Difficulty: Introductory. Prerequisites: familiarity with direct vs. indirect costs, product vs. period costs (Part 1 of these notes).
Once you know what category a cost belongs to, the next question is how it behaves when activity changes. This matters because managers need to predict costs at different production levels, choose between income statement formats, and decide which costs are relevant to a particular decision. Cost behaviour, the contribution-format income statement, and the distinction between differential, opportunity, and sunk costs form the analytical backbone of the course. Everything from CVP analysis to special-order decisions in later chapters depends on your ability to separate variable costs from fixed costs and to ignore sunk costs.
Variable costs change in total with activity; fixed costs stay constant in total within the relevant range; mixed costs have both elements. The traditional income statement groups costs by function (COGS vs. SG&A); the contribution format groups them by behaviour (variable vs. fixed). For decision-making, focus on differential costs (those that change between alternatives), consider opportunity costs (benefits foregone), and ignore sunk costs (already spent, unrecoverable).
Variable cost
A cost that varies, in total, in direct proportion to changes in the level of activity. Per-unit variable cost stays constant.
Think of it as: the more you make, the more you spend. Direct materials are the clearest example.
Fixed cost
A cost that remains constant in total regardless of changes in the level of activity, within the relevant range. Per-unit fixed cost decreases as volume rises.
In simple terms, you pay the same rent whether you produce 100 units or 10,000 units.
Mixed cost (semi-variable cost)
A cost with both a fixed component and a variable component. Total cost changes with activity, but not from zero.
Think of it as: a mobile phone plan with a base fee plus per-minute charges. A salesperson's compensation (base salary plus commission) is the textbook example.
Relevant range
The range of activity within which the assumed cost behaviour patterns (fixed costs stay fixed, variable cost per unit stays constant) are valid.
In simple terms, fixed costs hold steady only within a band. If the company doubles its capacity, it may need a second factory, and rent jumps.
Cost function
The mathematical relationship that describes how a cost changes with activity: Y = a + bX, where Y is total cost, a is the fixed component, b is the variable cost per unit of activity, and X is the activity level.
Contribution margin
Sales revenue minus all variable expenses. It represents the amount available to cover fixed costs and then generate profit.
Think of it as: what each sale contributes towards paying the bills.
Gross margin (gross profit)
Sales revenue minus cost of goods sold. Used in the traditional income statement format for external reporting.
Differential cost (incremental cost)
A cost that differs between two or more alternative courses of action being considered by management. Only differential costs are relevant to the decision.
Opportunity cost
The benefit foregone when one alternative is chosen over another. Opportunity costs are not recorded in accounting systems but are relevant to decisions.
Think of it as: what you give up. If you use factory space to make Product A, the profit you could have earned making Product B is the opportunity cost.
Sunk cost
A cost that has already been incurred and cannot be changed or recovered by any current or future decision.
In simple terms, money already spent. It is irrelevant to future decisions, no matter how large.
High-low method
A technique for separating the variable and fixed components of a mixed cost by using the highest and lowest activity levels observed.
Least-squares regression
A statistical method that fits a line through all data points to estimate the cost function. Produces an R-squared (R²) value measuring goodness of fit.
R-squared (R²)
A statistic between 0 and 1 that measures how well the regression line fits the data. An R² of 0.90 means the model explains 90% of the variation in cost.
Variable costs
Total variable cost rises and falls in direct proportion to activity.
Per-unit variable cost stays constant.
Examples: direct materials, direct labour, sales commissions, shipping costs.
Fixed costs
Total fixed cost stays constant within the relevant range.
Per-unit fixed cost drops as volume increases (cost is spread over more units).
Discretionary fixed costs (advertising budgets, training programmes) can be changed by management in the short term. Committed fixed costs (lease payments, depreciation on buildings) cannot.
Fixed costs hold only within the relevant range. A large enough change in activity may require new capacity, causing fixed costs to jump.
Mixed costs
Contain both a fixed element and a variable element.
Total cost increases with activity, but starts from a base rather than from zero.
Example: a salesperson earning a $40,000 base salary (fixed) plus a 5% commission on sales (variable).
Scatter plot: plot historical cost data against activity levels. Useful for visual inspection, identifying outliers, and judging whether a linear model is appropriate. Does not produce a precise equation.
High-low method: uses only the highest and lowest activity data points to estimate the variable cost per unit and the fixed cost. Simple but potentially unreliable because it ignores all other data.
Least-squares regression: uses all data points to fit a line mathematically. The most accurate of the three methods. Produces the cost equation (Y = a + bX) and an R² statistic indicating goodness of fit. Software handles the computation.
Traditional format (functional classification)
Used for external reporting under GAAP.
Groups costs by function: manufacturing vs. non-manufacturing.
Structure: Sales, minus COGS, equals Gross Margin, minus SG&A, equals Net Operating Income.
Contribution format (behavioural classification)
Used internally by management for decision-making.
Groups costs by behaviour: variable vs. fixed.
Structure: Sales, minus all Variable Expenses, equals Contribution Margin, minus all Fixed Expenses, equals Net Operating Income.
The contribution margin tells managers how much revenue is available to cover fixed costs and generate profit.
Both formats produce the same net operating income. They simply arrange costs differently.
Differential costs change between alternatives. If a decision would cause a cost to increase, decrease, or disappear, that cost is differential and relevant to the decision.
Opportunity costs are the benefits sacrificed by choosing one path over another. They do not appear in accounting records but must be considered in decision-making. If a company uses its spare capacity for Project A, the profit it would have earned from Project B is an opportunity cost of choosing A.
Sunk costs have already been incurred and cannot be recovered. They are irrelevant to any future decision, no matter how large. The price you paid for a machine last year should not influence whether to keep or replace it today.
General cost function: Y = a + bX where Y = total cost, a = total fixed cost, b = variable cost per unit of activity, X = activity level.
Variable cost only: Y = bX (fixed component is zero).
Fixed cost only: Y = a (variable component is zero).
Mixed cost: Y = a + bX (both components present).
High-low method: Variable cost per unit (b) = (Cost at highest activity, minus Cost at lowest activity) / (Highest activity, minus Lowest activity). Fixed cost (a) = Total cost at either point, minus (b multiplied by activity at that point).
Traditional income statement: Sales, minus COGS = Gross Margin. Gross Margin, minus SG&A = Net Operating Income.
Contribution format income statement: Sales, minus Variable Expenses = Contribution Margin. Contribution Margin, minus Fixed Expenses = Net Operating Income.
A ride-sharing company's cost per trip (fuel, driver payout) is variable. Its software development team's salaries are fixed. Its customer-support centre has a mixed cost structure: a base staffing level (fixed) plus overtime when demand spikes (variable). The contribution-format income statement helps the company understand how each additional ride contributes to covering its fixed costs.
Opportunity cost shows up constantly in business. A hotel deciding whether to convert a conference room into guest rooms weighs the lost conference revenue (opportunity cost) against the additional room revenue.
"Fixed costs never change." They can. Discretionary fixed costs (like an advertising budget) may be adjusted each year. What makes them "fixed" is that they do not change in response to activity within the relevant range.
"Variable cost per unit changes with volume." Per-unit variable cost stays constant. It is the total variable cost that changes with volume.
"Sunk costs are small costs that do not matter." Size is irrelevant. A $10 million machine purchased last year is a sunk cost. Its size does not make it relevant to future decisions.
"The contribution format and traditional format give different net income." They produce the same net operating income. Only the arrangement of line items differs.
Expect questions that give you a mixed cost and ask you to separate it into fixed and variable components using the high-low method.
The difference between the traditional and contribution income statement formats is tested frequently. You may be asked to reformat one into the other.
Questions on sunk costs often present a scenario designed to tempt you into considering a past expenditure. The correct answer is always to ignore it.
Opportunity cost questions typically describe a choice between two uses of a resource and ask what the opportunity cost of one choice is.
Understanding that per-unit fixed cost decreases with volume (while total fixed cost stays constant) is a recurring conceptual test point.
True or false: per-unit variable cost changes as activity increases. (False. Per-unit variable cost stays constant. Total variable cost changes.)
Fill in the blank: the cost function is expressed as Y = __________. (a + bX)
True or false: the contribution margin equals sales minus cost of goods sold. (False. That is gross margin. Contribution margin equals sales minus all variable expenses.)
Fill in the blank: a cost that has already been incurred and cannot be recovered is called a __________ cost. (Sunk cost.)
True or false: opportunity costs appear in the company's accounting records. (False. They are not recorded but are relevant to decisions.)
Q: A company's utility bill for its factory was $3,000 when it produced 1,000 units and $4,500 when it produced 2,000 units. Using the high-low method, what is the variable cost per unit and the fixed cost?
A: Variable cost per unit = ($4,500 minus $3,000) / (2,000 minus 1,000) = $1.50 per unit. Fixed cost = $3,000 minus ($1.50 multiplied by 1,000) = $1,500.
Q: A company has sales of $500,000, variable expenses of $300,000, and fixed expenses of $150,000. Prepare a contribution-format income statement and state the net operating income.
A: Sales $500,000, minus Variable Expenses $300,000 = Contribution Margin $200,000, minus Fixed Expenses $150,000 = Net Operating Income $50,000.
Q: You purchased a machine for $100,000 two years ago. It now has a market value of $20,000. You are deciding whether to keep it or replace it. Is the $100,000 purchase price relevant to the decision?
A: No. The $100,000 is a sunk cost. It has already been spent and cannot be recovered. The relevant figure is the $20,000 current market value (the differential cash flow from selling).
Q: A company can use its spare factory capacity to produce Product X (expected profit $30,000) or Product Y (expected profit $45,000). What is the opportunity cost of choosing Product X?
A: $45,000, the profit foregone from Product Y.
Q: Why might a manager prefer the contribution format income statement over the traditional format?
A: The contribution format separates variable and fixed costs, making it easier to analyse how changes in sales volume affect profit. It highlights the contribution margin, which is essential for CVP analysis, break-even calculations, and short-term decision-making.
Cost behaviour classification leads directly into cost-volume-profit (CVP) analysis, where you use the contribution margin to find break-even points and target profits. The high-low method and regression reappear in overhead estimation and budgeting. Differential and opportunity costs are central to special-order decisions, make-or-buy analysis, and other relevant costing problems later in the course.
The distinction between sunk and relevant costs is one of the most practically useful ideas in the course and will come back repeatedly.
Variable cost, fixed cost, mixed cost, semi-variable cost, relevant range, cost function, Y = a + bX, scatter plot, high-low method, least-squares regression, R-squared, goodness of fit, traditional income statement, contribution format income statement, gross margin, contribution margin, net operating income, COGS, SG&A, differential cost, incremental cost, opportunity cost, sunk cost, irrelevant cost, relevant cost, cost behaviour, cost-volume-profit, CVP, ACCT 3001, management accounting, managerial accounting