for which the annual volume is not great enough. Although predicting future volume, called forecasting, is a risky venture, it is an essential part of doing business. Product forecasts are typically available from marketing or upper management. The risky nature of production volume forecasting is one reason a manufacturing firm needs to see a quick payback of the automation investment. Thus, one must ascertain whether there is sufficient production volume to justify the investment in the automation. This can be accomplished by considering current and proposed methods’ fixed and variable manufacturing costs and performing a production volume breakeven point analysis.
A product’s manufacturing cost can be broken into two categories, fixed costs and variable costs. Fixed costs are costs that are independent of the quantity of product; i.e., they are incurred whether one part or one million parts are produced. These typically include building rent or mortgage costs, property taxes, equipment costs, and equipment maintenance, to name a few. Fixed costs are most conveniently expressed on an annual basis.
Variable costs, on the other hand, are dependent on the quantity of product. The higher the production, the more the cost incurred. Variable costs include direct labor, raw material costs, and energy costs to operate the equipment. Utilizing these concepts the total annual cost of a product can be represented by the following equation:
CT = CF + QCV,
where
| C T | = | total cost incurred on an annual basis ($/yr) |
| C F | = | fixed cost of product on an annual basis ($/yr) |
| Q | = | quantity of parts produced per year (parts/yr) |
| C V | = | variable cost per part ($/part). |
This formula’s use is demonstrated in the following example.
Example 2.15
Referring to the manual manufacturing method and information in Example 2.13, and given that the annual cost of maintenance for the machine is $8000 and the raw material cost is $1.25 per part, calculate total annual cost of producing 100,000 parts per year
Solution
The given information from the problem statement and taken from Example 2.13 is as follows:
PO = 100 parts/hr (production rate)
PI labor = $36/hr (2 operators at $18/hr)
PI capital = $25/hr
Q = 100,000 parts/yr
CF maint = $8000
raw material cost = $1.25/part.
The first step is to identify the variable costs, which include the labor wage rate, the machine’s capital cost, and the raw material cost. The labor and machine capital costs must be converted to units of $/part. This is accomplished by dividing the hourly cost by the production rate as follows:
CV labor = PI labor/PO = ($36/hr)/(100 parts/hr) = $0.36/part
CV capital = PI capital/PO = ($25/hr)/(100 parts/hr) = $0.25/part.
Next determine the total variable costs by summing each of the individual variable costs:
CV = CV labor + CV capital + CV material
= $0.36/part + $0.25/part + $1.25/part = $1.86/part.
The fixed cost is simply the annual maintenance costs:
CF = $8000/yr.
Solving for the total annual cost to make the product yields
CT = CF + QCV = $8000/yr + (100,000)($1.86/part) = $194,000/yr.
Performing a quantity breakeven analysis of two alternatives involves determining the number of parts that have to be produced that would realize the benefits of the alternative. This is significant because manual methods typically have a lower fixed cost and higher variable costs. Thus, when product volumes are low, manual methods are more cost effective. As production volumes increase the advantage goes to automated methods, which typically have a lower variable cost and higher fixed cost. This is illustrated in Figure 2-9.
Figure 2-9 Quantity breakeven point
Figure 2-9 is a plot showing the total annual cost of an automated method versus a manual method for the same theoretical task. The manual method has a lower fixed cost but higher variable costs. The lower fixed cost is evident in the graph by the lower starting point (zero parts produced). The steeper incline indicates higher variable costs. At around 15,000 parts the two lines cross, indicating the two methods have the same total annual cost. This is termed the quantity breakeven point. As the quantity produced is increased from this point, the automated method has a lower total annual cost. If the annual production is 25,000 parts, the cost savings that the automated method provides is the y-axis value difference between the two lines.
Thus, to determine the quantity breakeven point of two methods, the total annual cost equations are set equal to one another (i.e., equate the costs) and solved for the quantity (Q). This is the quantity at which the proposed and the current methods have the same production cost. Anything above this quantity favors the automated method over the manual method for cost efficiency. This is demonstrated in the following example.
Example 2.16
A new automated method is being developed to replace the manual method described in Example 2.15. The new method has a production rate of 165 parts/hr, requires only one operator, and has a capital cost of $45.50/hr. Additionally, the new method decreases material waste, thus reducing raw material costs to $1.00/part. Because of machine sophistication, yearly maintenance costs will increase to $16,000 per year. Perform a productivity analysis to compare the two alternatives for annual production of 100,000 parts/yr. Is the proposed method more productive? Calculate the quantity breakeven point. What is the total annual cost savings if the proposed method were to be used?
Solution
First, perform the productivity analysis (i.e., compare the current method’s hours and maintenance costs with the proposed). Most of the information can be substituted directly into a productivity calculation spreadsheet, with the
