Chapter 6 Cost Behaviour: Analysis and Use Solutions to Questions 6-1 An activity base is a measure of whatever causes the incurrence of a variable cost. 6-2 a. Unit fixed costs increase as volume decreases. b. Unit variable costs remain constant as volume decreases. c. Total fixed costs remain constant as volume decreases. d. Total variable costs decrease as volume decreases. 6-3 a. Cost behaviour: Cost behaviour refers to the way in which costs change in response to changes in a measure of activity such as sales volume, production volume, or orders processed. b. Relevant range: The relevant range is the range of activity within which assumptions about variable and fixed cost behaviour are valid. 6-4 A curvilinear cost is one where the relationship between the cost and activity is a curve rather than a straight line. Examples include: utilities where the amount charged per unit increases as the amount used increases; and wages where the rate per hour increases as more hours are worked and overtime is paid. 6-5 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 6-6 The linear assumption is reasonably valid providing that the cost formula is used only within the relevant range. 6-7 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. 6-8 a. Committed b. Discretionary c. Discretionary d. Committed e. Committed f. Discretionary © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 1 6-9 Yes. As the anticipated level of activity changes, the level of fixed costs needed to support operations may also change. Most fixed costs are adjusted upward and downward in large steps, rather than being absolutely fixed at one level for all ranges of activity. 6-10 The engineering approach to cost analysis is a detailed analysis of cost behaviour based on an industrial engineer’s evaluation of the inputs that are required to carry out an activity and of the costs of those inputs. It could be used to estimate the costs of a new product not previously produced. It could also be used to determine the cost of providing a particular service or department such as customer complaints. 6-11 The major disadvantage of the high-low method is that it uses only two data points, the highest and lowest levels of activity. If either of these points is an extreme value (well above or well below normal activity levels) the accuracy of the cost estimation model will be reduced. levels are being used to predict the costs, not vice-versa. Accordingly, the high-low activity levels provide the greatest possible variation in the selected cost driver. 6-13 The formula for a mixed cost is Y = a + bX. In cost analysis, the “a” term represents the fixed cost, and the “b” term represents the variable cost per unit of activity. 6-14 The contribution approach income statement organizes costs by behaviour, first deducting variable expenses to obtain contribution margin, and then deducting fixed expenses to obtain operating income. The traditional approach organizes costs by function, such as production, selling, and administration. Within a functional area, fixed and variable costs are intermingled. 6-12 The high-low activity levels are used instead of the high-low costs because activity © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 2 Managerial Accounting, 9th Canadian Edition Exercise 6-1 (15 minutes) 1. Smoothies Served in a Week 2,100 2,800 3,500 Fixed cost ...................................................................... $2,500 $2,500 $2,500 Variable cost ($0.75 per cup) .......................................... 1,575 2,100 2,625 Total cost ...................................................................... $4,075 $4,600 $5,125 Cost per smoothie served * ............................................ $1.94 $1.64 $1.46 * Total cost ÷ smoothies served in a week 2. The average cost of a smoothie declines as the number of smoothies served increases because the fixed cost is spread over more units. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 3 Exercise 6-2 (30 minutes) 1. The completed scattergraph is presented below: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 4 Managerial Accounting, 9th Canadian Edition Exercise 6-2 (continued) 2. (Students’ answers will vary considerably due to the inherent imprecision and subjectivity of the scattergraph method of estimating variable and fixed costs.) The approximate monthly fixed cost is $6,000—the point where the straight line intersects the cost axis. The variable cost per unit processed can be estimated as follows using the 8,000-unit level of activity, which falls on the straight line: Total cost at the 8,000-unit level of activity ........... Less fixed costs ................................................... Variable costs at the 8,000-unit level of activity ..... $14,000 6,000 $ 8,000 $8,000 ÷ 8,000 units = $1 per unit. Observe from the scattergraph that if the company used the high-low method to determine the slope of the line, the line would be too steep. This would result in underestimating the fixed cost and overestimating the variable cost per unit. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 5 Exercise 6-3 (20 minutes) 1. Month High activity level (August) .. Low activity level (October).. Change ............................... OccupancyDays 3,608 186 3,422 Electrical Costs $8,111 1,712 $6,399 Variable cost = Change in cost ÷ Change in activity = $6,399 ÷ 3,422 occupancy-days = $1.87 per occupancy-day Total cost (August) .................................................... Variable cost element ($1.87 per occupancy-day × 3,608 occupancy-days) Fixed cost element .................................................... $8,111 6,747 $1,364 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. 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. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 6 Managerial Accounting, 9th Canadian Edition Exercise 6-4 (20 minutes) 1 . The Rhythm Shop Income Statement—Acoustic Guitar Department For the Quarter Ended March 31 Sales ................................................................ Variable expenses: Cost of goods sold ($400 per guitar × $800,000 2,000 guitars*) ............................................ Selling expenses ($75 per guitar × 2,000 150,000 guitars) ....................................................... Administrative expenses (25% × 50,000 $200,000) ................................................... Contribution margin .......................................... Fixed expenses: Selling expenses (400,000-150,000) ................250,000 Administrative expenses(75% x 200,000) ........150,000 Operating income ............................................. $1,600,000 1,000,000 600,000 400,000 $ 200,000 *$1,600,000 sales ÷ $800 per guitar = 2,000 guitars. 2. Since 2,000 guitars were sold and the contribution margin totaled $600,000 for the quarter, the contribution of each guitar toward fixed expenses and profits was $300 ($600,000 ÷ 2,000 guitars = $300 per guitar). Another way to compute the $300 is: Selling price per guitar ....................... Less variable expenses: Cost per guitar ................................ Selling expenses.............................. Administrative expenses ($50,000 ÷ 2,000 guitar) .............. Contribution margin per guitar ............ $800 $400 75 25 500 $300 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 7 Exercise 6-4 (continued) 3. If the Rhythm Shop sells 100 more guitars in the quarter ending June 30, than they did for the quarter ending March 31, profits will increase by: 100 x $300* per guitar = $30,000 *$800 selling price - $500 total variable cost per guitar Total operating income for the quarter ended June 30 will be: Operating income for the Quarter ended March 31 Contribution margin from additional unit sales Total operating income** ** Check: 2,100 guitars sold x $300/guitar Less fixed expenses Total operating income $200,000 30,000 $230,000 $630,000 400,000 $230,000 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 8 Managerial Accounting, 9th Canadian Edition Exercise 6-5 (20 minutes) 1. The company’s variable cost per unit would be: $150,000 =$2.50 per unit. 60,000 units Taking into account the difference in behaviour between variable and fixed costs, the completed schedule would be: Units produced and sold Total costs: Variable costs ....................... Fixed costs ........................... Total costs .............................. Cost per unit: Variable cost ......................... Fixed cost ............................. Total cost per unit ................... *Given. 60,000 80,000 100,000 $150,000 * 360,000 * $510,000 * $200,000 360,000 $560,000 $250,000 360,000 $610,000 $2.50 6.00 $8.50 $2.50 4.50 $7.00 $2.50 3.60 $6.10 2. The company’s income statement in the contribution format would be: Sales (90,000 units × $7.50 per unit) ............................ Variable expenses (90,000 units × $2.50 per unit) ......... Contribution margin...................................................... Fixed expenses ............................................................ Operating income ......................................................... $675,000 225,000 450,000 360,000 $ 90,000 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 9 Exercise 6-6 (45 minutes) 1. High activity level ............ Low activity level ............. Change .......................... Units Shipped 8 2 6 Shipping Expense $3,600 1,500 $2,100 Variable cost element: Change in cost $2,100 = =$350 per unit Change in activity 6 units Fixed cost element: Shipping expense at the high activity level ................... Less variable cost element ($350 per unit × 8 units)..... Total fixed cost ........................................................... $3,600 2,800 $ 800 The cost formula is $800 per month plus $350 per unit shipped or Y = $800 + $350X, where X is the number of units shipped. 2. a. See the scattergraph on the following page. b. (Note: Students’ answers will vary due to the imprecision and subjective nature of this method of estimating variable and fixed costs.) Total cost at 5 units shipped per month [a point falling on the line in (a)] ...................................... Less fixed cost element (intersection of the Y axis).. Variable cost element............................................. $2,600 1,100 $1,500 $1,500 ÷ 5 units = $300 per unit. The cost formula is $1,100 per month plus $300 per unit shipped or Y = $1,100 + 300X, where X is the number of units shipped. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 10 Managerial Accounting, 9th Canadian Edition Exercise 6-6 (continued) 2. a. The scattergraph appears below: 3. The cost of shipping units is likely to depend on the weight and volume of the units shipped and the distance traveled as well as on the number of units shipped. In addition, higher cost shipping might be necessary to meet a deadline. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 11 Exercise 6-7 (20 minutes) 1. High level of activity ............ Low level of activity ............. Change ............................... Kilometres Driven 120,000 80,000 40,000 Total Annual Cost* $13,920 10,880 $ 3,040 * 120,000 kilometres × $0.116 per kilometre = $13,920 80,000 kilometres × $0.136 per kilometre = $10,880 Variable cost per kilometre: Change in cost = Change in activity $3,040____ = $0.076 per kilometre 40,000 kilometres Fixed cost per year: Total cost at 120,000 kilometres ........................... Less variable cost element: 120,000 kilometres × $0.076 per kilometre ........ Fixed cost per year .............................................. $13,920 9,120 $ 4,800 2. Y = $4,800 + $0.076X 3. Fixed cost ............................................................... Variable cost: 100,000 kilometres × $0.076 per kilometre .............................................................. Total annual cost ..................................................... $ 4,800 7,600 $12,400 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 12 Managerial Accounting, 9th Canadian Edition Exercise 6-8 (20 minutes) 1. High activity level (February)........ Low activity level (June) .............. Change ....................................... Blood Tests 3,500 1,500 2,000 Costs $14,500 8,500 $ 6,000 Variable cost per blood test: Change in cost = $6,000 = $3 per blood test Change in activity 2,000 blood tests Fixed cost per month: Blood test cost at the high activity level ................ Less variable cost element: 3,500 blood tests × $3.00 per test ..................... Total fixed cost .................................................... $14,500 10,500 $ 4,000 The cost formula is $4,000 per month plus $3.00 per blood test performed or, in terms of the equation for a straight line: Y = $4,000 + $3.00X where X is the number of blood tests performed. 2. Expected blood test costs when 2,300 tests are performed: Variable cost: 2,300 blood tests × $3.00 per test....... Fixed cost ............................................................... Total cost ................................................................ $6,900 4,000 $10,900 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 13 Exercise 6-9 (30 minutes) 1. The scattergraph appears below. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 14 Managerial Accounting, 9th Canadian Edition Exercise 6-9 (continued) 2. (Note: Students’ answers will vary considerably due to the inherent lack of precision and subjectivity of the scattergraph method.) Total costs at 2,500 blood tests per month [a point falling on the line in (1)] ......................................... $11,500 Less fixed cost element (intersection of the Y axis)..... 3,250 Variable cost element................................................ $8,250 $8,250 ÷ 2,500 blood tests = $3.30 per blood test. The cost formula is therefore $3,250 per month plus $3.30 per blood test performed. Written in equation form, the cost formula is: Y = $3,250 + $3.30X, where X is the number of blood tests performed. 3. The high-low method would not provide an accurate cost formula in this situation, since a line drawn through the high and low points would have a slope that is too flat. Consequently, the high-low method would overestimate the fixed cost and underestimate the variable cost per unit. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 15 Exercise 6-10 (30 minutes) 1. Monthly operating costs at 70% occupancy: 2,000 rooms × 70% = 1,400 rooms; 1,400 rooms × $21 per room per day × 30 days .. Monthly operating costs at 45% occupancy (given) . Change in cost ...................................................... Difference in rooms occupied: 70% occupancy (2,000 rooms × 70%)................. 45% occupancy (2,000 rooms × 45%)................. Difference in rooms (change in activity) .................. Variable cost= $882,000 792,000 $ 90,000 1,400 900 500 Change in cost $90,000 = =$180 per room. Change in activity 500 rooms $180 per room ÷ 30 days = $6 per room per day. 2. Monthly operating costs at 70% occupancy (above) .. Less variable costs: 1,400 rooms × $6 per room per day × 30 days ...... Fixed operating costs per month .............................. $882,000 252,000 $630,000 3. 2,000 rooms × 60% = 1,200 rooms occupied. Fixed costs .............................................................. Variable costs: 1,200 rooms × $6 per room per day × 30 days ...... Total expected costs ................................................ $630,000 216,000 $846,000 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 16 Managerial Accounting, 9th Canadian Edition Problem 6-11 (45 minutes) 1. Home Entertainment Income Statement For the Month Ended April 30 Sales (150 televisions × $1,500 per set) ............. Cost of goods sold (150 televisions × $900 per set) ...................... Gross margin .................................................... Selling and administrative expenses: Selling expenses: Advertising .................................................. Delivery of televisions (150 televisions × $40 per set) ................... Sales salaries and commissions [$2,900 + (4% × $225,000)] ..................... Utilities ........................................................ Depreciation of sales facilities ....................... Total selling expenses ..................................... Administrative expenses: Executive salaries ......................................... Depreciation of office equipment................... Clerical [$1,500 + (150 televisions × $40 per set)] . Insurance .................................................... Total administrative expenses .......................... Total selling and administrative expenses ............ Operating income .............................................. $225,000 135,000 90,000 $ 950 6,000 11,900 400 3,000 22,250 8,000 500 7,500 400 16,400 38,650 $ 51,350 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 17 Problem 6-11 (continued) 2. Home Entertainment Income Statement For the Month Ended April 30 Sales (150 televisions × $1,500 per set) ............. Variable expenses: Cost of goods sold (150 televisions × $900 per set) ................... Delivery of televisions (150 televisions × $40 per set) ..................... Sales commissions (4% × $225,000) ............... Clerical (150 televisions × $40 per set) ............ Total variable expenses................................. Contribution margin........................................... Fixed expenses: Advertising ..................................................... Sales salaries .................................................. Utilities........................................................... Depreciation of sales facilities .......................... Executive salaries ........................................... Depreciation of office equipment ..................... Clerical ........................................................... Insurance ....................................................... Total fixed expenses .......................................... Operating income .............................................. Total $225,000 Per Unit $1,500 135,000 900 6,000 9,000 6,000 156,000 69,000 40 60 40 1,040 $ 460 950 2,900 400 3,000 8,000 500 1,500 400 17,650 $ 51,350 3. Fixed costs remain constant in total but vary on a per unit basis with changes in the activity level. For example, as the activity level increases, fixed costs decrease on a per unit basis. Showing fixed costs on a per unit basis on the income statement make them appear to be variable costs. That is, management might be misled into thinking that the per unit fixed costs would be the same regardless of how many televisions were sold during the month. For this reason, fixed costs should be shown only in totals on a contribution-type income statement. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 18 Managerial Accounting, 9th Canadian Edition Problem 6-12 (45 minutes) 1. Cost of goods sold .................... Shipping expense ..................... Advertising expense ................. Salaries and commissions ......... Insurance expense ................... Depreciation expense ............... Variable Mixed Fixed Mixed Fixed Fixed 2. Analysis of the mixed expenses: High level of activity ..... Low level of activity ...... Change ........................ Units 4,500 3,000 1,500 Shipping Expense £56,000 44,000 £12,000 Salaries and Comm. Expense £143,000 107,000 £ 36,000 Variable cost element: Variable cost per unit = Shipping expense: Change in cost Change in activity £12,000 = £8 per unit 1,500 units Salaries and comm. expense: £36,000 = £24 per unit 1,500 units Fixed cost element: Cost at high level of activity ... Less variable cost element: 4,500 units × £8 per unit .... 4,500 units × £24 per unit... Fixed cost element ................ Shipping Expense £56,000 36,000 £20,000 Salaries and Comm. Expense £143,000 108,000 £ 35,000 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 19 Problem 6-12 (continued) The cost formulas are: Shipping expense: £20,000 per month plus £8 per unit or Y = £20,000 + £8X. Salaries and Comm. expense: £35,000 per month plus £24 per unit or Y = £35,000 + £24X. 3. Frankel Ltd. Income Statement For the Month Ended June 30 Sales revenue ............................................ Variable expenses: Cost of goods sold (4,500 units × £56* per unit) ................ Shipping expense (4,500 units × £8 per unit) .................... Salaries and commissions expense (4,500 units × £24 per unit) .................. Contribution margin.................................... Fixed expenses: Shipping expense .................................... Advertising .............................................. Salaries and commissions ......................... Insurance ................................................ Depreciation ............................................ Operating income ....................................... £630,000 £252,000 36,000 108,000 20,000 70,000 35,000 9,000 42,000 396,000 234,000 176,000 £ 58,000 *Per unit amount based on low level of sales activity: £168,000 ÷ 3,000 = £56 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 20 Managerial Accounting, 9th Canadian Edition Problem 6-13 (30 minutes) 1. a. b. c. d. e. f. g. h. i. 6 11 1 4 2 10 3 7 9 2. Without a knowledge of the underlying cost behaviour patterns, it would be difficult if not impossible for a manager to properly analyze the firm’s cost structure. The reason is that all costs don’t behave in the same way. One cost might move in one direction as a result of a particular action, and another cost might move in an opposite direction. Unless the behaviour pattern of each cost is clearly understood, the impact of a firm’s activities on its costs will not be known until after the activity has occurred. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 21 Problem 6-14 (45 minutes) 1. High-low method: High activity level .............. Low activity level ............... Change ............................. Number of Jobs Repair Costs 260 80 180 $24,000 9,600 $14,400 Variable cost per job: Change in cost = Change in activity $14,400 180 jobs = $80 per job Fixed cost: Total repair cost at high activity level ........ Less variable element: 260 jobs × $80 per job ......................... Fixed cost element .................................. $24,000 20,800 $ 3,200 Therefore, the cost formula is: Y = $3,200 + $80X. 2. Scattergraph method (see the scattergraph on the following page): (Note: Students’ answers will vary due to the inherent imprecision and subjectivity of the scattergraph method of estimating fixed and variable costs.) The line intersects the cost axis at about $4,250. The variable cost can be estimated as follows: Total cost at 180 jobs (a point that falls on the line) ... Less the fixed cost element (intersection of the Y axis on the graph) ........................................................ Variable cost element at 180 jobs (total) .................... $18,000 4,250 $13,750 $13,750 ÷ 180 jobs = $76.38 per job. Therefore, the cost formula is: Y = $4,250 + $76.38X. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 22 Managerial Accounting, 9th Canadian Edition Problem 6-14 (continued) The completed scattergraph follows: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 23 Problem 6-14 (continued) 3. Total predicted repair costs for 200 jobs: Y = $3,200 + $80(x) Y = $3,200 + $80(200) Y = $3,200 + $16,000 Y = $19,200 4. Neither of the formulas developed in parts 1 and 2 should be used to predict costs for a 600-job month because that level of activity appears to be well outside of the relevant range. The next closest activity level is only 260 jobs (May), which is less than half of the number of jobs the manager wants to predict costs for. Both fixed and variable costs could increase if the level of activity is 600 jobs. For example, additional mechanics may need to be hired, more repair equipment may be needed and facilities may need to be expanded (even temporarily) to accommodate an increase of that magnitude. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 24 Managerial Accounting, 9th Canadian Edition Problem 6-15 (45 minutes) 1. Maintenance cost at the 140,000 machine-hour level of activity can be isolated as follows: Total factory overhead cost ............. Deduct: Utilities cost @ $1.30 per MH* ...... Supervisory salaries ..................... Maintenance cost ........................... Level of Activity 80,000 MH 140,000 MH $340,400 $483,200 104,000 120,000 $116,400 182,000 120,000 $181,200 *$104,000 ÷ 80,000 MHs = $1.30 per MH 2. High-low analysis of maintenance cost: High activity level .............. Low activity level ............... Change ............................. Maintenance MachineCost Hours $181,200 116,400 $ 64,800 140,000 80,000 60,000 Note: in this problem the high level of activity (140,000 hours) does not correspond to the highest level of total overhead costs, which occurs in November. Variable cost per unit of activity: Change in cost = Change in activity $64,800 60,000 MHs = $1.08 per MH Total fixed cost: Total maintenance cost at the low activity level ............ $116,400 Less the variable cost element (80,000 MHs × $1.08 per MH) .................................. 86,400 Fixed cost element ..................................................... $30,000 Therefore, the cost formula is $30,000 per month plus $1.08 per machine-hour or Y = $30,000 + $1.08X, where X represents machinehours. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 25 Problem 6-15 (continued) 3. Maintenance cost .............. Utilities cost: $104,000/80,000 ............... Supervisory salaries cost .... Totals ............................... Variable Rate per Machine-Hour Fixed Cost $1.08 1.30 $2.38 $ 30,000 120,000 $150,000 Therefore, the cost formula would be $150,000 plus $2.38 per machinehour, or Y = $150,000 + $2.38X. 4. Fixed costs .......................................................... Variable costs: $2.38 per MH × 90,000 MHs.......... Total overhead costs ............................................ $150,000 214,200 $364,200 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 26 Managerial Accounting, 9th Canadian Edition Problem 6-16 (45 minutes) 1. Direct materials cost @ $15 per unit Direct labour cost @ $6 per unit ...... Manufacturing overhead cost .......... Total manufacturing costs ............... Add: Work in process, beginning ..... Deduct: Work in process, ending ..... Cost of goods manufactured ........... July—Low 9,000 Units $135,000 54,000 107,000 * 296,000 14,000 310,000 25,000 $285,000 October—High 12,000 Units $180,000 72,000 131,000 * 383,000 22,000 405,000 15,000 $390,000 *Computed by working backwards from cost of goods manufactured. 2. October—High level of activity .......... July—Low level of activity ................. Change ............................................ Variable cost = = Units Produced 12,000 9,000 3,000 Cost Observed $131,000 107,000 $ 24,000 Change in cost Change in activity $24,000 = $8 per unit 3,000 units Total cost at the high level of activity .................. Less variable cost element ($8 per unit × 12,000 units) ............................ Fixed cost element ............................................. $131,000 96,000 $ 35,000 Therefore, the cost formula is: $35,000 per month plus $8 per unit produced, or Y = $35,000 + $8X, where X represents the number of units produced. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 27 Problem 6-16 (continued) 3. The cost of goods manufactured if 9,500 units are produced: Direct materials cost (9,500 units × $15 per unit).. $142,500 Direct labour cost (9,500 units × $6 per unit) ....... 57,000 Manufacturing overhead cost: Fixed portion .................................................... $35,000 Variable portion (9,500 units × $8 per unit) ........ 76,000 111,000 Total manufacturing costs .................................... 310,500 Add: Work in process, beginning .......................... 16,000 326,500 Deduct: Work in process, ending .......................... 19,000 Cost of goods manufactured ................................ $307,500 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 28 Managerial Accounting, 9th Canadian Edition Problem 6-17 (30 minutes) 1. Maintenance cost at the 80,000 machine-hour level of activity can be isolated as follows: Level of Activity 60,000 MH 80,000 MH Total factory overhead cost .. 274,000 pesos Deduct: Indirect materials @ 1.50 pesos per MH* ............... 90,000 Rent ................................. 130,000 Maintenance cost ................ 54,000 pesos 312,000 pesos 120,000 130,000 62,000 pesos * 90,000 pesos ÷ 60,000 MHs = 1.50 pesos per MH 2. High-low analysis of maintenance cost: High activity level .............. Low activity level ............... Change observed............... Variable cost = = Maintenance Cost 62,000 pesos 54,000 8,000 pesos Machine-Hours 80,000 60,000 20,000 Change in cost Change in activity 8,000 pesos = 0.40 peso per MH 20,000 MHs Fixed cost element = Total cost – Variable cost element = 54,000 pesos – (60,000 MHs × 0.40 pesos) = 30,000 pesos Therefore, the cost formula is 30,000 pesos per year, plus 0.40 peso per machine-hour or Y = 30,000 pesos + 0.40 peso X. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 29 Problem 6-17 (continued) 3. Indirect materials (65,000 MHs × 1.50 pesos per MH) ....................... Rent ................................................ Maintenance: Variable cost element (65,000 MHs × 0.40 peso per MH) ................... 26,000 pesos Fixed cost element ......................... 30,000 Total factory overhead cost ............... 97,500 pesos 130,000 56,000 283,500 pesos © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 30 Managerial Accounting, 9th Canadian Edition Case 6-18 (30 minutes) 1. The completed scattergraph for the number of direct labour hours as the activity base is presented below: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 31 Case 6-18 (continued) 2. The completed scattergraph for the number of jobs as the activity base is presented below: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 32 Managerial Accounting, 9th Canadian Edition Case 6-18 (continued) 3. The number of direct labour-hours should be used as the activity base for predicting overhead costs. There are several reasons for this. First, a visual inspection of the scattergraphs suggest that it is easer to approximate the relationship between labour-hours and overhead costs with a straight line than it is for total number of jobs completed in a month. Although both activity measures appear to have linear relationship with overhead costs, direct labour-hours appears to a better fit. Second, jobs differ with respect to complexity with more complex jobs requiring more direct labour-hours since they take longer to complete. Thus more complex jobs would likely result in the incurrence of more variable overhead costs such as electricity. Evidence of the differing mix of job complexity is indicated by the fact that during several months, around 500 jobs were completed (January, July, September, and December) but overhead ranged from $75,045 to $83,434 across those months. Third, management has the flexibility to change the mix of welders used across jobs. More experienced welders are more efficient and waste less indirect materials suggesting labour-hours may be a better predictor of overhead costs. 4. August—High level of activity ............ May—Low level of activity ................. Change ............................................ Direct LabourHours 6,114 1,914 4,200 Overhead Costs $81,582 60,162 $ 21,420 Variable cost per unit of activity: Change in cost = Change in activity $21,420 4,200 DLHs = $5.10 per DLH Total cost at the high level of activity .................. Less variable cost element ($5.10 per unit × 6,114 hours) Fixed cost element ............................................. $81,582.0 0 31,181.4 0 $ 50,400. 60 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 33 Case 6-18 (continued) Therefore, the cost formula is: $ Y = $50,400.60 + $5.10X, where X represents the number of direct labour-hours. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 34 Managerial Accounting, 9th Canadian Edition CASE 6-19 (90 minutes) 1. Direct labour-hour allocation base: Electrical costs (a) ................................. Direct labour-hours (b)........................... Predetermined overhead rate (a) ÷ (b) ... Machine-hour allocation base: Electrical costs (a) ................................. Machine-hours (b) ................................. Predetermined overhead rate (a) ÷ (b) ... SFr 3,868,620 427,500 DLHs SFr 9.05 per DLH SFr 3,868,620 365,520 MHs SFr 10.58 per MH 2. Electrical cost for the custom tool job using direct labour-hours: Predetermined overhead rate (a) ............ SFr 9.05 per DLH Direct labour-hours for the job (b) .......... 30 DLHs Electrical cost applied to the job (a) × (b) SFr 271.50 Electrical cost for the custom tool job using machine-hours: Predetermined overhead rate (a) ............ SFr 10.58 per MH Machine-hours for the job (b) ................. 25 MHs Electrical cost applied to the job (a) × (b) SFr 264.50 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 35 CASE 6-19 (continued) The scattergraph for electrical costs and direct labour-hours appears below: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 36 Managerial Accounting, 9th Canadian Edition CASE 6-19 (continued) The scattergraph for electrical costs and machine-hours appears below: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 37 CASE 6-19 (continued) In general, the allocation base should actually cause the cost being allocated. If it doesn’t, costs will be incorrectly assigned to jobs. Incorrectly assigned costs are useless for decision-making. Examining the two scattergraphs reveals that electrical costs do not appear to be related to direct labour-hours. Electrical costs do vary, but apparently not in response to changes in direct labour-hours. On the other hand, looking at the scattergraph for machine-hours, electrical costs do tend to increase as the machine-hours increase. So if one must choose between machine-hours and direct labour-hours as an allocation base, machine-hours seems to be the better choice. Even so, it looks like little of the overhead cost is really explained even by machine hours. Electrical cost has a large fixed component and much of the variation in the cost is unrelated to machine hours. 4. High-low method: Week 2—High level of activity ........... Week 7—Low level of activity ............ Change ............................................ Machine Hours 8,620 6,000 2,620 Electrical Costs SFr 82,270 73,100 SFr 9,170 Variable cost per unit of activity: Total cost at the high level of activity .................. Less variable cost element SFr 3.50 per MH × 8,620 hours)……………………. Fixed cost element ............................................. SFr82,270 30,170 SFr 52,100 Therefore, the cost formula is: SFr Y = $52,100 + SFr 3.50X, where X represents the number of machine hours. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 38 Managerial Accounting, 9th Canadian Edition CASE 6-19 (continued) 5. The custom tool job requires 25 machine-hours. At SFr 3.50 per machine-hour, the electrical cost actually caused by the job would be only SFr 87.50. This contrasts with the electrical cost of SFr 271.50 under the old cost system and SFr 264.50 under the new ABC system calculated in part 2 above. Both the old cost system and the new ABC system grossly overstate the electrical costs of the job. This is because under both cost systems, the large fixed electrical costs of SFr 52,100 per week are allocated to jobs along with the electrical costs that actually vary with the amount of work being done. In practice, almost all categories of overhead costs pose similar problems. As a consequence, the costs of individual jobs are likely to be seriously overstated for decision-making purposes under both traditional and ABC systems. Both systems provide acceptable cost data for external reporting, but both provide potentially misleading data for internal decision-making unless suitable adjustments are made. 6. Electricity is used for heating and lighting the building as well as to run equipment. Therefore, consumption of electrical power is likely to be affected at least by the weather and by the time of the year as well as by how many hours the equipment is run. (Shorter days mean the lights have to be on longer.) © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 39 CASE 6-20 (90 minutes) Note to the instructor: This case requires the ability to build on concepts that are introduced only briefly in the text. To some degree, this case anticipates issues that will be covered in more depth in later chapters. 1. In order to estimate the contribution to profit of the charity event, it is first necessary to estimate the variable costs of catering the event. The costs of food and beverages and labour are all apparently variable with respect to the number of guests. However, the situation with respect overhead expenses is less clear. A good first step is to plot the labour hour and overhead expense data in a scattergraph as shown below. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 40 Managerial Accounting, 9th Canadian Edition CASE 6-20 (continued) This scattergraph reveals several interesting points about the behaviour of overhead costs: • The relation between overhead expense and labour hours is approximated reasonably well by a straight line. (However, there appears to be a slight downward bend in the plot as the labour hours increase— evidence of increasing returns to scale. This is a common occurrence in practice. • The data points are all fairly close to the straight line. This indicates that most of the variation in overhead expenses is explained by labour hours. As a consequence, there probably wouldn’t be much benefit to investigating other possible cost drivers for the overhead expenses. • Most (about $40,000) of the overhead expense appears to be fixed. Christine should ask herself if this is reasonable. Does the company have large fixed expenses such as rent, depreciation, and salaries? The overhead expenses can be decomposed into fixed and variable elements using the high-low method, least-squares regression method, or even the quick-and-dirty method based on the scattergraph. • The high-low method throws away most of the data and bases the estimates of variable and fixed costs on data for only two months. For that reason, it is a decidedly inferior method in this situation. Nevertheless, if the high-low method were used, the estimates would be computed as follows: High level of activity ...... Low level of activity ....... Change ...................... Labour Hours 4,500 1,500 3,000 Overhead Expense $67,750 48,400 $19,350 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 41 CASE 6-20 (continued) Variable cost per unit of activity: Change in cost = Change in activity Fixed cost element $19,350 3,000 MHs = $6.45 per DLH = Total cost – Variable cost = $67,750 – ($6.45 x 4,500) = $38,725 Using the high-low method estimate of the variable overhead cost per direct labour hour, the total variable cost per guest is computed as follows: Food and beverages ............................. Labour (0.5 hour @ $15 per hour) ........ Overhead (0.5 hour @ $6.45 per hour) . Total variable cost per guest ................. $19.00 7.50 3.22 $29.72 The total contribution from 200 guests paying $50 each is computed as follows: Revenue (200 guests @ $50.00 per guest) ......... Variable cost (200 guests @ $29.72 per guest) ... Contribution to profit ........................................ $10,000.0 0 5,944.00 $4,056.00 Fixed costs are not included in the above computation because there is no indication that any additional fixed costs would be incurred as a consequence of catering the cocktail party. If additional fixed costs were incurred, they should also be subtracted from revenue. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 42 Managerial Accounting, 9th Canadian Edition CASE 6-20 (continued) 2. Assuming that no additional fixed costs are incurred as a result of catering the charity event, any price greater than the variable cost per guest of $29.72 would contribute to profits. 3. Bidding slightly less than $45 to get the contract is advisable. Any bid above $29.72 would contribute to profits and a bid at the normal price of $50 is unlikely to land the contract. Apart from the contribution to profit, catering the event would also show off the company’s capabilities to potential clients. The danger is that a price that is lower than the normal bid of $50 might set a precedent for the future or it might initiate a price war among caterers. However, the price need not be publicized and the lower price could be justified to future clients because this is a charity event. Another possibility would be for Christine to maintain her normal price but throw in additional services at no cost to the customer. Whether to compete on price or service is a delicate issue that Christine will have to decide after getting to know the personality and preferences of the customer. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 43 Research and Application 6-21 Answers will vary among groups. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 44 Managerial Accounting, 9th Canadian Edition Exercise 6A-1 (20 minutes) 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. The solution below was calculated using Microsoft® Excel. The fixed cost element is estimated to be $3,426 per month, and the variable cost element is $2.80 per rental return. Expressed as an equation, the relation between cleaning costs and rental returns is Y = $3,426 + $2.80x where X is the number of rental returns. The R2 estimated by Excel, is 0.92, which is quite high, and indicates a strong linear relationship between cleaning costs and rental returns. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 45 Exercise 6A-1 (continued) 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 cleaning costs and rental returns. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 46 Managerial Accounting, 9th Canadian Edition Exercise 6A-2 (30 minutes) 1. Month January February March April May June July Units Shipped (X) 4 7 5 2 3 6 8 Shipping Expense (Y) $2,200 $3,100 $2,600 $1,500 $2,200 $3,000 $3,600 A spreadsheet application such as Microsoft® Excel or a statistical software package can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are: Intercept (fixed cost) ............... Slope (variable cost per unit) .... R2 ........................................... $1,011 $318 0.96 Therefore, the cost formula is $1,011 per month plus $318 per unit shipped or Y = $1,011 + $318X. Note that the R2 is 0.96, which means that 96% of the variation in shipping costs is explained by the number of units shipped. This is a very high R2 and indicates a very good fit. 2. Scattergraph method .......................... High-low method ................................ Least-squares regression method ........ Variable Cost per Unit $300 $350 $318 Fixed Cost per Month $1,100 $800 $1,011 Note that the high-low method gives estimates that are quite different from the estimates provided by least-squares regression. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 47 Exercise 6A-3 (30 minutes) 1. Units (X) 24 15 30 12 18 27 Total Quality Control Cost (Y) $540 $400 $620 $380 $480 $580 A spreadsheet application such as Microsoft® Excel or a statistical software package can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are: Intercept (fixed cost) ............... Slope (variable cost per unit) .... R2 ........................................... $215 $13.57 0.98 Therefore, the cost formula is $215 per week plus $13.57 per unit. Note that the R2 is 0.98, which means that 98% of the variation in quality control costs is explained by the number of units produced. This is a very high R2 and indicates a very good fit. 2. Y = $215 + $13.57X, where X is the number of units produced. 3. Total expected quality control costs if 20 units are produced: Variable cost: 20 units × $13.57 per unit .............. Fixed cost ........................................................... Total expected cost .............................................. $271.40 215.00 $486.40 4. It seems very plausible that as more units are produced, quality control costs would increase since each unit produced goes through a quality control process. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 48 Managerial Accounting, 9th Canadian Edition Problem 6A-4 (45 minutes) 1. Number of Leagues (X) 5 2 4 6 3 Total Cost (Y) $13,000 $7,000 $10,500 $14,000 $10,000 A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are: Intercept (fixed cost) .................. Slope (variable cost per unit) ....... R2 .............................................. $4,100 $1,700 0.96 Therefore, the variable cost per league is $1,700 and the fixed cost is $4,100 per year. Note that the R2 is 0.96, which means that 96% of the variation in cost is explained by the number of leagues. This is a very high R2 and indicates a very good fit. 2. Y = $4,100 + $1,700X 3. The expected total cost for 7 leagues would be: Fixed cost ......................................................... Variable cost (7 leagues × $1,700 per league)..... Total cost .......................................................... $ 4,100 11,900 $16,000 The problem with using the cost formula from (2) to estimate total cost in this particular case is that an activity level of 7 leagues may be outside the relevant range—the range of activity within which the fixed cost is approximately $4,100 per year and the variable cost is approximately $1,700 per league. These approximations appear to be reasonably accurate within the range of 2 to 6 leagues, but they may be invalid outside this range. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 49 Problem 6A-4 (continued) 4. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 50 Managerial Accounting, 9th Canadian Edition Problem 6A-5 (45 minutes) 1. Units Sold (000s) (X) 16 18 23 19 17 20 25 22 Shipping Expense (Y) $160,000 $175,000 $210,000 $180,000 $170,000 $190,000 $230,000 $205,000 A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are: Intercept (fixed cost) ............... Slope (variable cost per unit) .... R2 ........................................... $40,000 $7,500 0.99 Therefore the cost formula for shipping expense is $40,000 per quarter plus $7,500 per thousand units sold ($7.50 per unit), or Y = $40,000 + $7.50X, where X is the number of units sold. Note that the R2 is 0.99, which means that 99% of the variation in shipping cost is explained by the number of meals served. This is a very high R2 and indicates a very good fit. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 51 Problem 6A-5 (continued) 2. Mayer Company Budgeted Income Statement For the First Quarter of Year 3 Sales (21,000 units × $50 per unit) .................... $1,050,000 Variable expenses: Cost of goods sold (21,000 units × $20 per unit) ....................... $420,000 Shipping expense (21,000 units × $7.50 per unit) ..................... 157,500 Sales commission ($1,050,000 × 0.05) ............ 52,500 Total variable expenses ...................................... 630,000 Contribution margin........................................... 420,000 Fixed expenses: Shipping expenses .......................................... 40,000 Advertising expense ........................................ 170,000 Administrative salaries .................................... 80,000 Depreciation expense ...................................... 50,000 Total fixed expenses .......................................... 340,000 Operating income .............................................. $ 80,000 © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 52 Managerial Accounting, 9th Canadian Edition Case 6A-6 (90 minutes) 1a. Units Produced (X) 60,000 44,000 84,000 48,000 72,000 100,000 120,000 112,000 Utilities Cost (Y) $200,000 $180,000 $240,000 $300,000 $400,000 $420,000 $340,000 $480,000 A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are: Intercept (fixed cost) ............... Slope (variable cost per unit) .... R2 ........................................... $113,407 $2.58 0.47 Therefore, the cost formula using units produced as the activity base is $113,407 per month plus $2.58 per unit produced, or Y = $113,407 + $2.58X. Note that the R2 is 0.47, which means that only 47% of the variation in utility costs is explained by the number of units produced. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 53 Case 6A-6 (continued) b. The scattergraph plot of utility costs versus units produced appears below: © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 54 Managerial Accounting, 9th Canadian Edition Case 6A-6 (continued) 2a. DLHs (X) 15,000 9,000 12,000 18,000 30,000 27,000 24,000 33,000 Utilities Cost (Y) $200,000 $180,000 $240,000 $300,000 $400,000 $420,000 $340,000 $480,000 A spreadsheet application such as Excel or a statistical software package can be used to compute the slope and intercept of the least-squares regression line for the above data. The results are: Intercept (fixed cost) ............... Slope (variable cost per unit) .... R2 ........................................... $68,000 $12 0.94 Therefore, the cost formula using direct labour-hours as the activity base is $68,000 per quarter plus $12 direct labour-hour, or Y = $68,000 + $12X. Note that the R2 is 0.94, which means that 94% of the variation in utility costs is explained by the number of direct labour-hours. This is a very high R2 and is an indication of a good fit. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 55 Case 6A-6 (continued) b. The scattergraph plot of utility costs versus direct labour-hours appears below: 3. The company should probably use direct labour-hours as the activity base, since the fit of the regression line to the data is much tighter than it is with units produced. The R2 for the regression using direct labourhours as the activity base is twice as large as for the regression using units produced as the activity base. However, managers should look more closely at the costs and try to determine why utilities costs are more closely tied to direct labour-hours than to the number of units produced. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. 56 Managerial Accounting, 9th Canadian Edition Case 6A-6 (continued) 4. It is plausible that both units produced and direct labour hours would be related to utilities costs. However, because different models require different amounts of direct labour, it seems more plausible to expect a strong association between labour hours and utilities costs. Using units produced as the independent variable assumes no difference in labour hour requirements across the various models. Not surprisingly, the results of the regression analysis are consistent with the qualitative assessment of economic plausibility with a much higher R2 value for the model using direct labour hours. © McGraw-Hill Ryerson Ltd. 2012. All rights reserved. Solutions Manual, Chapter 6 57