Variable, Fixed & Mixed Costs

Overview

• What you’ll learn: Variable costs, fixed costs, mixed (semi-variable) costs, the relevant range concept, step costs, and how to identify cost behavior patterns for planning and decision-making.
• Prerequisites: Lesson 2 — Cost Objects, Cost Drivers & Cost Assignment
• Estimated reading time: 18 minutes

Introduction

The Grand Historian records: In the annals of cost accounting, no concept is more fundamental — or more treacherous — than cost behavior. The naive apprentice assumes all costs move in lockstep with production: make more widgets, spend more money. But the seasoned cost accountant knows that costs are creatures of varied temperament. Some march obediently with volume, increasing dollar for dollar as activity rises. Others stand like stone sentinels, unmoved whether the factory runs at full capacity or sits idle gathering dust. And still others exhibit the maddening personality of a mixed cost — part loyal soldier, part immovable fortress.

Understanding cost behavior is the key that unlocks every subsequent technique in this module: CVP analysis, budgeting, variance analysis, and pricing decisions all depend on knowing which costs will change and which will not when activity levels shift. Get this wrong, and your forecasts are fantasies. Get it right, and you can predict the financial consequences of any decision before committing a single dollar.

Variable Costs

A variable cost changes in total in direct proportion to changes in the level of activity. If activity doubles, total variable cost doubles. If activity drops to zero, total variable cost drops to zero.

Total vs. Per-Unit Behavior

This is where many students stumble, so let us be mercilessly clear:

Total variable cost is a straight line through the origin when plotted against activity. The slope of that line is the per-unit variable cost. This constancy per unit is what makes variable costs so beautifully predictable — and so useful for planning.

Examples of Variable Costs

• Direct materials: More units produced → more materials consumed
• Direct labor (piece-rate): Workers paid per unit produced
• Sales commissions: A percentage of revenue — more sales, more commission
• Shipping costs: More units shipped → higher freight charges
• Transaction processing fees: More transactions → more fees

Fixed Costs

A fixed cost remains unchanged in total regardless of changes in the level of activity — within the relevant range. Whether you produce one unit or one million units, total fixed costs remain the same obstinate amount.

Total vs. Per-Unit Behavior

This inverse relationship between per-unit fixed cost and volume is the source of economies of scale — the more you produce, the lower the fixed cost per unit, and therefore the lower the total cost per unit. This is why companies crave volume: it spreads fixed costs across more units, making each unit cheaper.

Examples of Fixed Costs

• Rent and lease payments: The landlord does not care how many widgets you make
• Insurance premiums: Annual premiums are set in advance
• Straight-line depreciation: Same charge each period regardless of usage
• Salaried employees: Their paychecks do not change with production volume
• Property taxes: Assessed on the property, not on production

Committed vs. Discretionary Fixed Costs

Not all fixed costs are created equal:

• Committed fixed costs: Arise from long-term decisions that cannot easily be reversed — building leases, equipment purchases, key executive salaries. These are the “must pay” costs; canceling them involves breaking contracts or selling assets.
• Discretionary fixed costs: Arise from annual management decisions — advertising campaigns, R&D budgets, employee training programs. These can be cut in a crisis without breaking contracts (though cutting them may have long-term consequences).

Mixed (Semi-Variable) Costs

A mixed cost contains both a fixed component and a variable component. It is the hybrid warrior of the cost world — part immovable, part responsive:

The cost function for a mixed cost is: Total Cost = Fixed Component + (Variable Rate × Activity Level)

Or in the language of algebra: Y = a + bX

Where Y = total cost, a = fixed component, b = variable rate per unit of activity, X = activity level.

Examples of Mixed Costs

• Electricity: A base charge (fixed) plus a per-kilowatt-hour charge (variable)
• Cell phone plan: Monthly fee (fixed) plus per-minute charges beyond the included minutes (variable)
• Sales representative compensation: Base salary (fixed) plus commission per sale (variable)
• Maintenance costs: Scheduled maintenance (fixed) plus repairs that increase with machine usage (variable)
• Delivery truck costs: Lease payment (fixed) plus fuel and mileage costs (variable)

For planning and CVP analysis, mixed costs must be separated into their fixed and variable components. We will learn the techniques for doing this — the high-low method and regression analysis — in Lessons 6 and 7.

The Relevant Range

The relevant range is the band of activity within which the assumed cost behavior patterns hold true. It is the operating zone where your cost assumptions are valid — step outside it, and all bets are off.

Consider factory rent: it is fixed at $120,000 per year as long as production stays between 0 and 50,000 units. But if demand surges to 80,000 units, you need a bigger factory — and rent jumps to $200,000. The fixed cost was only “fixed” within the relevant range of 0–50,000 units.

Similarly, variable costs per unit may not be truly constant across all volumes. At very high volumes, you might negotiate bulk discounts on materials (lowering per-unit cost). At very low volumes, you might pay premium prices for small orders (raising per-unit cost). The assumption of constant per-unit variable cost holds within the relevant range, not universally.

Step Costs

Some costs are fixed within a narrow range and then jump to a new level. These are step costs:

• Step-fixed costs: A supervisor can manage up to 20 workers. If you hire a 21st worker, you need another supervisor. Supervisor costs are fixed in steps of 20 workers.
• Step-variable costs: Similar pattern but with narrower steps. A delivery truck can carry 100 packages; the 101st package requires another truck.

Whether to treat step costs as fixed or variable depends on the width of the steps relative to the relevant range. If steps are wide relative to the range, treat as fixed. If narrow, treat as variable.

Visualizing Cost Behavior

Cost behavior is best understood through graphs. The x-axis represents the activity level (cost driver), and the y-axis represents total cost:

• Variable cost graph: A straight line from the origin, sloping upward. The slope equals the variable cost per unit.
• Fixed cost graph: A horizontal line at the fixed cost amount. It does not move regardless of activity.
• Mixed cost graph: A straight line that does NOT start at the origin. It starts at the fixed component (y-intercept) and slopes upward at the variable rate.
• Step cost graph: A staircase pattern — flat within each step, jumping vertically at the boundaries.

Being able to sketch and interpret these graphs is essential. If a cost pattern looks like a line through the origin, it is variable. If it looks like a horizontal line, it is fixed. If it looks like a line with a positive y-intercept, it is mixed. If it looks like stairs, it is a step cost.

Key Takeaways

• Variable costs change in total proportionally with activity but remain constant per unit.
• Fixed costs remain constant in total regardless of activity but decrease per unit as volume increases (economies of scale).
• Mixed costs contain both a fixed component and a variable component: Y = a + bX.
• The relevant range is the band of activity within which assumed cost behavior patterns are valid — cost assumptions may not hold outside this range.
• Step costs are fixed within narrow ranges and then jump to new levels.
• Fixed costs can be committed (long-term, hard to change) or discretionary (annual, manageable).
• Separating mixed costs into fixed and variable components is essential for CVP analysis and budgeting.

What’s Next

In Lesson 4, we will harness our knowledge of cost behavior to perform Cost-Volume-Profit (CVP) analysis — the technique that answers the most urgent question in business: “How many units must we sell to break even, and how many to earn our target profit?”