Fixed Cost

A fixed cost is a cost that does not change in total when production or another measure of business activity changes within a specified period and range. In economics and managerial accounting, it is distinguished from a variable cost, which changes with activity. Factory rent under an existing lease is a common example: the payment generally remains the same whether the factory produces many units, few units, or none. “Fixed” describes cost behavior, not permanence or an inability to change the expenditure under any circumstances. (openstax.org)

Time horizon and relevant range

In microeconomics, the short run is a period during which at least one production input cannot be adjusted. Costs associated with such inputs are fixed relative to changes in output. The long run allows all inputs to be adjusted, including plant size and equipment; consequently, the standard long-run model treats all production costs as variable. These periods are defined by adjustment possibilities rather than a universal number of months or years. (openstax.org)

Accounting analysis uses the relevant range: the activity interval within which an assumed cost relationship holds. A workshop’s rent may remain constant while output grows using existing space, but additional premises may become necessary beyond its capacity. Such changes create step costs, which remain constant over successive activity intervals and rise when thresholds are crossed. Fixed costs therefore need both a time horizon and an activity range to be meaningfully specified. (openstax.org)

Mathematical representation

Let $Q$ denote output, $F$ total fixed cost, and $V(Q)$ total variable cost. The total cost function is

The total fixed-cost curve is horizontal within the relevant range. If variable cost is zero at zero output, total cost at zero output equals $F$. Average fixed cost distributes the fixed amount across produced units:

It declines as output increases, although the total fixed expenditure remains unchanged. At zero output, this per-unit measure is undefined. (openstax.org)

Average total cost equals average fixed cost plus average variable cost. By contrast, marginal cost measures the additional cost of increasing output. While $F$ remains constant,

Thus, spreading fixed costs over additional units lowers their average contribution but does not itself lower marginal cost. A capacity expansion can change this relationship by introducing an additional fixed expenditure. (openstax.org)

Examples and classification

Examples commonly include premises rent, equipment leases, some administrative salaries, insurance premiums, and straight-line depreciation. Classification depends on the underlying arrangement: salaried labor may be fixed over a particular interval, whereas hourly labor may vary with hours worked. A payment combining a basic charge with usage charges is a mixed cost, containing both fixed and variable components. (openstax.org)

Accountants also distinguish committed fixed costs, associated with maintaining an organization’s operating capacity, from discretionary fixed costs, determined through periodic spending decisions. Equipment leases illustrate the former; advertising and employee-training budgets can illustrate the latter. A discretionary expenditure can be fixed relative to current output even though management can revise it for another budgeting period. (openstax.org)

Fixed costs and sunk costs

Fixed cost is not synonymous with sunk cost. Fixedness concerns how cost responds to activity; sunkness concerns whether an expenditure has already occurred and cannot be recovered. A future fixed payment may be avoidable if an activity is discontinued, while another fixed payment may remain contractually unavoidable. (openstax.org)

A relevant cost for a decision is a future cost that differs between alternatives. Consequently, an unchanged fixed expense does not affect the comparison between those alternatives, but a new equipment lease required by one option does. Opportunity cost, such as income forgone by using space rather than renting it out, may also matter despite not appearing as a recorded expenditure. (openstax.org)

Break-even analysis

Fixed costs are central to cost–volume–profit analysis. In a simple single-product model, let selling price per unit be $p$, variable cost per unit be $v$, and units sold be $Q$. Total revenue is $pQ$, and operating profit is

The difference $p-v$ is the per-unit contribution margin, which first covers fixed costs and then contributes to profit. When $p>v$, the break-even quantity is

For a hypothetical business with monthly fixed costs of $12,000, a $50 selling price, and $30 variable cost per unit, break-even sales are 600 units. This calculation assumes constant prices, constant unit variable costs, and unchanged fixed costs within the relevant range; multiple-product analysis additionally depends on the sales mix. (openstax.org)

Operating leverage and scale

Fixed costs contribute to operating leverage: the sensitivity of operating profit to changes in sales. Above break-even, additional sales can produce proportionally larger increases in profit because fixed expenses do not rise with each unit. Falling sales produce the reverse effect. The magnitude depends on contribution margin and the starting level of operating income, not simply the absolute amount of fixed expenditure. (openstax.org)

Declining average fixed cost is distinct from economies of scale. The former can occur by increasing utilization of an unchanged facility; the latter concerns declining long-run average cost as the scale of operations changes with all inputs adjustable. Expanding output within existing capacity and choosing a larger plant are therefore different analytical questions. (openstax.org)