Welcome to Cost Classification by Output and Behaviour!
Hi there! Welcome to one of the most fundamental chapters in your CIMA BA2 journey. Understanding how costs relate to output and how they behave as activity changes is essential for predicting profits, setting prices, and making smart business decisions. Don't worry if this seems a bit "maths-heavy" at first—we are going to break it down into simple, everyday examples that make complete sense.
1. Cost Classification in Relation to Output (Direct and Indirect Costs)
When classifying costs in relation to output, our main question is: Can this cost be traced directly and economically to a specific unit of output or cost object?
A cost object is any item, unit, or activity for which cost is ascertained—for example, a product (a pair of shoes), a service (a hotel stay), an activity, or a customer.
Direct Costs
Direct costs are costs that can be traced completely, specifically, and economically to a particular cost object.
- Direct materials: Raw materials that physically become part of the finished product (e.g. the leather used to make a pair of shoes, or timber for a dining table).
- Direct labour: Wages paid to workers who are directly involved in physically making the unit of output (e.g. the assembly worker stitching the shoe).
- Direct expenses: Other specific costs incurred exclusively for that cost object (e.g. royalties paid per unit produced, or hiring a specialist machine exclusively for a single customer job).
Prime Cost: The total of all direct costs is called the prime cost:
\( \text{Prime Cost} = \text{Direct Materials} + \text{Direct Labour} + \text{Direct Expenses} \)
Indirect Costs (Overheads)
Indirect costs (commonly called overheads) are costs that cannot be traced directly and exclusively to a single unit of output. They are shared across multiple units or support the business as a whole.
- Indirect materials: Items used in production that are difficult or uneconomic to trace to individual units (e.g. glue, cleaning fluids, and lubricating oils for machinery).
- Indirect labour: Wages of staff who support production but do not physically make individual units (e.g. factory supervisors, maintenance technicians, and security personnel).
- Indirect expenses: General operating costs such as factory rent, factory insurance, electricity, and machine depreciation.
Product Costs vs. Period Costs
In financial statements, costs are also distinguished by when they are recognized as expenses:
- Product costs: Costs directly associated with the purchase or manufacture of goods (direct materials, direct labour, and production overheads). These costs attach to units and are included in the valuation of inventory on the statement of financial position until the goods are sold.
- Period costs: Costs not tied to inventory valuation, charged as an expense directly to the statement of profit and loss in the accounting period in which they are incurred (e.g. administration expenses, selling and marketing costs, and financing costs).
2. What is Cost Behaviour?
Cost behaviour is the way a cost changes as the level of activity (output volume) changes. In a factory, the "activity" might be the number of shoes produced or machine hours worked. In a hospital, it might be patient days.
To manage a business, we need to know: if we produce one more unit, will our total costs go up? And by how much?
The Concept of the Relevant Range
Before examining cost behaviour patterns, you must keep in mind the relevant range. This is the range of activity within which specific cost behaviour patterns remain valid. For example, your factory rent stays flat between 0 and 1,000 units. If output expands to 5,000 units, you will need a larger facility, and rent will jump!
Quick Tip: Always assume operations remain within the relevant range unless the question specifies otherwise.
3. The Four Main Types of Cost Behaviour
A. Variable Costs
Variable costs increase in direct proportion to the level of activity. If activity increases by 20%, total variable costs also increase by 20%.
Example: Leather for shoes. If 1 pair uses \$10 of leather, 10 pairs require \$100 of leather.
- Total Variable Cost: Increases directly as activity increases.
- Variable Cost per unit: Remains constant (e.g. always \$10 per shoe).
B. Fixed Costs
Fixed costs remain constant in total regardless of how many units are produced (within the relevant range).
Example: Factory rent. Whether 1 shoe or 1,000 shoes are made, the rent remains the same.
- Total Fixed Cost: Stays constant as activity increases.
- Fixed Cost per unit: Decreases as activity increases (the fixed cost is spread over more units).
C. Stepped-Fixed Costs
Stepped costs are fixed for a specific range of activity, but once activity passes a certain threshold, the cost steps up to a higher fixed amount.
Example: A production supervisor earns a fixed salary and can supervise up to 10 workers. Hiring an 11th worker requires employing a second supervisor, causing total supervisory costs to jump up one step.
D. Semi-Variable Costs (Mixed Costs)
These costs contain both a fixed element and a variable element.
Example: Electricity bills often have a fixed standing connection charge per quarter plus a variable charge per kilowatt-hour consumed.
Key Takeaway Summary:
- Variable: Total varies with activity; per unit is constant.
- Fixed: Total is constant; per unit decreases as activity rises.
- Semi-Variable: Contains both a fixed baseline and a variable per-unit charge.
4. The Linear Equation of Costs
In management accounting, total cost behaviour within the relevant range is expressed using the linear cost equation:
\( y = a + bx \)
Where:
- \( y \) = Total Cost
- \( a \) = Total Fixed Cost (the vertical axis intercept)
- \( b \) = Variable Cost per unit (the gradient or slope of the cost line)
- \( x \) = Level of activity (number of units produced)
5. Separating Semi-Variable Costs: The High-Low Method
When given total cost data at different activity levels, the High-Low Method allows us to separate the semi-variable cost into its fixed and variable parts.
Step-by-Step Guide:
- Identify High and Low Points: Select the highest and lowest activity levels (and their associated costs) from the historical data.
- Calculate Variable Cost per unit (\( b \)):
\( b = \frac{\text{Total Cost at Highest Activity} - \text{Total Cost at Lowest Activity}}{\text{Highest Activity Level} - \text{Lowest Activity Level}} \) - Calculate Total Fixed Cost (\( a \)): Substitute \( b \) into either the highest or lowest activity data point:
\( a = \text{Total Cost} - (b \times x) \) - Formulate the Equation: Use \( y = a + bx \) to forecast total costs at any targeted activity level.
Example:
Lowest activity: 1,000 units at a total cost of \$5,000
Highest activity: 3,000 units at a total cost of \$9,000
Step 2 (Variable cost per unit):
\( b = \frac{\$9,000 - \$5,000}{3,000 - 1,000} = \frac{\$4,000}{2,000} = \$2\text{ per unit} \)
Step 3 (Total fixed cost):
Using the high level: \( a = \$9,000 - (\$2 \times 3,000) = \$9,000 - \$6,000 = \$3,000 \)
Step 4 (Cost function):
\( y = 3,000 + 2x \). If expected activity is 2,500 units, estimated total cost is \( \$3,000 + (\$2 \times 2,500) = \$8,000 \).
6. Common Mistakes to Avoid
- Selecting points by cost rather than activity: Always identify the high and low periods using the activity level (units, hours), not the cost amount.
- Confusing total fixed cost and unit fixed cost: Total fixed cost is constant, but fixed cost per unit declines as volume rises.
- Assuming direct costs are always variable: While most direct material and direct labour costs are variable, classification by output (direct vs. indirect) is based on traceability to the cost unit, whereas classification by behaviour (variable vs. fixed) is based on response to activity volume.
Quick Review Box
- Direct Costs: Traceable directly to a cost object (Direct Material + Direct Labour + Direct Expenses = Prime Cost).
- Indirect Costs: Overheads that cannot be traced directly to a single cost object.
- Variable Cost: Constant per unit; total changes with output.
- Fixed Cost: Constant in total; per unit decreases as output increases.
- High-Low Variable Rate: \( \frac{\text{Difference in Cost}}{\text{Difference in Activity}} \).
- Cost Line: \( y = a + bx \).