All credit for this text goes to...
Garrison, R. H., Webb, A., & Libby, T. (2024). Managerial Accounting (13th Canadian ed.). McGraw-Hill Ryerson.
Garrison, R. H., Noreen, E. W., Libby, T., Brewer, P. C., & Webb, A. (2015). Managerial accounting (10th ed.). McGraw Hill Ryerson.
Study Strategy
This chapter was studied after Chapter 7 (ABC). Chapter 3’s “activity base” maps directly to ABC’s “cost driver,” and what Chapter 3 calls “fixed” may be driven by batch, product, or facility-level activities. Use ABC thinking to deepen understanding, but answer exam questions using Chapter 3’s specific methods and vocabulary unless the question invites integration.
LO1: Describe how fixed and variable costs behave and how to use them to predict costs
How do variable costs behave?
A variable cost is constant per unit but varies in total with the activity level.
If Sledding Adventures pays 10 doesn’t change regardless of volume. But total refreshment cost scales directly: 100 customers = 8,000.
Per unit vs. total — the key distinction
Measure As volume increases Variable cost per unit Stays the same Total variable cost Increases proportionally Fixed cost per unit Decreases Total fixed cost Stays the same Fixed cost per unit is dangerous — it drops as volume increases, which can mislead pricing decisions. The textbook recommends dealing with fixed costs on a total basis rather than per unit.
What is an activity base?
An activity base is the measure of whatever causes a variable cost to be incurred.
Common activity bases: direct labour-hours, machine-hours, units produced, units sold, kilometres driven, beds occupied.
Whether a cost is variable depends on whether it is caused by the activity under consideration. The same cost could be variable relative to one activity base and fixed relative to another.
Cross-reference: FMGT-2294 Chapter 7 - Notes from the Textbook
Chapter 3’s “activity base” is the same concept as ABC’s “cost driver.” What Chapter 3 calls “fixed” is often just a cost driven by something other than units — ABC unpacks this into batch, product, and facility levels.
What is the difference between “variable cost per unit” and “variable cost per unit of activity”?
They’re the same only when the activity base is units produced/sold. They diverge when the activity base is something else.
| Term | What it means | Example |
|---|---|---|
| Variable cost per unit | Cost per widget | $10 per pair of skis |
| Variable cost per unit of activity | Cost per one unit of whatever drives the cost | $1.85 per occupancy-day |
A widget might consume multiple units of the activity base. If each widget takes 3 machine-hours and the variable cost is 5 but the variable cost per widget is $15.
What is the difference between true variable costs and step-variable costs?
True variable costs change in direct proportion to activity. Step-variable costs increase only in large, indivisible chunks.
| Type | Behavior | Example | Why it steps |
|---|---|---|---|
| True variable | Smooth, proportional to volume | Direct materials | You use exactly as much as you need |
| Step-variable | Flat within a step, jumps at threshold | Maintenance worker wages | People come in whole units (35 hrs/week) |
Management’s objective with step-variable costs: get the fullest use of services possible for each separate step. This is why managers assign more work — they’re paying for the full step regardless.
Unused step-variable capacity can't be inventoried
Unlike materials, if a maintenance worker has idle time, you can’t store it for next week. This is the textbook’s framing — though in practice, flex time and banked hours partially work around this. See Cost Behavior Is Horizon-Dependent for the nuance.
What is the relevant range?
The relevant range is the band of activity within which assumptions about cost behavior are valid.
Curvilinear costs can be approximated with a straight line within the relevant range. Outside that range, the approximation breaks down.
Non-linear variable costs have a per-unit amount that changes as activity level changes. Example: raw material quantity discounts — the more you buy, the lower the per-unit cost. This creates a stepped or curved total cost line rather than a straight one.
How do fixed costs behave?
Total fixed costs remain constant within the relevant range. Per-unit fixed cost decreases as volume increases.
The first customers have the greatest impact on reducing average fixed cost per unit. The curve flattens as volume grows — going from 100 to 200 customers halves the per-unit cost, but going from 700 to 800 barely moves it.
What are committed vs. discretionary fixed costs?
| Type | Definition | Planning horizon | Can you cut it short-term? | Examples |
|---|---|---|---|---|
| Committed | Investments in basic capacity for sustained operations | Multi-year | No — locked in | Depreciation, property taxes, insurance, top management salaries |
| Discretionary | Annual management decisions to spend in certain areas | Single year | Yes — with some consequences | Advertising, R&D, training programs |
Advertising isn't inherently a fixed cost
The textbook classifies advertising as discretionary fixed because it assumes a budget-based model: management decides a lump sum to spend. But if a company uses performance marketing with ROI/engagement targets, spending must flex with volume — making it variable or mixed. The classification depends on how management has structured the spending, not the cost category itself. See Cost Behavior Is Horizon-Dependent.
How do fixed costs and the relevant range interact?
Fixed costs appear to step across wide ranges of activity — similar to step-variable costs visually, but with two key differences:
| Dimension | Step-variable | Fixed cost steps |
|---|---|---|
| Cause of the step | Resource is indivisible (whole people, whole machines) | Capacity boundary reached (need second facility) |
| Width of each step | Narrow — maybe 40 hours | Wide — thousands or tens of thousands of hours |
| Short-term flexibility | Can hire/lay off relatively easily | Locked in once committed |
Because step-variable steps are narrow relative to the relevant range, they’re treated as variable for most purposes. Because fixed cost steps are wide, they’re treated as fixed within the entire relevant range.
Beyond the Textbook
The textbook treats cost behavior as an inherent property of costs. Microeconomics reveals it’s horizon-dependent — the same cost shifts from fixed to variable as the decision timeframe extends. Visually, the same phenomenon produces straight lines (one relevant range), staircases (multiple ranges), and smooth curves (zoomed way out). But the cause of stepping matters: indivisible resources (step-variable) vs. capacity boundaries (fixed). See Cost Behavior Is Horizon-Dependent for the full framework linking accounting classifications to microeconomic time horizons.
⚠️ Don’t confuse: Step-variable and fixed costs can produce the same staircase pattern visually, but the cause differs — indivisible resources (step-variable) vs. capacity boundaries (fixed). The cause determines how you manage it.
LO2: Analyze mixed costs using various approaches
What are mixed costs?
Mixed costs contain both a fixed element and a variable element. Also called semi-variable costs.
Expressed as: Y = a + bX
| Symbol | Meaning | Example (Sledding Adventures) |
|---|---|---|
| Y | Total cost | Total vehicle costs |
| a | Fixed cost element | $400/month lease |
| b | Variable cost per unit of activity | $0.20/km |
| X | Activity level | Kilometres driven |
Even at zero activity, the fixed portion is still incurred.
What are the approaches to analyzing mixed costs?
Four methods, each with different strengths:
| Method | How it works | Data required | Precision |
|---|---|---|---|
| Account analysis | Analyst classifies each account as fixed, variable, or mixed based on judgment and knowledge of the business | Knowledge of the business, chart of accounts | Low — subjective |
| Engineering approach | Detailed analysis of physical inputs required to produce output | Physical input-output specifications | High for direct costs, can’t handle indirect |
| High-low method | Uses highest and lowest activity data points to calculate slope (variable rate) and intercept (fixed cost) | At least two periods of cost and activity data | Low — only two data points |
| Least-squares regression | Statistical fit using all available data points | Full historical dataset | Highest — uses all data |
For account analysis, the textbook states: “the variable cost per unit is estimated by dividing the sum of the costs for the accounts that have been classified as variable by the total activity.”
Cross-reference: FMGT-2294 Chapter 5 - Notes from the Textbook
This calculation — total costs ÷ total activity = rate — is structurally identical to computing POHR. The difference is what goes in the numerator and why:
Context Numerator Purpose Account analysis (Ch 3) Only variable costs Separate behavior to predict future costs POHR (Ch 5) All MOH (fixed + variable blended) Assign overhead to jobs
The engineering approach can't handle manufacturing overhead on its own
The textbook states it’s “often used only for direct materials and labour” because tracing physical input-output relationships for indirect items is too time-consuming. It requires a supplemental method (account analysis, high-low, or regression) for overhead and indirect costs.
How does the high-low method work?
What is the correct sequence for analyzing mixed costs?
The sequence is a funnel — each step depends on the output of the previous one.
- Account analysis — classify the obvious costs first (rent = fixed, materials = variable). This narrows down which costs even need further analysis. Only mixed costs go forward.
- Scattergraph — plot the remaining mixed costs. This is the diagnostic gate: is the relationship linear? One relevant range or two? Outliers? If non-linear, don’t proceed with a linear method.
- High-low method — once the scattergraph confirms a roughly linear relationship, use the two extreme activity points to calculate variable rate and fixed component.
- Express as Y = a + bX — package the high-low outputs into the cost formula. This can’t come before step 3 because you don’t have the values yet.
The scattergraph is a gate
If the scattergraph shows a continuously curving relationship (not stepping, not breaking into two linear segments, but actually bending), a straight-line formula from the high-low method will underestimate costs at some volumes and overestimate at others. The scattergraph is permission to proceed with a linear method.
Step 1: Plot a scattergraph to visually confirm the relationship is approximately linear.
Step 2: Identify the periods with the highest and lowest activity levels (not costs).
The Trap
Pick high and low based on activity, not cost. The period with the highest cost may not be the period with the highest activity. The method needs maximum variation in the independent variable (activity).
Step 3: Calculate variable cost per unit of activity:
| Formula | Meaning | Example (Hamilton Hotel) |
|---|---|---|
| Variable rate = (Cost₂ − Cost₁) ÷ (Activity₂ − Activity₁) | Change in cost ÷ Change in activity (rise over run) | (1,773) ÷ (3,610 − 190) = $1.85/occupancy-day |
The textbook shows two versions of this formula
“Variable cost per unit” using (Y₂ − Y₁) / (X₂ − X₁), and “Variable cost per unit of activity” using Change in cost / Change in activity. These are the same formula — the second is just the first restated in plain English. No mathematical difference.
Step 4: Calculate fixed cost using either data point:
Fixed cost = Total cost − (Variable rate × Activity level) = 1.85 × 3,610) = $1,421.50
Step 5: Express as cost formula:
Y = 1.85X
Limitation of the high-low method
Uses only two data points, which may be extreme/unusual periods. The cost formula may misrepresent normal cost behavior. Use least-squares regression if greater accuracy is needed.
What is the purpose of a scattergraph?
The scattergraph is the diagnostic step before any calculation. It lets you:
- Visually assess whether the cost-activity relationship is linear
- Detect if there are multiple relevant ranges (like the Hamilton Hotel cleaning staff — flat up to 1,500 occupancy-days, then mixed above that)
- Spot outliers that might distort calculations
The cleaning staff example (Exhibit 3–10) is critical: a single straight line would be a poor fit. Two lines with different relevant ranges (0–1,500 and 1,501–4,000) are needed.
Beyond the Textbook
The four cost analysis methods aren’t competing choices — they’re a layered workflow in practice. Start with account analysis (judgment), use engineering for new or direct costs, then apply high-low or regression to remaining mixed costs. Method choice is itself a cost-benefit decision: higher-stakes decisions justify more sophisticated methods. See Cost Analysis Method Selection for practical application.
LO3: Prepare an income statement using the contribution format
Why use the contribution format instead of the traditional format?
The traditional format organizes costs by function (production, selling, admin). The contribution format organizes costs by behavior (variable, then fixed). Same operating income — different visibility.
The traditional format lumps variable and fixed costs together under functional headings. This hides cost behavior, making it difficult to predict how costs change with volume. The contribution format was developed specifically to support internal decision-making that depends on understanding cost behavior.
Managers apply knowledge of cost behavior when:
- Predicting costs at different activity levels
- Calculating break-even sales
- Estimating the impact of volume changes on profit
- Costing products
- Preparing budgets
- Deciding whether to keep or drop a product
- Deciding whether to make internally or outsource
What is the contribution margin?
Contribution margin = Sales − all variable expenses.
It’s the amount that contributes toward covering fixed expenses and then toward profit.
“Contribution toward fixed expenses and profits” is the textbook’s way of describing what the contribution margin does — it covers fixed costs first, and whatever remains is profit. It’s one number, not two.
Contribution margin per unit = Selling price per unit − all variable costs per unit.
Total contribution margin = Total sales − total variable costs, OR contribution margin per unit × units sold.
How do gross margin and contribution margin differ?
The Trap
Gross margin ≠ contribution margin. This distinction is critical for manufacturing companies and is a common exam mistake.
| Measure | Formula | What it includes |
|---|---|---|
| Gross margin | Sales − COGS | COGS contains both variable and fixed production costs mixed together |
| Contribution margin | Sales − all variable costs | Includes variable production, variable selling, AND variable admin |
For a merchandising company, COGS is all variable (they just buy and resell), so the difference between gross margin and contribution margin is only the variable selling and admin expenses.
For a manufacturing company, COGS includes fixed production overhead (depreciation on factory equipment, factory supervisor salaries, etc.), so gross margin and contribution margin can differ significantly.
Merchandising company shortcut
For merchandising companies, COGS = variable production costs on the contribution format. They don’t manufacture, so all production costs are the purchase cost of goods, which is entirely variable. If the question gives inventory data instead of a per-unit cost, calculate COGS first:
COGS = Beginning Inventory + Purchases − Ending Inventory
Why is merchandising COGS all variable but manufacturing COGS is not?
A merchandising company buys finished goods and resells them. Every dollar of COGS is a purchase cost that scales directly with units sold — buy one more widget, COGS goes up by the purchase price. No widget purchased, no cost.
A manufacturing company makes the product. COGS includes not just direct materials and direct labor (variable), but also MOH — which contains fixed costs like factory rent, equipment depreciation, and supervisor salaries that exist regardless of production volume.
| Company type | What’s in COGS | Why |
|---|---|---|
| Merchandising | Purchase cost of goods | You only pay for what you buy — pure variable |
| Manufacturing | DM + DL + MOH | MOH includes fixed production costs that don’t vary with volume |
Beyond the Textbook
The textbook’s claim that merchandising COGS is “all variable” assumes you buy exactly what you sell at a constant per-unit price with no contractual commitments. Applying the Seven lenses reveals situations where this breaks down:
- Mechanism: Minimum order quantities — supplier requires lots of 500, you sell 300. The excess isn’t driven by your sales volume.
- Conditions: Take-or-pay contracts — committed annual purchases regardless of sales. The committed portion behaves as fixed.
- Scale: Quantity discounts change the per-unit cost as volume changes, creating non-linear behavior.
- Actors: Private-label products (e.g., Costco’s Kirkland) may include fixed costs for product development, tooling, or packaging design embedded in the supplier relationship.
- Trade-offs: Companies deliberately convert variable COGS into fixed costs through bulk prepurchases and forward contracts to reduce risk.
- Scope: Franchise or licensing fees to sell certain branded products are fixed costs tied to the right to merchandise, not to units sold.
For exam purposes, treat merchandising COGS as all variable. In practice, examine the supplier agreements.
How to prepare a contribution format income statement
Exam requirement
The professor requires formatting the contribution format income statement from memory including all titles, headings, and categories. Memorize this template.
Contribution Format Template (Memorize)
[COMPANY NAME]
Contribution Income Statement
For the [Period] Ended [Date]
Sales $XXX,XXX
Less variable expenses:
Variable production (or COGS) $XX,XXX
Variable selling XX,XXX
Variable administrative XX,XXX XXX,XXX
--------
Contribution margin $XXX,XXX
Less fixed expenses:
Fixed production $XX,XXX
Fixed selling XX,XXX
Fixed administrative XX,XXX XXX,XXX
--------
Operating income $ X,XXX
========
Traditional Format Template (Memorize for comparison)
[COMPANY NAME]
Income Statement
For the [Period] Ended [Date]
Sales $XXX,XXX
Less cost of goods sold XXX,XXX
--------
Gross margin $XXX,XXX
Less operating expenses:
Selling expenses $XX,XXX
Administrative expenses XX,XXX XXX,XXX
--------
Operating income $ X,XXX
========
Side-by-Side Comparison
| Traditional format | Contribution format |
|---|---|
| Sales | Sales |
| Less: COGS (variable + fixed production mixed) | Less: all variable expenses (production, selling, admin) |
| Gross margin | Contribution margin |
| Less: operating expenses (selling + admin mixed) | Less: all fixed expenses (production, selling, admin) |
| Operating income | Operating income |
Both formats produce the same operating income
The contribution format just reorganizes where costs appear. Nothing is added or removed — the total is identical.
LO4: (Appendix 3A) Analyze a mixed cost using least-squares regression
Exam expectation (pending confirmation)
The textbook does not walk through Excel steps for running regression, and the professor did not cover it in class. Likely expectation: interpret outputs (a, b, R²), write the cost formula, assess economic plausibility. Probably NOT expected to run regressions in Excel. Email sent to professor to confirm.
What is least-squares regression?
Least-squares regression fits a line Y = a + bX to all available data points by minimizing the sum of squared errors (vertical distances between actual data points and the line).
Same output format as high-low — you get a (fixed cost) and b (variable cost per unit of activity). But regression also gives you R², which high-low cannot.
"Regression" in this course means simple linear regression
The textbook states the scattergraph must confirm a linear relationship before using regression. This is because the course only covers simple linear regression (fitting a straight line). Regression as a broader statistical technique can handle non-linear relationships (polynomial, logarithmic, exponential models) — but that’s beyond the course scope. For exams: scattergraph confirms linear → proceed. Scattergraph shows non-linear → neither high-low nor simple regression applies.
How does regression compare to the high-low method?
| Feature | High-Low | Least-Squares Regression |
|---|---|---|
| Data points used | 2 (highest and lowest activity) | All available |
| Output | a (fixed) and b (variable) | a, b, and R² |
| Precision | Low — extreme points may be unrepresentative | Higher — uses full dataset |
| Ease of use | Calculator math | Requires software (Excel, SPSS, R, SAS) |
| When to use | Quick estimate, limited data | Defensible numbers, sufficient historical data |
Hamilton Hotel — same data, different results
Method Cost Formula High-low Y = 1.85X Regression Y = 1.86X The difference exists because high-low only uses August and October (the extremes), while regression incorporates all 12 months. Regression’s R² of 99.9% confirms the fit is near-perfect.
What is R² and how do you interpret it?
R² (goodness of fit) measures the percentage of variation in cost explained by variation in the activity. Ranges from 0% (no fit) to 100% (perfect fit).
| R² Value | Interpretation |
|---|---|
| 95–100% | Excellent — activity base explains nearly all cost variation |
| 80–95% | Good — most variation explained, but some other factor likely present |
| 50–80% | Weak — significant unexplained variation, consider a different activity base |
| Below 50% | Poor — this activity base is not a useful predictor |
An R² of 87% means 87% of cost variation is explained by the activity base. The remaining 13% is driven by something else not captured in the model.
What is economic plausibility?
Economic plausibility asks: does it make causal sense that a change in the independent variable would cause a change in the cost? High R² alone is not enough.
The Trap
High R² without causal logic is a statistical trap. The textbook example: number of cleaning staff might correlate with electrical costs (high R²) because both are driven by occupancy-days. But cleaning staff don’t cause electricity usage. Using cleaning staff as the predictor would produce a formula that works historically but fails when the underlying relationship breaks (e.g., hotel automates cleaning but occupancy stays the same).
The fix: Always ask — “If I changed only the independent variable, would the cost actually change?” If yes, economically plausible. If no, you’ve found correlation without causation.
Always pair regression with a scattergraph
Even with regression, plot the data first. The scattergraph can reveal non-linear relationships, multiple relevant ranges, or outliers that R² alone won’t catch. A high R² on a curved relationship still produces a misleading straight-line formula.
What is multiple regression?
When more than one activity drives a cost, use multiple independent variables. Example: shipping costs driven by both units shipped and weight.
Same principle as simple regression, but uses adjusted R² instead of R² to account for the number of independent variables. Economic plausibility must be evaluated for each independent variable in the model.