The relevant range refers to a specific activity level that is bounded by a minimum and maximum amount. Within the designated boundaries, certain revenue or expense levels can be expected to occur. Outside of that relevant range, revenues and expenses will likely differ from the expected amount. The concept of the relevant range is particularly useful in two forms of analysis, which are noted below.
Budgeting Relevant Range
When a company constructs a budget for a future period, it makes assumptions about the relevant range of activities within which the business is likely to operate. As long as the actual activity volume falls somewhere within the relevant range, and other assumptions are valid, budgeted revenues and expenses are more likely to be correct. In this case, the relevant range is most likely to be fairly close to the current activity level of a business, with minor modifications.
Cost Accounting Relevant Range
The assumed cost of a product, service, or activity is likely to be valid within a relevant range, and less valid outside of that range. in particular, a "fixed" cost is likely to remain fixed only within a relevant range of activity. Also, volume discounts from suppliers are only valid for certain purchasing volume quantities.
Examples of Relevant Range
For example, ABC Company constructs a budget within a relevant revenue range of no more than $20 million. If actual sales were to exceed that amount, then ABC would need to construct a new manufacturing facility.
As another example, ABC Company assumes that the cost of a green widget is $10.00 within a relevant range of no less than 5,000 units per year and no more than 15,000 units per year. If the actual unit volume is less than 5,000 units, the purchased cost of materials increases sufficiently to make the assumed cost of $10.00 per unit too low. Conversely, if the actual unit volume is higher than 15,000 units, the purchased cost of materials decreases sufficiently to make the assumed cost of $10.00 per unit too high.
As a third example, if ABC Company were to produce more than 20,000 of its yellow LED lights, it would need a third shift to produce them, which would require an additional $70,000 annual salary for a shift supervisor. Thus, the initial cost of the LED light is only valid for a relevant range that stops at 20,000 units. Above that amount, a new relevant range can be assumed for a different cost that assumes the inclusion of the cost of the shift supervisor in the cost of the product.
As a fourth example, ABC Company constructs a manufacturing facility, which has a fixed cost of $10 million to operate and maintain every year. However, if production levels exceed 3 million units per year, then this fixed cost will increase, because of additional wear and tear on the facility. Thus, the relevant range of this fixed cost is up to a maximum of 3 million units per year.
Cost Behavior: Analysis and Use
Learning Objectives
1. Explain the effect of a change in activity on both total variable costs and per unit variable costs.
2. Explain the effect of a change in activity on both total fixed costs and fixed costs expressed on a per unit basis.
3. Use a cost formula to predict costs at a new level of activity.
4. Analyze a mixed cost using the high-low method.
5. Prepare an income statement using the contribution format.
Lecture Notes
A. Types of Cost Behavior Patterns. Three cost behavior patterns-variable, fixed, and mixed-are found in most organizations. Of course, there are many other types of cost behavior patterns but these three patterns are fairly common and the mixed cost model can be used to provide approximations to more complex cost behavior patterns within a relevant range. It is important for managers to understand the behavior of each type of cost.
1. Variable Costs. A variable cost is one whose total dollar amount varies in direct proportion to changes in the activity level. When expressed on a per unit basis, variable costs are constant. Examples of costs that are normally variable with respect to output volume are listed in Exhibit 5-2. Be careful to point out to students that some of these costs may be fixed in some organizations. This is particularly true of direct labor and other employee wages and salaries that may be effectively fixed due to labor laws in a country, custom, labor contracts, or the organization's personnel policies. Exhibit 5-8 in the text points out that there is wide variation in practice in how some of these costs are classified by individual firms.a. Activity base (cost driver). For a cost to be variable, it must be variable with some activity base. An activity base is a measure of whatever causes the incurrence of a variable cost. Some of the most common activity bases are machine-hours, units produced, and units sold. A measure of activity should be used to allocate a cost for decision-making purposes only if it actually causes the cost.b. True variable and step-variable costs. Some variable costs, such as direct materials, vary in direct proportion to the level of activity. These costs are called true variable costs. A cost that is obtainable only in large chunks and that increases or decreases in response to fairly wide changes in the activity level is known as a step-variable cost. For example, direct labor may be a step-variable cost when workers are only hired on a full-time basis. The difference between a true variable and a step-variable cost is displayed in Exhibit 5-3 in the text.
c. In reality, many costs behave in a curvilinear fashion. Most frequently, costs increase less than proportionately with activity. Nevertheless, within any given narrow band of activity even a curvilinear cost function is approximately linear. This narrow band of activity within which a particular straight line is a reasonable approximation to the true underlying cost function is called its relevant range.
- Thus, within the relevant range, variable cost per unit can be assumed to be constant. Exhibit 5-4 in the text illustrates a curvilinear cost and the notion of the relevant range.
- There is often confusion about the meaning of relevant range. Some individuals refer to the relevant range as the range of activity within which the company expects to operate or has operated in the recent past. That is not what we mean by the relevant range. The relevant range, as we use the term, is the range of activity within which a particular straight line provides a reasonable approximation to the real underlying cost function.
2. Fixed Costs. A fixed cost remains constant in total dollar amount within the relevant range. Since fixed costs remain constant in total, the amount of cost computed on a per unit basis will become progressively smaller as the number of units produced increases. Care must be exercised in interpreting fixed costs that have been expressed on a per unit basis; they should not be misinterpreted as variable costs.
a. For planning purposes, fixed costs can be viewed as either committed or discretionary.
- Committed fixed costs. Committed fixed costs relate to investment in buildings, equipment, and the basic organizational structure of a firm. Committed fixed costs are long-term in nature and can't be significantly reduced even for a short period of time without seriously impairing long-run goals.
- Discretionary fixed costs. Discretionary fixed costs are those which management adjusts periodically. Examples of discretionary fixed costs include advertising, research, and management development programs. The planning horizon for discretionary fixed costs is fairly short-usually a single year. Management may be able to adjust these fixed costs as circumstances change.
b. The relevant range for a fixed cost is that range of activity over which total fixed cost does not change. Exhibit 5-6 in the text illustrates this idea.
3. Mixed Costs. A mixed cost is one that contains both variable and fixed cost elements. Many costs are mixed and can be expressed in terms of the cost formula Y = a + bX, where Y is the total estimated cost, a is the estimated total fixed cost, b is the estimated variable cost per unit of activity, and X is the number of units of activity. Even when the underlying cost is not linear, this formula can provide a reasonable approximation to the underlying cost function within the relevant range.
4. Classification of costs. A cost that is considered variable in one firm may be considered fixed in another due, for example, to differing employment policies. Exhibit 5-8 in the text shows that there is a great deal of variation in how firms classify costs in terms of behavior.
B. Analysis of Mixed Costs. For planning and control purposes, mixed costs should be broken down into variable and fixed components. A number of methods can be used to analyze mixed costs. Account analysis and the engineering approach are mentioned briefly in this chapter and are covered in more detail in later chapters. This chapter discusses in more depth three techniques for analyzing past records of cost and activity-the high-low method, the scattergraph method, and least-squares regression. We are going to focus on the High-Low method only.
1. The High-Low Method. The high-low method of analyzing mixed costs focuses exclusively on the high and low levels of activity. The difference in cost observed at these two extremes is divided by the change in activity in order to determine the amount of variable cost involved.A major defect of the high-low method is that it utilizes only two points and ignores all of the other data. Generally, two points are not enough to produce accurate results. Moreover, the periods in which the high and low activity levels occur are often not typical of most periods.
C. The Contribution Format. There are two major approaches to preparing an income statement. The difference between these two approaches centers on the way in which costs are organized.
1. The Traditional Approach. The traditional approach to the income statement organizes data in a functional format, based on the functions of production, administration, and sales. No attempt is made to identify the behavior of costs included under each functional heading. This approach is used to prepare income statements for external reporting purposes.2. The Contribution Approach. The contribution approach to the income statement organizes costs by behavior, rather than by function.
a. The contribution approach separates costs into fixed and variable categories. Variable expenses are deducted to obtain the contribution margin. Fixed expenses are then deducted from the contribution margin to obtain net income.b. The contribution approach to the income statement makes it much easier for managers to understand the relations between volume and expenses, and volume and profits. Variable and fixed costs are not lumped together. Since planning and decision-making often involve changes in the level of activity, contribution income statements can be very useful to managers.