Chapter-3-Answer - COST BEHAVIOR: ANALYSIS AND USE PDF

Preview

Summary

COST ACCOUNTING AND CONTROL – Solutions ManualCHAPTER 3 COST BEHAVIOR: ANALYSIS AND USEI. Answers to Questions 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 ...

Description

COST ACCOUNTING AND CONTROL – Solutions Manual CHAPTER 3 COST BEHAVIOR: ANALYSIS AND USE

I. Answers to Questions 1.

a. b. c.

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

2.

a. b. c. d.

Unit fixed costs will decrease as volume increases. Unit variable costs will remain constant as volume increases. Total fixed costs will remain constant as volume increases. 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. 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.

b.

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.

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.

3-1

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 64 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. 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

3-2

d. e.

to use. Disadvantages: uses only two selected data points and is, therefore, subjective. 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. 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. 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. 3-3

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 selfevaluation 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. 19. An activity base is a measure of whatever causes the incurrence of a variable cost. Examples of activity bases include units produced, units sold, letters typed, beds in a hospital, meals served in a cafe, service calls made, etc. 20. (a) Variable cost: A variable cost remains constant on a per unit basis, but increases or decreases in total in direct relation to changes in activity. (b) Mixed cost: A mixed cost is a cost that contains both variable and fixed cost elements. (c) Step-variable cost: A step-variable cost is a cost that is incurred in large chunks, and which increases or decreases only in response to fairly wide changes in activity.

Mixed Cost Variable Cost

Cost

Step-Variable Cost

Activity

21. The linear assumption is reasonably valid provided that the cost formula is used only within the relevant range. 3-4

22. A discretionary fixed cost has a fairly short planning horizon—usually a year. Such costs arise from annual decisions by management to spend on certain fixed cost items, such as advertising, research, and management development. A committed fixed cost has a long planning horizon—generally many years. Such costs relate to a company’s investment in facilities, equipment, and basic organization. Once such costs have been incurred, they are “locked in” for many years. 23. a. b. c.

Committed Discretionary Discretionary

d. e. f.

Committed Committed Discretionary

24. The high-low method uses only two points to determine a cost formula. These two points are likely to be less than typical since they represent extremes of activity. 25. The term “least-squares regression” means that the sum of the squares of the deviations from the plotted points on a graph to the regression line is smaller than could be obtained from any other line that could be fitted to the data. 26. Ordinary single least-squares regression analysis is used when a variable cost is a function of only a single factor. If a cost is a function of more than one factor, multiple regression analysis should be used to analyze the behavior of the cost. II. Answers to Exercises Exercise 1 (Cost Classification) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

b f e i e h l a j k c or d g

Exercise 2 (Cost Estimation; Account Classification) Requirement 1 Fixed Costs: 3-5

Rent Depreciation Insurance Advertising Utilities Mr. Black’s salary Total Variable Costs: Wages CD Expense Shopping Bags Total Variable Costs Per Unit

P10,250 400 750 650 1,250 18,500 P31,800 P17,800 66,750 180 P84,730 = P84,730 / 8,900 = P95.20

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

3-6

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 3 (Cost Estimation Using Graphs; Service) Requirement 1

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. Exercise 4 (Fixed and Variable Cost Behavior) Requirement (1) 3-7

Cups of Coffee Served in a Week 1,800 1,900 2,000 P11,000 P11,000 P11,000 4,680 4,940 5,200 P15,680 P15,940 P16,200 P8.71 P8.39 P8.10

Fixed cost Variable cost Total cost Cost per cup of coffee served * * Total cost ÷ cups of coffee served in a week Requirement (2)

The average cost of a cup of coffee declines as the number of cups of coffee served increases because the fixed cost is spread over more cups of coffee. Exercise 5 (High-Low Method) Requirement (1) Month High activity level (August)......................... Low activity level (October)......................... Change...........................................................

Occupancy-Days 3,608 186 3,422

Electrical Costs P8,111 1,712 P6,399

Variable cost = Change in cost ÷ Change in activity = P6,399 ÷ 3,422 occupancy-days = P1.87 per occupancy-day Total cost (August)......................................................................................................... P8,111 Variable cost element (P1.87 per occupancy-day × 3,608 occupancy-days)............................................... 6,747 Fixed cost element......................................................................................................... P1,364 Requirement (2) Electrical costs may reflect seasonal factors other than just the variation in occupancy days. For example, common areas such as the reception area must be lighted for longer periods during the winter. This will result in seasonal effects on the fixed electrical costs. Additionally, fixed costs will be affected by how many days are in a month. In other words, costs like the costs of lighting common areas are variable with respect to the number of days in the month, but are fixed with respect to how many rooms are occupied during the month.

3-8

Other, less systematic, factors may also affect electrical costs such as the frugality of individual guests. Some guests will turn off lights when they leave a room. Others will not. Exercise 6 (Least-Squares Regression) The least-squares regression estimates of fixed and variable costs can be computed using any of a variety of statistical and mathematical software packages or even by hand. Month January............................................ February.......................................... March.............................................. April................................................ May................................................. June................................................. July.................................................. August............................................. September....................................... October........................................... November....................................... December........................................ Intercept Slope RSQ

Rental Returns 2,310 2,453 2,641 2,874 3,540 4,861 5,432 5,268 4,628 3,720 2,106 2,495

Car Wash Costs P10,113 P12,691 P10,905 P12,949 P15,334 P21,455 P21,270 P19,930 P21,860 P18,383 P 9,830 P11,081

P2,296 P3.74 0.92

The intercept provides the estimate of the fixed cost element, P2,296 per month, and the slope provides the estimate of the variable cost element, P3.74 per rental return. Expressed as an equation, the relation between car wash costs and rental returns is Y = P2,296 + P3.74X where X is the number of rental returns. Note that the R 2 is 0.92, which is quite high, and indicates a strong linear relationship between car wash costs and rental returns. While not a requirement of the exercise, it is always a good to plot the data on a scattergraph. The scattergraph can help spot nonlinearities or other problems with the data. In this case, the regression line (shown below) is a reasonably good approximation to the relationship between car wash costs and rental returns. 3-9

III. Answers to Multiple Choice Questions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A D B A B B C D C A

11. 11. 12. 13. 14. 15. 16. 17. 18. 19.

C* C* C A D C D B C C

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

C D C A D B D B A D

* Supporting Computations : 11. (10,000 x 2) – (P3,000 x 2) – P5,000 = P9,000

3-10

31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

D B A B A D B C B D

41. B 42. D 43. C

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

IV. Answers to Problems Problem 1 Requirement (a) High level of activity............................... Low level of activity................................ Difference...........................................

Miles Driven 120,000 80,000 40,000

Total Annual Cost* P13,920 10,880 P 3,040

* 120,000 miles x P0.116 = P13,920. 80,000 miles x P0.136 = P10,880. Variable cost per mile: Change in cost, P3,040 Change in activity, 40,000 = P0.076 per mile. Fixed cost per year: Total cost at 120,000 miles............................................ Less variable cost element: 120,000 x P0.076............. Fixed cost per year.....................................................

P13,920 9,120 P 4,800

Requirement (b) Y = P4,800 + P0.076X Requirement (c) Fixed cost.............................................................................. Variable cost: 100,000 miles x P0.076................................ Total annual cost............................................................

P 4,800 7,600 P12,400

Problem 2 Requirement 1 Cost of goods sold............................................................... Shipping expense................................................................ Advertising expense............................................................ Salaries and commissions................................................... Insurance expense............................................................... Depreciation expense.......................................................... Requirement 2 3-11

Variable Mixed Fixed Mixed Fixed Fixed

Analysis of the mixed expenses:

High level of activity.................... Low level of activity.................... Difference..............................

Salaries and Comm. Expense P143,000 107,000 P 36,000

Shipping Expense P56,000 44,000 P12,000

Units 4,500 3,000 1,500

Variable cost element: Change in cost Change in activity = Variable rate Shipping expense:

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

Salaries and comm. expense:

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

Fixed cost element: Cost at high level of activity..................... Less variable cost element: 4,500 units x P8.................................. 4,500 units x P24................................

Shipping Expense P56,000

Salaries and Comm. Expense P143,000

36,000 108,000

Fixed cost element..................................... P20,000 P 35,000 The cost elements are: Shipping expense: P20,000 per month plus P8 per unit or Y = P...