Chapter 18 - Answer
Content
MANAGEMENT ACCOUNTING (VOLUME II) - Solutions Manual
CHAPTER 18 APPLICATION OF QUANTITATIVE TECHNIQUES IN PLANNING, CONTROL AND DECISION MAKING II
I. Questions 1. PERT is superior to Gantt Charts in complex projects because: a. PERT charts are flexible and can reflect slippage or changes in plans, but Gantt charts simply plot a bar chart against a calendar scale. b. PERT charts reflect interdependencies among activities; Gantt charts do not. c. PERT charts reflect uncertainties or tolerances in the time estimates for various activities; Gantt charts do not. 2. The use of PERT provides a structured foundation for planning complex projects in sufficient detail to facilitate effective control. A workable sequence of events that comprise the project are first identified. Each key event should represent a task; then the interdependent relationships between the events are structured. After the network of events is constructed, cost and time parameters are established for each package. Staffing plans are reviewed and analyzed. The “critical path” computation identifies sequence of key events with total time equal to the time allotted for the project’s completion. Jobs which are not on the critical path can be slowed down and the slack resources available on these activities reallocated to activities on the critical path. Use of PERT permits sufficient scheduling of effort by functional areas and by geographic location. It also allows for restructuring scheduling efforts and redeployment of workers as necessary to compensate for delays or bottlenecks. The probability of completing this complex project on time and within the allotted budget is increased. 3. Time slippage in noncritical activities may not warrant extensive managerial analysis because of available slack, but activity cost usually increases with time and should be monitored.
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Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
4. The critical path is the network path with the longest cumulative expected activity time. It is critical because a slowdown along this path delays the entire project. 5. Crashing the network means finding the minimum cost for completing the project in minimum time in order to achieve an optimum tradeoff between cost and time. The differential crash cost of an activity is the additional cost of that activity for each period of time saved. 6. Slack is the amount of time an event can be delayed without affecting the project’s completion date. Slack can be utilized by management as a buffer against bottlenecks that may occur on the critical path. 7. Unit gross margin are typically computed with an allocation of fixed costs. Total fixed costs generally will not change with a change in volume within the relevant range. Unitizing the fixed costs results in treating them as though they are variable costs when, in fact, they are not. Moreover, when multiple products are manufactured, the relative contribution becomes the criterion for selecting the optimal product mix. Fixed costs allocations can distort the relative contributions and result in a suboptimal decision. 8. This approach will maximize profits only if there are no constraints on production or sales, or if both products use all scarce resources at an equal rate. Otherwise management would want to maximize the contribution per unit of scarce resource. 9. The opportunity cost of a constraint is the cost of not having additional availability of the constrained resources. This is also called a shadow price. 10. The feasible production region is the area which contains all possible combinations of production outputs. It is bounded by the constraints imposed on production possibilities. The production schedule which management chooses must come from the feasible production region. 11. The accountant usually supplies the contribution margin data that is used in formulating a profit-maximizing objective function. In addition, the accountant participates in the analysis of linear programming outputs by assessing the costs of additional capacity or of changes in product mix. 12. a. b. c. d. e. f. Hourly fee for inventory audit Salary of purchasing supervisor Costs to audit purchase orders and invoices Taxes on inventory Stockout costs Storage costs charged per unit in inventory
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(C) (N) (P) (C) (P) (C)
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
g. h. i. j.
Fire insurance on inventory Fire insurance on warehouse Obsolescence costs on inventory Shipping costs per shipment
(C) (N) (C) (P)
13. Although the inventory models are developed by operations researchers, statisticians and computer specialists, their areas of expertise do not extend to the evaluation of the differential costs for the inventory models. Generally, discussions of inventory models take the costs as given. It is the role of the accountant to determine which costs are appropriate for inclusion in an inventory model. 14. Cost of capital represents the interest expense on funds if they were borrowed or opportunity cost if funds were provided internally or by owners. It is included as carrying cost of inventory because funds are tied up in inventory. 15. Costs that vary with the average number of units in inventory: Inventory insurance Inventory tax Total Purchase price Insurance on shipment Total P 2.80 2.05 (P102.25 x 2%) P 4.85 P102.25 1.50 P103.75
Costs that vary with the number of units purchased:
Total carrying cost = (25% x P103.75) cost of capital + P4.85 = P25.94 + P4.85 = P30.79 Order costs: Shipping permit Costs to arrange for the shipment Unloading Stockout costs Total P201.65 21.45 80.20 122.00 P425.30
II. Problems Problem 1 (Solution is found on the next page.) Problem 2
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Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Requirement (a) The critical path through each of the three alternative paths calculated as the longest is 0 - 1 - 6- 7- 8. 0-1-2-5-8 0-1-3-4-7-8 0-1-6-7-8 ________
* critical
2 + 8 + 10 + 14 2+8+7+5+3 2 + 26 + 9 + 3
= = =
34 25 40*
Requirement (b) 40 - 3 - 5 = 32 Requirement (c) If path 4 - 7 has an unfavorable time variance of 10, this means it takes a total time of 15 to finish this activity rather than 5. This gives the path 0 - 1 - 3 - 4 - 7 - 8 a total time of 35, but since this is less than the critical path of 40, it has no effect. Requirement (d) The earliest time for reaching event 5 via 0 - 1 - 2 - 5 is 20, the sum of the expected times. Problem 3 No, they didn’t make a right decision, since they included fixed costs which do not differ in the short run. If they had used contribution margin instead of gross margin, they would have had P5 for G1 and P6.50 for G2, therefore they would have decided to produce G2 exclusively.
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Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
Problem 1 Requirement (a)
TASKS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Hobbing
Order 1
Order 3 Order 1 X X Order 3
Order 4 X X X
Order 2 Order 4 Order 2
Machini X X X X ng ___________ X Dead Time
Requirement (b) 28 days are required for the four orders.
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Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Problem 4 Order costs P Carrying costs S a. Carrying costs: QS 2 = 250 x P109.40 2 = P13,675.00 = = = = Insurance P860 + + + + Other order costs P18 Cost of capital on inventory 20% x P222 = P119.40 = P878
Out-of-pocket costs P65
Order costs: AP Q Total b. Economic order quantity: Q* = = 1,500 x P878 250 = P 5,268.00 P18,943.00
√
=
2 x 1,500 x P878 P109.40
= √ 24,077
=
155 units
Carrying costs: QS 2 Order costs: AP Q Total Problem 5 = 1,500 x P878 155 = P 8,496.77 P16,975.27 155 x P109.40 2 = P 8,478.50
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Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
It is necessary to evaluate the annual carrying costs and expected stockout costs at each safety-stock level. The carrying cost will be P24.40 for each unit in safety stock. With the given order size, there are 15 orders placed a year (i.e., 39,000/2,600 = 15). Based on these computations, we prepare the following schedule:
Safety Stock 0 150 175 250 Carrying Costs of Safety Stock 0 150 x P24.40 = P3,660 175 x P24.40 = P4,270 250 x P24.40 = P6,100b Expected Stockout Costs 0.50 x 15a x P1,650 = P12,375 0.20 x 15a x P1,650 = P 4,950 0.05 x 15a x P1,650 = P 1,273.5 0.01 x 15a x P1,650 = P 247.5 Total Costs P12,375 8,610 5,507.5 (optional) 6,347.5
Additional computations:
a b
15 is the number of orders per year. It should be evident that at this level the carrying costs alone exceed the total costs at a safety stock of 175 units. Therefore, it is not possible for this or any safety-stock level larger than 250 to be less costly than 175 units. Indeed, given a total cost at 175 units of P5,507.5, stockout costs would have to occur with probability zero for any safety stock greater than 225.72 units (i.e., P5,507.5 / P24.40 = P225.72).
III. Multiple Choice Questions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. C B D B D C A A A C 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. D C A A A C C D C D 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. D C C D D B D E B A 31. 32. 33. 34. 35. 36. 37. 38. C D A C D C D D
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CHAPTER 18 APPLICATION OF QUANTITATIVE TECHNIQUES IN PLANNING, CONTROL AND DECISION MAKING II
I. Questions 1. PERT is superior to Gantt Charts in complex projects because: a. PERT charts are flexible and can reflect slippage or changes in plans, but Gantt charts simply plot a bar chart against a calendar scale. b. PERT charts reflect interdependencies among activities; Gantt charts do not. c. PERT charts reflect uncertainties or tolerances in the time estimates for various activities; Gantt charts do not. 2. The use of PERT provides a structured foundation for planning complex projects in sufficient detail to facilitate effective control. A workable sequence of events that comprise the project are first identified. Each key event should represent a task; then the interdependent relationships between the events are structured. After the network of events is constructed, cost and time parameters are established for each package. Staffing plans are reviewed and analyzed. The “critical path” computation identifies sequence of key events with total time equal to the time allotted for the project’s completion. Jobs which are not on the critical path can be slowed down and the slack resources available on these activities reallocated to activities on the critical path. Use of PERT permits sufficient scheduling of effort by functional areas and by geographic location. It also allows for restructuring scheduling efforts and redeployment of workers as necessary to compensate for delays or bottlenecks. The probability of completing this complex project on time and within the allotted budget is increased. 3. Time slippage in noncritical activities may not warrant extensive managerial analysis because of available slack, but activity cost usually increases with time and should be monitored.
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Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
4. The critical path is the network path with the longest cumulative expected activity time. It is critical because a slowdown along this path delays the entire project. 5. Crashing the network means finding the minimum cost for completing the project in minimum time in order to achieve an optimum tradeoff between cost and time. The differential crash cost of an activity is the additional cost of that activity for each period of time saved. 6. Slack is the amount of time an event can be delayed without affecting the project’s completion date. Slack can be utilized by management as a buffer against bottlenecks that may occur on the critical path. 7. Unit gross margin are typically computed with an allocation of fixed costs. Total fixed costs generally will not change with a change in volume within the relevant range. Unitizing the fixed costs results in treating them as though they are variable costs when, in fact, they are not. Moreover, when multiple products are manufactured, the relative contribution becomes the criterion for selecting the optimal product mix. Fixed costs allocations can distort the relative contributions and result in a suboptimal decision. 8. This approach will maximize profits only if there are no constraints on production or sales, or if both products use all scarce resources at an equal rate. Otherwise management would want to maximize the contribution per unit of scarce resource. 9. The opportunity cost of a constraint is the cost of not having additional availability of the constrained resources. This is also called a shadow price. 10. The feasible production region is the area which contains all possible combinations of production outputs. It is bounded by the constraints imposed on production possibilities. The production schedule which management chooses must come from the feasible production region. 11. The accountant usually supplies the contribution margin data that is used in formulating a profit-maximizing objective function. In addition, the accountant participates in the analysis of linear programming outputs by assessing the costs of additional capacity or of changes in product mix. 12. a. b. c. d. e. f. Hourly fee for inventory audit Salary of purchasing supervisor Costs to audit purchase orders and invoices Taxes on inventory Stockout costs Storage costs charged per unit in inventory
18-2
(C) (N) (P) (C) (P) (C)
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
g. h. i. j.
Fire insurance on inventory Fire insurance on warehouse Obsolescence costs on inventory Shipping costs per shipment
(C) (N) (C) (P)
13. Although the inventory models are developed by operations researchers, statisticians and computer specialists, their areas of expertise do not extend to the evaluation of the differential costs for the inventory models. Generally, discussions of inventory models take the costs as given. It is the role of the accountant to determine which costs are appropriate for inclusion in an inventory model. 14. Cost of capital represents the interest expense on funds if they were borrowed or opportunity cost if funds were provided internally or by owners. It is included as carrying cost of inventory because funds are tied up in inventory. 15. Costs that vary with the average number of units in inventory: Inventory insurance Inventory tax Total Purchase price Insurance on shipment Total P 2.80 2.05 (P102.25 x 2%) P 4.85 P102.25 1.50 P103.75
Costs that vary with the number of units purchased:
Total carrying cost = (25% x P103.75) cost of capital + P4.85 = P25.94 + P4.85 = P30.79 Order costs: Shipping permit Costs to arrange for the shipment Unloading Stockout costs Total P201.65 21.45 80.20 122.00 P425.30
II. Problems Problem 1 (Solution is found on the next page.) Problem 2
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Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Requirement (a) The critical path through each of the three alternative paths calculated as the longest is 0 - 1 - 6- 7- 8. 0-1-2-5-8 0-1-3-4-7-8 0-1-6-7-8 ________
* critical
2 + 8 + 10 + 14 2+8+7+5+3 2 + 26 + 9 + 3
= = =
34 25 40*
Requirement (b) 40 - 3 - 5 = 32 Requirement (c) If path 4 - 7 has an unfavorable time variance of 10, this means it takes a total time of 15 to finish this activity rather than 5. This gives the path 0 - 1 - 3 - 4 - 7 - 8 a total time of 35, but since this is less than the critical path of 40, it has no effect. Requirement (d) The earliest time for reaching event 5 via 0 - 1 - 2 - 5 is 20, the sum of the expected times. Problem 3 No, they didn’t make a right decision, since they included fixed costs which do not differ in the short run. If they had used contribution margin instead of gross margin, they would have had P5 for G1 and P6.50 for G2, therefore they would have decided to produce G2 exclusively.
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Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
Problem 1 Requirement (a)
TASKS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Hobbing
Order 1
Order 3 Order 1 X X Order 3
Order 4 X X X
Order 2 Order 4 Order 2
Machini X X X X ng ___________ X Dead Time
Requirement (b) 28 days are required for the four orders.
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Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Problem 4 Order costs P Carrying costs S a. Carrying costs: QS 2 = 250 x P109.40 2 = P13,675.00 = = = = Insurance P860 + + + + Other order costs P18 Cost of capital on inventory 20% x P222 = P119.40 = P878
Out-of-pocket costs P65
Order costs: AP Q Total b. Economic order quantity: Q* = = 1,500 x P878 250 = P 5,268.00 P18,943.00
√
=
2 x 1,500 x P878 P109.40
= √ 24,077
=
155 units
Carrying costs: QS 2 Order costs: AP Q Total Problem 5 = 1,500 x P878 155 = P 8,496.77 P16,975.27 155 x P109.40 2 = P 8,478.50
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Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
It is necessary to evaluate the annual carrying costs and expected stockout costs at each safety-stock level. The carrying cost will be P24.40 for each unit in safety stock. With the given order size, there are 15 orders placed a year (i.e., 39,000/2,600 = 15). Based on these computations, we prepare the following schedule:
Safety Stock 0 150 175 250 Carrying Costs of Safety Stock 0 150 x P24.40 = P3,660 175 x P24.40 = P4,270 250 x P24.40 = P6,100b Expected Stockout Costs 0.50 x 15a x P1,650 = P12,375 0.20 x 15a x P1,650 = P 4,950 0.05 x 15a x P1,650 = P 1,273.5 0.01 x 15a x P1,650 = P 247.5 Total Costs P12,375 8,610 5,507.5 (optional) 6,347.5
Additional computations:
a b
15 is the number of orders per year. It should be evident that at this level the carrying costs alone exceed the total costs at a safety stock of 175 units. Therefore, it is not possible for this or any safety-stock level larger than 250 to be less costly than 175 units. Indeed, given a total cost at 175 units of P5,507.5, stockout costs would have to occur with probability zero for any safety stock greater than 225.72 units (i.e., P5,507.5 / P24.40 = P225.72).
III. Multiple Choice Questions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. C B D B D C A A A C 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. D C A A A C C D C D 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. D C C D D B D E B A 31. 32. 33. 34. 35. 36. 37. 38. C D A C D C D D
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