared, standard error, t-values,…) to help asses which regression equation is best.

Predicted cost for a 2,400 square foot house with 8 openings, using equation one:

P107 + P1.134 x 2,400 = P2,828.60

We cannot predict with equation 2 or equation 3 since 8 openings are outside the relevant range, the range for which the high-low equation was developed.

Requirement 2

Figure 9-A shows that the relationship between costs and square feet is relatively linear without outliers, while Figure 9-B shows a similar result for

9-7


the relationship between costs and number of openings. From this perspective, both variables are good cost drivers.

Figure 9-A

P0

P500

P1,000

P1,500

P2,000

P2,500

P3,000

P3,500

P4,000

P4,500

P5,0002,3

75

2,4

50

2,6

00

2,6

00

2,6

50

2,7

00

2,8

00

2,8

50

3,0

10

3,5

50

3,7

00

4,0

50

Square Feet

Co

st

Figure 9-B

9-8


Cost versus No. of Openings

P0

P500

P1,000

P1,500

P2,000

P2,500

P3,000

P3,500

P4,000

P4,500

P5,000

10 11 11 12 12 13 13 13 15 16 16 19

Number of Openings

Co

st

Exercise 3 (Cost Estimation; Account Classification)

Requirement 1

Fixed Costs:Rent P10,250Depreciation 400Insurance 750Advertising 650Utilities 1,250Mr. Black’s salary 18,500

Total P31,800Variable Costs:

Wages P17,800CD Expense 66,750Shopping Bags 180

Total P84,730

Variable Costs Per Unit = P84,730 / 8,900 = P95.20

9-9


Cost Function Equation: y = P31,800 + P95.20 x (CD’s sold)

Requirement 2

New Sales = 8,900 x 1.25 = 11,125 units

= round to 11,130

Total Costs = P31,800 + P95.20 x (11,130) = P137,760

Per Unit Total Costs = P137,760 / 11,130 = P123.80

Add P1 profit per disc: P123.80 + P10 = P133.80

Requirement 3

Adjusted New Sales = 8,900 x 11.50 = 10,240 units

Revenue = P133.80 x (10,240) = P137,010

Total Cost = P31,800 + P95.20 x (10,240) = P129,280

Cost Per Disc = P129,280 / 10,240 = P126.30

Profit Per Disk = P133.80 – P126.30 = P7.50

Exercise 4 (Cost Estimation Using Graphs; Service)

Requirement 1

9-10


Sales and Advertising Expense

P0

P20,000

P40,000

P60,000

P80,000

P100,000

P120,000

P140,000

P160,000

P2,5

00

P3,0

00

P3,5

00

P4,0

00

P4,5

00

P5,0

00

P5,5

00

Advertising Expense

Sale

s

Requirement 2

There seems to be a positive linear relationship for the data between P2,500 and P4,000 of advertising expense. Llanes’ analysis is correct within this relevant range but not outside of it. Notice that the relationship between advertising expense and sales changes at P4,000 of expense.

III. Problems

Problem 1

Requirement (a) Miles Driven

Total Annual Cost*

High level of activity........................ 120,000 P13,920Low level of activity......................... 80,000 10,880

Difference.................................... 40,000 P 3,040

* 120,000 miles x P0.116 = P13,920. 80,000 miles x P0.136 = P10,880.

Variable cost per mile:

9-11


Change in cost, P3,040 Change in activity,40,000

Fixed cost per year:Total cost at 120,000 miles.................................. P13,920Less variable cost element: 120,000 x P0.076..... 9,120

Fixed cost per year........................................... P 4,800

Requirement (b)

Y = P4,800 + P0.076X

Requirement (c)

Fixed cost.................................................................. P 4,800Variable cost: 100,000 miles x P0.076...................... 7,600

Total annual cost................................................. P12,400

Problem 2

Requirement 1

Cost of goods sold.................................................... VariableShipping expense..................................................... MixedAdvertising expense................................................. FixedSalaries and commissions......................................... MixedInsurance expense.................................................... FixedDepreciation expense................................................ Fixed

Requirement 2

Analysis of the mixed expenses:

Units Shipping Expense

Salaries and Comm.

ExpenseHigh level of activity.............. 4,500 P56,000 P143,000Low level of activity............... 3,000 44,000 107,000

Difference......................... 1,500 P12,000 P 36,000

Variable cost element: Change in cost

Change in activity

9-12

= P0.076 per mile.

= Variable rate

P12,000 1,500 units = P8 per unit.


Shipping expense:

Salaries and comm. expense:

Fixed cost element:Shipping Expense

Salaries and Comm. Expense

Cost at high level of activity............... P56,000 P143,000Less variable cost element:

4,500 units x P8........................... 36,0004,500 units x P24.........................

108,000

Fixed cost element............................. P20,000 P 35,000

The cost elements are:Shipping expense: P20,000 per month plus P8 per unit or Y = P20,000 + P8X.

Salaries and comm. expense: P35,000 per month plus P24 per unit or Y = P35,000 + P24X.

Requirement 3 LILY COMPANY Income Statement

For the Month Ended June 30

Sales in units................................................. 4,500 Sales revenues............................................... P630,000Less variable expenses:

Cost of goods sold (@P56)....................... P252,000Shipping expense (@P8)........................... 36,000Salaries and commission expense

(@P24).................................................. 108,000 396,000 Contribution margin...................................... 234,000

Less fixed expense:Shipping expense...................................... 20,000Advertising............................................... 70,000Salaries and commissions......................... 35,000

9-13

P36,000 1,500 units = P24 per unit.


Insurance.................................................. 9,000Depreciation............................................. 42,000 176,000

Net income.................................................... P 58,000

Problem 3

Requirement 1

YearNumber of

Leagues (X)Total Cost

(Y) XY X2

2004 5 P13,000 P 65,000 252005 2 7,000 14,000 42006 4 10,500 42,000 162007 6 14,000 84,000 362008 3 10,000 30,000 9

20 P54,500 P235,000 90

n ( XY) - ( X) ( Y) n (X2) - (X)2

5 (235,000) - (20) (54,500) 5 (90) - (20)2

= 1,700

( Y) - b( X) n

(54,500) - 1,700 (20) 5

= P4,100

Therefore, the variable cost per league is P1,700 and the fixed cost is P4,100 per year.

Requirement 2

Y = P4,100 + P1,700X

9-14

b =

=

a =

=


Requirement 3

The expected value total would be:

Fixed cost............................................................ P 4,100Variable cost (7 leagues x P1,700)....................... 11,900

Total cost........................................................ P16,000

The problem with using the cost formula from (2) to derive this total cost figure is that an activity level of 7 sections lies outside the relevant range from which the cost formula was derived. [The relevant range is represented by a solid line on the graph in requirement 4 below.]

Although an activity figure may lie outside the relevant range, managers will often use the cost formula anyway to compute expected total cost as we have done above. The reason is that the cost formula frequently is the only basis that the manager has to go on. Using the cost formula as the starting point should not present a problem so long as the manager is alert for any unusual problems that the higher activity level might bring about.

Requirement 4

Problem 4 (Regression Analysis, Service Company)

Requirement 1

9-15

P16,000

P14,000

P12,000

P10,000

P8,000

P6,000

P4,000

P2,000

P-0 1 2 3 8 6 5 4 7

Y

X


Figure 9-C plots the relationship between labor-hours and overhead costs and shows the regression line.

y = P48,271 + P3.93 X

Economic plausibility. Labor-hours appears to be an economically plausible driver of overhead cost for a catering company. Overhead costs such as scheduling, hiring and training of workers, and managing the workforce are largely incurred to support labor.

Goodness of fit. The vertical differences between actual and predicted costs are extremely small, indicating a very good fit. The good fit indicates a strong relationship between the labor-hour cost driver and overhead costs.

Slope of regression line. The regression line has a reasonably steep slope from left to right. The positive slope indicates that, on average, overhead costs increase as labor-hours increase.

Requirement 2

The regression analysis indicates that, within the relevant range of 2,500 to 7,500 labor-hours, the variable cost per person for a cocktail party equals:

Food and beverages P15.00Labor (0.5 hrs. x P10 per hour) 5.00Variable overhead (0.5 hrs. x P3.93 per labor-hour) 1.97Total variable cost per person P21.97

Requirement 3

To earn a positive contribution margin, the minimum bid for a 200-person cocktail party would be any amount greater than P4,394. This amount is calculated by multiplying the variable cost per person of P21.97 by the 200 people. At a price above the variable costs of P4,394, Bobby Gonzales will be earning a contribution margin toward coverage of his fixed costs.

Of course, Bobby Gonzales will consider other factors in developing his bid including (a) an analysis of the competition – vigorous competition will limit Gonzales’ ability to obtain a higher price (b) a determination of whether or not his bid will set a precedent for lower prices – overall, the prices Bobby Gonzales charges should generate enough contribution to cover fixed costs

9-16


and earn a reasonable profit, and (c) a judgment of how representative past historical data (used in the regression analysis) is about future costs.

Figure 9-CRegression Line of Labor-Hours on Overhead Costs for Bobby Gonzales’ Catering Company

P0

P10,000

P20,000

P30,000

P40,000

P50,000

P60,000

P70,000

P80,000

P90,000

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

Cost Driver: Labor-Hours

Ove

rhea

d C

ost

s

Problem 5 (Linear Cost Approximation)

Requirement 1

The linear cost function is plotted in Figure 9-D.

9-17

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

= P529,000 – P400,0007,000 – 4,000

= P43.00

Constant (a) = P529,000 – P43.00 (7,000)

= P228,000

Cost function = P228,000 + P43.00 (professional labor-hours)


No, the constant component of the cost function does not represent the fixed overhead cost of the ABS 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.

Requirement 2

A comparison at various levels of professional labor-hours follows. The linear cost function is based on formula of P228,000 per month plus P43.00 per professional labor-hours.

Total overhead cost behavior:

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6Actual total overhead

costs P340,000 P400,000 P435,000 P477,000 P529,000 P587,000Linear approximation 357,000 400,000 443,000 486,000 529,000 572,000Actual minus linear

approximation P(17,000) P 0 P (8,000) P (9,000) P 0 P15,000Professional labor-

hours3,000 4,000 5,000 6,000 7,000 8,000

The data are shown in Figure 9-D. The linear cost function overstates costs by P8,000 at the 5,000-hour level and understates costs by P15,000 at the 8,000-hour level.

Requirement 3

Based on Actual

Based on Linear Cost

FunctionContribution before deducting incremental

overhead P38,000 P38,000Incremental overhead 35,000 43,000Contribution after incremental overhead P 3,000 P (5,000)

The total contribution margin actually forgone is P3,000.Figure 9-DLinear Cost Function Plot of Professional Labor-Hourson Total Overhead Costs for ABS Consulting Group

9-18


P0

P100,000

P200,000

P300,000

P400,000

P500,000

P600,000

P700,000

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

Professional Labor-Hours Billed

To

tal O

verh

ead

Co

sts

IV. Multiple Choice Questions

1. A 11. C * 21. C 31. D 41. B2. D 11. C * 22. D 32. B 42. D3. B 12. C 23. C 33. A 43. C4. A 13. A 24. A 34. B5. B 14. D 25. D 35. A6. B 15. C 26. B 36. D7. C 16. D 27. D 37. B8. D 17. B 28. B 38. C9. C 18. C 29. A 39. B10. A 19. C 30. D 40. D

* Supporting Computations:

11. (10,000 x 2) – (P3,000 x 2) – P5,000 = P9,000

12. [(P20 + P3 + P6) x 2,000 units] + (P10 x 1,000 units) = P68,000

9-19

Mngt. Acctg. chapter 9

Documents

Transcript of Mngt. Acctg. chapter 9