MANAGEMENT ACCOUNTING - Solutions Manual CHAPTER COST BEHAVIOR: ANALYSIS AND USE I 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 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 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 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 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 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 9-1 Chapter Cost Behavior: Analysis and Use 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 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 The two assumptions are: A linear cost function usually approximates cost behavior within the relevant range of the cost driver Changes in the total costs of a cost object are traceable to variations or changes in a single cost driver 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 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 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 9-2 Cost Behavior: Analysis and Use Chapter 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 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 9-3 Chapter Cost Behavior: Analysis and Use 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 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 9-4 Cost Behavior: Analysis and Use Chapter 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 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 9-5 Chapter Cost Behavior: Analysis and Use Mixed Cost Variable Cost Cost Step-Variable Cost Activity 21 The linear assumption is reasonably valid providing that the cost formula is used only within the relevant range 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 Committed b Discretionary c Discretionary d Committed e Committed f 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 9-6 Cost Behavior: Analysis and Use Chapter of more than one factor, multiple regression analysis should be used to analyze the behavior of the cost II Exercises Exercise (Cost Classification) 10 11 12 b f e i e h l a j k c or d g Exercise (Cost Estimation; High-Low Method) Requirement (1) Cost equation using square fee as the cost driver: Variable costs: P4,700 – P2,800 4,050 – 2,375 = P1.134 Fixed costs: P4,700 = Fixed Cost + P1.134 x 4,050 Fixed 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: 9-7 Chapter Cost Behavior: Analysis and Use Variable costs: P4,700 – P2,800 19 – 11 = P237.50 Fixed costs: P4,700 = Fixed Cost + P237.50 x 19 Fixed Cost = P187.50 Equation Two: Total Cost = P187.50 + P237.50 x openings Cost equation using 10 openings as the cost driver: Variable costs: P4,700 – P2,875 19 – 10 = P202.78 Fixed costs: P4,700 = Fixed Cost + P202.78 x 19 Fixed 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 9-8 Cost Behavior: Analysis and Use Chapter 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 openings, using equation one: P107 + P1.134 x 2,400 = P2,828.60 We cannot predict with equation or equation since openings are outside the relevant range, the range for which the high-low equation was developed Requirement 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 the relationship between costs and number of openings From this perspective, both variables are good cost drivers Figure 9-A 9-9 Chapter Cost Behavior: Analysis and Use Figure 9-B 9-10 Cost Behavior: Analysis and Use Chapter where X is the number of rental returns Note that the R 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 III Problems Problem Requirement (a) High level of activity 9-17 Miles Driven 120,000 Total Annual Cost* P13,920 Chapter Cost Behavior: Analysis and Use Low level of activity Difference 80,000 40,000 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 P13,920 Less 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 4,800 Variable cost: 100,000 miles x P0.076 7,600 Total annual cost P12,400 Problem Requirement Cost of goods sold Shipping expense Advertising expense Salaries and commissions Insurance expense Depreciation expense Variable Mixed Fixed Mixed Fixed Fixed Requirement Analysis of the mixed expenses: High level of activity Low level of activity Difference 9-18 Units 4,500 3,000 1,500 Shipping Expense P56,000 44,000 P12,000 Salaries and Comm Expense P143,000 107,000 P 36,000 Cost Behavior: Analysis and Use Chapter Variable cost element: Change in cost = Variable rate Change in activity Shipping expense: P12,000 = P8 per unit 1,500 units P36,000 Salaries and comm expense: 1,500 units = P24 per unit Fixed cost element: Shipping Expense Cost at high level of activity Less variable cost element: 4,500 units x P8 4,500 units x P24 P56,000 Fixed cost element P20,000 Salaries and Comm Expense P143,000 36,000 108,000 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 LILY COMPANY Income Statement For the Month Ended June 30 Sales in units 4,500 Sales revenues P630,000 Less variable expenses: Cost of goods sold (@P56) P252,000 9-19 Chapter Cost Behavior: Analysis and Use Shipping expense (@P8) 36,000 Salaries and commission expense (@P24) 108,000 396,000 Contribution margin 234,000 Less fixed expense: Shipping expense 20,000 Advertising 70,000 Salaries and commissions 35,000 Insurance 9,000 Depreciation 42,000 176,000 Net income P 58,000 Problem Requirement Number of Leagues (X) 20 Year 2004 2005 2006 2007 2008 b a Total Cost (Y) P13,000 7,000 10,500 14,000 10,000 P54,500 = n (∑XY) - (∑X) (∑Y) n (∑X2) - (∑X)2 = (235,000) - (20) (54,500) (90) - (20)2 = 1,700 = (∑Y) - b(∑X) n = (54,500) - 1,700 (20) = P4,100 XY P 65,000 14,000 42,000 84,000 30,000 P235,000 X2 25 16 36 90 Therefore, the variable cost per league is P1,700 and the fixed cost is P4,100 per year Requirement 9-20 Cost Behavior: Analysis and Use Chapter Y = P4,100 + P1,700X Requirement The expected value total would be: Fixed cost P 4,100 Variable 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 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 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 Y P16,000 P14,000 P12,000 P10,000 P8,000 P6,000 P4,000 P2,000 P- 9-21 X Chapter Cost Behavior: Analysis and Use Problem (Regression Analysis, Service Company) Requirement 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 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 P15.00 Labor (0.5 hrs x P10 per hour) 5.00 Variable overhead (0.5 hrs x P3.93 per labor-hour) 1.97 Total variable cost per person P21.97 Requirement 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 9-22 Cost Behavior: Analysis and Use Chapter 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 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-C Regression Line of Labor-Hours on Overhead Costs for Bobby Gonzales’ Catering Company 9-23 Chapter Cost Behavior: Analysis and Use Problem (Linear Cost Approximation) Requirement Slope coefficient (b) = = Constant (a) Difference in cost Difference in labor-hours P529,000 – P400,000 = 7,000 – 4,000 P43.00 = P529,000 – P43.00 (7,000) = P228,000 Cost function = P228,000 + P43.00 (professional labor-hours) The linear cost function is plotted in Figure 9-D 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 9-24 Cost Behavior: Analysis and Use Chapter 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 Actual total overhead costs Linear approximation Actual minus linear approximation Professional laborhours P340,000 357,000 P(17,000) 3,000 Month P400,000 400,000 P 4,000 Month Month P435,000 443,000 P477,000 486,000 P (8,000) 5,000 P (9,000) 6,000 Month Month P529,000 529,000 P 7,000 P587,000 572,000 P15,000 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 Contribution before deducting incremental overhead Incremental overhead Contribution after incremental overhead Based on Actual Based on Linear Cost Function P38,000 35,000 P 3,000 P38,000 43,000 P (5,000) The total contribution margin actually forgone is P3,000 Figure 9-D Linear Cost Function Plot of Professional Labor-Hours on Total Overhead Costs for ABS Consulting Group 9-25 Chapter Cost Behavior: Analysis and Use Problem (Cost Behavior) The variable cost per hour can be computed as follows: P20,000 / 5,000 hours = P4 per hour Therefore, the missing amounts are as follows: 5,000 Total costs: Variable costs (@ P4 per hour) Fixed costs Total costs Cost per hour: Variable cost P 20,000 168,000 P 188,000 5,000 P 4.00 9-26 Hours of Operating Time 6,000 7,000 P 24,000 168,000 P 192,000 P 28,000 168,000 P 196,000 8,000 P 32,000 168,000 P 200,000 Hours of Operating Time 6,000 7,000 P 4.00 P 4.00 8,000 P 4.00 Cost Behavior: Analysis and Use Chapter Fixed cost Total cost per hour P 33.60 37.60 P 28.00 32.00 P 24.00 28.00 P 21.00 25.00 Observe that the total variable costs increase in proportion to the number of hours of operating time, but that these costs remain constant at P4 if expressed on a per hour basis In contrast, the total fixed costs not change with changes in the level of activity They remain constant at P168,000 within the relevant range With increases in activity, however, the fixed cost per hour decreases, dropping from P33.60 per hour when the boats are operated 5,000 hours a period to only P21.00 per hour when the boats are operated 8,000 hours a period Because of this troublesome aspect of fixed costs, they are most easily (and most safely) dealt with on a total basis, rather than on a unit basis, in cost analysis work Problem (High-Low Method) Requirement (1) The first step in the high-low method is to identify the periods of the lowest and highest activity Those periods are November (1,100 patients admitted) and June (1,900 patients admitted) The second step is to compute the variable cost per unit using those two data points: Month High activity level (June) Low activity level (November) Change Variable cost = = Number of Patients Admitted 1,900 1,100 800 Admitting Department Costs P15,200 12,800 P 2,400 Change in cost Change in activity P240,000 800 patients admitted = P3 per patient admitted 9-27 Chapter Cost Behavior: Analysis and Use The third step is to compute the fixed cost element by deducting the variable cost element from the total cost at either the high or low activity In the computation below, the high point of activity is used: Fixed cost element = = = Total cost – Variable cost element P15,200 – (P3 per patient admitted x 1,900 patients admitted) P9,500 Requirement (2) The cost formula is Y = P9,500 + P3X Problem (Scattergraph Analysis; Selection of an Activity Base) Requirement (1) The completed scattergraph for the number of units produced as the activity base is presented below: 5,000 4,500 Janitorial Labor Cost 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0 20 40 60 80 100 120 140 Units Produced Requirement (2) The completed scattergraph for the number of workdays as the activity base is presented below: 9-28 Cost Behavior: Analysis and Use Chapter Requirement (3) 5,000 4,500 Janitorial Labor Cost 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0 10 12 14 16 18 20 22 24 Number of Janitorial Workdays The number of workdays should be used as the activity base rather than the 9-29 Chapter Cost Behavior: Analysis and Use number of units produced There are several reasons for this First, the scattergraphs reveal that there is a much stronger relationship (i.e., higher correlation) between janitorial costs and number of workdays than between janitorial costs and number of units produced Second, from the description of the janitorial costs, one would expect that variations in those costs have little to with the number of units produced Two janitors each work an eight-hour shift—apparently irrespective of the number of units produced or how busy the company is Variations in the janitorial labor costs apparently occur because of the number of workdays in the month and the number of days the janitors call in sick Third, for planning purposes, the company is likely to be able to predict the number of working days in the month with much greater accuracy than the number of units that will be produced Note that the scattergraph in part (1) seems to suggest that the janitorial labor costs are variable with respect to the number of units produced This is false Janitorial labor costs vary, but the number of units produced isn’t the cause of the variation However, since the number of units produced tends to go up and down with the number of workdays and since the janitorial labor costs are driven by the number of workdays, it appears on the scattergraph that the number of units drives the janitorial labor costs to some extent Analysts must be careful not to fall into this trap of using the wrong measure of activity as the activity base just because it appears there is some relationship between cost and the measure of activity Careful thought and analysis should go into the selection of the activity base IV Multiple Choice Questions 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 31 32 33 34 35 36 37 38 39 40 * Supporting Computations: 11 (10,000 x 2) – (P3,000 x 2) – P5,000 = P9,000 9-30 D B A B A D B C B D 41 B 42 D 43 C Cost Behavior: Analysis and Use Chapter 12 [(P20 + P3 + P6) x 2,000 units] + (P10 x 1,000 units) = P68,000 9-31 ... costs and number of openings From this perspective, both variables are good cost drivers Figure 9-A 9-9 Chapter Cost Behavior: Analysis and Use Figure 9-B 9-1 0 Cost Behavior: Analysis and Use Chapter. .. P2,000 P- 9-2 1 X Chapter Cost Behavior: Analysis and Use Problem (Regression Analysis, Service Company) Requirement Figure 9-C plots the relationship between labor-hours and overhead costs and shows... Processed 9-1 4 8,000 10,000 Cost Behavior: Analysis and Use Chapter Requirement (2) (Students’ answers will vary considerably due to the inherent imprecision and subjectivity of the quick -and- dirty