4 Cost Behaviour APPLY WHAT YOU HAVE LEARNED 1. 1. V Direct material 2. V Direct labour 3. F Cost of factory security guard 4. F Straight-line amortization on production equipment 5. M Maintenance on production equipment 6. M Maintenance on factory building 7. V Cost of cleaning supplies used in the factory 8. F Rent on the factory building 9. F Salary for the two factory supervisors 10. F Vice president of manufacturing’s salary 11. M/V Cost of electricity used in the factory 12. M Cost of production machine lubricants 2. 1. 2. F F 3. M/V 4. V 5. F 6. F 82 Cost of the car Insurance cost (or M - Can vary depending upon insurance company) Maintenance cost Cost of gasoline The cost of a college parking permit CAA membership Chapter 4 – Cost Behaviour 3. 1. 2. 3. 4. 5. 6. F F V V F F or M Rent for the party hall Cost of the band Cost of cold drinks Cost of food Cost of party decorations Cost of renting tables and chairs 4. 1. 2. 3. 4. F V or M V F Cost of the new office building Basic telephone service Cost of lawyers’ salaries Cost of the receptionist’s wages 5. 1. F 2. 3. 4. 5. 6. 7. F F F or M F M or V V Cost of store rent. (or M if the store has entered into a bonus rent situation) Basic telephone service Cost of salaries for the two salespeople Cost of advertising Cost of store displays Cost of electricity Cost of merchandise sold 6. The accounting department finds it difficult to use the scatter diagram because this diagram does not present a very linear pattern. Without a clear linear pattern, the cost estimates used might bear little correlation to the actual cost behaviour of the truck maintenance. The accounting department could derive precise calculations of the cost behaviour for truck maintenance with a regression analysis. Because no one knows how to accomplish this, the accountants can use the high-low method, which approximates the results obtained with regression analysis. The high-low method is a quick, easy, and low-cost method to approximate the fixed and variable cost of truck maintenance. Chapter 4 – Cost Behaviour 83 7. Diagram (a) is preferred because the relationship between the x and y is more linear and, therefore, it is easier to predict outcomes at various levels of production. 8. a. High Low Difference Sales $2,860,000 2,300,000 $ 560,000 Selling Expense $369,400 347,000 $ 22,400 Variable rate = $22,400 / $560,000 = $0.04 of selling expense for each $1 of sales b. TC = FC + (unit variable rate x volume) $347,000 = FC + (0.04 x $2,300,000) FC = $347,000 – $92,000 FC = $255,000 or TC = FC + (unit variable rate x volume) $369,400 = FC + (0.04 x $2,860,000) FC = $369,400 – $114,400 FC = $255,000 c. 84 TC = FC + (unit variable rate x volume) TC = $255,000 + (.04 x $2,500,000) TC = $255,000 + $100,000 TC = $355,000 Chapter 4 – Cost Behaviour 9. a. High Low Difference Units 15,300 14,500 800 Packaging Cost $33,191 32,567 $ 624 Variable rate = $624 / 800 units = $0.78 packaging cost for each unit packaged b. TC = FC + (unit variable rate x volume) $32,567 = FC + ($0.78 x 14,500) FC = $32,567 – $11,310 FC = $21,257 or TC = FC + (unit variable rate x volume) $33,191 = FC + ($0.78 x 15,300) FC = $33,191 – $11,934 FC = $21,257 c. TC = FC + (unit variable rate x volume) TC = $21,257 + ($0.78 x 15,000) TC = $21,257 + $11,700 TC = $32,957 Chapter 4 – Cost Behaviour 85 10. a. High Low Difference Inspections 48,600 41,950 6,650 Inspection Cost $83,790 77,273 $ 6,517 Variable rate = $6,517 / 6,650 inspections = $0.98 of inspection cost for each inspection b. TC = FC + (unit variable rate x volume) $77,273 = FC + ($0.98 x 41,950) FC = $77,273 – $41,111 FC = $36,162 or TC = FC + (unit variable rate x volume) $83,790 = FC + ($0.98 x 48,600) FC = $83,790 – $47,628 FC = $36,162 c. TC = FC + (unit variable rate x volume) TC = $36,162 + ($0.98 x 45,000) TC = $36,162 + $44,100 TC = $80,262 86 Chapter 4 – Cost Behaviour 11. Machine Hours a. High 120,000 Low 100,000 Difference 20,000 Electricity Cost $221,600 188,000 $ 33,600 Variable rate = $33,600 / 20,000 hours = $1.68 of electricity for each machine hour b. TC = FC + (unit variable rate x volume) $221,600 = FC + ($1.68 x 120,000) FC = $221,600 – $201,600 FC = $20,000 or TC = FC + (unit variable rate x volume) $188,000 = FC + ($1.68 x 100,000) FC = $188,000 – $168,000 FC = $20,000 c. TC = FC + (unit variable rate x volume) TC = $20,000 + ($1.68 x 122,500) TC = $20,000 + $205,800 TC = $225,800 Chapter 4 – Cost Behaviour 87 12. Copies Produced a. High 77,800 Low 52,550 Difference 25,250 Cost $2,592.82 1,961.57 $ 631.25 Variable rate = $631.25 / 25,250 copies = $0.025 of service and supply cost for each copy produced b. TC = FC + (unit variable rate x volume) $1,961.57 = FC + ($0.025 x 52,550) FC = $1,961.57 – $1,313.75 FC = $647.82 or TC = FC + (unit variable rate x volume) $2,592.82 = FC + ($0.025 x 77,800) FC = $2,592.82 – $1,945 FC = $647.82 c. 88 TC = FC + (unit variable rate x volume) TC = $647.82 + ($0.025 x 75,000) TC = $647.82 + $1,875 TC = $2,522.82 Chapter 4 – Cost Behaviour 13. a. High Low Difference Parts Handled 185,400 154,300 31,100 Cost $10,675.37 9,244.77 $ 1,430.60 Variable rate = $1,430.60 / 31,100 copies = $0.046 of service and material handling cost for each part handled b. TC = FC + (unit variable rate x volume) $10,675.37 = FC + ($0.046 x 185,400) FC = $10,675.37 – $8,528.40 FC = $2,146.97 or TC = FC + (unit variable rate x volume) $9,244.77 = FC + ($0.046 x 154,300) FC = $9,244.77 – $7,097.80 FC = $2,146.97 c. TC = FC + (unit variable rate x volume) TC = $2,146.97 + ($0.046 x 160,000) TC = $2,146.97 + $7,360 TC = $9,506.97 Chapter 4 – Cost Behaviour 89 14. High Low Difference Units 18,000 15,000 3,000 Shipping Cost $35,400 30,000 $ 5,400 Variable rate = $5,400 / 3,000 units = $1.80 of shipping expense for each unit sold TC = FC + (unit variable rate x volume) $35,400 = FC + ($1.80 x 18,000) FC = $35,400 – $32,400 FC = $3,000 TC = FC + (unit variable rate x volume) TC = $3,000 + ($1.80 x 16,500) TC = $3,000 + $29,700 TC = $32,700 15. High Low Difference Flight Hours Operating Cost 1,875 $2,148,125 1,250 1,563,750 625 $ 584,375 Variable rate = $584,375 / 625 hours = $935 of operating expense per flight hour TC = FC + (unit variable rate x volume) $2,148,125 = FC + ($935 x 1,875) FC = $2,148,125 – $1,753,125 FC = $395,000 TC = FC + (unit variable rate x volume) TC = $395,000 + ($935 x 1,500) TC = $395,000 + $1,402,500 TC = $1,797,500 90 Chapter 4 – Cost Behaviour 16. High Low Difference Number 190 150 40 Operating Cost $8,601 7,741 $ 860 Variable rate = $860 / 40 = $21.50 of operating expense for each charter TC = FC + (unit variable rate x volume) $8,601 = FC + ($21.50 x 190) FC = $8,601 – $4,085 FC = $4,516 TC = FC + (unit variable rate x volume) TC = $4,516.00 + ($21.50 x 185) TC = $4,516.00 + $3,977.50 TC = $8,493.50 17. a. High Low Difference Number 3,000 1,000 2,000 Operating Cost $140,000 80,000 $ 60,000 Variable rate = $60,000 / 2,000 = $30 of operating expense per purchase order b. TC = FC + (unit variable rate x volume) $140,000 = FC + ($30 x 3,000) FC = $140,000 – $90,000 FC = $50,000 c. TC = FC + (unit variable rate x volume) TC = ($50,000 x 4) + ($30 x 7,000) TC = $200,000 + $210,000 TC = $410,000 Chapter 4 – Cost Behaviour 91 18. a. 92 Chapter 4 – Cost Behaviour 18. (Continued) Note to Instructor: Each student’s graph will vary. Likewise, each of their calculations of variable cost per purchase order and fixed costs will vary. When you examine a number of the students’ computations of the total cost, you will find that they are reasonably similar. The variable cost per purchase order is found by comparing two coordinates on the graph: Orders Cost 3,500 $155,000 1,500 100,000 2,000 $ 55,000 $55,000 / 2,000 = $27.50 a. The fixed cost for one quarter is $60,000 b. TC = FC + (UVC x V) TC = ($60,000 x 4) + ($27.50 x 7,000) TC = $240,000 + 192,500 TC = $432,500 Note to Instructor: To judge the merits of each method, consider that the regression model for these data computes fixed costs per quarter at $59,000 and the variable cost per order at $28. Using the regression model, the total cost formula is: TC = FC + (UVC x V) TC = ($59,000 x 4) + ($28 x 7,000) TC = $236,000 + $196,000 TC = $432,000 Chapter 4 – Cost Behaviour 93 19. a. High Low Difference Number 15,000 9,000 6,000 Operating Cost $58,231.51 46,297.51 $11,934.00 Variable cost = $11,934 / 6,000 = $1.989 of operating expense per invoice b. c. TC = FC + (UVC x V) $58,231.51 = FC + ($1.989 x 15,000) FC = $58,231.51 – $29,835.00 FC = $28,396.51 TC = FC + (UVC x V) TC = ($28,396.51 x 4) + ($1.989 x 45,000) TC = $113,586.04 + $89,505.00 TC = $203,091.04 20. a. High Low Difference Number 130 105 25 Operating Cost $26,529.16 25,212.91 $ 1,316.25 Variable cost = $1,316.25 / 25 = $52.65 of operating expense per repair b. TC = FC + (UVC x V) $26,529.16 = FC + ($52.65 x 130) FC = $26,529.16 – $6,844.50 FC = $19,684.66 c. TC = FC + (UVC x V) TC = ($19,684.66 x 4) + ($52.65 x 450) TC = $78,738.64 + $23,692.50 TC = $102,431.14 94 Chapter 4 – Cost Behaviour 21. a. High Low Difference Number 12,100 7,000 5,100 Production Cost $20,500 14,992 $ 5,508 Variable cost = $5,508 / 5,100 = $1.08 of production cost per broom. b. TC = FC + (UVC x V) $20,500 = FC + ($1.08 x 12,100) FC = $20,500 – $13,068 FC = $7,432 c. TC = FC + (UVC x V) TC = $7,432 + ($1.08 x 12,000) TC = $7,432 + $12,960 TC = $20,392 Chapter 4 – Cost Behaviour 95 22. a. 96 Chapter 4 – Cost Behaviour 22. (Continued) Note to Instructor: Each student’s graph will vary. Likewise, each of their calculations of variable cost per broom produced and fixed costs will vary. When you examine a number of the students’ computations of the total cost, you will find that they are reasonably similar. The variable cost per broom produced is found by comparing two coordinates on the graph: Brooms Cost 14,000 $22,000 6,000 14,000 8,000 $ 8,000 $8,000 / 8,000 = $1.00 b. c. The total fixed cost per the graph is $9,000. TC = FC + (UVC x V) TC = $9,000 + ($1.00 x 12,000) TC = $9,000 + $12,000 TC = $21,000 Note to Instructor: To judge the merits of each method, consider that the regression model for these data computes fixed costs per quarter at $8,017 and the variable cost per broom at $0.9861. Using the regression model, the total cost formula is: TC = FC + (UVC x V) TC = $8,017 + ($0.9861 x 12,000) TC = $8,017 + $11,833 TC = $19,850 Chapter 4 – Cost Behaviour 97 23. a. High Low Difference Number 35 15 20 Cost $78,000 42,000 $36,000 Variable rate = $36,000/20 = $1,800 of cost per session b. TC = FC + (UVC x V) $78,000 = FC + ($1,800 x 35) FC = $78,000 – $63,000 FC = $15,000 per quarter c. TC = FC + (UVC x V) TC = $15,000 + ($1,800 x 25) TC = $15,000 + $45,000 TC = $60,000 98 Chapter 4 – Cost Behaviour 24. a. Chapter 4 – Cost Behaviour 99 24. Note to Instructor: Each student’s graph will vary. Likewise, each of their calculations of variable cost per session and fixed costs will vary. When you examine a number of the students’ computations of the total cost, you will find that they are reasonably similar. The variable cost per session is found by comparing two coordinates on the graph: Sessions Cost 40 $90,000 10 30,000 30 $60,000 $60,000 / 30 = $2,000 b. The total fixed costs from the graph are $10,000. c. TC = FC + (UVC x V) TC = $10,000 + ($2,000 x 25) TC = $10,000 + $50,000 TC = $60,000 Note to Instructor: To judge the merits of each method, consider that the regression model for these data computes fixed costs per quarter at $11,250 and the variable cost per session at $1,980. Using the regression model, the total cost formula is: TC = FC + (UVC x V) TC = $11,250 + ($1,980 x 25) TC = $11,250 + $49,500 TC = $60,750 100 Chapter 4 – Cost Behaviour 25. a. High Low Difference Tests 140,000 50,000 90,000 Testing Cost $1,860,000 1,290,000 $ 570,000 Variable cost = $570,000 / 90,000 = $6.333 of testing cost for each test given b. TC = FC + (UVC x V) $1,860,000 = FC + ($6.333 x 140,000) FC = $1,860,000 – $886,620 FC = $973,380 c. TC = FC + (UVC x V) TC = $973,380 + ($6.333 x 125,000) TC = $973,380 + $791,625 TC = $1,765,005 Chapter 4 – Cost Behaviour 101 26. a. 102 Chapter 4 – Cost Behaviour 26. (Continued) Note to Instructor: Each student’s graph will vary. Likewise, each of their calculations of variable cost per test performed and fixed costs will vary. When you examine a number of the students’ computations of the total cost, you will find that they are reasonably similar. The variable cost per test is found by comparing two coordinates on the graph: Tests Cost 160,000 $1,960,000 20,000 1,150,000 140,000 $ 810,000 $810,000/140,000 = $5.786 per test b. c. Fixed costs from the graph are $1,025,000 TC = FC + (UVC x V) TC = $1,025,000 + ($5.786 x 125,000) TC = $1,025,000 + $723,250 TC = $1,748,250 Note to Instructor: To judge the merits of each method, consider that the regression model for these data computes fixed costs per quarter at $1,026,101 and the variable cost per test at $5.82. Using the regression model, the total cost formula is: TC = FC + (UVC x V) TC = $1,026,101 + ($5.82 x 125,000) TC = $1,026,101 + $727,500 TC = $1,753,601 Chapter 4 – Cost Behaviour 103 27. Cost of Goods Sold High Low Difference Cost $920,000 800,000 $120,000 Sales $1,150,000 1,000,000 $ 150,000 Variable cost = $120,000 / $150,000 = $0.80 of COGS for each dollar of sales TC = FC + (UVC x V) $920,000 = FC + ($0.80 x 1,150,000) FC = $920,000 – $920,000 FC = 0 Sales Commissions Cost High $17,250 Low 15,000 Difference $ 2,250 Sales $1,150,000 1,000,000 $ 150,000 Variable cost = $2,250 / $150,000 = $0.015 of sales commission per sales dollar TC = FC + (UVC x V) $17,250 = FC + ($0.015 x 1,150,000) FC = $17,250 – $17,250 FC = 0 Store Rent High Low Difference Cost $3,000 3,000 0 Sales $1,150,000 1,000,000 $ 150,000 Variable cost = $0 / $150,000 = $0.0 of store rent for each dollar of sales TC = FC + (UVC x V) $3,000 = FC + ($0 x 1,150,000) FC = $3,000 104 Chapter 4 – Cost Behaviour 27. (Continued) Amortization High Low Difference Cost $20,000 20,000 $ 0 Sales $1,150,000 1,000,000 $ 150,000 Variable cost = $0 / $150,000 = $0.0 of Amortization for each dollar of sales TC = FC + (UVC x V) $20,000 = FC + ($0 x 1,150,000) FC = $20,000 Maintenance High Low Difference Cost $4,100 3,800 $ 300 Sales $1,150,000 1,000,000 $ 150,000 Variable cost = $300 / $150,000 = $0.002 of maintenance cost per sales dollar TC = FC + (UVC x V) $4,100 = FC + ($0.002 x 1,150,000) FC = $4,100 – $2,300 FC = $1,800 Office Salaries High Low Difference Cost $35,500 34,000 $ 1,500 Sales $1,150,000 1,000,000 $ 150,000 Variable cost = $1,500 / $150,000 = $0.01 of office salaries for each dollar of sales Chapter 4 – Cost Behaviour 105 27. (Continued) TC = FC + UVC x V $35,500 = FC + ($0.01 x 1,150,000) FC = $35,500 – $11,500 FC = $24,000 28. Direct Material High Low Difference Units 326,000 257,000 69,000 Cost $775,880 611,660 $164,220 Variable rate = $164,220 / 69,000 = $2.38 of Direct Material for each unit TC = FC + (UVC x V) $775,880 = FC + ($2.38 x 326,000) FC = $775,880 – $775,880 FC = 0 Direct Labour High Low Difference Units 326,000 257,000 69,000 Cost $2,109,220 1,662,790 $ 446,430 Variable rate = $446,430 / 69,000 = $6.47 of Direct Labour for each unit TC = FC + (UVC x V) $2,109,220 = FC + ($6.47 x 326,000) FC = $2,109,220 – $2,109,220 FC = 0 106 Chapter 4 – Cost Behaviour 28. (Continued) Manufacturing Overhead Units High 326,000 Low 257,000 Difference 69,000 Cost $1,868,760 1,781,820 $ 86,940 Variable rate = $86,940 / 69,000 = $1.26 of manufacturing overhead per unit TC = FC + (UVC x V) $1,868,760 = FC + ($1.26 x 326,000) FC = $1,868,760 – $410,760 FC = $1,458,000 Chapter 4 – Cost Behaviour 107 29. Cost of Goods Sold Cost High $112,500 Low 75,000 Difference $ 37,500 Sales $150,000 100,000 $ 50,000 Variable cost = $37,500 / $50,000 = $0.75 of COGS for each dollar of sales TC = FC + (UVC x V) $112,500 = FC + ($0.75 x 150,000) FC = $112,500 – $112,500 FC = 0 Sales Commissions Cost High $ 7,500 Low 5,000 Difference $ 2,500 Sales $150,000 100,000 $ 50,000 Variable cost = $2,500 / $50,000 = $0.05 of sales commission per dollar of sales TC = FC + (UVC x V) $7,500 = FC + ($0.05 x 150,000) FC = $7,500 – $7,500 FC = 0 Store Rent High Low Difference Cost $ 1,000 1,000 $ 0 Sales $150,000 100,000 $ 50,000 Variable cost = $0 / $50,000 = $0.0 of Store Rent for each dollar of sales 108 Chapter 4 – Cost Behaviour 29. (Continued) TC = FC + (UVC x V) $1,000 = FC + ($0 x 150,000) FC = $1,000 – $0 FC = $1,000 Amortization High Low Difference Cost $ 500 500 $ 0 Sales $150,000 100,000 $ 50,000 Variable cost = $0 / $50,000 = $0.0 of amortization for each dollar of sales TC = FC + (UVC x V) $500 = FC + ($0 x 150,000) FC = $500 – $0 FC = $500 Maintenance High Low Difference Cost $ 250 200 $ 50 Sales $150,000 100,000 $ 50,000 Variable cost = $50 / $50,000 = $0.001 of maintenance per dollar of sales TC = FC + (UVC x V) $250 = FC + ($0.001 x 150,000) FC = $250 – $150 FC = $100 Chapter 4 – Cost Behaviour 109 29. (Continued) Office Salaries Cost High $6,000 Low 5,000 Difference $1,000 Sales $150,000 100,000 $ 50,000 Variable rate = $1,000 / $50,000 = $0.02 of office salaries per dollar of sales TC = FC + (UVC x V) $6,000 = FC + ($0.02 x 150,000) FC = $6,000 – $3,000 FC = $3,000 b. 30. 1. 2. 3. 4. 110 The information provided in requirement a describes the cost behaviour of each cost. This helps decision makers budget costs for the future. Y c f a d b b X a b Chapter 4 – Cost Behaviour 31. The high-low method approximates the true relationship between fixed and variable costs in a total cost formula. It is quick and easy to compute, but only considers two observations from the entire body of available data. It does not afford the opportunity to determine if a linear relationship exists between the costs and the volume in the given situation. The scatter graph method presents a visual picture of the total cost behaviour over a number of measurement points. The picture allows the reader to see how linear the relationship is and any data that fall outside the normal results. The decision maker must attempt to draw a line that represents the mean of the data points. The point at which the line intersects the Y axis at zero activity is the fixed cost amount. The slope of the line is the variable cost per unit. The line provides the total cost for any activity amount along the line. Even though this method uses visual estimation, the method provides a more robust result than the high-low method, because all of the observations are incorporated into the solution and the decision maker can visually evaluate the linearity of the data. Regression analysis provides a very accurate description of the relationship between cost and activity. Although most spreadsheet software contains regression models that are easy to use, regression analysis requires more knowledge than either the scatter graph method or the high-low method. The data output is as easy to use as the data output of the other methods. 32. Students’ answers will vary but should include the basic information contained in the answer to Problem 31 plus their own recommendation. Chapter 4 – Cost Behaviour 111 33. Delivery Expense Number Expense High 700 $26,480 Low 600 25,480 Difference 100 $ 1,000 Variable cost = $1,000/100 = $10 of Delivery Expense for each delivery TC = FC + (UVC x V) $26,480 = FC + ($10 x 700) FC = $26,480 – $7,000 FC = $19,480 2004: Number of Deliveries Cost under Proposal @ $30 Cost under Current System Savings over Proposal 1,250 $37,500 31,980 (19,480 + [1,250 x 10]) $ 5,520 2005: Number of Deliveries Cost under Proposal @ $30 Cost under Current System Savings over Proposal 1,775 $53,250 37,230 (19,480 + [1,775 x 10]) $16,020 Sznadel should reject the proposal because as the number of deliveries grows, the cost of outsourcing the deliveries will become much higher than delivering within the organization. 112 Chapter 4 – Cost Behaviour 34. Each student group’s analysis will vary but should describe the fixed costs of the merchandising business including such things as straight-line amortization of furniture and equipment, insurance, monthly salaries, and rent. The variable costs should include product and packaging. Mixed costs include many other costs such as telephone, utilities, wages, and advertising. 35. To: Mr. Al Palmer From: The costs of your new playground will consist of a number of fixed, variable, and mixed costs. A fixed cost is the same regardless of the number of hours of operation, variable costs relate directly to the number of hours of operation, and mixed costs have some fixed amount and some variable amount. The fixed cost of the playground includes the amortization that will occur each year on the equipment and the building addition. In addition, the property taxes and property insurance will increase because of the building and equipment. You might also need to increase the personal injury liability insurance to include the risk of children being hurt, lost, or endangered. Variable costs of operating the playground include the salary of the childcare workers, payroll taxes, employee benefits, paper supplies, food and drink that you might serve, and utilities. These will vary in proportion to the number of hours of operation. Mixed costs include repairs and maintenance on the equipment and space because these costs will be partly routine and partly dependent upon the amount of usage. If we can analyze each of these costs, we can determine the overall fixed costs of the operation and the variable cost per hour. We can construct the projected revenues and expenses to allow you to make the best possible decision about this project. Chapter 4 – Cost Behaviour 113