Segregating Costs: Fixed vs. Variable Costs

THOMAS BUTTROSS: One of several topics to cover when talking about basic cost concepts is the segregation of costs and the fixed and variable costs. Any discussion of fixed versus variable cost requires a discussion of mixed and step costs.

The learning objective is to understand and be able to use cost categories, that is segregation of costs that underline managerial accounting. Be aware that these cost categories are fundamental and are used throughout the study of cost or managerial accounting.

One way to segregate costs is fixed versus variable costs, including mixed and step costs, which is covered here. Another way is direct versus indirect costs, which is covered separately. A third way is the segregation of costs in financial accounting for financial reporting purposes by functional categories, such as separating rent expense from utilities, expense from interest expense, which is not covered in managerial accounting, an important point that there are different segregations of the same cost for different purposes. Note that these categories are not mutually exclusive. For example, a fixed cost can be direct or indirect and a variable cost can be direct or indirect.

These methods used to segregate costs apply to all kinds of organizations, as well as to individuals such as you. Any organization that incurs costs, whether it is in manufacturing, merchandising, service not for profit or government can segregated its costs. All organizations are likely to have some costs that are fixed and some that are variable with respect to a particular cost object.

The concept of fixed and variable cost does not make any sense unless one first considers two factors, the time frame and the relevant range. Most costs are fixed in the extreme short run. Given a 24-hour time frame, it would be difficult to change most costs. For example, terminating an employee generally requires severance pay. That stops the costs from disappearing immediately.

On the other hand, all costs are variable in the extreme long run. Given a 40-year time frame even multibillion dollar plants can be retired [INAUDIBLE]. Managerial accounting generally uses a time frame of one year for classification of a cost as fixed or variable. Given an infinite range of activity, no cost would be fixed.

Let's consider depreciation of manufacturing facilities. It if it takes one $2 billion plant to make 500,000 automobiles per year, then it will take two such plants to make one million, three such plants to make one million five, et cetera. No organization expects to operate over an infinite range of activity.

If the above auto company expects the relevant range of demand for its vehicles to be between $1.3 million and $1.5 million vehicles, then it will attempt to operate with three plants, no more and no less. With six million invested in plants, depreciation will be fixed for quite a few years even though we are only interested in one year.

Keep in mind that different organizations have different relevant ranges. For example, Toyota and GM build more cars than BMW. So their relevant range would be much higher than BMW's relevant range. Also, because different organizations have different relevant ranges, a fixed cost for one organization can be a step cost for another. This will be more apparent when you cover the part of this presentation on stepped cost.

The formula for a straight line comes from your math courses earlier in life and is used in your college statistics course when covering linear regression. This would be a great time to use Google to revisit the Cartesian plane. At the time this was prepared one good place to go is, quote, "line geometry, unquote, in Wikipedia.

The formula for a straight line utilizes the northeast quadrant of that Cartesian plane. The formula is y equals a plus bx, where y equals the dependent variable, because its value depends on the value of the other variables in the equation. When graphing, the vertical axis is the y-axis. In accounting, y is usually monetary representing either revenue or cost. Most often, in cost or managerial accounting, y will be a cost.

x equals the independent variable, because it comes from outside the equation, meaning its value does not depend on any other values in the equation. x is a measure of activity. When graphing, the horizontal axis is the x-axis. In accounting, x is usually units sold, where y is revenue, or x is units produced, where y is cost. However, x could be something else, such as miles driven, where y is automobile operating cost.

Most often in cost or managerial accounting, x will be units produced. a equals the intercept. It is the value of y when x is 0. In accounting, it is the fixed cost portion of the equation. b equals the slope defined as the rise divided by the run or the change in y over the change in x. It is the rate of change in y as x changes. In accounting, it is the variable cost portion of the equation. An overview of fixed and variable mixed and step costs is presented here. Examples are presented and discussed on the slides that follow.

A fixed cost is a cost that remains unchanged in total when activity changes. In terms of the equation, it is the value of y when x equals 0, which is y equals a. The example we will cover shortly is straight line depreciation on a factory building.

A variable cost is a costly changes in total, in total proportionally, which is the same as saying linearly as activity changes. In terms of the equation, it is the value of y when a equals 0, which is y equals bx. The example we will cover shortly is direct material used in a product.

A mixed cost is a that is partially fixed and partially variable. In terms of the equation it is the value of y when both a and b exist, which is y equals a plus bx. The example we will cover shortly is factory utilities. To use Excel to separate in mix cost see the article "Forecasting with Excel Regression Analysis Can Help Predict Revenues and Costs" by James A Weisel, Journal of Accountancy, February, 2009 pages 62 through 67.

A step cost also known as step variable or step fixed is a cost that varies in batches as activity changes. It does not fit into the equation presented because it is not linear. The example we will cover shortly is salary for factory supervisors.

The graph of straight line depreciation of a factory building displays a fixed cost. The planned depreciation will remain at $20,000 during the next year, regardless of the level of units produced. In terms of the equation for a straight line, y equals a equals 20,000.

This graph of direct material cost displays a variable cost. The direct material cost changes proportionally with any change in the units produced. To change proportionally, the cost has to be linear, meaning it has to plot as a straight line. In terms of the equation for a straight line, y equals bx equals 2x.

The variable cost is a slope of the blue line that is going up the graph assuming you're looking at a color version of the graph. Slope is rise over run. And this comes from mathematics, not from accounting. We're simply using mathematics to do this plot. Note that the cost rises from 0 to 10,000 as the activity runs from 0 to 5,000 units.

Rise over run is $10,000 minus $0 dollars divided by 5,000 units minus 0 units equals $10,000 over 5,000 units equals 2 or $2 of cost rise for every one unit produced. The graph of factory electricity displays a mixed cost, a cost that is partially fixed and partially variable.

The factory electricity costs $4,000 even when there is no activity. This might be the cost of heating and cooling the building and having the lights on, independent of production. In addition, the cost changes proportionally with any change in the units produced, which is the activity level. An additional $2 in electricity is used each time a unit is produced. In terms of the equation for a straight line, y equals a plus bx equals 4,000 plus 2x.

You can easily divide a mixed cost into its fixed and variable components. For example, if you're doing a budget and you wanted to divide this factory electricity into fixed and variable, you would say fixed electricity is $4,000 and variable factory electricity is 2x or two times the number of units produced. So it's easy once you have the formula for the mix cost to divide it into fixed and variable.

The hard part with the mixed cost is getting that formula. The utility company does not send you a bill saying, you owe $9,500. $4,000 was fixed and $5,500 was variable. No. It sends a bill simply saying, you owe $9,500. You have to figure out how much is fixed and how much is variable.

The good news is that it's easy to do that using the regression function within Excel, that is you could take your last 12 utility bills and throw in the amount you paid for utilities, this is the y values, and your volume of output, this is the x values, and Excel will estimate the a and b values for y equals a plus bx. You may not remember this from statistics, but the problem is that if you have only 12 data points, your estimates of a and b don't tend to be stable.

Statisticians would tell you need about 60 data points. To get 60 data points, you would need five years of monthly electric bills. The problem with long periods of time is that the data may not be stable, that is your electric rates may have changed during the last five years, so you're comparing apples and oranges and that doesn't work well. As long as you realize you're probably going to end up using the last 12 months of electric bills to get values for a and b, and those values will not be perfect, and as long as you can live with that imperfection, that's probably the way to go.

A step costs is a cost that increases after a batch of units. In this case, consider the example of factory supervisors salary. Let's assume one supervisor can supervise up to 10 workers. Supervisors cost $20,000 per year each. I know this is a ridiculously low number. Let's also assume that one worker can make 200 units per day.

If the company is going to make between 1 and 2000 units, it is going to need between 1 and 10 employees. At this level, it is going to need 1 supervisor at a cost of 20,000. So the line starts at 20,000 and goes out until it hits 2000 units.

Once a company exceeds 2000 units, it will need to hire more employees and therefore more supervisors. From 2,001 to 4,000 units will require 11 to 20 employees and 2 supervisors at a total cost of 40,000. from 4,001 to 6,000 hours use will require 21 to 30 employees and 3 supervisors at a total cost of 60,000.

Now what can you do with that step cost? There are a couple ways to handle it. But any way you handle it, you have to break it down into fixed or variable cost. We will cover two ways.

One way the simple way to handle it is to have a relevant range that is on a single step. So if production is expected to be between $4,000 and 6,000 units, then the organization needs 3 supervisors at a fixed cost of 60,000. Often a step cost cannot be converted into a fixed cost because the relevant range cannot be restricted to one step.

So a second way to handle it is to draw a line starting at the minimum of 20,000 for 1 supervisor through the center of the remaining steps, and then use the slope of that line as a variable cost. What you end up doing is turning the step cost into a mixed cost. In this case, you only get the correct costs at the midpoint of each step. Below the midpoint of the step, you underestimate the cost. And above the midpoint of the step, you overestimate the cost.

Now you have an opportunity to practice what you go through to make sure you understand the concept. Classify each of the following costs as fixed, variable, mixed, or step with respect to the units of product produced. Factory maintenance crew salaries, is it fixed, variable, mixed, or step? Pause the presentation until you have an answer.

Here we have what is probably a step cost. Why is it a step cost? It may be that you have a maintenance crew of 10 people and you need a maintenance crew of 10 people in order to build the one million units you expect to build this year. But if you increase production, you're going to run the machines more, and need more maintenance, and you have to hire more people for the maintenance crew once you reach a certain level of production.

And the same is true if you cut production. You can lay off some of the people in the maintenance crew, but it may take a 5,000 unit change in production before you need to add or terminate a maintenance worker.

Factory electricity, is it fixed, variable, mixed, or step? Pause the recorded presentation until you have a solution. If you said mixed, you are correct, because there would be a certain amount of utility bill that would be incurred just from having the lights on, and then there would be a dish utilities consumed as units went down the assembly line.

Factory building straight line depreciation, is it fixed, variable, mixed, or step? Pause the recorded presentation until you have a solution. If you said fixed, you are correct, because once you calculate straight line depreciation it varies with time, not the number of units that are produced. It is a certain amount that will be the same whether you produce 0 units or you produce the maximum number of units that could possibly that you could possibly produce in that plant.

Factory machinery units of output depreciation, is it fixed, variable, mixed, or step? Pause the presentation until you have an answer. When you compute units of output depreciation, you're saying depreciation is a certain amount per unit, therefore it varies directly with the number of units produced, making it variable, or it is at least acting as a variable cost.

Factory supervisor salaries, is it fixed, variable, mixed, or step? Pause the recorded presentation until you have an answer. Like the maintenance crew salaries it is a step cost.

Factory land and building property taxes, is it fixed, variable, mixed, or step? Pause the presentation until you have an answer. The property tax is based on the value of the property, not the number of units produced on the property, therefore like the factory building straight line depreciation it is a fixed cost. This is the end of fixed versus variable cost discussion.