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2. Cost Behavior Analysis

Good managers must not only be able to understand the conceptual underpinnings of cost behavior, but they must also be able to apply those concepts to real world data that do not always behave in the expected manner. Cost data are impacted by complex interactions. Consider for instance the costs of operating a vehicle. Conceptually, fuel usage is a variable cost that is driven by miles. But, the efficiency of fuel usage can fluctuate based on highway miles versus city miles. Beyond that, tires wear faster at higher speeds, brakes suffer more from city driving, and on and on. Vehicle insurance is seen as a fixed cost; but portions are required (liability coverage) and some portions are not (collision coverage). Furthermore, if you have a wreck or get a ticket, your cost of coverage can rise. Now, the point is that assessing the actual character of cost behavior can be more daunting than you might first suspect. Nevertheless, management must understand cost behavior, and this sometimes takes a bit of forensic accounting work. Let's begin by considering the case of "mixed costs."

2.1. Mixed Costs

Many costs contain both variable and fixed components. These costs are called mixed or semi variable. If you have a cell phone, you probably know more than you wish about such items. Cell phone agreements usually provide for a monthly fee plus usage charges for excess minutes, text messages, and so forth. With a mixed cost, there is some fixed amount plus a variable component tied to an activity. Mixed costs are harder to evaluate, because they change in response to fluctuations in volume. But, the fixed cost element means the overall change is not directly proportional to the change in activity.

To illustrate, assume that Butler's Car Wash has a contract for its water supply that provides for a flat monthly meter charge of $1,000, plus $3 per thousand gallons of usage. This is a classic example of a mixed cost. Below is a graphic portraying Butler's potential water bill, keyed to gallons used:

Look closely at the data in the spreadsheet, and notice that the "variable" portion of the water cost is $3 per thousand gallons. For example, spreadsheet cell B12 is $2,100 (700 thousand gallons at $3 per thousand); observe the formula for cell B12 in the upper bar of the spreadsheet (=(A12/1000)*3). In addition, the "fixed" cost is $1,000, regardless of the gallons used. The total in column D is the summation of columns B and C. The cost components are mapped in the diagram at the right.

Hopefully, the preceding illustration is clear enough. But, what if you were not given the "formula" by which the water bill is calculated? Instead, all you had was the information from a handful of past water bills. How hard would it be to sort it out? Could you estimate how much the water bill should be for a particular level of usage? This type of problem is frequently encountered in business, as many expenses (individually and by category) contain both fixed and variable components.

2.2. High-Low Method

One approach to sorting out mixed costs is the high-low method. It is perhaps the simplest technique for separating a mixed cost into fixed and variable portions. However, beware that it can return an imprecise answer if the data set under analysis has a number of rogue data points. But, it will work fine in other cases, as with the water bills for Butler's Car Wash. Information from Butler's actual water bills is shown at above right. Butler is curious to know how much the August water bill will be if 650,000 gallons are used. Assume that the only data available are from the aforementioned four water bills.

With the high-low technique, the highest and lowest levels of activity are identified for a period of time. The highest water bill is $3,550, and the lowest is $2,020. The difference in cost between the highest and lowest level of activity represents the variable cost ($3,550 - $2,020 = $1,530) associated with the change in activity (850,000 gallons on the high end and 340,000 gallons on the low end yields a 510,000 gallon difference). The cost difference is divided by the activity difference to determine the variable cost for each additional unit of activity ($1,530/510 thousand gallons = $3 per thousand).

The fixed cost can be calculated by subtracting variable cost (per-unit variable cost multiplied by the activity level) from total cost. The table at above right reveals the application of the high-low method. An electronic spreadsheet can be used to simplify the high-low calculations. The website includes a link to an illustrative spreadsheet for Butler.

 
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