Accounting

Fixed Costs

A fixed cost is constant in total amount regardless of changes in activity level. Costs such as the plant managers' salary, depreciation, insurance, and rent usually remain the same regardless of whether the plant is above or below its expected level of operations. At McDonald's, the cost of heating the restaurant would be a fixed cost.

Important characteristics of a fixed cost are:

Fixed cost is a lump of costs that is not normally divisible and does not change as activity or volume changes. A fixed cost remains constant across a reasonable range of activity. The fixed cost per unit decreases as activity or volume increases and increases as activity or volume decreases.

For example, March's rent is quoted as a dollar amount for that month, not as an amount per unit of output or even per hour of use.

By definition, total fixed costs are constant, causing the fixed cost per unit to vary at different levels of activity. Figure 1.10 shows the behavior of fixed costs on a per unit basis and in total. When a company produces a greater number of units, the fixed cost per unit decreases. Conversely, when fewer units are produced, the fixed cost per unit increases. This variability of fixed costs per unit creates problems in product costing. The cost per unit depends on the number of units produced or on level of activity.

Figure 1.10: Behavior of fixed costs

Certain fixed costs can be changed by management action. These are discretionary fixed costs. Discretionary fixed costs are expenditures that managers can elect to spend or not to spend. For example, a company might budget the cost of consultants at $20,000 per month for the coming year. But the contract states that the company can cancel the contract at any time. Management maintains discretionary control over the spending. On the other hand, if the contract guarantees the consultant a 12-month relationship and the contract has been signed, a committed fixed cost has been created. A committed fixed cost is one over which a manager has no control and must incur. Advertising cost for McDonald's would be a discretionary fixed cost. Depreciation on McDonald's restaurant equipment would be a committed fixed cost.

An interesting observation is necessary here. Managers can, with time and intent, change the cost behavior of certain activities. For example, variable direct labor costs can be converted into a fixed cost by guaranteeing full-time employment for some period, such as a three-year union contract. Or equipment could be leased on a short-term basis (day-today or even hourly) instead of purchased—converting a fixed cost into a variable cost. Also, automated equipment with a fixed rent or depreciation could replace variable-cost manual labor. Thus, we recognize that managers can act to change certain cost behavior, particularly over time.

Contemporary Practice 1.2

Fixed vs. Variable Expenses

"You can get quality people to invent, develop and design products for you on a percentage of the products' billing—in other words, on a variable expense basis. Many will want to work on upfront fees only, a fixed expense. Salesmanship on your part can get them to charge your way. If they're sold on your company, you personally, or the product, they're more likely to comply with your wishes. Sometimes a compromise is required where you pay a modest upfront fee and a modest percentage on sales of the product." (Reiss, 2010)

Expressing Variable and Fixed Costs–A Cost Function

Since a variable cost is a rate, it is a function of an independent variable—an activity or output level. Variable costs can be converted into total variable costs only by knowing the activity or output level. Fixed costs are first expressed as an amount, a constant. Fixed costs can be converted into a rate per unit only if the activity or output level is known. In the following example, the cost per unit of $7 and total costs of $700,000 can be found only if the output of 100,000 units is known.

If the production level increases to 120,000, both the cost per unit and total costs change. A decrease in the cost per unit from $7 to $6.50 results from spreading fixed costs of $300,000 over more units—120,000 instead of 100,000. The increase in total cost equals the variable costs for the additional 20,000 units. A decrease in volume has similar reverse impacts—the cost per unit increases, but total costs decline.

Three factors must generally be known to perform cost analyses:

The variable cost rate,

The fixed cost amount, and

The level of activity or output.

Notice that if we know the bold numbers in the example above and the activity level, we can calculate all other numbers.

These factors can be brought together in a cost function—an expression that mathematically links costs, their behavior, and their cost driver. In the example, the expression is:

Total costs = $300,000 + $4 (X), where X is the number of units produced.

This expression can be symbolically shown as:

Total costs = a + b (X), where a is fixed costs and b is variable costs per unit.

This is an important formula in managerial accounting. Understanding these relationships can give insight into cost behavior for planning, control, and decision making. By knowing the activity level and cost function, we can find either total costs or costs per unit. The reverse is also true.

Finding the Cost Function Using Total Costs and Activity Levels

In this example, let's assume we know the total costs ($700,000 and $780,000) at both activity levels (100,000 and 120,000 units). How do we find the cost function? First, we calculate the variable cost per unit as follows:

This is b in our cost function. The change in cost from a change in activity yields the slope of the total variable cost line.

To find the fixed cost, which is a in the cost function, we take the total costs at either activity level and subtract the variable costs at that level, as follows:

$780,000 – ($4 × 120,000 units) = $300,000

or

$700,000 – ($4 × 100,000 units) = $300,000

We now have both a and b. The cost function is $300,000 + $4 (X).

Finding the Cost Function Using Per Unit Costs and Activity Levels

Using the same example, per unit costs were $7 at the 100,000 units activity level and $6.50 at 120,000 units. First, we find total costs at each level by multiplying the cost per unit by the activity level as follows:

$7 per unit × 100,000 = $700,000 and $6.50 per unit × 120,000 =$780,000

Second, we follow the same procedure as shown previously in converting total costs into the cost function. The same calculations could be applied separately to total variable costs for b and to total fixed costs for a. Calculations at both levels produce the same cost function.

One danger in converting fixed cost lumps into cost per unit is that the unit cost can be misinterpreted. It might be assumed that $7 is the variable cost—forgetting that the $300,000 is a fixed cost. At different activity levels, the per unit cost will be different. Even in solving homework problems, students are in danger of missing the impact of volume changes on total costs and unit costs if only costs per unit or total costs are used.

Relevant Range

In Figures 1.8 and 1.9, activity is assumed to start at zero and go to very high levels. Realistically, the cost function holds only for a much narrower range of activity—a relevant range. A relevant range is the normal range of expected activity. Management does not expect activity to exceed a certain upper bound nor to fall below a lower bound. Production activity is expected to be within this range, and costs are budgeted for these levels. In cost analysis, costs are expected to behave as defined within the relevant range. The cost function is assumed to be valid for this range of activity. Usually, past experience establishes the relevant range.

Fixed costs are fixed and variable costs are variable within the relevant range. In the above example, the volume range was between 100,000 and 120,000 units. The cost function of $300,000 plus $4 per unit is valid between 100,000 and 120,000 units as shown in Figure 1.11. If planned production were 130,000 units, our cost function might not be valid or useful.

Figure 1.11: Cost patterns using a relevant range

Semivariable and Semifixed Costs

Figure 1.12 illustrates cost functions that are neither strictly variable nor fixed. In the real world, very few costs are truly variable or fixed. Semivariable costs change but not in direct proportion to the changes in output. Some semivariable costs, called mixed costs, may be broken down into fixed and variable components, thus making it easier to budget and control costs. Using the cost function techniques shown previously, fixed and variable parts can identified. In Example A of Figure 1.12, telephone expenses may include a monthly basic connection fee (fixed) plus a charge for each local call (variable).

Semifixed costs or step-fixed costs are typified by step increases in costs with changes in activity as shown in Example B. Activity can be increased somewhat without a cost increase. However, at some activity level, additional fixed cost must be incurred to expand capacity. If many narrow steps exist, a step-cost pattern may approximate a variable cost. Or with wide steps, one step may encompass the entire relevant range and the step cost appears as a fixed cost.

Figure 1.12: Examples of semivariable and semifixed cost patterns

Example C shows a cost that increases but at a lower cost per unit as activity increases. An example is increased worker efficiency as activity increases, resulting in a lower per unit cost. This is a nonlinear cost. Example D shows a piece-wise linear cost. It is a constant variable rate until a certain activity level is reached, then the variable cost per unit increases. Perhaps an electric utility offers a low per kilowatt rate for the first 500 kilowatts and a higher rate beyond that level.

Many expenses have both fixed and variable components. Chapter 2 examines techniques that can help separate the fixed and variable portions and that can quantify the cost function.