2-2.
Figure 2-2 Manufacturing process expenses
Figure 2-2 is a pie chart showing the relative percentage of expenses that make up the final selling price of a representative product. Note that the manufacturing cost is only 40%. Figure 2-3 is a pie chart of the relative percentage of expenses that make up total manufacturing cost for this product. Notice how the categories in Figure 2-3 relate to the partial productivity measures. Direct labor coincides with labor, capital equipment costs with capital; indirect labor is often absorbed into the capital equipment or direct labor costs; materials and supplies category would represent both material and energy. When an automation project is undertaken, its goal is to decrease one or more of the expenses shown in the figure. Thus, these expenses need to be accurately reflected in the productivity calculations. One accomplishes this by expressing the partial productivity measures in $/hr.
Figure 2-3 Manufacturing cost percentages
When one evaluates an existing process, labor rate, energy cost, and raw material costs are typically readily available from the manufacturing firm’s accounting office. Additionally, the capital costs of the existing equipment would be available as well. These rates will include allocated overhead costs. However, capital costs of an alternative—new automated equipment—process must be estimated.
Estimation of capital costs of a proposed automation can be done through simple calculations that take into account the time value of money in conjunction with allocated factory overhead. When a manufacturing firm invests in a capital expenditure, it expects the investment will yield a return. Most firms have a standard rate of return. This figure, expressed as a percentage, should be readily available from a firm’s upper management. With the rate in hand, the automation engineer can begin to make estimated capital cost calculations.
The goal of the capital cost calculations is to represent the cost of the proposed automation in terms that can be used in the productivity calculations. Thus, cost needs to be expressed in terms of $/hr. The calculation breaks the initial cost of the equipment into an annual cost, then spreads that annual cost over the hours the machine is estimated to run in a year; finally, it adds in factory overhead expenses. The estimated hourly capital cost of the automation can be calculated with the following equation:
Cc = Ca(1 + rfoh),
where
Cc = estimated hourly capital cost of the automation ($/hr)
Ca = estimated hourly cost of automation ($/hr)
rfoh = factory overhead rate.
The hourly estimated cost of the automation can be determined from the equation
Ca = (CIfcr)/ha,
where
| C I | = | initial cost of the automation ($) |
| f cr | = | capital recovery factor |
| ha | = | time that machine is in operation annually (hr). |
The initial cost of the automation (CI) will be known and hours of machine operation annually (ha) can be readily determined. The capital recovery factor (fcr) is determined by the equation
fcr = r(1 + r)n / [(1 + r)n − 1],
where
r = desired rate of return (%)
n = number of years of the service life of the machine.
Figure 2-4 Typical factory overhead costs
Factory overhead rate (rfoh) is the ratio of factory overhead costs to those of the machine under consideration. This is found by distributing the overhead over some variable such as direct labor costs. Typical factory overhead costs are given in Figure 2-4. For any given factory this can be accomplished by taking all of the overhead costs of the firm for one year and dividing it by the total cost spent on direct labor. The formula for this calculation is:
rfoh = Cfoh/Cdl,
where
| C foh | = | annual cost of factory overhead ($/yr) |
| C dl | = | annual direct labor costs ($/yr). |
The following example demonstrates the use of these formulas.
Example 2.12
An automated work cell is being considered to replace an existing process. The cell will cost $150,000 to purchase and is anticipated to have a 4-year service life. The machine will operate for 2080 hours per year. The company spent $2,300,000 on factory overhead and $6,500,000 on direct labor costs last year. Estimate the hourly capital cost to operate the new automated work cell if the manufacturing firm desires a 15% return on its investment.
Solution
The governing equations are
| C c | = | Ca(1 + rfoh ) |
| C a | = | (CIfcr)/ha |
| f cr | = | r(1 + r)n /[(1 + r)n − 1] |
| r foh | = | Cfoh/Cdl. |
The values are given as
| r foh | = | 35% |
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C
I
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