The power to compete: the new math of precision management.

The rise of activity based costing (ABC) in the new manufacturing environment has come about mainly as a need for more accurate product costing in an ever-changing and very competitive marketplace. An important result of this search for better data is more accurate and relevant costing information that is useful for decision making. This article will describe the use of data developed in an ABC system as it applies to the multiproduct cost-volume-profit (CVP) analysis model. Data derived under ABC can be integrated into traditional decision-making techniques to make these models more accurate and relevant.

The traditional way of determining CVP information in a one-product firm is to use a variation on the following income equation:

I = PX - VX - FC

In this equation, I is income, P is price of product X, V is the variable cost per unit of X and FC is the fixed cost component. To determine the breakeven level in units of product X, the formula becomes:

X = FC/(P - V)

The term P - V is the contribution margin of product X.

The conversion of the single product model to a multiproduct model rests on the assumption of the product sales mix. The denominator for the multiproduct model represents a weighted average contribution margin, i.e., weighted by the sales mix of the individual products. The breakeven point for a multiproduct firm, therefore, will ultimately depend on the sales mix of the products. For example, in a two-product firm, if the product with the larger contribution margin is also the largest seller, then the overall breakeven point of the firm in units will be lower than if the lower contribution margin product was the dominant seller.

The traditional multiproduct CVP model suffers from two flaws. The first concerns the determination of the variable cost component. This cost component is assumed volume-based and is generally regarded to be influenced by only one activity level or cost driver, most commonly production output. This assumption works fairly well for a single product firm or a multiproduct firm that uses resources in a homogeneous manner across its product lines. But in a firm where the product lines are diverse and incur costs in different proportions, determination of the variable cost component must become more detailed to accurately determine the contribution margins of the products.

The second flaw of the traditional CVP model for multiproduct firms deals with the fixed cost component. The CVP formula treats fixed costs as joint or common to the individual products. Little effort is made to develop additional cost drivers to help explain cost behavior. Individual product CVP analysis is, for the most part, useless if there is little or no tracing of fixed costs to the individual products. In order to make individual product CVP analysis relevant, as much of the total fixed costs as possible must be traced to the individual product lines. Fortunately, ABC is structured to do exactly this.

Activity Based Costing and CVP Analysis

To more accurately use CVP analysis in an ABC environment, the traditional model must be modified to correct the flaws discussed above. Specifically, the model must accommodate:

* units of product that have variable costs that are volume based on not just one but multiple cost drivers; and

* nonvolume costs that are traceable to individual product lines. Under an ABC system, the costs necessary for CVP analysis are broken down into the following categories:

1. Volume-based costs: dependent on volume-based activities such as production, direct labor hours or machine hours. Examples would be direct materials (production) and machining costs (machine hours per unit). These can be classified as unit level activities, i.e., they are performed each time a unit is produced. Each product may have volume (variable) costs that are dependent on different cost drivers.

2. Nonvolume-based traceable costs: incurred each time a batch of goods is produced. They are generally fixed with respect to individual units of product but are traceable to product lines. Examples of this type of cost are setup costs, which are dependent upon number of setups; and shipping costs, dependent upon the number of orders received.

3. Nonvolume-based, non-traceable costs: facility level activities that sustain a facility's operations; also referred to as common costs. They are also fixed and cannot be traced to individual products and are therefore arbitrarily allocated for product costing purposes.

One of the goals of ABC is to try to trace and match as many of these costs as possible to specific cost drivers.

Table 1 demonstrates the CVP model in an ABC environment. Assume a three-product firm.

Under the traditional approach, the first requirement is to distinguish between variable and fixed costs. This is done for all costs, including manufacturing and administrative. The activity level or cost driver used is a single, volume-based measure. In the example above, the activity level or cost driver chosen is machine hours. This is the largest overhead cost of the production process. Statistical analysis would indicate that with respect to machine hours, all the other costs would show little correlation. This can be seen if the consumption ratios of the individual production costs are examined. The consumption ratio shows how much each product "consumes" of the total individual cost. The ratios for production costs are shown in Table 2.

The material handling consumption ratio is calculated by multiplying total production by parts per unit. This gives the total amount of the cost driver, parts per unit. So (15,000 units x 40 parts per unit for Prod1) + (10,000 x 60) + (2,500 x 100) = 1,450,000 parts. Prod1 consumption ratio is then 600,000/1,450,000 = 41%. Production scheduling uses total production orders for its cost driver. So 200 + 90 + 100 = 390. Prod1 gets 200/390 = 51%. And so on.

The ratios show that there is diversity in the amount of resources (costs) used or consumed among the products. Since the ratios of the resources consumed by the three products are different, arbitrarily choosing one cost driver will ultimately lead to product cost distortion, as it will then be assumed that all costs are consumed in the same or approximate ratios as the driver chosen.

With the exception of machining costs, the other production costs would be considered fixed in the analysis. In this example, there are 245,000 total machine hours |(15,000 x 9~ + (10,000 x 8) + (2,500 x 12). Cost per machine hour would be \$750,000/245,000 = \$3.06/hour. For simplicity sake, it is assumed that TABULAR DATA OMITTED the machining costs are strictly variable. Total variable overhead for Prod1 would be \$27.54 (\$3.06 x 9 machine hours per unit), \$24.48 (\$3.06 x 8) for prod2, and \$36.72 (\$3.06 x 12) for prod3. The \$750,000 represents only about 39% of the total overhead production costs of \$1,910,000. Under the traditional model, the rest of overhead production costs would be considered common or facility level costs.
```Table 2

Prod1 Prod2 Prod3 Total

Material 41% 41% 18% 100%
Production scheduling 51 23 26 100
Setup time 40 30 30 100
Machining 55 32 13 100
Finishing 32 50 18 100
Inspection 53 27 20 100
```

With respect to the marketing and administrative expenses, the traditional approach would generally pick up commissions as a variable expense. In this example, commission is set at 3% of the selling price. Total commission expense represents 38% of total marketing and administrative expenses of \$430,000.

Exhibit 1 below shows the relationship between the variable (traceable or volume based) and nontraceable (fixed or nonvolume based) costs in the traditional model.

Breakeven under the traditional model can be determined from the above data. The contribution margin for each of the products is calculated in Table 3.

The weighted average contribution margin is determined by multiplying the product's contribution margin by its sales mix. So, for Prod1:

\$102.21 x 55% = \$56.22.

Total weighted average contribution margin = \$121.10 Breakeven point = Total fixed costs/weighted avg. contrib. margin = \$1,425,000/\$121.10 = 11,767 units

The fixed costs in the numerator are all the costs in the example except direct materials, machining and selling commissions.

The analysis provides limited and misleading data. While a specific breakeven point has been determined, given an assumed sales mix, it would be difficult to say anything specific about the individual product lines. The fixed costs represent about 40% of the total costs and about 61% of all costs minus direct materials. Due to the lack of developed cost drivers, the fixed costs cannot be traced to the specific products under traditional CVP analysis.

Additionally, the analysis infers that machine hours are the only mechanism available to control overhead production costs. But changes in output would affect not just machining costs but other volume-based costs as well. By limiting the analysis to basically one volume-driven cost driver for production costs, the analysis falls short of being very useful for management decision making.

CVP Analysis with Activity Based Costing

Improvement in the accuracy and the relevance of CVP analysis begins with the ability to trace costs to specific products or product lines. It is in this area that ABC has great value. We can relieve the restriction that the traditional model makes with respect to having one cost driver affecting all costs. ABC uses as many cost drivers as are needed to explain the specific cost structure under investigation. These cost drivers may be volume driven, such as units or direct labor hours, or nonvolume driven, such as production orders or number of setups. Nonvolume costs are often traceable to specific products or product lines.
```Table 3

Prod1 Prod2 Prod3

Selling price \$175.00 \$225.00 \$250.00

Direct material \$40.00 \$50.00 \$60.00
Selling (commissions) 5.25 6.75 7.50
Total variable costs \$72.79 \$81.23 \$104.22

Contribution margin \$102.21 \$143.77 \$145.78

Weighted average cont mgn \$56.22 \$51.76 \$13.12
```

In addition to direct materials, there are five volume-based costs. The volume-based costs and their related cost drivers are shown in Table 4.

The remaining costs in the example are nonvolume-based costs. These costs can be distinguished between nonvolume costs that are traceable to specific products and common costs that are not traceable and would have to be arbitrarily allocated to the products for costing purposes. The nonvolume traceable costs are production scheduling, setup time, inspection and shipping. The remaining costs are common manufacturing and common marketing and administrative costs.
```Table 4

Cost Driver Cost

Direct materials Units produced \$1,250,000
Machining Machine hours 750,000
Material handling Parts per unit 400,000
Selling expense 3% of (selling price) 165,000
Warehousing Weight/unit 50,000
Finishing Direct labor hours 120,000

Total volume costs \$2,735,000
Table 5

Cost per Prod1 Prod2 Prod 3
Driver

Machining \$3.06 \$27.54 \$24.48 \$36.72
Matl handling .28 11.03 16.80 28.00
Selling .03 5.25 6.75 7.50
Warehousing .51 1.53 2.04 2.55
Finishing .86 2.58 6.02 8.60

Total Volume Costs \$47.93 \$56.09 \$83.37
```

Given the distinction between the volume and nonvolume cost, a new CVP analysis can be performed. First, volume-based costs on a per unit base are determined. These are as shown in Table 5.

The machining cost and selling expense (commissions) are calculated the same way as in the traditional approach. As a further example, material handling is based on parts per unit. Given the output levels above, total parts are 1,450,000. Cost per part is \$400,000/1,450,000 = \$.28 per part. Prod1's cost then is \$.28 x 40 parts = \$11.03 per unit. Finishing is \$120,000 cost/140,000 total direct labor hours or \$.86 per hour. And so on.

Exhibit 2 shows the new relationship between the traceable and nontraceable costs.

As can be seen, the cost structure has changed substantially with ABC.

The new contribution margins using data from ABC for the three products are shown in Table 6.

The fixed costs for this model consist of the traceable nonvolume costs plus the common costs. These costs are shown in Table 7.
```Table 6

Prod1 Prod2 Prod3

Selling price \$175.00 \$225.00 \$250.00
Direct material 40.00 50.00 60.00
Volume costs 47.93 56.09 83.37
Total volume costs \$87.93 \$106.09 \$143.37
Contribution margin \$87.07 \$118.91 \$106.63

Weighted average cont mgn \$47.89 \$42.81 \$9.60

Total weighted average contribution margin \$100.30
Table 7

Cost Amount

Production scheduling \$150,000
Setup time 180,000
Inspection 210,000
Shipping 140,000
Common - mfg 100,000
Total \$855,000

Breakeven point \$855000/\$100.30 = 8525 units
```

Results using ABC data differ dramatically from the results under the traditional analysis. Including volume-based costs in the contribution margin shows that these costs can be affected by changes in output. This is not apparent in the traditional analysis. Material handling cost, warehousing and finishing costs, which were treated as fixed costs in the traditional approach, are all affected by movement in volume of output.

The results have further implications for decision making. The additional volume-based costs can be seen to be affected if activity changes. This is important for decisions about special orders, make or buy decisions and other relevant decision-making situations.

Product Line Analysis

Under traditional analysis, tracing of fixed costs to individual products is not done. This makes it virtually impossible to make specific inquiries about each product line. But with ABC, nonvolume-based costs may still be traceable to specific products at the batch level--that is, not changing on a unit-specific basis but still incurred as part of the product line.

In this example, nonvolume traceable costs are production scheduling, setup time, inspection and shipping. These costs are traced to the individual products as shown in Table 8.

The amount of nonvolume traceable costs represents 19% of the total costs. The remaining common are \$175,000 and are not traceable to any of the individual products. The additional traceability of the nonvolume costs also allows for more accurate decision making. Product TABULAR DATA OMITTED related decisions can be analyzed more accurately because fixed costs, under the traditional method considered common and not relevant, become traceable and relevant under ABC.

A breakeven point by product line can be calculated for each product by dividing the products nonvolume traceable costs by each product's contribution margin. In this example, the product-by-product breakeven points are: Prod1, 3,533; Prod2, 1,688; and Prod3, 1,611 units. The fact that the sum of the individual product's breakeven points does not equal the overall breakeven occurs because the common costs were not included in the individual product's calculation. These costs are not traceable to the individual products. Any allocation of the \$175,000 would be purely arbitrary and of little value.

The individual breakeven point estimates are more accurate than under the traditional approach, which assumes all costs are common and is generally not true. In this example, only about 5% of total costs are common (\$175,000/\$3,590,000). As more and more of the fixed costs become traceable, a more accurate estimate of individual product line CVP data becomes available. The ABC model is very valuable here because tracing costs to product lines is a major objective of ABC.

Summary

We have attempted to demonstrate the usefulness of ABC for more accurately developing decision making information for managers. Specifically, this article shows how properly developed data can be used in a CVP analysis model. The possibilities for ABC data analysis in the decision making area are extensive. In the rapidly changing and competitive marketplace that firms currently face, improving the accuracy and relevance of cost data is in itself a real competitive advantage.

References

1 Cooper R, "Cost Classification in Unit-Based and Activity-Based Manufacturing Cost Systems," The Journal of Cost Management, Fall 1990, pp. 4-14.

2 Hanson D, Management Accounting, PWS-KENT Publishing Company. Boston, MA. 1990.

3 Wolk H, Q Gerber and G Porter, Management Accounting, PWS-KENT Publishing. Boston, MA. 1988.

Lawrence M. Metzger, PhD, CPA, is associate professor of accounting at Loyola University of Chicago.
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