# Fixed vs Variable Cost - Explained

What is a Variable Cost?

# What is a Variable Cost?

A variable cost is an expense that varies in accordance with the level of output. Such costs tend to go up or down as per the production activities of a company. Variable costs will increase in case the production increases and decrease in case production falls. For example: costs associated with raw materials, utilities and packaging costs.

# What is a Fixed Cost?

A fixed cost remains constant or does not vary with the output of an organization. For example, facility rent may remain the same whether the company produces 1 unit or 1 million units of product.

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## Committed Versus Discretionary Fixed Costs

Organizations often view fixed costs as either committed or discretionary.

A committed fixed cost is a fixed cost that cannot easily be changed in the short run without having a significant impact on the organization. Examples of committed fixed costs include salaried employees with long-term contracts, depreciation on buildings, and insurance.

A discretionary fixed cost is a fixed cost that can be changed in the short run without having a significant impact on the organization. Examples of discretionary fixed costs include advertising, research and development, and training programs.

In general, management looks to cut discretionary fixed costs when sales and profits are declining, since cuts in this area tend not to have as significant an impact on the organization as cutting committed fixed costs.

Difficulties arise when struggling organizations go beyond cutting discretionary fixed costs and begin looking at cutting committed fixed costs.

## What are Mixed Costs?

We have now learned about two types of cost behavior patternsvariable costs and fixed costs.

However, there is a third type of cost that behaves differently in that both total and per unit costs change with changes in activity. This cost behavior pattern is called a mixed cost

The term mixed cost describes a cost that has a mix of fixed and variable costs.

For example, a monthly salary plus a commission is a mixed cost because it has a fixed component per month and a variable component of \$per unit.

Because this cost is depicted with a straight line, we can use the equation for a straight line to describe a mixed cost:

Total mixed cost = Total fixed cost + (Unit variable cost × Number of units)

or

Y = + vX where

Y = total mixed costs (this is the y-axis)

= total fixed costs

= variable cost per unit

X = level of activity (this is the x-axis)

## Methods Used to Estimate Fixed and Variable Costs

Four common approaches are used to estimate fixed and variable costs:

• Account analysis
• High-low method
• Scattergraph method
• Regression analysis

The goal of each cost estimation method is to estimate fixed and variable costs and to describe this estimate in the form of Y = vX.

That is, Total mixed cost = Total fixed cost + (Unit variable cost × Number of units)

### Account Analysis

The account analysis approach is perhaps the most common starting point for estimating fixed and variable costs.

This approach requires that an experienced employee or group of employees review the appropriate accounts and determine whether the costs in each account are fixed or variable.

Totaling all costs identified as fixed provides the estimate of total fixed costs.

To determine the variable cost per unit, all costs identified as variable are totaled and divided by the measure of activity (units produced is often the measure of activity).

Remember, the goal is to describe the mixed costs in the equation form Y = f + vX.

Estimate monthly production costs = (Y)

Fixed Costs = f

Variable cost per unit = v

How many units produced = (X).

### High-Low Method

Accountants who use this approach are looking for a quick and easy way to estimate costs, and will follow up their analysis with other more accurate techniques.

The high-low method uses historical information from several reporting periods to estimate costs.

All of the data points from are plotted on the graph. Although a graph is not required using the high-low method, it is a helpful visual tool.

Draw a straight line using the high and low activity levels from these data.

The goal of the high-low method is to describe this line mathematically in the form of an equation stated as Y = + vX, which requires calculating both the total fixed costs amount (f) and per unit variable cost amount (v).

Four steps are required to achieve this using the high-low method:

Step 1. Identify the high and low activity levels from the data set. Identify the months with the highest and lowest level of activity (level of production). Note that we are identifying the high and low activity levels rather than the high and low dollar levels—choosing the high and low dollar levels can result in incorrect high and low points.

Step 2. Calculate the variable cost per unit (v). Because the slope of the line shown represents the variable cost per unit, the goal here is to calculate the slope of the line using the high and low points identified in step 1 (the slope calculation is often referred to as “rise over run” in math courses).

The calculation of the variable cost per unit: Unit variable cost (v) = (Cost at highest level − Cost at lowest level) / Highest Units - Lowest Units)

Step 3. Calculate the total fixed cost (f). After completing step 2, the equation to describe the line is partially complete and stated as Y = f + \$vX.  The goal of step 3 is to calculate a value for total fixed cost (f). Simply select either the high or low activity level, and fill in the data to solve for f (total fixed costs).

Total fixed cost =  total costs - total variable costs.

You will get the same number for either the high or low month.

Step 4. State the results in equation form Y = vX. We know from step 2 the variable cost per unit, and from step 3 that total fixed cost. Thus we can state the equation used to estimate total costs as

Y = f + vX

Now it is possible to estimate total production costs given a certain level of production (X).

## What is the Scattergraph Method?

Many organizations prefer to use the scattergraph method to estimate costs.

Accountants who use this approach are looking for an approach that does not simply use the highest and lowest data points.

The scattergraph method considers all data points, not just the highest and lowest levels of activity.

Again, the goal is to develop an estimate of fixed and variable costs stated in equation form Y = f + vX.

Follow the five steps associated with the scattergraph method:

Step 1. Plot the data points for each period on a graph. This step requires that each data point be plotted on a graph. The x-axis (horizontal axis) reflects the level of activity (units produced in this example), and the y-axis (vertical axis) reflects the total production cost.

Step 2. Visually fit a line to the data points and be sure the line touches one data point. Once the data points are plotted as described in step 1, draw a line through the points touching one data point and extending to the y-axis. The goal here is to minimize the distance from the data points to the line (i.e., to make the line as close to the data points as possible).

Step 3. Estimate the total fixed costs (f). The total fixed costs are simply the point at which the line drawn in step 2 meets the y-axis. This is often called the y-intercept.  Remember, the line meets the y-axis when the activity level (units produced in this example) is zero.  Fixed costs remain the same in total regardless of level of production, and variable costs change in total with changes in levels of production. Since variable costs are zero when no units are produced, the costs reflected on the graph at the y- intercept must represent total fixed costs.

Step 4. Calculate the variable cost per unit (v). After completing step 3, the equation to describe the line is partially complete.  The goal of step 4 is to calculate a value for variable cost per unit (v).  Simply use the data point the line intersects and fill in the data to solve for v (variable cost per unit) as follows:

Step 5. State the results in equation form Y = f vX. We know from step 3 that the total fixed costs and from step 4 the variable cost per unit.  Now it is possible to estimate total production costs given a certain level of production (X).

### Regression Analysis

Regression analysis is similar to the scattergraph approach in that both fit a straight line to a set of data points to estimate fixed and variable costs.

Regression analysis uses a series of mathematical equations to find the best possible fit of the line to the data points and thus tends to provide more accurate results than the scattergraph approach.

Rather than running these computations by hand, most companies use computer software, such as Excel, to perform regression analysis.

Now it is possible to estimate total production costs given a certain level of production (X).

Regression analysis tends to yield the most accurate estimate of fixed and variable costs, assuming there are no unusual data points in the data set.

It is important to review the data set first—perhaps in the form of a scattergraph—to confirm that no outliers exist.

## The Relevant Range and Nonlinear Costs

Two important assumptions must be considered when estimating costs using the methods described in this chapter.

1. When costs are estimated for a specific level of activity, the assumption is that the activity level is within the relevant range.

2. Costs are estimated assuming that they are linear.

Both assumptions are reasonable as long as the relevant range is clearly identified, and the linearity assumption does not significantly distort the resulting cost estimate.

The assumption is that total fixed costs and per unit variable costs will always be at the levels shown in regardless of the level of production.

As defined earlier, the relevant range is a term used to describe the range of activity for which cost behavior patterns are likely to be accurate.

It is up to the cost accountant to determine the relevant range and make clear to management that estimates being made for activity outside of the relevant range must be analyzed carefully for accuracy.

The accountant may determined that a sales level of units is within the relevant range. However, if the company is quickly approaching full capacity. If sales were expected to increase in the future, the company would have to increase capacity, and cost estimates would have to be revised.

Another important assumption being made is that all costs behave in a linear manner.

Variable, fixed, and mixed costs are all described and shown as a straight line. However, many costs are not linear and often take on a nonlinear pattern.

If a company produces just a few units each month, workers (direct labor) do not gain the experience needed to work efficiently and may waste time and materials. This has the effect of driving up the per unit variable cost.

Recall that the slope of the line represents the unit cost; thus, when the unit cost increases, so does the slope.

If the company produces more units each month, workers gain experience resulting in improved efficiency, and the per unit cost decreases (both in materials and labor). This causes the total cost line to flatten out a bit as the slope decreases.

This is fine until the company starts to reach its limit in how much it can produce (called capacity). Now the company must hire additional inexperienced employees or pay its current employees overtime, which once again drives up the cost per unit.

Thus the slope begins to increase.

Although this is probably a more accurate description of how variable costs actually behave for most companies, it is much simpler to describe and estimate costs if you assume they are linear.

As long as the relevant range is clearly identified, most companies can reasonably use the linearity assumption to estimate costs.

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