I. IntroductionThis paper aims to examine why all costs can be classified as either fixed or variable. While because of this classification, mixed costs or more commonly called semi-variable costs have emerged, these semi-variable costs can still be broken down by means of a set of mathematical segregation formulas.
The paper starts by defining the two classifications of costs according to behavior–fixed and variable costs, and their innate characteristics with regard to the level of activity in production. Then, semi-variable costs are explored in relation to their emergence because of the difficulty in classification. Then, a set of mathematical formula is introduced that aims to segregate the fixed and variable components of a semi-variable costs. This proves that even costs with mixed components can still be classified as either fixed or variable costs, in the end.
II. Fully explain why all costs can be determined as either fixed or variable, including those composed of fixed and variable elements can be unarguably split between the fixed and variable.
A. Fixed and variable costs differentiated
In classifying costs according to their behavior, two classifications are used—the fixed costs and the variable costs. Variable costs are defined as costs that change depending on the change in the cost driver on a pro rata basis (McDonald 2005). According to the traditional economic theory, the unit variable cost is fixed, and as volume rises, this unit variable cost is multiplied according to the level of activity, which comprises the total variable cost to a company (Weiner 1960).
The other classification of cost is called the fixed cost. Fixed costs are costs that are not directly affected by the cost driver (McDonald 2005). According to the traditional economic theory, fixed costs are costs that are usually indivisible, because their behavior is not dependent on the change in the level of activity (Machlup 1934). Fixed costs, according to the theory is treated as fixed not according to the level of performance, but is fixed as to time (Gordon & Cook 1973). According to Fekrat, however, fixed costs over the long period of time is also considered variable because of the concept of relevant range (1972). Fixed costs can only be fixed within a relevant range, and outside that range, it changes according to the increase in activity, although not directly and proportionately like variable costs.
For different costing techniques such as absorption and contribution costing, these distinctions are used in order to determine unit costs (Fekrat 1972). Classifying costs into fixed or variable categories is also important in conducting a break-even analysis (Stephens 1966).
B. The emergence of semi-variable costs
Traditional costing systems have lead to difficulties in terms of classifying costs whether they are fixed or they are variable (Weiner 1960). According to the traditional economic theory, variable costs change depending on the changes in the level of activity of production (Weiner 1960). So if the level of activity, or the volume increases, the total variable costs are expected to increase as well in direct proportion to the change in the volume. However, not all variable costs have been found to adhere to this theory (Weiner 1960). There are variable costs that do not increase proportionately with the increase in the company’s level of activity, or volume produced (Stephens 1966). This has lead to the emergence of another category, the semi-variable costs.
Semi-variable costs are later found out as costs that have both fixed and variable components (Weiner 1960). This has been the major reason why, for every increase in the company’s level of activity, these costs do not increase proportionately. In order to further distinguish semi-variable from variable costs, Goliger concretely defines the two concepts as follows: “a semi-variable expense is an expense with a ratio of increase (or decrease) lower than the ratio of the sales volume increase (or decrease) with which it is compared (1949);” according to him, “a variable expense is an expense with a ratio of increase (or decrease) equal to or higher than the ratio of the sales volume increase (or decrease) with which it is compared (1949).”
C. Breaking down semi-variable costs
Semi-variable costs, however are not useful in conducting break-even analysis. In order for these costs to be used in the analysis, academicians have found a way to break them down in the form of a mathematical segregation formulas (Goliger 1949). This proves that any cost, even those with both the fixed and variable components can all be broken down and classified as either fixed or variable.
This mathematical segregation formulas can be stated as follows:
Step 1: R = (E-e) / (S-s)
Step 2: V = R x S and V= R x s
Step 3: F = E – V and e-V; F should be a constant as the difference
where: E = any semi-variable expense at high volume
e = any semi-variable expense at low volume
S = Sales at high volume
s = Sales at low volume
V = Variable part of expense
F = Fixed part of expense
R = Ratio of variable part to any sales volume
These set of formulas aims to segregate the fixed costs from the high and the low scenarios. After the variable components are determined and are deducted from the semi-variable expense, what remains is the fixed component. The fixed components under these two scenarios are the same, which proves that the computation is correct. Therefore, it is proven that even semi-variable costs can also be broken down into fixed and variable costs.
Weiner has also provided some statistical model in order to prove this formula (1960). However, he extends the formula by not just looking at the fixed cost component, but also, in order to address the emerging common knowledge that fixed cost is variable over the long time, because of the concept of relevant range, he looks for the ‘invariability range (Weiner 1960).’ This can be done, however by gathering some data and getting the differences in percentages in each range (Weiner 1960). But the aim is the same, in costs that are considered mixed, these should be segregated by getting the proportionate figures and determining the common figures in the different levels of activities, which is the fixed figure.
In classifying costs according to their behavior in relation to a firm’s level of activity, there are two types of classification—the fixed and variable costs. Fixed costs are not directly affected by the changes in the volume or the level of activity in terms of production; variable costs are. Variable costs change in direct proportion to the changes in the volume. However, not all variable costs adhere to the traditional economic theory of changing proportionately to the production’s level of activity. This has lead to another classification—semi-variable costs.
However, academicians have later found out an explanation why semi-variable costs do not proportionately increase or decrease depending on the increase or decrease in the company’s production volume. This is because, semi-variable costs have fixed component as well. These components can be segregated by means of a set of mathematical formulas that aims to determine the fixed cost as the common cost in both the high and low volume production scenarios. Therefore, semi-variable costs do not exist fully, and these costs can unarguably be classified further into fixed and variable costs, especially for purposes of break-even analysis and finding the unit cost in terms of contribution costing.
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