COSTS OF MANUFACTURING OPERATIONS
Decisions on automation and production systems are usually based on the relative costs of alternatives. In this section we examine how these costs and cost factors are determined.
1 Fixed and Variable Costs
Manufacturing costs can be classified into two major categories: (1) fixed costs and (2) variable costs. A fixed cost is one that remains constant for any level of production output. Examples include the cost of the factory building and production equipment, insurance, and property taxes. All of the fixed costs can be expressed as annual amounts. Expenses such as insurance and property taxes occur naturally as annual costs. Capital investments such as building and equipment can be converted to their equivalent uniform annual costs using interest rate factors.
A variable cost is one that varies in proportion to the level of production output. As output increases, variable cost increases. Examples include direct labor, raw materials, and electric power to operate the production equipment. The ideal concept of variable cost is that it is directly proportional to output level. When fixed cost and variable cost are added, we have the following total cost equation:
where TC=total annual cost ($ yr), FC=fixed annual cost ($ yr), VC=variable cost ($ pc), and Q=annual quantity produced (pc yr).
When comparing automated and manual production methods (Section 1.4), it is typical that the fixed cost of the automated method is high relative to the manual method, and the variable cost of automation is low relative to the manual method, as pictured in Figure 2.4. Consequently, the manual method has a cost advantage in the low quantity range, while automation has an advantage for high quantities. This reinforces the arguments presented in Section 1.4.1 on the appropriateness of manual labor for certain production situations.
2 Direct Labor, Material, and Overhead
Fixed versus variable are not the only possible classifications of costs in manufacturing. An alternative classification separates costs into: (1) direct labor, (2) material, and (3) overhead. This is often a more convenient way to analyze costs in production. The direct labor cost is the sum of the wages and benefits paid to the workers who operate the production equipment and perform the processing and assembly tasks. The material cost is the cost of all raw materials used to make the product. In the case of a stamping plant, the raw material consists of the steel sheet stock used to make stampings. For the rolling mill that made the sheet stock, the raw material is the iron ore or scrap iron out of which the sheet is rolled. In the case of an assembled product, materials include component parts manufactured by supplier firms. Thus, the definition of “raw material” depends on the company. The final product of one company can be the raw material for another company. In terms of fixed and variable costs, direct labor and material must be considered as variable costs.
Overhead costs are all of the other expenses associated with running the manufacturing firm. Overhead divides into two categories: (1) factory overhead and (2) corporate overhead. Factory overhead consists of the costs of operating the factory other than direct labor and materials. The types of expenses included in this category are listed in Table 2.7. Factory overhead is treated as fixed cost, although some of the items in our list could be correlated with the output level of the plant. Corporate overhead is the cost of running the company other than its manufacturing activities. A list of typical corporate overhead expenses is presented in Table 2.8. Many companies operate more than one factory, and this is one of the reasons for dividing overhead into factory and corporate categories. Different factories may have significantly different factory overhead expenses.
J. T. Black  provides some typical percentages for the different types of manufacturing and corporate expenses. These are presented in Figure 2.5. We might make several observations about these data. First, total manufacturing cost represents only about 40% of the product’s selling price. Corporate overhead expenses and total manufacturing cost are about equal. Second, materials (and parts) make up the largest percentage of total manufacturing cost, at around 50%.And third, direct labor is a relatively small proportion of total manufacturing cost: 12% of manufacturing cost and only about 5% of final selling price.
Overhead costs can be allocated according to a number of different bases, including direct labor cost, material cost, direct labor hours, and space. Most common in industry is
direct labor cost, which we will use here to illustrate how overheads are allocated and subsequently used to compute factors such as selling price of the product.
The allocation procedure (simplified) is as follows. For the most recent year (or most recent several years), all costs are compiled and classified into four categories: (1) direct labor, (2) material, (3) factory overhead, and (4) corporate overhead. The objective is to determine an overhead rate (also called burden rate) that could be used in the following year to allocate overhead costs to a process or product as a function of the direct labor costs associated with that process or product. In our treatment, separate overhead rates will be developed for factory and corporate overheads. The factory overhead rate is calculated as the ratio of factory overhead expenses (category 3) to direct labor expenses (category 1); that is,
where FOHR=factory overhead rate, FOHC=annual factory overhead costs ($ yr); and DLC=annual direct labor costs ($ yr).
The corporate overhead rate is the ratio of corporate overhead expenses (category 4) to direct labor expenses:
where COHR=corporate overhead rate, COHC=annual corporate overhead costs ($ yr), and DLC=annual direct labor costs ($ yr). Both rates are often expressed as percentages. If material cost were used as the allocation basis, then material cost would be used as the denominator in both ratios. Let us present two examples to illustrate (1) how overhead rates are determined and (2) how they are used to estimate manufacturing cost and establish selling price.
EXAMPLE 2.7 Determining Overhead Rates
Suppose that all costs have been compiled for a certain manufacturing firm for last year. The summary is shown in the table below. The company operates two different manufacturing plants plus a corporate headquarters. Determine: (a) the factory overhead rate for each plant and (b) the corporate overhead rate. These rates will be used by the firm in the following year.
EXAMPLE 2.8 Estimating Manufacturing Costs and Establishing Selling Price
A customer order of 50 parts is to be processed through plant 1 of the previous example. Raw materials and tooling are supplied by the customer. The total time for processing the parts (including setup and other direct labor) is 100 hr.
Direct labor cost is $10.00 hr. The factory overhead rate is 250% and the corporate overhead rate is 600%. Compute the cost of the job.
Solution: (a) The direct labor cost for the job is (100 hr)($10.00 hr)=$1000.
(b) The allocated factory overhead charge, at 250% of direct labor, is ($1000)(2.50)=$2500.
(c) The allocated corporate overhead charge, at 600% of direct labor, is ($1000)(6.00)=$6000.
Interpretation: (a) The direct labor cost of the job, representing actual cash spent on the customer’s order=$1000. (b) The total factory cost of the job, including allocated factory overhead=$1000+$2500=$3500. (c) The total cost of the job including corporate overhead=$3500+$6000=$9500. To price the job for the customer and to earn a profit over the long run on jobs like this, the price would have to be greater than $9500. For example, if the company uses a 10% markup, the price quoted to the customer would be (1.10)($9500) = $10,450.
3 Cost of Equipment Usage
The trouble with overhead rates as we have developed them here is that they are based on labor cost alone. A machine operator who runs an old, small engine lathe whose book value is zero will be costed at the same overhead rate as an operator running a new CNC turning center just purchased for $500,000. Obviously, the time on the machining center is more productive and should be valued at a higher rate. If differences in rates of different production machines are not recognized, manufacturing costs will not be accurately measured by the overhead rate structure.
To deal with this difficulty, it is appropriate to divide the cost of a worker running a machine into two components: (1) direct labor and (2) machine. Associated with each is an applicable overhead rate. These costs apply not to the entire factory operations, but to individual work centers. A work center is a production cell consisting of (1) one worker and one machine, (2) one worker and several machines, (3) several workers operating one machine, or (4) several workers and machines. In any of these cases, it is advantageous to separate the labor expense from the machine expense in estimating total production costs.
The direct labor cost consists of the wages and benefits paid to operate the work center. Applicable factory overhead expenses allocated to direct labor cost might include state taxes, certain fringe benefits, and line supervision.The machine annual cost is the initial cost of the machine apportioned over the life of the asset at the appropriate rate of return used by the firm. This is done using the capital recovery factor, as follows:
where UAC=equivalent uniform annual cost ($ yr); IC=initial cost of the machine ($); and (A P,i,n)=capital recovery factor that converts initial cost at year 0 into a series of equivalent uniform annual yearend values, where i=annual interest rate and n=number of years in the service life of the equipment. For given values of i and n, (A P,i,n) can be computed as follows:
Value of (A P, i, n) can also be found in interest tables that are widely available. The uniform annual cost can be expressed as an hourly rate by dividing the annual
cost by the number of annual hours of equipment use. The machine overhead rate is based on those factory expenses that are directly assignable to the machine. These include power to drive the machine, floor space, maintenance and repair expenses, and so on. In separating the factory overhead items in Table 2.7 between labor and machine, judgment must be used; admittedly, the judgment is sometimes arbitrary. Total cost rate for the work center is the sum of labor and machine costs. This can be summarized as follows:
where Co=hourly rate to operate the work center ($ hr), CL=direct labor wage rate ($ hr), FOHRL=factory overhead rate for labor, Cm=machine hourly rate ($ hr), and FOHRm=factory overhead rate applicable to machines.
It is the author’s opinion that corporate overhead expenses should not be included in the analysis when comparing production methods. Including them serves no purpose other than to dramatically increase the costs of the alternatives. The fact is that these corporate overhead expenses are present whether or not either or none of the alternatives is selected. On the other hand, when estimating costs for pricing decisions, corporate overhead should be included because over the long run, these costs must be recovered through revenues generated from selling products.
EXAMPLE 2.9 Hourly Cost of a Work Center
The following data are given: direct labor rate=$10.00 hr; applicable factory overhead rate on labor=60%; capital investment in machine=$100,000; service life of the machine=8 yr; rate of return=20%; salvage value in 8 yr=0; and applicable factory overhead rate on machine=50%. The work center will be operated one 8hr shift, 250 day yr. Determine the appropriate hourly rate for the work center.
Solution: Labor cost per hour=CLA 1+FOHRLB =$10.00(1+0.60)= $16.00 hr. The investment cost of the machine must be annualized, using an 8yr service life and a rate of return=20%. First we compute the capital recovery factor:
Now the uniform annual cost for the $100,000 initial cost can be determined:
UAC=$100,000(A P, 20%, 8)=100,000(0.2606)=$26,060.00 yr
The number of hours per year=(8 hr day)(250 day yr)=2000 hr yr. Dividing this into UAC gives 26,060 2000=$13.03 hr. Then applying the factory overhead rate, we have
CmA 1+FOHRmB =$13.03(1+0.50)=$19.55 hr Total cost rate is
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