Difficulty: Introductory | Prerequisites: Part 1 study notes (Obj. 2.1 and 2.2), understanding of cost, cost object, direct and indirect cost.
Once you can classify a cost as direct or indirect, the next question is how that cost behaves when activity levels change. This is the variable-versus-fixed distinction, and it drives every budget, break-even analysis and pricing decision in the course. Understanding unit costs (and the trap of using them carelessly) rounds out the foundation. Together, Objectives 2.3 and 2.4 give you the tools to predict what will happen to costs when production or sales volume moves up or down.
Variable costs change in total when activity changes but stay constant per unit. Fixed costs stay the same in total regardless of activity but change per unit as volume moves. A cost driver is whatever causes total costs to change. All of this holds only within the relevant range. Unit cost (average cost) is total cost divided by units, and managers should think in total costs rather than unit costs when making decisions, because unit costs shift with volume.
Variable cost
A cost that changes in total in proportion to changes in the level of activity or volume. Per unit, a variable cost stays constant. Think of direct materials: each extra unit uses the same amount of material, so total material cost rises with output but cost per unit is flat.
Fixed cost
A cost that remains unchanged in total for a given time period, despite changes in the level of activity or volume. Per unit, a fixed cost falls as volume rises and rises as volume falls. Think of monthly rent: the bill is the same whether you make 100 units or 10,000.
Cost driver
A variable, such as the level of activity or volume, that causally affects total costs over a given time span. There is a cause-and-effect relationship between the driver and the cost. For distribution costs, the driver might be miles driven; for direct labour, it might be production hours.
Relevant range
The band of normal activity or volume within which the assumed cost-volume relationships hold. Inside this range, total fixed costs stay flat and variable costs change proportionally. Outside it, those relationships may break down (for example, you might need to lease a second factory).
Unit cost (average cost)
Total cost divided by the number of units. It is a blended figure that mixes variable and fixed components, which is why it changes whenever volume changes.
Cost behaviour
How costs react to a change in the level of activity. This is the umbrella concept for the variable/fixed distinction.
Variable costs in total vs per unit
Total variable costs increase when activity increases and decrease when activity decreases. Variable cost per unit stays the same regardless of volume. If each motorcycle belt costs $20 and you produce 2,000 motorcycles, total belt cost is $40,000. Produce 3,000 and total belt cost is $60,000, but cost per belt is still $20.
Fixed costs in total vs per unit
Total fixed costs do not change with volume within the relevant range. Fixed cost per unit, however, falls as production rises and rises as production falls. If monthly rent is $22,000, producing 100 units gives a fixed cost per unit of $220. Producing 200 units drops it to $110. This is the key insight for understanding why unit costs decline with higher volume.
A fixed cost is fixed only within boundaries
Fixed costs are fixed only in relation to a given range of activity and for a given time span (usually a budget period). If a union contract sets annual salaries, labour costs are fixed for that year. If volume doubles beyond the current plant capacity, you may need new facilities, and a new level of fixed cost kicks in.
Cost drivers and cause-and-effect
A cost driver is a variable that causally affects costs. The cost driver for distribution might be number of miles driven; for direct labour, it might be production hours; for human resources, it might be number of job applications processed. Fixed costs do not have cost drivers over the short run because, by definition, they do not change with activity in the short run.
The relevant range
Within the relevant range, a change in the cost driver will cause total variable costs to change while total fixed costs stay the same. Outside the relevant range, variable costs may not change proportionally (volume discounts, overtime premiums) and fixed costs may jump to a new level.
Classifying costs on two dimensions at once
A cost can be classified on both the direct/indirect axis and the variable/fixed axis simultaneously. For example, wood for a chair manufacturer is a direct variable cost (traceable to the chair and changes with volume). The plant supervisor's salary is an indirect fixed cost (shared across products and stays the same regardless of output). A belt for a motorcycle is a direct variable cost. Property taxes on the factory are an indirect fixed cost.
How unit cost is calculated
Unit cost = Total cost / Number of units produced. It is also called average cost. This is the figure that appears on financial reports and is used for inventory valuation.
The unit-cost trap
Managers should think in terms of total costs, not unit costs, when making decisions about product mix and pricing. Unit cost blends variable and fixed components, so it changes whenever volume changes. If you use a unit cost calculated at one volume to predict costs at a different volume, you will get the wrong answer.
Worked example: expanding production
Swansea Manufacturing produces 3,000 tyres per month. Per-unit data at 3,000 tyres: direct materials $38, direct manufacturing labour $14, variable manufacturing overhead $19, fixed manufacturing overhead $20. Total manufacturing cost per unit is $91.
The plant can handle 5,000 tyres. What is the total cost of producing 4,000 tyres?
Variable costs per unit stay the same: $38 + $14 + $19 = $71 per tyre.
Total variable costs at 4,000 tyres: $71 x 4,000 = $284,000.
Total fixed costs do not change. At 3,000 tyres, total fixed manufacturing overhead = $20 x 3,000 = $60,000.
Total cost at 4,000 tyres: $284,000 + $60,000 = $344,000.
New unit cost: $344,000 / 4,000 = $86.00 (down from $91, because fixed costs are spread over more units).
If you had simply multiplied $91 by 4,000, you would have got $364,000, overstating the cost by $20,000. That is the unit-cost trap.
What happens when volume changes
When production increases within capacity, total manufacturing costs rise (because variable costs rise) but unit manufacturing costs fall (because the fixed component per unit shrinks). When production decreases, the reverse happens: total costs fall but unit costs rise.
\text{Unit Cost} = \frac{\text{Total Cost}}{\text{Number of Units}}\text{Total Cost} = \text{Total Fixed Costs} + (\text{Variable Cost per Unit} \times \text{Number of Units})\text{Operating Income} = \text{Sales} - \text{Variable Costs} - \text{Fixed Costs}When sales halve, variable costs halve too, but fixed costs stay the same. This is the pattern tested in projected operating income questions.
Students often believe variable cost per unit changes with volume. It does not. Total variable cost changes; per-unit variable cost stays constant within the relevant range.
Students often assume fixed cost per unit is constant. It is not. Total fixed cost is constant; fixed cost per unit falls as volume rises and rises as volume falls.
Students often apply a unit cost calculated at one production level to predict total costs at a different level. This gives a wrong answer because the fixed-cost component per unit has changed. Always separate variable and fixed components before scaling.
Students often think that all costs have cost drivers in the short run. Fixed costs do not have cost drivers in the short run because they do not change with activity levels.
Questions asking what happens to fixed cost per unit when volume decreases are common. The answer: fixed cost per unit increases.
Projected operating income questions give you current sales, variable costs and fixed costs, then ask you to halve sales. Remember: variable costs halve, fixed costs stay the same.
Expect questions asking you to identify the most likely cost driver for a given function (e.g. number of purchase orders for purchasing, number of miles driven for distribution).
The relevant range concept is frequently tested. Within it, fixed costs are flat and variable costs are proportional. Outside it, those assumptions break.
Unit cost is also called average cost. This definition point appears in true/false questions.
True or false: Variable costs per unit vary with the level of production. (False. Variable costs per unit are constant.)
True or false: Fixed cost per unit falls with an increase in production volume. (True.)
Fill in the blank: A band of normal activity in which cost-volume relationships hold is called the ________. (Relevant range.)
True or false: A unit cost is computed by dividing total cost by the number of units. (True.)
True or false: Managers should focus on unit costs rather than total costs when making product mix decisions. (False. They should focus on total costs.)
Q: Rally Synthesis makes 100 bottles a day. Fixed costs are $22,000 and variable costs for 100 bottles are $30,000. Each bottle sells for $1,200. How does daily profit change if sales drop 10%?
A: Variable cost per unit = $300. Profit at 100 bottles = $120,000 - $52,000 = $68,000. Profit at 90 bottles = $108,000 - ($22,000 + $27,000) = $59,000. Profit falls by $9,000.
Q: If each motorcycle requires a $20 belt and 2,000 motorcycles are produced, the total belt cost is classified as what?
A: A direct variable cost. It is traceable to the product (direct) and changes with the number of motorcycles produced (variable).
Q: Wonderful Products has sales of $43,000, variable costs of $14,000 and fixed costs of $11,000. If sales halve next month, what is projected operating income?
A: ($43,000 / 2) - ($14,000 / 2) - $11,000 = $21,500 - $7,000 - $11,000 = $3,500.
Q: A plant produces 4,000 bicycles with a unit cost of $89 (including $14 of fixed overhead). What is the per-unit cost if production expands to 5,000?
A: Variable cost per unit = $53 + $10 + $12 = $75. Total fixed costs = $14 x 4,000 = $56,000. Total cost at 5,000 = ($75 x 5,000) + $56,000 = $431,000. Unit cost = $431,000 / 5,000 = $86.20.
Cost behaviour feeds directly into cost-volume-profit analysis (Chapter 3), which uses the variable/fixed split to find break-even points and target profits. It also connects to the manufacturing cost classifications in Obj. 2.5 and 2.6, where you will use these same categories to build income statements and cost-of-goods-manufactured schedules. The unit-cost trap reappears in Chapter 9 (decision-making), where using the wrong unit cost can lead to incorrect make-or-buy decisions.
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