Relevant Range

The relevant range is the range of activity over which a company's cost behavior assumptions are expected to remain valid. Within that range, total fixed costs stay the same and the variable cost per unit stays constant. If activity moves above or below the range, those assumptions can break down: the business may need another machine, another shift or a bigger warehouse, or it may get volume discounts on materials.

The concept is a basic part of cost behavior analysis in managerial accounting. Every cost formula, budget and break-even calculation implicitly assumes that the company will operate inside a relevant range, so the range sets the limits on how far those tools can be trusted.

In theory, accountants describe costs with straight lines: fixed costs are flat and variable costs rise in proportion to activity. In reality, costs are rarely that tidy over all possible volumes. A factory's rent and supervisory salaries are fixed only until it runs out of space or staff; beyond that, costs step up. Variable costs per unit may fall at high volumes because of bulk buying, or rise when overtime premiums kick in. The relevant range is the stretch of activity where the straight-line description is a good enough approximation.

Fixed costs that rise in jumps are often called step costs. A supervisor might handle up to 20 workers; employing 21 to 40 needs a second supervisor. Within each band the cost is fixed, and each band is its own relevant range.

A bakery's plant can produce between 20,000 and 50,000 loaves a month with one shift. Within this range its fixed costs are $60,000 a month and its variable cost is $0.80 per loaf. The total cost formula is:

Here $\text{Fixed costs}$ are the period costs that do not change within the range, $\text{Variable cost per unit}$ is the extra cost of each loaf and $\text{Units}$ is the number of loaves produced. At 40,000 loaves the bakery expects total cost of $60,000 plus $32,000, or $92,000, an average of $2.30 a loaf. If demand rose to 70,000 loaves, the formula would predict $116,000, but that answer is outside the relevant range. A second shift would add perhaps $25,000 of fixed supervisory and utility costs, and night-shift wages might raise the variable cost. The real total could be well above $140,000.

• Cost-volume-profit analysis: cost-volume-profit charts and the break-even point rely on fixed costs and unit contribution margin being stable, which is only true inside the relevant range.
• Budgeting: a flexible budget restates costs for the actual level of activity, but its formulas apply only within the range for which they were built.
• Cost estimation: methods such as the high-low method and regression analysis estimate fixed and variable components from past data, and the results should only be applied to activity levels similar to those in the data.
• Pricing and capacity decisions: a special order that pushes output beyond the range must carry the extra fixed costs it triggers, not just the normal variable cost.

The relevant range is a practical assumption, not a precise figure, and it can shift as a business changes its equipment, staffing or suppliers. It is usually defined for a particular time period, such as a month or a year, because over longer periods almost all costs can be changed. Economists describe the same issue in terms of marginal cost, which can rise or fall with scale. Accountants use the relevant range to remind managers that a simple cost formula is a model of the business as it currently operates, and that large changes in volume need a fresh analysis of mixed costs and capacity.