LEARNING OBJECTIVES

After you have read and studied this chapter, you should be able to:
1. Explain how activity based costing (ABC) fits into an overall cost accounting system.
2. Describe the two main problems that tend to occur when companies use traditional costing.
3. Discuss the causes and directions of product cost distortions that occur in traditional costing.
4. Explain the logic underlying ABC.
5. Discuss how the concepts of fixed and variable costs are viewed in ABC.
6. Explain the distinction between production volume and activity volume.
7. Describe how activity measures are chosen when using the ABC approach.
8. Describe the ABC cost hierarchy.
9. Explain the conceptual distinction between activities, drivers and activity measures.
10. Outline four steps involved in designing an activity based costing system or sub-system.²
11. Outline three additional steps required to obtain ABC product costs.
12. Compute product cost in relatively simple ABC problems.
13. Discuss CAM-I's involvement in developing and implementing ABC concepts and techniques.
14. Discuss a controversial issue concerning how ABC should be used.
15. Discuss the connection between ABC and the dichotomy of capitalism.

The main purpose of this chapter is to introduce the concepts and terminology associated with activity based costing and to discuss how activity based concepts are used to produce more accurate product costs than those obtained in the traditional cost systems presented in Chapters 4, 5 and 6. This chapter contains two relatively long sections and three fairly short sections. The first section places emphasis on the conceptual material underlying activity based costing and addresses the first nine learning objectives listed above. The second section outlines the steps involved in using the ABC technique and provides two related examples that illustrate and compare ABC with traditional costing. This section covers learning objectives 10 through 12. Sections three and four include a discussion of the CAM-I organization's involvement in the development and implementation of ABC concepts and a short discussion of a controversial issue concerning how ABC should be used. The last section relates the emergence of activity based costing to the dichotomy of capitalism framework discussed in Chapter 1.

ABC CONCEPTS

This sub-section places activity based costing within the five part cost accounting system structure illustrated in Exhibit 2-1 of Chapter 2. Is ABC an input measurement basis, an inventory valuation method, a cost accumulation method, a cost flow assumption, a measure relating to the timing of data availability, or none of the above?

From our previous discussions in Chapters 2 and 6 recall that activity based product costing may be used as an alternative to the traditional inventory valuation methods, or as a separate stand alone, microcomputer based system designed only to obtain more accurate information for management decisions. If ABC replaces traditional full absorption, or variable costing, it becomes the company's inventory valuation method. Then, activity based costs flow through the perpetual inventory accounts. However, if ABC is used as a separate management decision support system where activity based product cost are determined only once per year, then ABC is not serving as the company's inventory valuation method.

More importantly, whether ABC is used as a replacement for traditional inventory valuation or as a stand alone method, it provides information about how and why resources are consumed. Thus, according to ABC advocates, it is not just an inventory valuation method, or just a separate product costing method. Activity based costing is a resource consumption model that can provide a wealth of information to aid in decisions concerning product and process improvements.³ We will return to this idea in Chapter 8 under the heading of activity based management (ABM).

Another clarification regarding how ABC fits into the overall cost accounting system has to do with cost accumulation. Remember that there are two basic cost accumulation methods, job order costing and process costing. Activity based costing is not a cost accumulation method, therefore it does not replace these methods, but instead ABC is used to enhance the accuracy of the product costs determined in both job cost and process cost environments. Most of the illustrations of ABC in textbooks and articles are based on two to four products which seems to imply a process orientation. However, since there are likely to be more product variations or differences in a job cost environment than in a process cost environment, it is logical to assume that the potential benefits of using ABC are greater for companies that produce a large number of products to customer specifications, than for companies that have more focused processes dedicated to a few generic products.

Two main problems tend to occur when traditional inventory valuation methods are used to provide information for management decision purposes. One has to do with product cost distortions, or cross-subsidies and the other relates to the exclusiveness of traditional product costing.

First, in traditional costing, only production volume related measures are used to allocate overhead costs to products, even though many products do not consume indirect resources (overhead) in proportion to the volume of products produced. Since many types of indirect resource costs are caused by, or driven by, non-production volume related product characteristics such as size and complexity, traditional costing tends to distort product costs. This means that too much overhead cost is allocated to some products, while too little overhead cost is allocated to other products. These distortions are frequently referred to as cross-subsidies. Generally, ABC solves this problem by separating overhead costs into different cost categories referred to as cost pools. Costs that are caused by, or driven by, the same activity are pooled together and then allocated, or traced, to products using an appropriate measure of the activity volume.

A second problem with traditional cost systems is that tracing product related administrative, marketing and distribution costs to product inventories is not a generally acceptable procedure allowable for external reporting. However, engineering design, marketing, distribution and customer service costs are clearly part of the costs of placing a product in the hands of the customer. Since these non-manufacturing costs may differ substantially from product to product and from customer to customer, ABC traces these costs to products and customers using additional cost pools and activity measures. Thus, the ABC approach provides the potential for more accurate product costs for management decisions concerning product planning, product design and introduction, product design changes, product pricing, make versus buy, product distribution, product service and product discontinuance. ABC also provides potential benefits to many service oriented industries such as banking, insurance, health care, and transportation.

To keep the illustrations in this chapter fairly simple, we will concentrate on manufacturing costs, but remember that non-manufacturing costs are also traced to products and services using the ABC approach.

THE CAUSES OF PRODUCT COST DISTORTIONS

There are two main causes of product cost distortions in traditional costing, i.e., where a single production volume based overhead rate is used by each product department. These include product volume differences (or product volume diversity) and product differences (or product diversity).

Cost distortions from product volume differences occur when a company produces one, or more, high volume products (i.e., a relatively large number of units) and one, or more low volume products (i.e., a relatively small number of units). Generally, the low volume products will receive too little overhead when a single production volume based departmental rate is used and high volume products will receive too much overhead. Conceptually, the idea is that each type of product requires engineering, purchasing, inspection and other support, regardless of the number of units produced, thus these support costs do not vary in proportion to the number of units, but instead vary with other factors that are unrelated to production volume. If the costs of support activities are allocated to products on the basis of a production volume related measurement such as direct labor hours, low volume products will not receive cost allocations in proportion to their demands on these activities.

Cost distortions from product differences occur when there are variations in product size and product complexity. Small products tend to require less production volume related input (such as direct labor time) than large products, although they do not require less support in proportion to their size. Therefore small products tend to be undercosted, while large products tend to be overcosted.

Product complexity generally refers to product design complexity. Products with complex designs are likely to require more engineering work, more materials related support (e.g., purchasing and materials movement), perhaps longer machine setups and more inspections than less complex products. These additional demands on the various support activities generally cause relatively complex products to be undercosted and relatively simple products to be overcosted. In addition, products that require a relatively large number of parts, unique parts and relatively more, long or complex machine setups tend to be undercharged with overhead while products that require relatively few parts, common parts, relatively few setups, short or simple setups tend to be overcharged.

The generalizations in the previous paragraphs are summarized in Exhibit 7-1. The effects of product volume differences and product sized differences are illustrated in the examples below. The effects of differences in product complexity are illustrated in some of the problems at the end of this chapter.

EXHIBIT 7-1
SUMMARY OF COST DISTORTIONS
THAT TEND TO OCCUR IN TRADITIONAL COST SYSTEMS

Activity based costing is based on the following ideas. First, designing, producing and distributing products and services requires many activities to be performed. Performing these activities requires resources to be purchased and used. Purchasing and using resources causes costs to be incurred. Restated in reverse order, the ABC logic is that resources generate costs, activities consume resources and products consume activities. Thus, a company's activities are identified, then costs are traced to these activities (or activity cost pools) based on the resources that they require. Then, costs are assigned, or traced from each of these activity cost pools to the company's products (or services) in proportion to the demands that each product (or service) places on each activity. In ABC, a measure of the relevant activity volume is used to trace each type of costs, rather than exclusively using measurements (or allocation bases) related to the volume of the products or services produced. Using this logic, ABC tends to solve the problems created by traditional cost or inventory valuation methods. The ABC logic is illustrated in Figure 7-1.

There are still two stages in assigning costs to products in a manufacturing environment, i.e., 1) from service departments (activities) to producing departments, and 2) from producing department activity cost pools to products.

The traditional concepts of fixed and variable costs are frequently de-emphasized in activity based costing. This is because the ABC logic looks at costs from a long run perspective while the traditional fixed/variable cost behavior methodology is based on a short run perspective. The ABC designer explicitly recognizes that all costs tend to be variable in the long run. Therefore, one of the objectives of ABC is to determine the main causes of these long run cost variations. ABC designers attempt to answer the following question. What creates the demand for the output of each of the company's main activities?

To help managers understand the conceptual difference between the long run and short run perspectives, Cooper and Kaplan utilize an idea they refer to as the "Rule of One". According to this rule, if a support department, or activity, uses only one unit of a particular type of resource, such as one person or one machine, then the cost of that resource can be classified as fixed. However, if more than one unit of the resource is required, then classifying the resource cost as fixed is not beneficial for product costing purposes. Something caused the demand for the resource to be greater than one. Perhaps this driver can be identified and used to trace the costs more accurately to the products or services that ultimately consume the resource through activities. Although some activity costs tend to be fixed, i.e., not respond to short run changes in activity volume, these fixed costs represent management commitments that are made to support a past, present or expected future activity level. Generally, all costs are driven by something, even if the driver appears to be inactive.

Does the de-emphasis on the fixed-variable cost methodology in ABC mean that activity cost cannot be separated into short run fixed and variable cost categories? The answer is that fixed and variable activity costs can be identified and traced to products and services using separate activity based rates. One potential advantage of using separate rates for fixed and variable costs is that idle capacity (or unused resource) costs can be identified for each activity if the activity rates are based on practical capacity rather than normal or planned activity volume (See the note on denominator activity levels for more on this issue). There is another potential advantage in the area of cost control. If ABC is used as the company's inventory valuation method, it would allow variance analysis to be performed for each activity.

The answer to this question is controversial. Some critics argue that the fixed/variable cost methodology should be eliminated because it motivates managers to add more business volume and variety in an attempt to lower the fixed costs per unit without adequately considering the long run effects. However, the additional product variety and diversity tends to cause the so called fixed costs to increase, which defeats the original purpose. Thus, the whole process is much like a dog chasing it's tail.⁴ This is an interesting issue that we will return to in Chapter 11.

Activity volume refers to an input or output measurement of the quantity of work performed to accomplish an activity. These activity volume measurements may represent the frequency, duration or physical volume of an activity.⁵ However, the key difference between traditional costing and activity based costing is that ABC uses both production volume and non production volume activity measures to trace costs to products. Some examples of common activities and representative activity measures are presented in Exhibit 7-2.

EXHIBIT 7-2
EXAMPLES OF ACTIVITY COST POOLS AND ACTIVITY MEASURES

* This classification scheme is discussed below.

A key idea in ABC is to find an activity measure for each activity that is closely related (correlated) to the activity costs involved. As indicated in Exhibit 7-2, a production volume related measure might be appropriate for some types of costs, (e.g., machine hours for machining ), but non-production volume related measures are more appropriate for other types of activity costs. For example, the number of purchase orders might be an appropriate choice as the activity measure for purchasing costs, while the number of engineering work orders might be a more appropriate basis for tracing engineering costs. The cost classification scheme referred to in the right hand column of Exhibit 7-2 is discussed below.

ABC designers normally use interviews with knowledgeable managers to define activities, cost pools and cost driver relationships. Although the statistical tools discussed in Chapter 3 might also be used to aid in this process, there are some serious problems that limit their usefulness for this purpose. First, analyzing short run data may produce very misleading results. This is because performing correlation analysis with short run data is not likely to reveal the drivers of long run variable costs, i.e., the costs identified as fixed costs in traditional costing. Another key idea in ABC is that reducing the volume of a particular activity measurement will not necessarily have a short run effect on the cost of the activity. Reductions in activity requirements may simply create idle or excess capacity. Data collected for a longer period (e.g., two or three years) might be more useful for identifying drivers and activity measures for long run variable costs, but the data would have to be adjusted to remove the influence of non stationary factors such as changes in production processes, inflation and seasonal variations. As indicated in Chapter 3, these factors can cause autocorrelation which tends to confuse rather than clarify the relationships involved.

There is a second potential problem when attempting to use statistical correlation analysis to identify cost drivers and activity measures to represent them. The overall correlation between an activity measure and the overall demands placed on the activity by the company's products may be fairly high, although the correlation of the activity measure with the demands of some specific products is relatively low. For example, if ninety-eight percent of a company's products require short machine setups, (e.g., one hour) while the other two percent require long setups, (e.g., eight hours) then, the overall correlation between the number of setups required and setup costs would probably be fairly high. However, assigning setup costs to products on the basis of the number of setups would tend to undercost the products that require long setups and overcost the products that require short setups. The main point of this discussion is that accurate cost tracing requires high correlation between the activity measure and the demands of each specific product, not just high overall, or average correlation.⁶

A cost classification scheme, sometimes referred to as the ABC cost hierarchy, places all costs into one of the following categories:⁷

    1. Unit level - the cost of an activity required once each time a unit of product is produced.

    2. Batch level - the cost of an activity required each time a batch of products is produced.

    3. Product level - the cost of an activity required to support a specific type of product.

    4. Facility level - the cost of an activity associated with maintaining the facility or plant.

    5. Customer level - the cost of an activity required to support a specific customer.

Batch and Product Level Activities

Although it is not clear how each activity cost would be classified by a particular company, the probable cost classifications for the activities in Exhibit 7-2 are indicated in the right-hand column of the exhibit. Most of the examples in the exhibit are either product or batch level activities. If an activity is triggered mainly by the orders, lots, or batches of products produced, then it fits into the batch level category. For example, if the activities associated with purchasing, receiving and storing materials are initiated mainly by production orders for the production of batches of products, then these are batch level activities. On the other hand, if these same activities are performed mainly to keep an average inventory of raw materials available without regard for specific batches, then they might be classified as product level activities.

Examples of customer level activities include accounts receivable, special packaging, distribution or shipping requirements and certain types of non-routine customer services. Examples of facility level costs include building maintenance, property taxes and insurance, plant security and the plant manager's salary. Most of the facility level costs are common to all products and according to one view need not be assigned to products for management decision purposes. Others disagree and consider full cost to be more appropriate. We will not dwell on this controversy except to note that it is one of the many unresolved issues in accounting.

The ABC cost classification scheme helps emphasize the difference between traditional costing and activity based costing. In assigning cost to products, traditional costing treats all manufacturing costs as unit level costs, therefore they are referred to as production volume based (PVB), or unit based allocations. On the other hand, ABC recognizes that many of the support costs in a company are either related to activities associated with producing batches of products, or to other activities that are performed to support specific products. In addition, traditional costing treats marketing, distribution and customer service costs as period costs, while ABC traces, or attempts to trace, these product level and customer level costs to products and customers.

Conceptually, the three terms activity, driver and activity measure have different meanings although these terms are frequently used interchangeably in accounting literature. The purpose of this section is to clarify the conceptual distinction between activities, drivers and activity measures.

Activities represent the types of work performed in an organization. For example, purchasing represents a main activity for a company. The activities chosen in the ABC design process usually represent main activities that are made up of many sub-activities, tasks and sub-tasks. For example, many different types of work must be performed in the purchasing department, but all of this work may be conveniently classified as purchasing so that the complexity of the ABC design is kept to a manageable level. The different types of activities, along with some examples, are summarized at the top of Exhibit 7-3.

EXHIBIT 7-3
ABC CONCEPTS AND TERMINOLOGY

Cost drivers and activity drivers are essentially the same. A driver is an underlying cause of a cost. Normally, whatever drives an activity also drives the costs of the activity. Conceptually, there are primary drivers and secondary drivers. A primary driver represents the initial cause of an activity. A secondary driver represents an activity or event that is caused by a previous activity or event. For example, the primary drivers of purchasing costs may be factors such as customer demands, product design characteristics (e.g., number of parts required) and the number of vendors selected. Therefore, purchasing is technically a secondary driver of purchasing costs. This terminology is summarized in the middle section of Exhibit 7-3.

To obtain a better grasp of these concepts consider the following idea. All of a company's functions and activities require resources that generate costs, therefore all activities are cost drivers. However, all functions and activities are performed to support the company's objectives, e.g., to generate profits, increase market share etc., thus all functions and activities are technically subordinate to these primary drivers. Activities merely represent secondary cost drivers, although the distinction between primary and secondary is likely to be forgotten or ignored after the system is designed. It is also useful to note that although activities are cost drivers, drivers do not have to be activities. Drivers may be events or other phenomena.

Conceptually, an activity measure is not necessarily an activity, or a cost driver or an activity driver. An activity measure is instead a unit of measurement chosen to represent the activity volume and the primary driver. The activity measure provides the basis for tracing or linking the activity costs to the products that consume the activity.

To understand the difference between the activity measure and the activity driver, consider the following example. The number of purchase orders might be chosen to represent the volume of work performed by the purchasing department, but the number of purchase orders is driven by whatever drives the purchasing activity. Primary, or higher level drivers are likely to be such things as the number of products produced, the number of raw materials and parts required for each product, whether the parts are common to many products or unique requirements for a single product and the number of vendors involved. Thus, to say that the number of purchase orders is the driver for purchasing costs tends to confuse the issue. Although ordering causes costs, the number of purchase orders is secondary. The number of purchase orders is a dependent variable because it is caused by something else.⁸ However, since there may not be a convenient measure of the primary driver, or drivers, the number of purchase orders often serves as a reasonably accurate substitute for tracing purchasing cost to products.

Another example may help to clarify the point. The number of direct labor hours is frequently used in traditional cost systems as the basis for allocating overhead costs to products. As a result, accountants frequently say that direct labor time is the cost driver. However, the number of direct labor hours depends upon, or is caused by, the level of production activity which in turn is driven by the company's objectives and customer demands. Thus, the number of direct labor hours is simply a convenient activity measure chosen to represent production activity.

The lower section of Exhibit 7-3 summarizes the terminology that relates to activity measures. There are different types of measures including frequency, duration and physical measurements. Simple frequency measures that indicate the number of times an activity is performed are appropriate when each occurrence of an activity requires the same amount of time and resources, e.g., where each purchase order requires the same amount of time to prepare on a standard form. Duration measurements and physical measurements are more appropriate where the time or resources needed to perform an activity are not uniform.

FOUR STEPS IN DESIGNING AN ABC SYSTEM OR SUB-SYSTEM⁹

The concepts discussed in the previous sections of this chapter can be summarized into four steps. Designing an ABC model, system or sub-system requires: 1) identifying a company's main activities, 2) determining the primary and secondary drivers for these activities, 3) aggregating activities into homogenous cost pools and 4) selecting activity measures to represent each pool. Homogeneous activity costs are those costs that are consumed in the same proportions. Recognizing these relationships allows the designer to combine homogenous costs into a single cost pool to simplify the system. Although this concept is somewhat vague when stated in this simple way, it should become clear to you after studying the examples presented below.

After the system has been designed, ABC costs per unit can be calculated using historical costs or budgeted costs. ABC calculations can be based on annual activity costs obtained from historical records, or budget estimates made for a subsequent period. In either case, three steps are required to determine unit ABC costs once the data is available. These steps include:

1) Calculate the activity overhead rates for each activity cost pool by dividing the total annual cost of each cost pool by the total annual quantity of the activity measure associated with each pool. More precisely in equation form:

    where: Rj = the activity overhead rate for activity j.
                     j = the number of the activity.

If historical information is used to develop ABC unit costs, i.e., data from a prior period, then the annual costs and quantities in the calculation are established by the prior period activity levels achieved. If the ABC system is designed with budgeted data, then the annual cost estimates and annual quantities of the activity measures would depend on the capacity level chosen. Popular alternatives include practical capacity, normal or average capacity, and planned volume.

2) Determine the total annual costs of each product by multiplying the activity overhead rates by the activity quantities associated with each product as follows,

    where: Ci = Total annual cost of product i.
                 Di = Direct cost of product i.
                Aji = Quantity of activity j consumed by product i.
                 Rj = the activity overhead rate for activity j.
                    j = the number of the activity.
                    i = the number of the product.
                G = Greek sigma or summation sign meaning "the sum of".

3) Calculate each product's unit costs by dividing the total annual costs for each product i by the number of units of product i produced.

These three steps are illustrated in the examples provided below.

A variety of illustrations could be provided to show how product cost distortions occur in traditional production volume based (PVB) costing and how these distortions are eliminated when activity based costing is used. Two related examples are provided to show how product volume differences and product size differences tend to affect product costs. Some other types of cost distortions appear in the problems provided at the end of this chapter. Although the examples are based on manufacturing firms, similar cost distortions frequently occur in service organizations.

Assume that Company A produces two products, V1 and V2 with the annual production volumes and product characteristics presented in Exhibit 7-4.¹⁰ To emphasize the key issues involved without unnecessary complications, assume that the firm has only one production department so that all service department costs are allocated to this single department in stage 1 cost allocations.¹¹ This simplifying assumption allows us to ignore the first stage allocations that would only distract from the issue that we want to examine. To further simplify the illustrations, we will also assume that the activity costs are perfectly correlated to the activity measures chosen. Of course this is an unrealistic assumption, but when there are only two products, it allows us to isolate the cost distortions caused by production volume differences and product size differences precisely.

EXHIBIT 7-4
ANNUAL PRODUCT DATA FOR COMPANY A

The company's main activities have been combined into five activity cost pools along with appropriate activity measures based on management interviews. These five cost pools and the activity measurements associated with each cost pool appear in Exhibit 7-5.

EXHIBIT 7-5
ANNUAL ACTIVITY COSTS FOR COMPANY A

The way this illustration is designed, we can further simplify the problem by aggregating, or combining these five cost pools into only two homogeneous cost pools, one for non-production volume related costs and one for production volume related costs. This is possible because the consumption proportions for the three non-production related costs pools (purchasing/receiving, engineering and setups) are the same and the consumption proportions for the two production related cost pools (machining/power/maintenance, and materials planning/ handling) are the same. Since each unit of V2 requires twice as much of each type of non-production related costs as each unit of V1, these three cost pools can be combined into a single homogeneous cost pool and traced to products using any one of the three activity measures, i.e., number of purchase orders, engineering work orders or setups. Each of these measures reflects the 2 to 1 consumption ratio. Since each unit of V2 requires the same amount of direct material and direct labor as V1, the two production volume related cost pools can be combined and traced to products using either direct labor hours or materials dollars. Both of these measures reflect the 1 to 1 consumption of production volume related resources. The activity costs and measurements after combining the homogeneous cost pools are presented in Exhibit 7-6.

EXHIBIT 7-6
ANNUAL ACTIVITY COSTS FOR COMPANY A
COMBINED HOMOGENEOUS COST POOLS

Activity overhead rates for the two cost categories in Example 7-1 are calculated as follows:

1. Non-production volume related = $66,600 ÷ 3* = $22,200 per purchase order.

* Total purchase orders = 1 for V1 and 2 for V2.

2. Production volume related = $33,000 ÷ 1,100* = $30 per direct labor hour.

* Total direct labor hours = 100 for V1 and 1,000 for V2.

The calculations for steps 2 and 3 are presented in Exhibit 7-7. In step 2 the activity overhead rates are multiplied by the quantities of the appropriate activity measures to obtain the overhead costs traced to each product. Then in step 3, the unit ABC costs are determined by dividing the cost traced to each product by the annual production quantities from Exhibit 7-4, i.e., 100 units for V1 and 1,000 units for V2. Direct material and direct labor costs are also included in the exhibit to show the total unit cost for each product. As indicated at the bottom of Exhibit 7-7, the unit ABC costs are $312 for V1 and $134.40 for V2.

Comparing ABC With Traditional PVB Costing For Products V1 and V2

Now suppose Company A uses the traditional production volume based (PVB) costing approach where all overhead costs are allocated to products using direct labor hours as a single allocation basis. Then the total overhead rate would be calculated by dividing the total activity overhead costs in Exhibit 7-5 (or Exhibit 7-6) by the total number of direct labor hours, i.e., 1,100 total units multiplied by 1 hour per unit. This calculation produces a total overhead rate of $90.55 per direct labor hour ($99,600 ÷1,100 DLHs = 90.54545). Overhead costs for each product are $90.55 since each product requires 1 direct labor hour. This is very different from the ABC unit overhead cost of $252 for V1 and $74.40 for V2 that are calculated in Exhibit 7-7. Adding direct material and direct labor costs of $60 provides a total unit cost of $150.55 for each product. Thus, the traditional costing approach would understate the unit cost of the low volume product V1 by $161.45 and overstate the unit cost of the higher volume product V2 by $16.15.

EXHIBIT 7-7
COMPANY A
COSTS TRACED TO PRODUCTS V1 AND V2
USING AN ACTIVITY BASED COST (ABC) SYSTEM

Using Proportions Rather than Activity Rates

A different way to solve relatively simple ABC problems is use proportions as illustrated in Figure 7-2 below. Although the non-production volume related costs could be combined as above, each activity cost pool is kept separate in Figure 7-2 to provide a somewhat different view of the solution. The proportions used are based on the data in Exhibit 7-4. For example, V1 required 1 purchase order and V2 required 2 purchase orders, therefore purchasing and receiving costs are allocated 1/3 to V1 and 2/3 to V2.

To understand why the traditional production volume based (PVB) approach distorts product costs per unit, consider the more detailed PVB unit costs calculated in Exhibit 7-8. This exhibit illustrates the cost allocations obtained in a traditional PVB system where direct labor hours are used as the allocation basis. The separate overhead cost pools are maintained to show where the distortions occur. Therefore separate overhead rates are needed for each pool. Dividing the annual costs of the non-production volume related pool ($66,600 from Exhibit 7-6) by 1,100 direct labor hours generates a rate of $60.5455 per direct labor hour. Of course the rate for the production volume related pool is still $30 per hour, i.e., $33,000 ÷ 1,100, because the activity measure for this pool is direct labor hours in both the ABC and PVB systems.

Production volume based allocations based on direct labor hour proportions are illustrated in Figure 7-3 below for each activity cost pool. 

We can see from Exhibit 7-8 and Figure 7-3 that each unit of V1 and V2 receive the same amount of cost in each overhead cost category. This is because each product requires the same number of direct labor hours per unit (i.e., 1 hour each). At first, this may appear to be a fair and accurate way to allocate overhead. However, since Company A produces ten times as many V2's as V1's, traditional PVB costing assigns ten times as much overhead costs to V2 as it assigns to V1. More specifically, V2 receives ten elevenths (1,000/1,100) or 90.9% of the overhead, while V1 receives only one eleventh (100/1,100) or 9.1%. This distorts the product costs per unit because V2 consumes only two thirds of the non-production volume related activities , i.e., 2 out of 3 purchase orders, 8 out of 12 engineering work orders and 4 out of 6 setups, while V1 consumes the other one third. The resulting unit cost distortions are summarized in Exhibit 7-9 where ABC and PVB unit costs are compared.

EXHIBIT 7-9
COMPANY A
ABC AND PVB UNIT COST COMPARISONS

The unit cost comparisons in Exhibit 7-9 reveal that the high volume product V2 subsidizes the low volume product V1. Each high volume product is overcosted by $16.15 while each low volume product is undercosted by $161.45. Since Company A produces only 100 units of V1, the distortion per unit is more significant for V1 than for V2. The graphic illustration in Figure 7-4 shows this in a somewhat more dramatic way. The unit cost distortion that occurs for V1 is greater than the traditional PVB unit cost estimate.

Although the unit cost distortions are not equal, the total cost distortions are always equal, except for small rounding errors. The approximate equality of the distortions for Company A can be verified by multiplying the unit cost distortions by the number of units involved, i.e., (100)(161.45) is approximately equal to (1,000)(16.15). To avoid the rounding error, we can compare the total costs in Exhibits 7-7 and 7-8, i.e., the total understatement for V1 is 31,200 - 15,054.55 = $16,145.45, while the total overstatement for V2 is 150,545.45 - 134,400 = $16,145.45.

Note from Exhibit 7-9 that the production volume related costs are not distorted by the traditional PVB approach. This reinforces the point made earlier that a production volume related basis may be an appropriate activity measure for tracing certain types of overhead costs to products, although it cannot be used as the only basis in cases where all costs are not consumed in proportion to production volume.

Assume that Company B produces two products V2 and V3 where Product V2 is the same small high volume product that Company A produces. However, V3 is a larger size, high volume product that requires more direct material and direct labor because of it's size, but no additional support from purchasing, engineering or setups. Also assume that Company B has the same cost structure as Company A except for the differences between the two companies related to production volume and product size. Activity costs are still perfectly correlated to the activity measures chosen for the ABC system.

The data for Company B are presented in Exhibits 7-10 and 7-11. The same two aggregated cost pools used for Company A can also be used for Company B because the consumption proportions are the same for each of the three non-production volume related activities. The products consume all three non-production volume related activities in the same proportions. If V3 consumed ½ of the purchase orders, 1/3 of the engineering work orders and 1/5 of the setups, then we would not be able to combine these costs into a single homogeneous pool.

EXHIBIT 7-10
ANNUAL PRODUCT DATA FOR COMPANY B

EXHIBIT 7-11
ANNUAL ACTIVITY COSTS FOR COMPANY B
SEPARATE AND COMBINED HOMOGENEOUS COST POOLS

Activity overhead rates for the two cost categories in Example 7-2 are calculated as follows:

1. Non-production volume related = $88,800 ÷ 4* = $22,200 per purchase order.
* Total purchase orders = 2 for V2 and 2 for V3.

2. Production volume related = $330,000 ÷ 11,000* = $30 per direct labor hour.
* Total direct labor hours = 1,000 for V2 and 10,000 for V3.

EXHIBIT 7-12
COMPANY B
COST TRACED TO PRODUCTS V2 AND V3
USING AN ACTIVITY BASED COST (ABC) SYSTEM

The calculations for steps 2 and 3 are presented in Exhibit 7-12.

Comparing ABC With Traditional PVB Costing For Products V1 and V2

Exhibit 7-13 illustrates the cost allocations obtained for Company B in traditional PVB costing where direct labor hours are used as the allocation basis. The separate overhead cost pools are maintained, as in the previous example, to show where the distortions occur. Thus, separate overhead rates are needed for each pool. Dividing the annual cost of the non-production volume related pool ($88,800 from Exhibit 7-11) by 11,000 direct labor hours generates a rate of $8.0727 per direct labor hour. Of course the rate for the production volume related pool is still $30 per hour, i.e., $330,000 ÷ 11,000, because direct labor hours are used as the activity measure for this pool in both the ABC and PVB calculations.

EXHIBIT 7-13
COMPANY B
COST TRACED TO PRODUCTS V2 AND V3 USING A
TRADITIONAL PRODUCTION VOLUME BASED (PVB) COST SYSTEM

Exhibit 7-13 shows that in PVB costing each unit of V3 receives ten times as much overhead costs as V2 in each overhead cost category, i.e., ten elevenths or 90.9% for V3 as opposed to one eleventh or 9.1% for V2. This is because each unit of V3 requires ten direct labor hours while each unit of V2 requires only one hour. The PVB approach distorts product costs because V3 consumes only fifty percent of the non-production related support, i.e., 2 out of 4 purchase orders, 8 out of 16 engineering work orders and 4 out of 8 setups. The resulting unit cost distortions are summarized in Exhibit 7-14 where ABC and PVB unit costs are compared. The PVB approach understates the unit cost of the relatively small product V2 by $36.33 and overstates the unit cost of the relatively large product V3 by $36.33. The unit cost distortions are equal because the production volumes for V2 and V3 are equal.

EXHIBIT 7-14
COMPANY B
ABC AND PVB UNIT COST COMPARISONS