Unformatted text preview: CHAPTER 10 DETERMINING HOW COSTS BEHAVE 101 The two assumptions are 1. Variat ions in the level o f a single act ivit y (the cost driver) explain t he variat ions in the related total costs. 2. Cost behavior is approximated by a linear cost funct ion within the relevant range. A linear cost funct ion is a cost funct ion where, within the relevant range, the graph of total costs versus the level o f a single act ivit y forms a straight line. 102 Three alternat ive linear cost functions are 1. Variable cost funct ion––a cost funct ion in which total costs change in proportion to the changes in the level o f activit y in the relevant range. 2. Fixed cost funct ion––a cost funct ion in which total costs do not change wit h changes in the level o f act ivit y in the relevant range. 3. Mixed cost funct ion––a cost funct ion that has both variable and fixed elements. Total costs change but not in proportion to the changes in the level of act ivit y in the relevant range. 103 A linear cost funct ion is a cost function where, within the relevant range, the graph o f total costs versus the level of a single act ivit y related to that cost is a straight line. An example o f a linear cost funct ion is a cost funct ion for use of a telephone line where the terms are a fixed charge o f $10,000 per year plus a $2 per minute charge for phone use. A nonlinear cost funct io n is a cost funct ion where, within the relevant range, the graph o f total costs versus the level o f a single activit y related to that cost is not a straight line. Examples include econo mies o f scale in advert ising where an agency can double the number o f advertisements for less than twice the costs, stepcost funct ions, and learningcurvebased costs. 104 No. High correlat ion merely indicates that the two variables mo ve together in the data examined. It is essent ial also to consider econo mic plausibilit y before making inferences about cause and effect. Without any economic plausibilit y for a relationship, it is less likely that a hig h level of correlation observed in one set of data will be similarly found in other sets of data. 105 1. 2. 3. 4. Four approaches to estimat ing a cost funct ion are Industrial engineering method. Conference method. Account analysis method. Quant itative analysis o f current or past cost relat ionships. 106 The conference method est imates cost funct ions on the basis of analysis and opinio ns about costs and their drivers gathered fro m various departments of a co mpany (purchasing, process engineering, manufacturing, emplo yee relat ions, etc.). Advantages o f the conference method include 1. The speed with which cost estimates can be develo ped. 2. The pooling of knowledge fro m experts across functional areas. 3. The improved credibilit y o f the cost funct ion to all personnel. 101 107 The account analysis method est imates cost funct ions by classifying cost accounts in the subsidiary ledger as variable, fixed, or mixed wit h respect to the ident ified level o f activit y. Typically, managers use qualitat ive, rather than quant itative, analys is when making these cost classificat ion decisio ns. 108 The six steps are 1. Choose the dependent variable (the variable to be predicted, which is so me type of cost). 2. Ident ify 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 funct ion. 6. Evaluate the cost driver of the estimated cost functio n. Step 3 typically is the most difficult for a cost analyst. 109 Causalit y in a cost function runs fro m the cost driver to the dependent variable. Thus, choosing the highest observat ion and the lowest observat ion of the cost driver is appropriate in the highlow method. 1010 1. 2. 3. Three criteria important when choosing amo ng alternat ive cost funct ions are Economic plausibilit y. Goodness of fit. Slope of the regressio n line. 1011 A learning curve is a function that measures how laborhours per unit decline as units o f production increase because workers are learning and becoming better at their jo bs. Two models used to capture different forms of learning are 1. Cumulat ive averaget ime learning model. The cumulat ive average t ime per unit declines by a constant percentage each time the cumulat ive quant it y of unit s produced doubles. 2. Incremental unittime learning model. The incremental t ime needed to produce the last unit declines by a constant percentage each t ime the cumulat ive quantit y o f units produced doubles. 1012 Frequent ly encountered problems when co llecting cost data on variables included in a cost funct ion are 1. The time period used to measure the dependent variable is not properly matched wit h the time period used to measure the cost driver(s). 2. Fixed costs are allo cated 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 ho mogeneous relationship between the individual cost items in the dependent variable cost pool and the cost driver(s) does not exist. 6. The relat ionship between the cost and the cost driver is not stationary. 7. Inflat ion has occurred in a dependent variable, a cost driver, or both. 102 1013 Four key assumptions examined in specificat ion analysis are 1. Linearit y of relat ionship 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 distribut ion of residuals. 1014 No. A cost driver is any factor whose change causes a change in the total cost of a related cost object. A causeandeffect relat ionship underlies selection of a cost driver. Some users o f regression analys is include numerous independent variables in a regressio n model in an attempt to maximize goodness of fit, irrespect ive o f the econo mic plausibilit y o f the independent variables included. Some of the independent variables included may not be cost drivers. 1015 No. Mult ico llinearit y exists when two or more independent variables are highly correlated with each other. 1016 (10 min.) Estimating a cost function. 1. Difference in costs Slope coefficient = Difference in machinehours = $5, 400 - $4, 000 10, 000 - 6, 000 $1, 400 = $0.35 per machinehour 4, 000 = Constant = Total cost – (Slope coefficient ´ Quantit y of cost driver) = $5,400 – ($0.35 ´ 10,000) = $1,900 = $4,000 – ($0.35 ´ 6,000) = $1,900 The cost funct ion based on the two observations is Maintenance costs = $1,900 + $0.35 ´ Machinehours 2. The cost funct ion in requirement 1 is an est imate of how costs behave within the relevant range, not at cost levels outside the relevant range. If there are no months wit h zero machine hours represented in the maintenance account, data in that account cannot be used to estimate the fixed costs at the zero machinehours level. Rather, the constant component of the cost funct ion provides the best available starting po int for a straight line that approximates how a cost behaves within the relevant range. 103 1017 (15 min.) Identifying variable, fixed, and mixedcost functions. 1. 2. See Solut ion Exhibit 1017. 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. Contract 1 2 3 Cost Function Fixed Mixed Variable 3. SOLUTION EXHIBIT 1017 Plots of Car Rental Contracts Offered by Pacific Corp. Co n tract 1: Fi xe d C o s ts $160 Car R e n tal Co sts 140 120 100 80 60 40 20 0 0 50 100 150 M il e s Trave l e d p e r D ay Co n tract 2: M i xe d Co s ts $160 140 120 100 80 60 40 20 0 0 100 50 M il e s Trave l e d p e r D ay 150 C ar Re n t al C os ts Co n tract 3: Vari ab l e Co s ts Car R e n tal Co sts $160 140 120 100 80 60 40 20 0 0 50 100 M il e s Trave l e d p e r D ay 150 104 1018 1. 2. 3. 4. 5. 6. 7. 8. 9. (20 min.) Various costbehavior patterns. K B G J Note that A is incorrect because, alt hough the cost per pound eventually equals a constant at $9.20, the total do llars o f cost increases linearly fro m that point onward. I The total costs will be the same regardless o f the volume level. L F This is a classic stepcost function. K C 1019 (30 min.) Matching graphs with descriptions of cost and revenue behavior. a. b. c. d. e. f. (1) (6) (9) (2) (8) (10) A stepcost function. It is data plotted on a scatter diagram, showing a linear variable cost funct ion wit h constant variance of residuals. The constant variance o f residuals implies that there is a uniform dispersio n of the data points about the regression line. g. h. (3) (8) 1020 (15 min.) Account analysis method. 1. Variable costs: Car wash labor $260,000 Soap, cloth, and supplies 42,000 Water 38,000 Electric power to move conveyor belt 72,000 Total variable costs $412,000 Fixed costs: Depreciat ion $ 64,000 Salaries 46,000 Total fixed costs $110,000 Some 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. Some costs are classified as fixed because the total costs in these categories do not vary wit h the number of cars washed. If the conveyor belt moves regardless o f the number of cars on it, the electricit y costs to power the conveyor belt would be a fixed cost. 2. Variable costs per car = $412,000 = $5.15 per car 80,000 Total costs estimated for 90,000 cars = $110,000 + ($5.15 × 90,000) = $573,500 105 1021 ( 15 min.) Account analysis 1. The electricit y cost is clearly variable since it ent irely depends on number of kilowatt hours used. The Waste Management contract is a fixed amount if the cost object is not number of quarters, since it does not depend on amount of activit y or output during the quarter. The telephone cost is a mixed cost because there is a fixed component and a component that depends on number of calls made. 2. The electricit y rate is $573 ÷ 3000 kw hour = $0.191 per kw hour The waste management fixed cost is $270 for three months, or $90 (270 ÷ 3) per month. The telephone cost is $20 + ($0.03 per call ´ 1,200 calls) = $56 Adding them together we get: Fixed cost of utilit ies = $90 (waste management) + $20 (telephone) = $110 Utilities cost = $110 + ($0.191 per kw hour kw hours used) + ($0.03 per call ´ number of calls) per month Utilit cos 3. or F ies t = $146 + ($0.191 per kw hour 4000 hours) + ($0.03 per call ´ 1,200 calls) f ebruary = $146 + $764 + $36 = $910 106 1022(30 min.) Account analysis method. 1. Manufacturing cost classification for 2009: Total Costs (1) $300,000 225,000 37,500 56,250 60,000 75,000 95,000 100,000 $948,750 % of Total Costs That is Variable Fixed Variable Variable Costs Costs Cost per Unit (2) (3) = (1) ´ (2) (4) = (1) – (3) (5) = (3) ÷ 75,000 100% 100 100 20 50 40 0 0 $300,000 225,000 37,500 11,250 30,000 30,000 0 0 $633,750 $ 0 0 0 45,000 30,000 45,000 95,000 100,000 $315,000 $4.00 3.00 0.50 0.15 0.40 0.40 0 0 $8.45 Account Direct materials Direct manufacturing labor Power Supervision labor Materialshandling labor Maintenance labor Depr eciation Rent, property taxes, admin Total Total manufacturing cost for 2009 = $948,750 Variable costs in 2010: Unit Variable Increase in Cost per Variable Variable Cost Unit for Percentage Cost per Unit Total Variable 2009 Increase per Unit for 2010 Costs for 2010 (6) (7) (8) = (6) ´ (7) (9) = (6) + (8) (10) = (9) ´ 80,000 $4.00 3.00 0.50 0.15 0.40 0.40 0 0 $8.45 5% 10 0 0 0 0 0 0 $0.20 0.30 0 0 0 0 0 0 $0.50 $4.20 3.30 0.50 0.15 0.40 0.40 0 0 $8.95 $336,000 264,000 40,000 12,000 32,000 32,000 0 0 $716,000 Account Direct materials Direct manufacturing labor Power Supervision labor Materialshandling labor Maintenance labor Depr eciation Rent, property taxes, admin. Total 107 Fixed and total costs in 2010: Dollar Fixed Increase in Fixed Costs Costs Percentage Fixed Costs for 2010 for 2009 Increase (13) = (14) = (11) (12) (11) ´ (12) (11) + (13) Variable Costs for 2010 (15) Total Costs (16) = (14) + (15) Account Direct materials $ 0 Direct manufacturing labor 0 Power 0 Supervisio n labor 45,000 Materialshandling labor 30,000 Maintenance labor 45,000 Depreciat ion 95,000 Rent, property taxes, admin. 100,000 Total $315,000 0% 0 0 0 0 0 5 7 $ 0 0 0 0 0 0 4,750 7,000 $11,750 $ 0 $336,000 $ 336,000 0 264,000 264,000 0 40,000 40,000 45,000 12,000 57,000 30,000 32,000 62,000 45,000 32,000 77,000 99,750 0 99,750 107,000 0 107,000 $326,750 $716,000 $1,042,750 Total manufacturing costs for 2010 = $1,042,750 2. Total cost per unit, 2009 Total cost per unit, 2010 $948,750 = $12.65 75,000 $1,042,750 = = $13.03 80,000 = 3. Cost classificat ion into variable and fixed costs is based on qualitative, rather than quant itative, analys is. How good the classificat ions are depends on the knowledge o f individua l managers who classify the costs. Gower may want to undertake quant itative analysis o f costs, using regressio n analys is on timeseries or crosssect ional data to better estimate the fixed and variable co mponents of costs. Better knowledge of fixed and variable costs will help Gower to better price his products, to know when he is getting a posit ive contribut ion margin, and to better manage costs. 108 1023 (15–20 min.) Estimating a cost function, highlow method. 1. The key point to note is that the problem provides highlow values o f X (annual round trips made by a helicopter) and Y ¸ X (the operating cost per round trip). We first need to calculate the annual operating cost Y (as in co lumn (3) below), and then use those values to estimate the funct ion using the highlow method. Cost Driver: Annual Round Trips (X) (1) 2,000 1,000 1,000 Operating Cost per RoundTrip (2) $300 $350 Annual Operating Cost (Y) (3) = (1) ´ (2) $600,000 $350,000 $250,000 Highest observat ion of cost driver Lowest observat ion of cost driver Difference Slope coefficient = $250,000 ¸ 1,000 = $250 per roundtrip Constant = $600,000 – ($250 ´ 2,000) = $100,000 The est imated relat ionship is Y = $100,000 + $250 X; where Y is the annual operating cost of a helicopter and X represents the number of round trips it makes annually. 2. The constant a (estimated as $100,000) represents the fixed costs of operating a helicopter, irrespect ive o f the number o f round trips it makes. This would include items such as insurance, registration, depreciat ion on the aircraft, and any fixed co mponent of pilot and crew salaries. The coefficient b (est imated as $250 per roundtrip) represents the variable cost of each round trip—costs that are incurred only when a helicopter actually flies a round trip. The coefficient b may include costs such as landing fees, fuel, refreshments, baggage handling, and any regulatory fees paid on a perflight basis. 3. If each helicopter is, on average, expected to make 1,200 round trips a year, we can use the estimated relationship to calculate the expected annual operating cost per helicopter: Y = $100,000 + $250 X X = 1,200 Y = $100,000 + $250 ´ 1,200 = $100,000 + $300,000 = $400,000 Wit h 10 helicopters in its fleet, Reisen’s est imated operating budget is 10 ´ $400,000 = $4,000,000. 109 1024 (20 min.) Estimating a cost function, highlow method. 1. See Solut ion Exhibit 1024. There is a posit ive relat ionship between the number o f service reports (a cost driver) and the customerservice depart ment costs. This relat ionship is economically plausible. 2. Number of CustomerService Service Reports Department Costs Highest observat ion of cost driver 436 $21,890 Lowest observat ion of cost driver 122 12,941 Difference 314 $ 8,949 Customerservice department costs = a + b (number of service reports) $8, 949 = $28.50 per service report 314 Constant (a) = $21,890 – $28.50 ´ 436 = $9,464 = $12,941 – $28.50 ´ 122 = $9,464 Customerservice = $9,464 + $28.50 (number of service reports) department costs Slopecoefficient (b) = 3. Other possible cost drivers of customerservice department costs are: a. Number o f products replaced wit h a new product (and the do llar value o f the new products charged to the customerservice department). b. Number of products repaired and the time and cost of repairs. SOLUTION EXHIBIT 1024 Plot of Number of Service Reports versus CustomerService Dept. Costs for Capitol Products CustomerService Department Cost s $25,000 20,000 15,000 10,000 5,000 $0 0 100 200 300 400 500 Number of Service Reports 1010 1025 (30–40 min.) Linear cost approximation. 1. Slope coefficient (b) = Difference in cost $529,000 - $400,000 = = $43.00 Difference in laborhours 7,000 - 4,000 Constant (a) = $529,000 – ($43.00 × 7,000) = $228,000 Cost funct ion = $228,000 + $43.00 ´ professio nal laborhours The linear cost funct ion is plotted in Solut ion Exhibit 1025. No, the constant component of the cost funct ion does not represent the fixed overhead cost of the Memphis Group. The relevant range o f professio nal laborhours is fro m 3,000 to 8,000. The constant component provides the best available starting po int for a straight line that approximates how a cost behaves wit hin the 3,000 to 8,000 relevant range. 2. A co mparison at various levels o f professio nal laborhours follows. The linear cost funct ion is based on the formula o f $228,000 per month plus $43.00 per professio nal laborhour. Total overhead cost behavior: Month 1 Professio nal laborhours 3,000 Actual total overhead costs $340,000 Linear approximat ion 357,000 Actual minus linear approximat ion $(17,000) Month 2 Month 3 Month 4 Month 5 Month 6 4,000 5,000 6,000 7,000 8,000 $400,000 $435,000 $477,000 $529,000 $587,000 400,000 443,000 486,000 529,000 572,000 $ 0 $ (8,000) $ (9,000) $ 0 $ 15,000 The data are shown in So lut ion Exhibit 1025. The linear cost funct ion overstates costs by $8,000 at the 5,000hour level and understates costs by $15,000 at the 8,000hour level. 3. Contribut ion before deducting incremental overhead Incremental overhead Contribut ion after incremental overhead The total contribut ion margin actually forgone is $3,000. Based on Actual $38,000 35,000 $ 3,000 Based on Linear Cost Function $38,000 43,000 $ (5,000) 1011 SOLUTION EXHIBIT 1025 Linear Cost Funct ion Plot of Professio nal LaborHours on Total Overhead Costs for Memphis Consult ing Group $700,000 Total Overhead Costs 600,000 500,000 400,000 300,000 200,000 100,000 0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 Professional LaborHours Billed 1026 (20 min.) Costvolumeprofit and regression analysis. 1a. Average cost of manufacturing = Total manufactur ng costs i 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 2009 of $30 per frame and mult iply it by 36,000 bicycle frames to determine the total cost of manufacturing 36,000 bicycle frames. The reason is that some o f the $900,000 (or equivalent ly the $30 cost per frame) are fixed costs and so me are variable costs. Without dist inguishing fixed fro m 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 cont inue 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 so me costs are fixed and so me are variable, the cost of manufacturing 36,000 frames will be somewhere between $900,000 and $1,080,000. Some students could argue that another reason for not being able to determine the cost of manufacturing 36,000 bicycle frames is that not all costs are output unitlevel costs. If so me costs are, for example, batchlevel costs, more informat ion would be needed on the number o f 1012 batches in which the 36,000 bicycle frames would be produced, in order to determine the cost of manufacturing 36,000 bicycle frame...
View Full Document
- Spring '10
- Cost Accounting, representative, cost funct ion, Bob Jones