CH-10-12 Managing and Allocating Support-Service Costs – Cost Management: Strategies for Business Decisions : Chapter Notes

This Document Contains Chapters 10 to 12 Chapter 10 Managing and Allocating Support-Service Costs Chapter Outline A. Cost Management Challenges — There are three challenges offered in this chapter. 1. Since cost allocation is arbitrary, does it matter how costs are allocated in an organization? 2. How can a cost allocation approach be chosen that allows proper evaluation of tradeoffs that may result from the allocations made? 3. How can managers be educated to understand the complexities of the cost allocation process chosen? B. Learning Objectives: 1. The chapter explains the importance of managing support service costs and why these costs are allocated. 2. It provides understanding of the need to choose single or multiple cost pools and to separate the cost of resources supplied and the cost of resources used. 3. It illustrates how to choose appropriate allocation bases. 4. Chapter 10 illustrates two methods used to allocate support department costs — the direct and step. 5. The chapter evaluates the consequences of choosing among the cost allocation methods. 6. Reciprocal method of cost allocation is explained in the Appendix. C. Service cost challenges exist in virtually every type of organization. Organizations exist for a variety of purposes. For-profit organizations exist to provide goods and services that generate profit. Non-profit organizations and government units operate to provide goods and services that benefit members of a community or society at large. Most of the focus on use of resources in organizations is properly placed on the resources used to meet the objectives of the organization. However, resources are also used to support productive processes. Employees provide services such as Human Resources, information systems, accounting, janitorial services, and top executives’ expertise. Additional resources are expended to house and equip these services. Historically, support services have been viewed as relatively minor costs compared to costs of productive activity. As these costs have increased though, organizations have shifted some of the cost management focus to controlling, reducing, and minimizing costs of support services. 1. Support services may be outsourced. Some organizations have chosen to focus exclusively on their core business. These organizations have consciously chosen to eliminate in-house performance of support activities. When making a decision to outsource or not, there are several factors that should be considered. a. The knowledge base that outsourcing service providers need must be considered. If the skills or expertise needed to successfully perform services cannot be obtained outside of an organization, they must be completed internally. On the other hand, there are some activities that an organization may not have the skills or expertise to perform. For instance, an organization that is expanding into the global market may not have in-house expertise in dealing with complex customs and trade laws or international tax issues. In these instances, it may be more practical to obtain such expertise from outside sources. b. Some information or certain activities may be too sensitive to outsource. In this case, an organization must retain control of these support-service activities by providing them internally. c. The costs of outsourcing compared to the cost of performing services internally must also be considered. d. The reliability of outside service providers must also be considered. This is particularly important if outsourced activities are associated in some way with the reputation of the organization. D. For those support services that continue to be performed internally, the costs of these services must be managed. There are several options for managing support-service costs. Two opposing views are to either provide the services to internal customers at no charge, or to charge internal customers for support services. Each is discussed below. 1. Internal customers who receive support services might be charged nothing for the services. In that case, support service costs are recovered from revenues generated from sale of product (or as illustrated in the text, by tax revenues). Users of the support services do not have the financial information that helps them to recognize the costs of using support services. While this approach is simple, it does nothing to encourage efficient, cost-effective use of the services offered. 2. The costs of support services can be charged to using departments, and costs can be recovered from these internal customers. This is accomplished by use of a system of cost allocations. Since support services cannot be directly traced to users, allocation is the only way that support department costs can be assigned. Allocation of support department costs is arbitrary and may not be accurate measures of resource use. Assigning costs may also create tension and dissension internally if managers do not agree with the charges to their department for the use of support department services. E. Support services exist to facilitate direct or production activities. Direct activities may also be referred to as line activities. Direct services or production activities exist to meet the objectives of an organization. Support services exist only to help the entire organization to function more smoothly. 1. Direct or production departments are those departments that generate revenue. Even in the case of non-profit organizations or government agencies, certain departments are the source of cash inflow and can be viewed as direct departments. Support-service departments, on the other hand, only generate costs. a. Support-service costs are often facility-level resource costs that don’t vary directly with production activity. 2. The use of support department costs is not easily observable. For instance, unit-level production costs are directly related to production activity, and changes in production costs can be traced to changes in unit-level activity. Support department costs cannot be traced this way, even though costs may be indirectly related to unit-level production activities. For instance, support services of the Payroll Department are necessary because of employees in direct and other departments. In other words, without the production activities, there would be no need for a Payroll Department. However, since Payroll Department employees are paid a salary that is not based purely on production activities, there is no direct way to trace Payroll Department activities to different production departments. Even if Payroll Department costs could justifiably be assigned based on number of employees in each production department, they would not be directly traceable to units of product unless labor costs themselves could be traced that way. F. Allocation of support service costs is really a full cost problem, similar to the problems described in Chapter 4. Recall, in Chapter 4, the problem of assigning higher-level production costs to lower-level activities made cost allocation necessary. Allocation of support-services costs creates the same type of problem, because non-production facility-level costs are allocated to production departments. 1. The impact of cost allocation on managers’ decision-making activities must be considered. Cost allocation from support departments should be excluded from consideration in making certain decisions. For instance, decisions about profitability of products or product lines should not include support department cost allocations. a. Cost allocations from support departments should be used to highlight the fact that direct departments are the reason for support department costs. The costcausing direct department should pay for support department costs. In order for them to pay though, there must be a way to determine the amounts due. b. Allocation of costs to direct (production) departments makes the cost-causers conscious of the need to manage these costs. If there is no cost attached to support services, then users may not be efficient in their use of such services. c. Allocation of costs aids managers in planning and budgeting. To the extent that support department costs change with direct department activity, managers can better anticipate these changes in support department costs. For example, if a production department anticipates that a large number of new hires will be necessary in the coming year, it should also be conscious of the attendant costs that will occur in the Human Resources Department. 2. In addition to managing support-service needs of internal customers, there may be other reasons for allocating support department costs. a. Some organizations may be required to report allocations to government agencies. b. Cost-plus contracts, which are often used by government agencies, nonprofit organizations, and academic institutions, make support department allocations critical to recovery of the entire cost of providing products and services to external customers. c. Allocation of facility-level support service costs, like the salaries of top executives, motivates managers at lower levels to increase profits needed to cover these higher-level costs. 3. Once the decision to allocate support-service costs is made, a system for allocating these costs must be chosen and implemented. G. The choice of methods for cost allocation from support departments to internal customers should accomplish several objectives. A key objective is to allocate costs in a way that motivates using departments to use support services wisely. A second objective is to choose an allocation procedure that is fair and does not cause internal disputes. A third objective is to help managers of an organization know what amounts of support services are necessary. A fourth objective is to assure that the costs of the allocation system do not outweigh the benefits. There are four steps to use that aid in the degree of success achieved in meeting these objectives. These steps are explained in detail below. H. Step 1. Costs of support-services must be identified, and decisions must be made regarding how or if various support-service activities should be combined (pooled). 1. Support service spending must be identified. Identifying support department costs depends on how and at what level support departments acquire resources. The use of resources may also differ by level (i.e., facility- or lower-level). Some support department costs can be traced to direct departments. More often, however, support-service costs cannot be traced, and must be allocated. a. Support-service costs can be identified and pooled based on resource type. For instance, human resource costs could be separated from equipment and space costs for a given support department, or one type of support department may be separated from another type of support department. 2. Support service uses must be identified. Organizations may identify and then pool costs based on uses of facility-level support-service resources. This is especially useful when a support department has both facility-level and lower-level components. a. Managers need to be cognizant of the costs associated with having many cost pools. At the same time, expanding the number of cost pools will increase the accuracy of cost allocations. There is a tradeoff between controlling the costs of having an accurate allocation system and limiting the degree of accuracy the system can provide. b. Often, organizations may have support-service department pools for each department, or for each function, or for broad categories of functions. 3. Costs to be allocated must be measured. Allocation of support department costs cannot be based on the actual costs, because they are not known early enough to allocate them. This makes it necessary to develop estimates of support-service costs. 4. Cost of resources supplied must be separated from cost of resources used. For example, you may have five guards in facilities even though three of them are essentially needed for now. Users should be charged for the cost of resources used and not with the total cost of resources supplied. I. Step 2. Choose the appropriate cost allocation bases and calculate rates. Once the costs and cost pools are identified, an allocation base must be chosen and allocation rates, or amounts to allocate, must be calculated. The allocation base should mirror, as closely as is practical, a costdriver base. This means that the base should be indicative of a causal link between the cost and the cost allocation. Such a link improves the planning and decision-making activities of managers. It may also influence behavior if managers see that their actions affect support-service costs. 1. An activities-based cost approach can be used to assign support department costs. This entails the following. a. Measure each support department’s resource spending (costs) by level. This means that unit, batch, product, customer, and facility-level costs must be identified. b. Identify and measure activities demanded by internal customers that require support-service spending. This allows cost-driver bases to be chosen. c. Derive cost-driver rates by dividing costs by the activity. 2. A cost allocation approach that is more traditional than ABC is used by many organizations. Traditional cost allocations often use allocation bases such as number of employees, space occupied, hours of use, or other activities that are more general than those used in an ABC system. a. If allocation bases are not cost drivers, they must at a minimum be justifiable for use as an allocation base. J. Step 3. A cost allocation method must be selected and implemented. Two commonly used methods are the direct method and the step method. A third method, the reciprocal method, is not widely used and is presented in the appendix to Chapter 10. The direct and step methods are described below. 1. The direct method of cost allocation charges support department costs only to internal customers in direct (production) departments. This allocation method ignores the use of support services between support service departments. The direct method places emphasis on the fact that, ultimately, all support-service costs are paid for by production departments. a. Suppose that an organization has two support departments, S1 and S2, and it has two production departments, P1 and P2. Costs of department S1 would be allocated to departments P1 and P2. Costs of department S2 would be allocated to departments P1 and P2. With the direct method, no costs of department S1 would be allocated to department S2, and no S2 costs would be allocated to department S1. b. The chief criticism of the direct method is that it ignores the use of support departments by other support departments. For instance, the Accounting Department hires new employees and therefore uses the services of the Human Resources Department. Human Resources uses the Accounting Department whenever it needs to have a bill paid. Neither of these support departments receives a cost allocation from the other support department. This is justifiable for two reasons. First, support department costs are fairly small relative to production department costs, so the degree of accuracy needed in assigning support department costs to other support departments need not be extensive. Second, since all support department costs are ultimately allocated to production departments anyway, an interim allocation between support departments is viewed by some as an unnecessary complication. 2. The step method partially addresses the criticisms leveled against the direct method. The step method allocates costs from the support department with the largest proportion of its total allocation base in other support departments to other support and production departments. This first support department is the most general support department. Then costs from the second most general support department are allocated to the remaining support departments and all of the production departments. The support department with the smallest proportion of its costs in other support departments has its costs allocated only to production departments. a. Once a support department’s costs are allocated, nothing is ever allocated back to it, even though it may use the services of the remaining support departments. Thus, allocations from support departments are made in only one direction. b. Using the example presented in the discussion of the direct method, suppose there are two support departments, S1 and S2, and two production departments, P1 and P2. If department S1 is the most general support department, then its costs will be allocated to departments S2, P1, and P2. Department S2 would then have its own costs plus the allocated amount it received from department S1. Then department S2’s adjusted cost would be allocated to production departments P1 and P2. c. The step method is viewed as an improvement over the direct method, because it partially recognizes the reciprocal relationships among support departments. Many companies opt for the direct method because it is easier to use and maintain, particularly if interdepartmental services are insignificant. d. When using step allocation, one must allocate the service department with the largest percentage of service provided to other service departments first, before proceeding to the second department and so forth. 3. Critics of the step method argue that, if a more complex method is to be used, it should be the reciprocal method. The reciprocal method assigns costs of every support department to every other department that uses it. Thus, if department S1 uses department S2, and department S2 uses department S1, then each support department will receive an allocation from the other support department. The main criticism of the reciprocal method is that it unnecessarily complicates the cost allocation process, particularly since all of the support department costs end up being allocated to the production departments anyway. K. Step 4. Evaluation of the choices among allocation methods should reveal whether the desired results will be achieved by the allocation method chosen. The desired results include accuracy, effects on departments, and linkage between costs and benefits. 1. The allocation process cannot be perfectly accurate. Since cost allocations are always arbitrary to some extent, managers must balance their degree of tolerance for the inaccuracy against their degree of tolerance for costs of having a more expensive allocation method. It may not be cost-effective to modify allocation of support department costs to improve accuracy. 2. Another way to evaluate cost-allocation methods is to look at the effects of alternative methods on production departments. If costs are allocated to managers of production departments, managers will be resistant to any allocation method that increases support department costs to their department. a. One factor that should influence the choice of methods — ABC, reciprocal, step, or direct — is the amount of support services used by other support departments. If the amount of use is high between support departments, use of the direct method will distort the true costs of support services used by the various production departments. b. If support department costs are used to evaluate managers, then managers will prefer whichever cost allocation method assigns the least cost to them, but this should not be a real concern of cost managers. c. All support department allocation methods are assigning the same amount of total cost to production departments. However, the method chosen can change the amount of cost allocated to individual departments. An undesirable result of assigning support department costs to a production department is that the manager of the production department may cut back on the use of the support departments’ services just to reduce his or her departments’ costs. While this may have the desired effect in that production department, it simply means that the cost will be reassigned to another department in the short run. In the long run, costs and services would be reduced, and that manager would have access to lower levels of service. Suppose a trucking company revised its cost allocations in such a way that resulted in truck maintenance costs (a support service) being allocated differently. If the allocation base is mechanic hours, then the manager of a truck facility would be tempted to reduce mechanics’ time to reduce maintenance costs. This is certainly not a desired effect of cost allocation. d. The choice of allocation method could affect amounts allocated in cost-plus contracts. If an organization has a mix of external customers, some with cost-plus contracts, and others with market-based contracts, the tendency would be to allocate as much support department cost to the cost-plus contracts. Customers with such contracts need to recognize this tendency and must insist on knowing how costs are determined and assigned. Many federal government contracts are cost-plus, and contractors are given very specific limits on allocation methods and amounts. 3. A third consideration in evaluating which cost allocation method to choose is the relation between costs and benefits of setting up, administering, and maintaining the system. Complex systems are much more difficult to maintain than simple systems. Each year, allocation bases and cost estimates change. New rates must be calculated for every cost base used. Organizational structure also changes, making it necessary to revise estimates of the use of support department services. a. At times it is necessary to fine-tune an allocation system, especially if it is causing undesirable results. b. Ethical considerations may lead to challenges in how cost allocations are made, especially in cost-plus contracts, or when government agencies charge taxes based on cost-plus estimates of taxes charged. L. Reciprocal method of cost allocation allows for interdepartmental (reciprocal) use of services. For example, if personnel department uses services of payroll department, and payroll department receives services of personnel department, there should theoretically be a recognition of this reciprocal service; i.e., each department should be charged with a fair share of the other department’s costs. A mathematical model can be established to allow for accounting of such interdepartmental services. Software packages may be utilized for such accounting. Essentially, we need set up reciprocal equations. Total departmental costs (P) = Direct cost of the dept.($) + service costs to be allocated to the dept. (S). Assume S1 = 86,000 + .20 S2 while S2 = 30,000 + .40 S1. We can continue with these equations as follows: S1 = 86,000 + .20 (30,000 + .40 S1) S1 = 86,000 + 6,000 - .08 S1 S1 - .08 S1 = 92,000 .92S1 = 92,000 / .92 S1 = 100,000. Now that we have S1, we can solve for S2. S2 = 30,000 + (.40 * 100,000) S2 = 70,000. Problem 1 – Chapter 10 Cost allocation and management decisions LO: 1 and 4 Time required: 45 minutes Saba Electronics has two service departments computer services (S1) and personnel (S2) as well as two production departments (P1 and P2). S1 costs amount to $285,000 and S2 costs amount to $98,500. Direct overhead of production departments amount to $495,000 and $386,500 respectively. S1 department is equipped to provide a total of 600 CPU hours of service. Currently, however, S2 uses 100 hours, P1 150 hours and P2 200 hours of this service. S2’s costs are allocated to production units based on number of employees. P1 has 120 and P2 has 280 employees. P2 has indicated that due to the exorbitant costs of S1, it will contract out 100 hours of its work to an outside contractor which charges $350 for one hour of CPU time. Required: 1) Using step-down allocation, allocate costs assuming that all resources provided are charged to the end units. 2) Using step-down allocation, allocate costs assuming that only resources used are charged to the end units. 3) Using step-down allocation, allocate costs assuming that P2 contracts out 100 hours of its work as indicated in the problem. Charging is based on resources used by departments. 4) Discuss the alternatives and various implications of cost management for the computer services department. Solution: 1) S1 S2 P1 P2 Direct cost 285,000 98,500 495,000 386,500 S1 allocated (CPU hours) 450 100 150 200 S1 allocated $'s 285,000 63,333 95,000 126,667 S2 allocated (No of employees) 120 280 161,833 48,550 113,283 2) S1 S2 P1 P2 Unused Direct cost 285,000 98,500 495,000 386,500 S1 allocated (CPU hours) 600 100 150 200 150 S1 allocated $'s 285,000 47,500 71,250 95,000 71,250 S2 allocated (No of employees) 120 280 146,000 43,800 102,200 3) S1 S2 P1 P2 Direct cost 285,000 98,500 495,000 386,500 S1 allocated (CPU hours) 600 100 150 100 250 S1 allocated $'s 285,000 47,500 71,250 47,500 118,750 S2 allocated (No of employees) 120 280 146,000 43,800 102,200 5) It appears that computer department has considerable excess capacity. If the cost is not charged to the final using departments, it would be absorbed as a loss. Furthermore, based on P2’s decision, it appears that computer cost per hour is significantly higher than what outsiders can provide for this type of service. Management should ask some hard questions. Can S1 ever become competitive? Can the excess capacity either be reduced or the excess capacity utilized or rented out? In the long-run, S1 has to become competitive. Otherwise, the service should be outsourced. In the short-run, management should see whether partial outsourcing of P2 would reduce S1 costs at least by the amount paid out by P2 for outsourcing. Otherwise, it would be advantageous for the company to continue the service internally while looking for long-term solutions. P2 may be compensated by the higher management for the amount that it is sacrificing for buying the service internally. Problem 2 LO: 1, 2, 3 Managing service department costs and finding appropriate allocation bases: Estimated time: 20 minutes Omid Printing had three service departments; Graphic Design, Personnel, and Accounting. The producing departments for the firm were copying and printing. Other data regarding these departments follow: Item Graphic Design Personnel Accounting Copying Printing Design Effort 20% 80% Number of employees 5 7 10 25 70 Accounting effort 4% 6% 10% 80% Direct cost $200,000 $140,000 300,000 $600,000 $1,400,000 Allocation DL hours Machine Hrs. Omid has assigned you to determine a cost allocation method for the company. Discuss a) the pros and cons of each method, b) the pros and cons of no allocation charge, c) the sequence that the service departments need to be allocated and the reasoning behind it, d) what allocation bases you use for each cost pool and why. Answer: a) Direct method is the easiest but the least accurate. Reciprocal method is most accurate but the most complicated. Step allocation method falls in between the two. b) If no allocation is made to the final users, the producing department will not understand or be concerned about the cost of service departments and their use and request of services from those departments may be unreasonable and unrealistic. In addition, the cost related to each manufacturing department will not be properly identified, and there will be no way that one can come up with a reasonable costing method for the organization. c) Generally, the department that provides the most service to other service departments and has the highest cost should be allocated first (in case of step method of cost allocation) to come up with the most reasonable answer. It does not make any difference in case of the other two methods of cost allocation. Accordingly, in this problem, Accounting needs to be allocated first (highest cost and provides the most service), followed with Personnel (because Personnel provides service to Graphic Design, but Graphic Design does not provide service to Personnel. d) As illustrated in the above Table, the Accounting Manager and Graphic Design may estimate based on experience the amount of time needed for servicing each department. Personnel cost may be allocated based on some more objective basis such as number of employees. Problem 3. General Dual Allocation Estimated time: 15 minutes Consider the budget and actual cost of computer services for Saba Company: Item Budget Actual Supervision $4,800,000 $4,650,000 Data Entry 3,200,000 3,900,000 Computer Lease 6,200,000 6,078,000 Supplies 420,000 785,000 Production Division A’s share of the above service 30% 20% Production Division B’s share of the above service 70% 80% Required: What would be the most logical way of allocating the computer department costs to division A and B? Try to be analytical as well as logical in coming up with an innovative and useful method of cost allocation in this particular case. Answer: The most logical system of cost allocation in this case is a dual allocation method where actual fixed costs would be allocated based on budgeted percentages – because the department commits capacity utilization based on production managers’ estimated need of those services, and actual variable costs would be allocated based actual usage of those services (such as the amount of printing paper needed), based on actual usage of those services regardless of what the budgeted percentages were. Alternatively, one could use budgeted fixed costs and budgeted percentages for fixed cost portion, and budgeted rate for variable costs and actual volume of services used for variable costs. In this situation, inefficiencies of the service department will not be transferred to the final using departments, and managers remain accountable for services provided and services used based on agreed upon rates. This approach makes performance evaluation more feasible and meaningful with variances charged directly to some loss account rather than being transferred to the final users of those services. This is like having concluded an agreement with an outside firm (like outsourcing), and the producing departments knowing ahead of time the rates for which they will be charged for the services that they request from such outside sources. Problem 4. Omid Manufacturing has two service departments (Personnel and Maintenance) and two manufacturing departments (M1 and M2). Personnel is allocated based on number of employees. Maintenance based on service hours provided. M1 is finally allocated based on machine hours and M2 is allocated based on direct labor hours. The outputs of the firm are products A and B. A uses $145 of material, $22 of labor, 1.2 machine hours in M1 and 2.8 hours of labor hours in M2. Other information follows: Item Personnel Maintenance Manufacturing 1 Manufacturing 2 Number of employees 5 25 30 70 Maintenance hours 100 200 600 1900 Direct overhead $32,000 $68,000 $494,880 $981,920 Machine hours 2,400 1,600 Labor hours 3,200 8,800 Required: a) Use direct allocation to close service department costs, determine the overhead rates in M1 and M2, and compute the final cost of product A. b) Use step allocation to close service departments with Maintenance to be allocated first, determine the overhead rates in P1 and P2, and compute the final cost of product A. c) Use reciprocal allocation to close service departments, determine the overhead rates in M1 and M2, and compute the final cost of product A. Solution: a) Item S1 S2 M1 M2 Total Direct overhead 32,000 68,000 494,880 981,920 1,576,800 S1 allocated (32,000) 9,600 22,400 S2 allocated (68,000) 16,320 51,680 Totals - - 520,800 1,056,000 1,576,800 Allocation base 2,400 8,800 Rate per hour Cost of Product A: 145+22+(1.2*217)+(2.8*120) = $763.40 b) 217 120 Direct overhead 68,000 32,000 494,880 981,920 1,576,800 S2 allocated (68,000) 2,615 15,692 49,692 - - (34,615) 10,385 24,231 - Total - - 520,957 1,055,843 1,576,800 Allocation base 2,400 8,800 Rate per hour 217.07 119.98 The difference in cost using direct or step method is quite minimal as you see from the above worksheets. Accordingly, direct allocation of costs would have been adequate. c) Reciprocal allocation S1: 32,000 + (100/2600) S2 S2: 68,000 + (25/125) S1 Solving for S1 results in $34,883.71 Solving for S2 results in $74,976.57 Item S2 S1 M1 M2 Total Direct overhead 68,000 32,000 494,880 981,920 1,576,800 (74,976) 2,884 17,302 54,790 0 6,976 (34,884) 8,372 19,535 - Totals - - 520,554 1,056,245 1,576,800 Allocation base 2,400 8,800 Overhead rates 216.90 120.03 The same logic applies here. The difference between direct, step, and reciprocal methods used is minimal. Therefore, using direct method for cost allocation must be adequate. Sample Quiz 1. The reason(s) stated for cost allocation often include a. the requirements for tax regulations and financial accounting. b. determination of the fair value of cost-plus contracts for reimbursement purposes. c. influencing management’s behavior in cost control. d. choosing a basis even though it may appear somewhat arbitrary. e. all of the above Answer: e Learning Objective: 1 2. Support services to be allocated a. use only one allocation base in each department. b. may use several allocation bases for each pool of costs. c. could charge some departments for specialized services without allocation. d. b and c e. a and c Answer: d Learning Objective: 1 3. A reasonable allocation base for heating and air conditioning costs may be a. quantity of material used. b. volume occupied. c. space occupied. d. number of documents. e. None of the above. Answer: b Learning Objective: 2 Use the following data to respond to questions 4 through 15. Omid Printing has two service departments (S1 and S2) and two manufacturing departments (M1 and M2). S1 is allocated based on number of employees. S2 is allocated based on maintenance hours. The company produces two products (P1 and P2). P1 uses $167 of labor and material. It uses 1.2 machine hours in M1 and 2.8 labor hours in M2. P2 has the same labor and material cost but uses 3.2 machine hours in M1 and 1.6 labor hours in M2. Other data follows: Item S1 S2 M1 M2 Number of employees 15 25 30 70 Maintenance hours 100 200 600 1900 Direct overhead $32,000 $68,000 $495,000 $984,000 Machine hours 2400 Direct labor hours 8800 4. Using direct allocation, S1 charge to M1 amounts to a. $9,600 b. $22,400 c. $16,320 d. $51,680 e. None of the above. Answer: a Learning Objective: 4 5. Using direct allocation, S2 charge to M1 amounts to a. $9,600 b. $22,400 c. $16,320 d. $51,680 e. None of the above. Answer: c Learning Objective: 4 6. Using direct allocation, M1’s overhead rate per hour amounts to a. $217.05 b. $157.05 c. $120.24 d. $102.24 e. None of the above. Answer: a Learning Objective: 4 7. Using direct allocation, P1’s product cost per unit (rounded) amounts to a. $597 b. $764 c. $889 d. $1,056 e. None of the above. Answer: b Learning Objective: 4 8. Using direct allocation, P2’s share of overhead per unit (rounded) amounts to a. $597 b. $764 c. $889 d. $1,056 e. None of the above. Answer: c Learning Objective: 4 9. If step-allocation method is used, a. S1 should be allocated first because it provides more service to S2. b. S2 must be allocated first because it provides more service to S1. c. S1 should be allocated first because it is the order that the problem assumes. d. S2 should be allocated first because it has a higher total amount than S1. e. None of the above. Answer: b Learning Objective: 4 10. Using step allocation and assuming that S2 is allocated first, M1 share of S2 (rounded) amounts to a. $10,383 b. $15,694 c. $24,228 d. $49,694 e. None of the above. Answer: b Learning Objective: 4 11. Using step allocation and assuming that S2 is allocated first, M1 share of S1 (rounded) amounts to a. $10,383 b. $15,694 c. $24,228 d. $49,694 e. None of the above. Answer: a Learning Objective: 4 12. Using step allocation and allocating S2 first, overhead rate per hour for M2 amounts to a. $110.22 b. $120.22 c. $207.12 d. $217.12 e. None of the above. Answer: b Learning Objective: 4 13. Using step allocation and allocating S2 first, cost per unit of P2 (rounded) amounts to a. $764 b. $864 c. $954 d. $1,054 e. None of the above. Answer: d Learning Objective: 4 14. If reciprocal allocation is used, a. S1 should be allocated first because it is so listed in the problem. b. S2 should be allocated first because it provides more service to S1. c. S2 should be allocated first because it provides more service to P1. d. S2 should be allocated first because it provides more service to P2. e. Order of allocation does not make any difference. Answer: e Learning Objective: 6 15. Using reciprocal allocation, amount charged by S1 to S2 (rounded) amounts to a. $2,611 b. $2,790 c. $3,538 d. $4,538 e. None of the above. Answer: d Learning Objective: 6 16. Comparing direct allocation to reciprocal allocation, total costs after allocation a. tend to be higher using the first method. b. tend to be higher using the second method. c. are the same regardless of the method used. d. tend to be slightly different depending on the method used. e. none of the above. Answer: c Learning Objective: 6 17. Comparing step allocation to reciprocal allocation, total cost of service departments after allocation to other service departments is a. same as the costs before allocation. b. higher when reciprocal method is used. c. lower when reciprocal method is used. d. tends to be slightly different depending on the method used. e. None of the above. Answer: b Learning Objective: 6 18. Cost allocation has implications in a. managerial decisions. b. product or service costs. c. company income level from period to period. d. contractual compliance. e. all of the above. Answer: e Learning Objective: 5 19. Which of the following methods do NOT charge service department costs to a service department after its costs have been allocated? a. the step-down and reciprocal b. the direct and step-down c. the reciprocal and direct method d. he simultaneous equation method e. algebraic matrix method Answer: b Learning Objective: 5 20. The reciprocal cost allocation method begins with allocation of the costs of the service department that a. provides the greatest percentage of service to the production departments. b. provides the greatest percentage of its service to other service departments. c. has the total highest cost among the service departments. d. has the combination highest percentage and dollar amount of its service to other service departments. e. None of the above. Answer: d Learning Objective: 6 21. Computer dept. costs are allocated based on CPU time used. CPU time used by Personnel is 600 minutes, by machining 3,400 minutes, and by assembly 2,000 minutes. Total computer dept. cost amounts to $84,000. Personnel dept. costs are allocated based on number of employees. Its total cost amounts to $48,000. Computer dept. has 200 employees, machining 500, and assembly 300. What is Computer dept. cost using reciprocal method? a. $84,000 b. $86,612 c. $90,612 d. none of the above Answer: c LO: 6 C = 84,000 + .10 P; P = 48,000 + .20 C; therefore, C = 84,000 + .10 (48,000 + .20C); solving for C, We get $90,612. 22. Computer dept. costs are allocated based on CPU time used. CPU time used by Personnel is 600 minutes, by machining 3,400 minutes, and by assembly 2,000 minutes. Total computer dept. cost amounts to $84,000. Personnel dept. costs are allocated based on number of employees. Its total cost amounts to $48,000. Maintenance has 200 employees, machining 500, and assembly 300. What is Personnel dept. cost using reciprocal method? a. $48,000 b. $56,122 c. $66,122 d. $76,000 Answer: c LO: 6 C = 84,000 + .10 P; P = 48,000 + .20 C; therefore, C = 84,000 + .10 (48,000 + .20C); solving for C, We get $90,612. We can now use the cost obtained in the Personnel dept. equation: P = 48,000 + (.20 * 90,612) = $66,122.   Chapter 11 Cost Estimation Chapter Outline A. Cost Management Challenges 1. Why must an organization estimate costs? 2. What cost patterns exist in different organizations? 3. What is simple and multiple regression analysis? What is account analysis? How are the two similar and different from each other? 4. What is the engineering method of cost estimation, and how is it used? 5. How can cost estimation be used to predict profitability in the future? B. Learning Objectives 1. Chapter 11 explains why companies need to estimate the relation between costs and cost drivers. 2. The chapter demonstrates how to graph cost patterns when they are fixed, step (semivariable), and variable. The learning curve is also explained, and graphing of cost patterns when a learning curve is involved is presented. 3. Chapter 11 explains the uses of simple and multiple regression for cost estimation purposes. 4. It presents advantages and disadvantages of account analysis compared to multiple regression for cost estimation. 5. The engineering method of cost analysis is presented, and it is compared to regression and account analysis. 6. Understand how regression works. 7. Estimate and use learning curves in cost predictions. B. Cost estimation is the process of estimating the relation between costs and the cost drivers that cause them. Some costs are directly related to an activity and can be estimated based on the activity. Other costs are indirectly related to an activity and are not as easy to predict because they are indirect. This is one of the challenges that cost managers must address in estimating costs. Another challenge exists because costs and expenditures do not always occur at the same time. The main purposes of cost estimation are to manage costs, make decisions, and to plan and set standards. 1. A cost is what occurs when resources are acquired for production or other activity in an organization. Expenditures are the payments for the activities in an organization. Expenditures do not always occur at the same time as the cost. When there are big time differences between the cost activity and the expenditure for cost activity, cost managers need to distinguish between them. In most cases, managers assume that costs and expenditures match reasonably well. This simplifies the cost estimation process. 2. The understanding that “costs do not just happen” is tied to an understanding between costs and activities. Managers must identify activities that cause costs in order to estimate costs. They must then manage the activities in order to manage costs. C. There are three reasons why organizations find it necessary to estimate costs. Cost estimation is used to (1) manage costs, (2) make decisions, and (3) plan and set standards. 1. Cost management is best accomplished by determining which activities drive costs and then managing these activities. This topic has been addressed in Chapter 4 (ABC) and Chapter 5 (ABM). 2. Decision making in a business setting is based on cost and profit information. Since resources are limited, organizations are always confronted with choosing among alternatives. Given two cost-causing alternatives, managers must use estimated costs before deciding which alternative to choose. Cost estimation requires that managers understand the underlying behavior of costs being estimated. Cost behavior is described below. a. A simple cost behavior pattern is one in which costs are some combination of fixed and variable. Total variable costs change in proportion with total activity. In the simplest case, there is only one activity driving variable costs. Fixed costs are those costs that do not vary with activity. This simple cost pattern can be expressed mathematically. It is, TC = F + VX, where TC = Total costs F = Fixed costs V = The cost driver rate X = The number of cost driver units. This simple mathematical expression is just the equation for a line, suggesting that the cost pattern shows a linear relationship between costs and activity. D. Real-world applications of cost estimation can be depicted as a simple linear expression. However, a more realistic expression considers multiple cost drivers and complex cost behaviors. As always, managers must weigh the costs and benefits of using a more complex estimation method. 1. Another cost pattern commonly encountered is one with step costs, also known as semi- fixed costs. Step costs change with activity of the cost driver but not in direct proportion. These costs increase in chunks. For instance, rent on a store is a fixed cost. However, if the store is not large enough to accommodate rapidly increased sales activity, then a larger, more expensive store may be rented, increasing this seemingly fixed cost based on increased activity (units sold). 2. When trying to determine the pattern of costs, one must take into consideration the relevant range of activity. The relevant range is the range over which an organization expects to operate and over which assumed cost patterns are reasonably accurate. As long as the relevant range falls below the point where the next higher level of a step cost will be expended, one can assume the simpler cost estimation (TC = F + VX) model is useful for cost estimation. 3. Another cost pattern that might be encountered is a semi-variable cost. Semi-variable costs have elements of fixed costs and variable costs. Utility costs are a simple example. If, in a given month an organization shuts down, it would still have some amount of electricity costs. When that same organization is open and operating, electricity costs will rise because the use of electricity has risen. There are many semi-variable costs that occur in a business setting. 4. Some cost patterns are even more complex than the three just described. The simple cost line, semi-fixed, and semi-variable cost patterns are all linear in nature. Some cost patterns are curved, and trying to predict such costs is more difficult than costs that are linear. One type of non-linear cost is called a learning curve. When there is a relationship between the amount of experience in performing a task and the amount of time it takes to perform it, a learning phenomenon occurs. The more experienced a person becomes with a new task, the more quickly they can complete the task, until they are completely familiar with it. The cost pattern associated with this learning phenomenon can be expressed mathematically, based on the amount of experience in performing a task and the time required to perform it. Mathematically, the learning phenomenon is expressed as Y = aXb where Y = Average number of labor-hours required for X units of cost driver volume a = Number of labor-hours required for the first cost driver unit X = Cumulative number of cost driver units b = Index of learning equal to the log of the learning rate divided by the log of 2. For instance, a learning rate of 80%, commonly used in practice, would result in a value for “b” of -.322. The idea behind the learning phenomenon is that the greater the cost driver volume, the greater the experience. The learning phenomenon and the learning curve can be applied to new products or processes and is helpful to managers trying to estimate costs of a complex process. A process that appears to be very costly and time consuming might be rejected if managers do not factor learning into estimated time to complete the process. E. Once a cost pattern has been established for a cost or set of costs, the next step is to try to estimate those costs. There are three methods that are commonly used in practice: (1) statistical methods, especially simple and multiple regression analysis, (2) account analysis, and (3) engineering estimates. Since estimates may differ based on the estimation methods used, managers may choose two or all three of these methods to aid them in making the right decision. Each of these methods is discussed below. 1. Statistical cost estimation using regression analysis is one way to mathematically express the relation between costs and cost drivers. Regression analysis uses terminology that must be explained before the mechanics of its use can be illustrated. a. A dependent variable (or left-hand-side variable, or the “Y” variable) represents total costs in a cost model. b. The independent variable (or the right-hand-side variable, or the X variable) represents cost driver activity. The purpose of a regression model is to estimate the total costs, particularly the total cost driver amounts, given some level of activity. c. The independent variable (cost driver activity) drives the dependent variable (total cost). The dependent variable and the independent variable are correlated, meaning they move together. d. The regression model is used to estimate the Y variable. The estimate is based on historical cost observations of cost driver activity, paired with total costs. In order for a regression analysis to be informative, there must be a logical relationship between costs and the chosen cost driver. e. The regression model must be limited to analysis within the relevant range of activity. f. A simple regression model is based on the simple, linear cost estimation equation described earlier: TC = F + VX, where TC represents total costs, F represents fixed costs, V stands for variable costs per unit for the cost driver, and X is the cost driver quantity. In a simple regression model, there is only one independent variable. g. A simple regression problem can be graphed, using a scatter graph. The Y-axis shows total costs. The X-axis shows cost driver activity. The scatter graph can be used as a preliminary assessment of the validity of assumptions about the cost driver and total costs. If there is a linear relationship, the scatter graph will show a pattern that would allow a line to be drawn as a rough estimate of costs for any point in the graph. h. A method that is even simpler than the simple regression method is the high-low method. With the high-low method, the only information needed is the highest observation-pair of costs and activity and the lowest observation of cost and activity. The high-low method estimates the slope of one’s cost line. Mathematically, the high-low model is: Slope = (Highest cost – lowest cost)/(highest quantity of cost driver – lowest quantity of cost driver) The answer obtained by using the high-low method is the variable (cost driver) rate per unit. Armed with the cost driver rate, substitute this value into another equation that allows one to solve for the intercept. This equation is: Intercept = Total cost at lowest cost driver level – (Variable cost per unit X lowest quantity of cost driver). The intercept represents fixed costs. Using the highest cost-quantity pair will give the same answer for the intercept. Estimates of fixed costs and the variable rate using regression are more accurate because they use all observations. i. Interpretation of the regression model helps one to understand whether the results will be good predictors of future costs. The most important measure of the validity of the results is the “r-square (R2), which measures the proportion of the variation in the dependent variable (total costs) explained by the independent variable (cost driver activity). R2 can range in value from 0 to 1. An R2 of zero implies there is absolutely no relationship between the dependent and independent variables. An R2 of one implies the dependent and independent variable are perfectly correlated with each. A statistical rule of thumb is that an R2 that is greater than .30 implies there is some relationship between the dependent and independent variables. j. Here is an example of a regression problem’s results. Suppose one wanted to estimate monthly costs of electricity. The cost driver is kilowatt-hours. TC = $500 + .06X, where X is the number of kilowatt-hours. If 10,000 kilowatt- hours of electricity is used, then total cost would be an estimated $500 + $.06(10,000) = $500 + $600 = $1,100 per month. 2. A more complex and sophisticated type of regression analysis is useful when more than one cost driver affects total costs. This is called multiple regression. Multiple regression is a regression model that has more than one independent variable. Multiple regression is a better predictive model. However, it requires that more information be collected. A multiple regression model that is structured based on the hierarchies described in earlier chapters of the text would be an informative one to predict costs. A cost driver at the unitlevel, batch-level, product-level, and customer level would be a very useful predictive tool. The intercept could represent facility-level costs and activities. The regression model for different organizations could use such cost drivers in different combinations. a. For each total cost observation, the corresponding activity quantity must also be known in a multiple regression model. Each piece of information is used as input in the regression model. Notice that the R-square discussed in a simple regression model is replaced with an adjusted R-square in multiple regression. The interpretation is essentially the same. 3. Account analysis is another estimation tool that can be used by itself or in addition to regression analysis. Account analysis is based on past costs associated with each cost driver. Total costs are separated into categories that tie to the cost drivers. Costs are categorized by hierarchy (unit, batch, product, customer, and facility-level). With an activities-based cost system, total costs must be categorized into each activity. A complex ABC system with 100 cost drivers would greatly complicate account analysis. a. Account analysis gives results that are similar to multiple regression. It offers two benefits. First, it allows decision makers to have a comparison with regression results (to validate or invalidate them). Another benefit is that account analysis may help analysts to spot trends or errors that might be overlooked if a computerized regression analysis is used. Account analysis is more labor intensive and time consuming than regression analysis. 4. There are five data problems that might arise when using regression or account analysis. a. Missing data can lead to inaccuracies of results. The more detailed the analysis is, the more likely it is that this problem will arise. b. Outliers are extreme, unusual observations. Outliers should be taken out of the group of regular outliers. For instance, if an air conditioner manufacturer is trying to estimate production costs, the costs for a month of production during a recordbreaking heat wave may be an outlier. The manufacturer may have a lot of overtime and expedited costs for such an unusual month. c. Allocated and discretionary costs should be included in regression and account analysis with caution. Allocated costs may appear to be variable if they are allocated based on some volume of a cost driver. Discretionary costs like advertising may also appear to be variable when assigned to segments of an organization. d. Since historical costs are not usually adjusted for inflation, use of historical costs may give misleading results in highly inflationary periods. e. Activities may sometimes be mismatched with expenditures (for instance, billing for long distance costs may be a month later than recorded activity). Managers should recognize and correct such mismatches. 5. The engineering method is the third cost estimation method in use by organizations. Engineering estimates are cost estimates based on measurement and pricing of the work involved in the activities that go into a product. The engineering method differs from regression and account analysis in one important way. It uses cost and activity projections instead of historical costs. Cost analysts prepare detailed step-by-step analysis of each activity required to make a product, together with the costs involved. a. The engineering method has several advantages. The detailed cost information it provides allows managers to predict future costs with more accuracy than account analysis or regression. The detailed information provides a benchmark to be used to evaluate future activities. Since it does not rely on historical information, it can be used to estimate costs for totally new activities. The engineering method also helps managers to identify non-value-added activities. b. The engineering method has some drawbacks too. One obvious one is that it is expensive and time-consuming. Another is that it is based on estimates and may not be properly adjusted for conditions that are non-optimal. 6. The three cost estimation methods all have benefits and drawbacks. If all three methods are used, they may give conflicting results. 7. Use of the cost estimation analyses requires an understanding of which information to use when, and how to use it. Suppose an organization is using cost estimates to decide if part of their operations should be outsourced? The cost estimation analysis should be modified to show which costs will go away and which ones will be added. Estimation models can also be used for sensitivity analysis related to product and process variety and revised cost estimation, if the engineering method is used. F. Cost managers must resist any temptation to manipulate cost estimation results to their advantage. Statistics can be inappropriately used to support one’s decision, when the decision should probably be a different one. G. Managers must choose the estimation method or methods that are best for their organization. Regression is the least costly and probably the easiest to collect data for. Managers who want more detailed, insightful information should consider account analysis or the engineering method. The practical reality is that the cost of estimation procedures, as well as the human resources needed to develop, implement, and maintain the estimation models may be a driving factor in which method to choose. Managers must also consider how well their own costs fit the different estimation methods, using logic, good sense and judgment to decide which models make the most sense for them to use. 1. Regression analyses are the easiest but do not give a lot of insight into the underlying reasons for costs. 2. Account analyses allow one to look at patterns of cost and help managers to see how and why resources are being used. Account analysis is more labor-intensive and timeconsuming (and therefore more expensive) than regression analysis. 3. Engineering analyses force managers to think about every cost being incurred to achieve some objective and to help them identify non-value-added costs. It is very expensive to do, and most of the information is estimated. Thus, cost estimates are based on numbers that are also estimates. H. The Appendix provides an analysis of regression tools. Confidence in the coefficients is provided by calculating the t-statistic. “t” is the value of “b” divided by its standard error (SE). The standard error of b is a measure of the uncertainty about the “b”. The larger the SE, the more the dispersion of b values and the more uncertainty about its value. As a rule of thumb, a t of 2 or better is usually considered significant. The value of t times the SE of b added or subtracted from b provides the range of values for b; i.e., the upper and lower limits. 1. Multicollinearity occurs when cost is correlated to more than one cost driver. The question arises as to how much each cost driver impacts the cost involved. Problem 1 – Chapter 11 LO: 3 High-low method of cost estimation as compared to regression. Time needed: 45 minutes Carter Energy Company was very cost conscious, and the recent heating and bills have been on the manager’s mind. The average temperatures for the 12 preceding months and the cooling or heating bill involved are given below. You are asked to prepare a high-low analysis of the heating and cooling bills, and estimate the cooling cost for February and August of next year. The way the weather is these days, we have to have heating on from October 1st through March 31st, and have the air conditioning on from April 1st through September 30th of each year. Required: 1) using high-low method determine a) slope of the lines, b) intercepts, c) heating bill for next February assuming that the average temperature would be around 13 degrees, and d) cooling bill for next August assuming that the average temperature would be around 98 degrees. 2) use regression to determine the intercept and slope of the line with a 95% probability for the summer months. 3) discuss the difference in statistics between using the above two methods. Month Temperature Utility bill $'s January 25 3,240 February 19 4,123 March 41 1,658 April 67 496 May 78 1,385 June 87 2,140 July 92 3,371 August 94 3,249 September 83 1,670 October 56 1,237 November 49 2,112 December 29 2,949 1. Use of the high-low method: Solution: Slope - winter (78) Intercept 4123 - (-78*19) 5,605 Intercept 1237 - (-78*56) 5,605 Next Feburary 13 4,591 Slope - summer 102 Intercept 3249 - (102*94) (6,336) Intercept 496 - (102*67) (6,336) Next August 98 3,657 2. Use of the Regression method Observations 6 ANOVA df SS MS F Significance F Regression 1 5093800.885 5093801 99.76664 0.000564551 Residual 4 204228.6151 51057.15 Total 5 5298029.5 Upper Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% 95.0% Intercept -6461.609 850.9134664 -7.59373 0.001613 -8824.128467 -4099.09 -8824.1285 -4099.0896 X Variable 1 101.186935 10.13052046 9.988325 0.000565 73.06004248 129.3138 129.31382 73.060042 7 RESIDUAL OUTPUT PROBABILITY OUTPUT Observation Predicted Y Residuals 1 317.92 178.08 2 1430.97 -45.97 3 2341.65 -201.65 4 2847.59 137.41 5 3049.96 199.04 6 1936.91 -266.91 Percentile Y 8.33 496 25.00 1385 41.67 1670 58.33 2140 75.00 2985 91.67 3249 3.High-low method resulted in an intercept of – 6,336 and a slope of $102. Regression provides an intercept of – 6,461 and a slope of 101.86. The numbers are fairly close showing that the two months (highest and lowest) are fairly representative of costs. Regression uses all points observed and provides a more comprehensive picture. Additional statistics such as standard error, t-statistics, the upper and lower limits with a 95% confidence interval, coefficient of determination (r^2), predicted Y and residuals are also provided. Problem 2. LO: 4 Use and interpret account analysis for cost estimation Estimated time: 15 minutes Ryan Company had the following costs: Customer service $16,400, product engineering $17,800, batch processing $12,900, warehousing 18,600, quality control $24,200. It was determined that the primary cost driver for customer service was number of customers (200), for product engineering number of new products (89), for batch processing number of barches (258), for warehousing number of parts stored (9,300), and for quality control number of inspections (6,050). Determine cost per unit of service using account analysis technique and discuss the limitations of this method. Answer: Customer service 16,400 200 82.00 Product engineering 17,800 89 200.00 Batch processing 12,900 258 50.00 Warehousing 18,600 9,300 2.00 Quality control 24,200 6,050 4.00 Item Cost Driver per unit Account analysis is past oriented and cannot easily separate fixed from variable costs. Problem 3 LO 5 Use of engineering method for cost estimation Estimated time: 15 minutes Farhad company uses engineering techniques to estimate its labor and material requirements. Here are product A requirements in terms of direct material, direct labor, and related overhead requirements: Mixing Labor grade A ½ hour $8 an hour Calendaring Labor grade B ¼ hour $10 an hour Slitting Labor grade C ¼ hour $12 an hour Building Labor grade D ¾ hour $15 an hour Curing Labor grade E ¾ hour $18 an hour Finishing Labor grade F ¼ hour $20 an hour Materials needed: ABC ¼ lb $9 a lb BCD ¼ a gallon $10 a gallon CDF ½ a yard $12 a yard DFG ¾ a yard $16 a yard FGH 1 lb $18 a lb Related labor cost of moving, storage, cleaning, idle time, supervision, etc. amount to 200% of direct labor, and related overhead in terms of maintenance, utilities, depreciation, etc. amount to $150 per machine hour. Machine time attributed to each unit of A is about 1/3 of an hour. Determine cost per unit of A using the engineering method. Answer: Item Qty. Rate Amount Mixing 0.50 8.00 4.00 Calendaring 0.25 10.00 2.50 Slitting 0.25 12.00 3.00 Building 0.75 15.00 11.25 Curing 0.75 18.00 13.50 Finishing 0.25 20.00 5.00 Total direct labor 39.25 ABC material 0.25 9.00 2.25 BCD " 0.25 10.00 2.50 CDF 0.50 12.00 6.00 DFG 0.75 16.00 12.00 FGH 1.00 18.00 18.00 Total direct material 40.75 Labor relaed overhead 200% of DL 78.50 Machine related overhea 1/3 150.00 50.00 Total overhead 128.50 Total cost per unit of product A 208.50 Problem 4. LO: 3 High-low method of cost estimation Estimated time: 15 minutes Consider the following data for this company’s maintenance costs: Month Machine hours Amount $ January 200 $2,800 February 350 $3,000 March 450 $4,000 April 500 $5,000 May 600 $5,600 June 580 $5,800 What would be the estimated maintenance cost if the maintenance hours are 590 hours? What if it would be 690 hours? Answer: b = (5,600 – 2,800) / (600 – 200) = $7 estimated variable cost per maintenance hour a = 5,600 – (600 * 7) = $1,400 estimated fixed costs Or: 2,800 – (200 *7) = $1,400 estimated fixed costs Thus: Estimated maintenance cost for July: 1400 + (590 * 7) = $5,530. The computations at 690 hours will produce $6,230. However, as the hours forecasted are beyond our relevant range, we cannot state with any level of confidence that our costs would be in that range. Sample quiz 1. Fixed costs a. per unit remain the same regardless of total output. b. remain the same within the relevant range of output. c. increase in steps as the amount of the cost driver volume increases. d. have both fixed and variable components in them. e. None of the above. Answer: b Learning Objective: 2 2. Step costs a. per unit remain the same regardless of total output. b. remain the same within the relevant range of output. c. increase in steps as the amount of the cost driver volume increases. d. have both fixed and variable components in them. e. None of the above. Answer: c Learning Objective: 2 3. It takes this worker ten minutes to assemble a toy. With a learning curve of 70% as production doubles, the average time needed to make four units would be a. 4.9 minutes. b. 3.43 minutes. c. 3.33 minutes. d. 3.23 minutes. e. None of the above. Answer: a Learning Objective: 2 10 * 70% * 70% = 4.9 minutes 4. The cost to rebuild this race car engine is $1,500, and a buyer offers to buy four such engines for $6,000. Assuming a cumulative learning curve of 90% as production doubles, the profit will be a. – 0 – b. $600 c. $1,140 d. $1,215 e. None of the above. Answer: c Learning Objective: 2 1500 * .90 * .90 = $1,215 5. Independent variables are a. the cost drivers that appear to cause certain costs. b. the cost drivers that correlate with certain costs. c. caused or correlated with certain activities. d. a and/or b e. None of the above. Answer: d Learning Objective: 3 6. You have a situation where total costs amount to $6,000, when labor hours total is 400, and $5,000, when labor hours total is 300. Using the high-low method, what would be the total cost when labor hours amount to 450 hours? a. $4500 b. $5500 c. $6500 d. $7500 e. None of the above. Answer: c Learning Objective: 3 (6,000 – 5,000) / (400 – 300) = 10; 6000 – (400 * 10) = 2,000; 2000 + (450 * 10) = 6,500. 7. R-square is a. the proportion of the variation of dependent variable explained by dependent variables. b. the proportion of the variation of independent variable explained by the independent variables. c. the proportion of the variation of dependent variable explained by the independent variables. d. the proportion of the variation of independent variable explained by the dependent variable. e. None of the above. Answer: c Learning Objective: 3 8. Multiple regression is a. a regression equation with more than one independent variable. b. a regression equation with more than one dependent variable. c. a regression equation with more than one independent and dependent variables. d. a regression that considers unknown factors. e. none of the above. Answer: a Learning Objective: 3 9. Using multiple regression, you have identified $12,000 of unit level costs for 3,000 units, $1,000 of product level costs for 40 products, and $3,500 of customer-level costs for ten customers. The cost of job one which used 500 unit level activities, 10 product level activities, and 2 customer-level activities amounts to a. $3,450 b. $3,250 c. $3,050 d. $2,950 e. None of the above. Answer: d Learning Objective: 3 10. Account analysis compared to the regression method a. is based on past costs. b. needs a software that is often used to find the relation between each of the independent variables and costs. c. requires more data for analysis. d. a and b e. a and c Answer: e Learning Objective: 4 11. Regression as compared to account analysis a. is more accurate. b. is more expensive. c. has the burden of providing more information. d. b and c e. None of the above. Answer: e Learning Objective: 4 12. Engineering method compared to account analysis a. rely on data from the past. b. rely on present and future data. c. measure the work involved in the activities that go into a product. d. b and c e. a and c Answer: d Learning Objective: 5 13. This restaurant’s total cost for 5,000 meals served amounted to $100,000. The manager is convinced that he can sell the meals at an average of $20 per meal and make a profit if his volume increases because a. fixed costs per unit remain the same with a larger volume. b. total fixed costs would be lower with a larger volume. c. variable costs per unit is lower with a larger volume. d. total mixed costs remain the same with a larger volume. e. None of the above. Answer: e Learning Objective: 2 Total fixed costs remain the same. As volume increases, average cost per unit decreases. 14. In choosing variables for cost estimation, the following must be considered. a. economic plausibility b. goodness of fit c. significance of the independent variables d. All of the above. e. a and b Answer: d Learning Objective: 1 15. The t-statistic is a. the value of b divided by its standard error. b. a measure of uncertainty about b. c. the cost driver for X. d. less than 2 when regression results are not due to chance. e. None of the above. Answer: a Learning Objective: 3 16. Given a standard error of .8 and the b value of 5, the t value would amount to a. 4 b. 5 c. 6.25 d. 7.25 e. None of the above. Answer: c Learning Objective: 3 5 / .8 = 6.25 17. Given the b value of 5, an SE of .8, and a t-value of 2.5, the range of b would be between a. 3 to 7 b. 4 to 6 c. 3.5 to 5 d. 5 to 7.5 e. None of the above. Answer: a Learning Objective: 3 18. Given that SE = 1.6, b = 12, and t with a 70% probability is 1.25, the range of b with a 70% probability will be a. 8 – 16 b. 10 – 14 c. 6 – 18 d. 4 – 20 e. None of the above. Answer: b Learning Objective: 3 19. Residuals a. are the difference between the estimated Y values and the actual Y’s. b. must be normally distributed around the regression line for validity. c. must be independent of each other with regard to regression for validity. d. must have constant variance over the range of independent variables for validity. e. All of the above. Answer: e Learning Objective: 3 20. Presence of serial correlation a. does not affect the accuracy of the b in the regression equation. b. affects the accuracy of the b in the regression equation. c. affects the standard errors of the coefficients. d. a and c e. b and c Answer: d Learning Objective: 3 Chapter 12 Financial and Cost-Volume-Profit Models Chapter Outline A. Cost Management Challenges — Chapter 12 offers three cost management challenges. 1. How can organizations benefit from using a financial model? 2. Can financial models define future risks so that managers at least know what the uncertainties are? 3. Should organizations always try to maximize revenues or even the sales of products and services with the most throughput, contribution margin, or profit per unit? Are resource constraint an issue? B. Learning Objectives — This chapter has seven learning objectives. 1. Design financial models to match strategic and operational decisions, such as profit planning or optimal use of a scarce resource. 2. Build a basic cost-volume-profit (CVP) financial model. 3. Build a computerized financial planning model. 4. Build a financial model that reflects the effects of taxes, multiple products, and multiple cost drivers. 5. Apply scenario and sensitivity analyses to model the risk of decisions. 6. Manage scarce resources 7. Apply the Theory of Constraints to manage scarce resources (Appendix A) 8. Use linear programming to model decisions about the use of multiple scarce resources (Appendix B). C. Financial models are representations of reality in the business world. A model allows one to see how something is supposed to work. A financial model allows an organization to test the interaction of economic variables in a variety of settings. Financial models require that analysts develop a set of equations that represent a company’s operating and financial relationships. These may include things like the relation of sales to variable costs, inventory turnover, and the relative proportions of various products sold. Once a financial model is developed, it can be used to explore different combinations of the variables that interact with each other to see what outcomes to expect given different scenarios. Financial models offer several benefits to users. Once the model is developed, users can concentrate on business analysis instead of number crunching. It gives managers insight into possible business outcomes without the risk of trying them first. It is, therefore, possible to identify bad business decisions ahead of time. On a cautionary note, models are only as good as the information that goes into them. Faulty assumptions in building a model will lead to faulty predictions and bad business decisions. D. One model that has proven to be especially useful is the Cost-volume-profit (CVP) model. This model shows the effects of volume changes on an organization’s costs, revenues, and income. This basic model combines four important variables — volume of sales, costs, revenue, and profits. The basic model can be extended to assess the impact of price, cost, and volume changes, along with changes in product mix and income taxes. Although the model is called cost-volume-profit, it can be used by non-profit organizations as well. Such organizations perform analyses to assure that they spend only the funds they have. This is a special type of CVP analysis called breakeven analysis. 1. The breakeven point is the volume of activity that generates just enough revenue to cover all costs for an organization. It is the level of sales volume where an organization is not making any profit, but they are not losing money either. a. The breakeven point is best understood if costs and revenues are expressed in a manner that departs from the traditional presentation of costs and revenues. The format that aids in understanding how to achieve the breakeven point is called the contribution margin (CM) format. This type of profit-reporting approach splits costs into two categories — fixed costs and variable costs. b. The CM format of the income statement is shown in brief form as follows: Sales revenue Less Total Variable Cost = Total contribution margin Less total fixed costs = Operating income Less income taxes, other non-operating income = Net income This format is useful because variable costs change with sales activity. Since this is true, sales revenue, variable costs, and total contribution can all be expressed in terms of volume times a dollar amount per unit sold. For instance, suppose a product can be sold for $40. Variable cost for each unit is $25. This leaves a contribution per unit of $15 ($40 - $25). For every unit sold, $15 in contribution margin is generated. The contribution margin can be used first to cover fixed costs, and then, what is left after covering fixed costs and income taxes, is net income. c. Calculation of the breakeven point can be accomplished using the contributionmargin approach. In order to use this approach, the CM per unit must be known, and estimated fixed costs must be known. Suppose in the example given above, the CM of $15 per unit must be used to cover $45,000 in fixed costs. Then, $45,000/$15 = 3,000 units. To check the accuracy of this, multiply 3,000 units times the $15 CM, to get $45,000 in contribution margin. This is the breakeven point. To get the breakeven in dollars, we must use contribution margin ratio (CM/Sales) to determine the breakeven point. d. Another way to calculate the breakeven point is to use the equation approach. To see how the equation approach is derived, look at the equation showing how operating income is obtained: 1) Sales revenue – Total cost = Operating income. Total cost can be split into fixed and variable costs: 2) Sales revenue – Variable cost – Fixed cost = Operating income. Sales revenue and variable costs can be expressed differently, based on number of units sold: 3) (Selling price per unit * sales volume) – (Variable cost per unit * sales volume) – Fixed costs = Operating income. Since, at the breakeven point, Operating income is zero, the equation can be written as: 4) (Selling price per unit * sales volume) – (Variable cost per unit * sales volume) – Fixed costs = $0. Next, rearrange the equation by adding Fixed costs to both sides of the equation, to get: 5) (Selling price * sales volume) – (Variable cost per unit * sales volume) = Fixed costs. Rearrange the left-hand-side of the equation, combining the sales volume terms, to get: 6) (Selling price - Variable cost per unit) * Sales volume = Fixed costs. Finally, to get Sales volume on one side of the equation by itself, divide both sides by (Selling price – Variable cost): 7) Sales volume = Fixed costs/(Selling price – Variable cost). This gives you the sales volume at the breakeven point. Use the example given above to see if this approach works. Sales volume = $45,000/($40 - $25) = $45,000/$15 = 3,000 units, which is the same result obtained before. e. The CVP model can also be graphed. Graphing the model helps managers see what it will take to break even, and then they can see what it takes to make profit. It also shows how much sales would have to decline before an already profitable business begins to lose money. Two graphs are typically used. CVP graph that graphs the lines for sales, variable costs, and fixed costs, and shows the point of intersect (break- even point), and profit-volume graph that shows volume and the range of profit and loss as well as the break-even point. 2. Organizations in business to earn profits want to perform beyond the breakeven point. CVP analysis can be used to estimate the sales volume needed to attain target amounts of profit. If the target amount of operating income is known, then extending the CVP model beyond the breakeven point is fairly simple. All that is required is that target operating income be added to estimated fixed costs. In the example given above, suppose the organization wanted to earn operating income of $30,000. In order to determine the sales volume needed to achieve this income, use the equation form of the CM model: Sales volume = Fixed costs/(Selling price – Variable cost). This model needs to be expanded to include operating income of $30,000. Then, Sales volume = (Fixed costs + Target operating income)/(Selling price – Variable cost). Using the amounts given before, Sales volume = ($45,000 + $30,000)/$15 = 5,000 units. 3. Organizations making profit must also pay income taxes. A business only gets to keep income after taxes (net income). Thus, the CVP analysis is more informative if it shows what it will take to generate a target amount of net income. In order to calculate the sales volume needed to achieve a specified amount of net income, a tax rate as a percentage of operating income is assumed. Mathematically, the amount of net income can be expressed as a percentage of operating income. Look at the following equations to see why this is true. Let net income be represented by after-tax income and before-tax income represent operating income. Let t equal the tax rate. 1) After-tax income = Before-tax income – income taxes. The amount of income tax is Before-tax income * t. Restated: 2) After-tax income = Before-tax income – (Before-tax income * t). Rearrange the right-hand-side of the equation, to get: 3) After-tax income = Before-tax income * (1 – t). Divide both sides of the equation by (1 – t) to get: 4) After-tax income/(1 – t) = Before-tax income. Since organizations may establish target net income, now it is a straightforward step to calculate the amount of sales volume needed to achieve some target operating income as well. Extending the earlier example, suppose the tax rate is 20% and target operating income is, as before, $30,000. Then net income is 1 – the tax rate of 20%, or 80% of $30,000 = $24,000. Suppose the net income of $24,000 is the stated target and target operating income is not known. It can be obtained by using the rearranged equation above: After-tax income/(1 – t) = Before-tax income - $24,000/(1 - .20) = Before-tax income = $24,000/.80 = $30,000. Then, the sales volume needed could be determined as before. 4. The variables can be revised, manipulated, and rearranged, to see what the profit outcomes would be if assumptions about price, volume, and costs were changed. These changes are best accomplished using computer software and are referred to collectively as sensitivity analysis. Sensitivity analysis shows how the outcome of a decision process changes as one or more assumptions change. 5. A concept related to CVP is operating leverage (OL). OL reflects the risk of missing sales targets and is measured by the ratio of contribution margin to operating income. Companies with high fixed costs are riskier but more profitable at higher volumes of sales. The concepts is called operating leverage because a change in percentage in sales times the OL signifies the amount of change in income. Assume that company A has a contribution margin of $20,000 and an operating income of $10,000 resulting in an OL of 2. Company B has a contribution margin of $40,000 and the same operating income resulting in an OL of 4. Now if the sales of both companies increase by 20%, profits of company A will increase by 2 * 20% or 40% while profits of company B will increase by 4 * 20% or 80%. This is the power of the operating leverage. Note that the OL does not remain constant. As sales change so does profit and the degree of OL. 6. CVP analysis, as described so far, is useful for a very simple business with only one product and a simple cost structure. Most organizations have many products, adding complexity to the CVP analysis. The CVP model can quickly become a modeling tool that can only be used via computer software. A simple example with two or three products can be used to illustrate how a multiple-product CVP model works. In this simple example, another simplifying assumption is made. It is assumed that the relative proportions of each type of product sold remains the same. a. When two or more products are sold, and the sales mix is held constant, a weighted average unit contribution margin (WAUCM) can be computed. The best way to think about the WAUCM is to think of a “unit” as a bundle, consisting of the number of items in each bundle, for each product. For instance, if the sales mix for a beauty salon is five trims for every perm, then one “unit” will be five trims and one perm. The contribution margin will be the one that is generated by that bundle of products. b. When calculating the breakeven point or computing target income, the WAUCM must be revised any time the sales mix is revised. c. CVP uses the idea of sales mix in calculating the breakeven point and beyond the breakeven point. The sales mix assumptions are also used for performance evaluation and to assess profitability and for decision making related to which products to sell. d. When computing breakeven in dollars in a multi-product situation, we should take the sales weight in dollars for each product as a percentage of total times its contribution margin ratio to arrive at a weighted average contribution margin ratio. Alternatively, we should compute the weighted average contribution margin ratio by dividing total contribution by total sales for the mix of the products provided at a given product mix level. 7. There are limitations in the usefulness of the CVP model. First, the sales mix must be held constant in order to calculate a breakeven point or to estimate sales volume needed to achieve some target income amount. This is usually not a realistic assumption. Other variables are assumed to remain constant — costs, efficiency of operations, technology in operations, and cost characteristics. This assumption is also not a realistic one. We also start with a given sales price. A third assumption is that there is a linear relationship between revenues and costs, thus ignoring quantity discounts and other effects that threaten the accuracy of the model’s results. Perhaps the biggest criticism of the CVP model is the use of one activity — units sold — as the cost/activity driver. The CVP model ignores market conditions, such as product demand, competitive pricing, sales resulting in pricing changes, quality issues, general economic conditions, inflation, among other variables. Some argue that CVP is too simplistic to be useful as a management tool. Others argue that the model needs to be extended to an activities-based model. a. CVP and ABC together can provide managers with a comprehensive estimation model. By using an ABC approach and taking into account that costs can be categorized as unit, batch, product, customer, or facility-level costs, the CVP model needs to be modified so that the costs are characterized differently than simply fixed or variable. Total costs should be categorized as: (Unit variable cost * number of units) + (Batch costs * number of batches) + (Product cost *number of products) + (Customer cost * number of customer orders) + (Facility costs * facility cost driver). This characterization of costs takes some costs that might have been treated as fixed before and now treats them as variable, but the variability is based on activity other than number of units sold. b. By using account analysis and multiple regression (see Chapter 11), a CVP model can be extended to incorporate multiple layers of cost drivers and activity. The extension of the simple CVP model provides many benefits. The main benefit is that it provides much better information regarding what must be done to ensure profitability. It also clarifies different costs that exist. c. Although the CVP model is much more complex when adapted to allow inclusion of multiple cost drivers, it is easier to perform sensitivity analysis via computer software. Once the time and money are invested in an intricate system like the one described, it is to the advantage of the organization to use the model as much as possible in order to evaluate performance and examine profitability options. E. Excel worksheet is very conducive to creating computer models to solve CVP scenarios together with sensitivity analysis. It is important to use cells and cell references so that changing some assumptions would automatically result in recalculating the desired numbers. Target profit, target selling price, taxes, and costs can be all incorporated into the model. A sales mix or a product mix of different products with specific proportion of each can also be included into the model for a multi-product situation. In addition, ABC models can be incorporated into the equation to account for a new combination of factors that show variability by unit, by batch, by product, or by customer type. F. The CVP model is used primarily for short-term decision making. Four types of decisions for which the CVP model might provide helpful information are (1) the make-or-buy decision, (2) adding or dropping a business unit (e.g., a product line), (3) optimal use of scarce resources, and (4) accepting special orders. The question of the optimal use of scarce resources is discussed in this chapter. G. Choosing which goods and services to produce and sell is a common managerial decision. Successful organizations are likely to be confronted with limited capacity, at least in the short run. These limitations are called capacity constraints. Examples of capacity constraints include shortage of skilled tax accountants during tax season; not enough computer programmers to write code for new video games needed for holiday sales; or too few cooks at a large restaurant. Ideally, managers faced with capacity constraints should direct resources needed to alleviate the constraint before expending resources on less constrained activities. Sometimes it is not possible to correct the capacity constraint problem soon enough to avoid choosing between profit-making alternatives. 1. When an organization is faced with choosing among alternative profitable activities, the contribution margins generated by each alternative should be compared. The opportunity that provides the highest contribution margin per unit of the scarce resource is the one that should be chosen. 2. Although managers might have to resolve capacity constraints related to one bottleneck resource, it is often the case that two or more capacity constraints must be dealt with at the same time. When this is the case, the analysis of which activity or group of activities is optimal can be completed using a mathematical model called “linear programming.” Linear programming is a mathematical model used to maximize profits or minimize costs. H. One of the most common methods of assessing risk is sensitivity analysis. It tests a financial planning model for changes in outcomes caused by changes in each of the model’s parameters. 1. The what if analysis could be in terms of impact on profit with different sales volumes, sales prices, fixed costs, or variable costs, and any combination of these variables. 2. Another example could be a “scenario analysis” where profit levels will be explored under best, worst, and most likely cases. I. Linear programming can also be used to model decisions about the use of multiple scarce resources. 1. Linear programming shows how best to allocate multiple scarce resources among alternative courses of action in the short run when capacity cannot be increased. The objective could be maximization of sales or profits or minimization of costs. a. Objective function is a mathematical relation of inputs to outputs to be maximized or minimized. b. Feasible solution space is the combination of input and output values that satisfy the constraints. c. Optimum point is the set of inputs and outputs in the feasible solution space that maximizes or minimizes the objective function. 2. Linear programming model requires transforming data into equation form. If the objective is maximization of contribution margin (CM) of a three-item product mix with certain given contribution margins, the model could say: Maximize: $A + $B + $C Subject to certain constraints, such as Direct Material ?A + ?B + ?C <= ### Direct Labor ?A + ?B + ?C = ? Sales of B should be >= ? a. After entering the data into an Excel worksheet, you can go tools – add-in – solver and call in the required cells to solve a linear programming problem. Chapter 12 - Problem 1 LO: 4 Building a financial model that reflects the effects of taxes, multiple products, and multiple cost drivers. Time needed: 45 minutes XYZ Company has three products X, Y, and Z. X sells for $20 with a variable cost of $8, Y sells for $30 with a variable cost of $21, Z sells for $50 with a variable cost of $40. Fixed costs amount to $214,000. Furthermore, assume that for every 5 units of X that are sold, the company sells 3 units of Y and 2 units of Z. Required: Use an Excel worksheet 1) Determine break-even in units and dollars of each product. 2) Assuming a desired profit of $107,000, how much of each product should be sold? 3) Assuming a desired net profit of $149,800 and a tax rate of 30%, how much of each product should be sold? 4) At a targeted profit level of $53,500 (no taxes), by how much would profit increase if sales increase by 80%? Show the percentage and the amount. Solution: 1) X Y Z Selling price 20 30 50 Variable costs 8 21 40 Contribution margin 12 9 10 Sales mix 5 3 2 Fixed costs 214000 Weighted average CM 60 27 20 107 Breakeven in units 10000 6000 4000 2000 Breakeven in dollars 200000 180000 200000 580000 CM = FC at BE 120000 54000 40000 214000 2) Target profit 107000 Cost and profit to be covered 321000 Required units 15000 9000 6000 3000 Sales required in $ 300000 270000 300000 870000 3) Net income 149800 Tax rate 0.3 Income before tax 214000 FC and profit to be covered 428000 Sales required 20000 12000 8000 4000 Sales required in $ 400000 360000 400000 1160000 4) Operating income 53500 FC and profit to be covered 267500 Required units 12500 7500 5000 2500 Sales required in $ 250000 225000 250000 725000 Operating leverage 4 Sales increase 80% Profit increase 320% Problem 2 LO: 5 Sensitivity analysis Time needed: 20 minutes Arman Company has a total of $250,000 in fixed manufacturing and $150,000 in fixed administrative costs per period. The product sells for $20 and has a manufacturing variable cost of $12 and variable selling expense of $2 per unit. Required: a) Determine the breakeven point in units and in dollars. b) What would be the breakeven point in units and dollars if fixed manufacturing cost increase by $40,000? c) What would be the BE if fixed administrative costs decrease by $80,000? d) What would be the BE if selling price increase by $4 a unit? e) What would be the BE if variable manufacturing costs increase by one dollar? f) What would be the BE if variable selling expense decrease by one dollar? g) What would be the BE if the tax rate is at 30% of net income? Answer: Q FMC FAE Total F SP VMC VSE CM CM % BE units BE $ a) 250,000 150,000 400,000 20.00 12.00 2.00 6.00 0.30 66,667 1,333,333 b) 290,000 150,000 440,000 20.00 12.00 2.00 6.00 0.30 73,333 1,466,667 c) 250,000 70,000 320,000 20.00 12.00 2.00 6.00 0.30 53,333 1,066,667 d) 250,000 150,000 400,000 16.00 12.00 2.00 2.00 0.13 200,000 3,200,000 e) 250,000 150,000 400,000 20.00 13.00 2.00 5.00 0.25 80,000 1,600,000 f) 250,000 150,000 400,000 20.00 12.00 1.00 7.00 0.35 57,143 1,142,857 g) This is irrelevant because there are no taxes at breakeven point where profit is zero. Problem 3 LO: 6 & 7 Managing scarce resources and the theory of constraints Time needed: 25 minutes Product X requires 2 hours of labor time, ½ hour of machine time, and 3 lbs of material whereas, Product Y requires 1 ½ hour of labor time, one hour of machine time, and 4 lbs of material. X sells for $125 and Y sells for $179 a unit. Labor cost is $12 an hour; machine time costs $20 an hour, and material costs $16 a lb. Determine a) Optimal output where demand is unlimited. Production capacity is 1500 of each product b) Optimal output where demand for X and Y is one thousand units and we have a labor time constraint of 3,000 hours. c) Optimal output where demand is 1,000 units for each and machine time available is only 1,200 hours. d) Optimal output where demand is 1,000 units for each and material available is only 4,900 lbs. Solution: Product X Qty Cost Total Prod. Y Qty Cost Total Selling price 125.00 Selling price 179 Labor 2.00 12.00 24.00 Labor 1.50 12.00 18 Mach. Time 0.50 20.00 10.00 Mach. Time 1.00 20.00 20 Material 3.00 16.00 48.00 Material 4.00 16.00 64 Contribution margin 43.00 77.00 a) If demand is unlimited produce as much of each as both have positive contribution margin. b) With labor constraint, produce 1,000 of Y and give the balance to X (1500/2 = 750). c) With limited machine time, produce 1,000 units of Y and (200/.5) 400 units of X. d) With limited availability of materials, produce 1,000 Y and (900/3) 300 units of X. Problem 4 LO: 4 Multiple products breakeven model Estimated time: 15 minutes Gissue Bake Shop makes two kinds of pastries. Pastry X costs $12 and sells for $20. Pastry B costs $7 and sells for $10 each. The above costs are variable costs only. The shop’s fixed costs amount to $3,923. Current sales volume amounts to 300 units of A and 700 units of B. The same mix will hold in the future. Determine a) breakeven point, b) sales needed if the company expects a periodic profit of $2,000, c) sales needed if the company expects a net profit of $2,000 with a tax rate of 30%. Solution: Item Product A Product B Total Selling price 20 10 Contribution margin 10 3 Current sales volume 300 700 1,000 Total contribution margin 3000 2100 5,100.00 Sales 6000 7000 13,000.00 Contribution margin ratio 0.392307692 Fixed costs 3,923.00 Breakeven 9,999.80 b) sales with profit of $2,000 c) sales with a profit of $2,000; taxes at 30%: 15097.84 Profit before taxes: 6666.67 Sales needed 26993.27 Variable cost 10 7 Sample Quiz 1. AAA Company produced a product which had a selling price of $20 and a variable cost which amounted to 60% of sales. Given a fixed cost of $60,000, the breakeven sales will be a. 5,000 units b. 5,500 units c. 6,000 units d. 7,000 units e. 7,500 units Answer: e Learning Objective: 2 60,000 / 8 = 7,500; CM = 20 – (20 * .60) = 8 2. AAA Company produced a product which had a selling price of $20 and a variable cost which amounted to 40% of sales. The company wants a profit before tax of $15,000. The tax rate is 20% and fixed costs amount to $60,000. AAA must sell a. 6,250 b. 7,396 c. 9,375 d. 9,844 e. None of the above. Answer: a Learning Objective: 4 (60,000 + 15,000) / 12 = 6,250 units 3. AAA Company produced a product which had a selling price of $20 and a variable cost which amounted to 60% of sales. The company wants a profit after tax of $15,000. The tax rate is 20% and fixed costs amount to $60,000. AAA must sell a. 6,250 b. 7,396 c. 9,375 d. 9,844 e. None of the above. Answer: d Learning Objective: 4 15,000 / (1 - .20) = 18750; (60,000 + 18,750) / 8 = 9,844 4. AAA currently has a profit of $15,000 at a sales volume of 6250 and a variable cost of $8 and a selling price of $20. If variable costs increase to $9, by how much can the fixed costs change to still maintain the same profit? a. $6,000 decrease b. $6,250 decrease c. $6,000 increase d. $6,250 increase e. None of the above. Answer: b Learning Objective: 1 5. AAA currently has a profit of $15,000 at a sales volume of 9375 units and a fixed cost which amounts to $65,625 and a selling price of $20 per unit. Variable cost per unit should be a. $12.6 b. $12.0 c. $11.4 d. $11.0 e. None of the above. Answer: c Learning Objective: 2 6. ABC Company sells three products with exactly the same price of $20 a unit. However, A’s contribution margin amounts to 40%, B’s at 50%, and C’s at 60% of sales. Sales mix for A, B, and C is at 500, 1500, and 3000 units respectively. Fixed costs amount to $16,500. Breakeven sales for B should be a. 450 b. 600 c. 750 d. 1500 e. None of the above. Answer: a Learning Objective: 4 Sales mix: 10%, 30%, and 60% with CM of 8, 10, and $12 respectively. (10% * 8) + (30% * 10) + (60% * 12) = 11; 16,500 / 11 = 1,500; 1,500 * 30% = 450 7. ABC Company sells three products with exactly the same price of $20 a unit. However, A’s variable cost is at 40%, B’s at 50%, and C’s at 60%. Fixed costs amount to $18,000. An additional $9,000 needs to be spent on advertising to boost sales. Sales mix is at 500, 1500, and 3000 units for A, B, and C respectively. Sales in dollars for C at breakeven amounts to a. $18,000 b. $24,000 c. $36,000 d. $45,000 e. None of the above. Answer: c Learning Objective: 4 (10% * 12) + (30% * 10) + (60% * 8) = 9; 27,000 / 9 = 3,000; 3,000 * 60% * 20 = 36,000 8. ABC’s sales mix has drastically changed due to market conditions to 3000, 1500, and 500 units for A, B, and C respectively. Fixed costs have increased to $22,000 per period. The selling price is at $20 a unit for all products with a variable cost of 40%, 50%, and 60% for A, B, and C respectively. Breakeven units for A will be a. 300 b. 600 c. 900 d. 1,200 e. None of the above. Answer: b Learning Objective: 4 9. Omid Company produces and sells two products — M and N — for $29 and $19 a unit respectively. Variable costs amount to $14 for M and $12 for N per unit. It takes 1½ hours to make one unit of M and ½ hour to make one unit of N. Total manpower available is 1300 hours and maximum demand for is 1,800 units of M and 1,700 units of N. The optimum production of M to maximize profit should be a. 300 b. 900 c. 1700 d. 1800 e. None of the above. Answer: a Learning Objective: 6 10. Honda Company has decided that a fair selling price for its model 2003 Accord is $18,960 per vehicle. The dealer markup is 20% from the net manufacturer’s price. The freight to the dealer’s shops, which is paid by the manufacturer, comes to $450 per vehicle. An Accord inclusive of freight presents costs the company in the neighborhood of $15,950. Honda’s cost to manufacture per unit should be reduced by _______ in order to break even. a. $150 b. $600 c. $782 d. $1,232 e. None of the above. Answer: b Learning Objective: 4 11. Shahnaz has three products X, Y, Z with a throughput margin of $12, $18, and $24 respectively. It takes one hour to produce one unit of X, two hours to produce one unit of Y, and three hours to produce one unit of Z. If a total of 3000 hours are available, how much of which product(s) should be made? 3,000 units of X 1,500 units of Y 1,000 units of Z 1000 units of X and 1,000 units of Y 500 units of X, 500 units of Y, and 500 units of Z. Answer: a Learning Objective: 6 12. Shahnaz has three products X, Y, Z with a throughput margin of $12, $18, and $24 respectively. It takes one hour to produce one unit of X, two hours to produce one unit of Y, and three hours to produce one unit of Z. Given a demand of 900 units for each product, how much of each product should be made? 900 of each 900 of X, 750 of Y, and 200 of Z 800 of X, 800 of Y, and 200 of Z 900 units of X, 900 units of Y, and 100 units of Z none of the above. Answer: d Learning Objective: 6 13. Shahnaz has three products X, Y, Z with a throughput margin of $12, $18, and $24 respectively. It takes one hour to produce one unit of X, two hours to produce one unit of Y, and three hours to produce one unit of Z. Given a demand of 800 units for each product, the optimal throughput margin will amount to: $27,500 $28,800 $29,200 $31,600 $32,750 Answer: b Learning Objective: 6 14. Based on the data available, there is a 30% chance of selling 12,000 units of X at $15 a unit or 50% chance of selling 10,000 units at $16 a unit or 20% chance of selling 9,000 units at $18 a unit. The weighed average probability of sales amounts to $184,600 $168,400 $166,400 $164,600 none of the above Answer: c Learning objective: 5 15. Ryan Enterprises had sales amounting to $350,000, 40% of which was for variable costs with a profit amounting to $20,000. The company has an operating leverage of 9 times 8 times 7 times 6 times 5 times Answer: a Learning objective: 2 16. Ryan Enterprises had sales amounting to $350,000, 40% of which was for variable costs with a profit amounting to $20,000. If sales increase by 40%, profit will increase by 40% 120% 240% 300% 360% Answer: e Learning objective: 2 17. Ryan Enterprises had sales amounting to $350,000, 40% of which was for variable costs with a profit amounting to $20,000. If sales increase by 20%, profit will amount to $36,000 $36,000 $56,000 $66,000 none of the above Answer: c Learning objective: 2 18. Omid Printing expects its fixed costs to amount to $180,000. The company has an average selling price of $40 a unit with a variable cost of 60% and desired profit of 10% of sales. The company’s sales should amount to ___________ to meet its objectives: $500,000 $600,000 $700,000 $800,000 $900,000 Answer: b Learning objective: 4 19. The theory of constraint is the constraint or constraining factor is a process or resource in a system that limits the capacity of the system seeks to improve productive processes by focusing on the constraining factors a and b b and c Answer: c Learning objective: 7 20. Constraint is the constraint or constraining factor is a process or resource in a system that limits the capacity of the system seeks to improve productive processes by focusing on the constraining factors a and b b. and c Answer: b Learning objective: 7 17. Honda Company has decided that a fair selling price for its model 2000 Accords is $18,960 per vehicle. The dealer’s margin is 20% from the suggested selling price. If Honda wants a profit of 10% on its net invoiced price, its cost per vehicle should be a. $13,651 b. $14,220 c. $16,853 d. $17,556 e. None of the above. Answer: a Learning Objective: 4 18. XY Company’s product mix includes $720,000 in sale of X and $640,000 in sale of Y. X’s contribution margin is 60% and Y’s is 40% of sales. Fixed costs amount to $505,880. X’s sale at breakeven should amount to a. $640,000 b. $720,000 c. $529,400 d. $470,600 e. None of the above. Answer: c Learning Objective: 2 19. XY Company’s product mix includes $720,000 in sale of X and $640,000 in sale of Y. X’s contribution margin is 60% and Y’s is 40% of sales. Fixed costs amount to $505,880. Weighted average contribution margin ratio for Y amounts to a. .31764 b. .18824 c. .50588 d. .40000 e. None of the above. Answer: b Learning Objective: 2 20. Value engineering may involve a. benchmarking. b. activity-based costing. c. elimination of non-value-added costs. d. tearing apart competitive products for analysis. e. All of the above. Answer: e Learning Objective: 4 21. Sensitivity analysis answers what if questions such as possible impact of changes in a. sales prices b. variable costs c. fixed costs d. sales mix e. all of the above. Answer: e Learning Objective: 5 Instructor Manual for Cost Management: Strategies for Business Decisions Ronald W. Hilton, Michael W. Maher, Frank H. Selto 9780073526805, 9780072430332, 9780072830088, 9780072299021, 9780072881820, 9780072882551, 9780070874664, 9780072388404, 9780072343533