# 16.7.2 Exercise: Activity-Based Costing

### Intended learning outcomes: Calculate the cost accumulation for two products, given the material consumption as well as the standard time for the operations and the fixed and variable costs of two work centers, differentiating the fixed costs between investitures in machines and in in tools and devices.

Think again about products A and B described above. After reading Section 16.1.4, you know that tooling costs make up a sizable proportion of the fixed costs. If the costs of the tools used for products A and B are diffe­rent, this should be apparent in the cost accumulation. However, that can only be achieved if we view tool utilization as a process in its own right. Following the principle of ABC and the steps involved (see Section 16.4.2), the characteristic variables for this process are defined as follows:

• ABC process: tool utilization, or use.
• Process costs: the manufacturing or procurement costs of the tool.
• Activity cost driver: the number of units produced with the tool. Why? Usually, it is not the length of time that a tool is utilized that determines its wear, but rather production of a certain number of units of the product. A good example would be pressing tools.
• Process cost rate: process costs divided by the total quantity of product units that are produced using the tool until the tool is used up or worn out.

Figure 16.7.2.1 shows a breakdown of the fixed costs in machine costs and costs for tools and devices.

Fig. 16.7.2.1       Work center costs data.

As in exercise 16.7.1 above, the investitures in machines will be depreciated in 5 years, whereby 1000 productive hours are assumed annually. It is further assumed that a tool can be used to manufacture 20,000 products A or B before it is used up or worn out, no matter whether it is an expensive or inexpensive tool.

Since one hour of capacity is utilized for 40 units of products A or B, 200,000 products can be manufactured in 5000 productive hours. This means that, in that period, 10 tools will be required.

In the following, assume also that the same number of units of products A and B is manufactured. In this case, work center 1 will use 10 tools (5 T1 and 5 T2 tools), which represents an investment of \$100,000. Work center 2 uses 10 tools (5 T3 and 5 T4 tools), which represents an investment of \$50,000. The sum of fixed costs is thus the same as in exercise 5 above.

Determine the values marked “?” in the cost accumulation tables in Figures 16.7.2.2 and 16.7.2.3 below (compare Figure 16.2.2.1).

To calculate the process cost of the tool, use the following:

• The process quantity or quantity per for the ABC process “tool use for operation 1 (or 2)” is 1 (one use per unit produced).
• The total (target) quantity is the number of units produced.
• The process variable, or activity cost driver, is the “use of the tool.”
• The process cost rate (or cost per unit) is the cost of the tool divided by the number of units that can be produced until the tool is used up.
• The process costs (target) are the product of the total (target) quantity times the cost per unit.

Fig. 16.7.2.2       Graphical representation of the cost accumulation for a product A.

Fig. 16.7.2.3       Graphical representation of the cost accumulation for a product B.

Problem-solving hints:

The full cost of goods manufactured will not be the same for products A and B (why?): In fact, we calculate \$4.30 per unit produced of product A (or \$172 for a batch size of 40), and \$5.20 per unit produced of product B (or \$208 for a batch size of 40).