# Chapter 3: Cost Behaviour: Analysis and Use

### 1) Describe how fixed and variable costs behave and how to use them to predict costs.

Cost behaviour – How a cost will react or change as changes take place in the level of business activity.

• Essential for cost prediction under different circumstances.

Cost structure – The relative proportion of fixed, variable, and mixed costs found in an organization.

#### Variable Costs

Variable Cost – The one whose total dollar amount varies in direct proportion to changes in the activity level.

• i.e. double activity level = double variable costs.

Variable cost is constant if expressed on a per unit basis.

• Graphically - Total cost slopes upward and per unit cost is constant.

#### Activity Base

• A measure of whatever causes a variable cost to be incurred.
• i.e. total cost of direct materials increases as more goods are produced. This means that number of goods produced is an activity base for explaining cost of direct materials.
• Assume that the activity base is total volume of goods/services produced or sold by the organization.
• Specify if it is something other than total sales.

#### Extent of Variable Costs

• Number and type of variable costs present in an organization depend on its structure and purpose.
• i.e. merchandising companies have COGS, manufacturing companies have direct material costs, and some manufacturing overhead costs like indirect materials.

#### True Variable Costs vs Step-Variable Costs

• True Variable Costs – Amount used during a period varies in direct proportion to the level of production activity.
• For example - direct materials.
• Step Variable Costs – A cost that is obtainable only in large amounts and that increases and decreases only in response to fairly wide changes in activity level. (i.e. cost of a maintenance worker)
• Costs cannot be stored as inventory – It is lost if it is not used.
• Must be careful not to accumulate too many unneeded resources as a result. #### The Linearity Assumption and the Relevant Range

• Curvilinear Costs – Costs that show a curved relationship between cost and activity rather than a straight-line relationship.
• It can be approximated with a straight line within the band of activity (fairly linear part) or relevant range.
• Outside the relevant range, the straight line is a poor approximation.

#### Curvilinear Costs and the Relevant Range • Non-linear Variable Cost – A variable cost where the per unit amount increases or decreases as the activity level changes.
• i.e. unit of cost of raw materials used by manufacturing companies decreases as quantity purchased increases. (Costco and Bulk Barn anyone? xD)

#### Fixed Costs

• Total fixed costs remain constant within the relevant range of activity.
• This means that per unit fixed cost drops at a decreasing rate.
• First customers have the greatest impact on the average fixed costs per unit.
• To avoid confusion, fixed costs are expressed in total fixed cost. #### Types of Fixed Cost

• Committed Fixed Costs – Fixed costs that are difficult to change in the short term and that relate to the investment in facilities, equipment, and the basic organizational structure of a firm.
• Firms are locked into these costs, they must pay them even if operations change level.
• Discretionary Fixed Costs – Fixed costs arising from annual decisions by management to spend in certain areas, such as advertising and research.
• Planning horizon is typically short term, and may be canceled with minimum damage to objectives
• Can be adjusted from year to year, or during a year if necessary.
• Trend towards fixed costs
• Many companies prefer greater fixed costs than variable costs.
• i.e. Competition to satisfy customer needs has led to automating business processes.
• Also, demand for knowledge workers is higher.

#### Fixed Costs and the Relevant Range

• As relevant range is the range of activity over which the graph of the cost is graph.
• The width of steps for fixed costs is so wide, that they must be treated as being fixed for the entire relevant range of activity. #### Mixed Costs

• Contains both variable and fixed cost elements.
• Graphically, the fixed element causes a vertical intercept with a slope upward as the variable cost element is added to the fixed cost. • Equation for a straight line expresses relationship between mixed cost and level of activity
• Y = a + bX
• Y - total mixed cost
• a - the total fixed cost (vertical intercept)
• b - the variable cost per unit of activity (slope of the line)
• X - level of activity

### 2) Analyze mixed costs using various approaches.

• Fixed portion – Basic minimum cost of having an activity ready and available for use.
• Variable Portion – Cost incurred for actual consumption of the activity.

#### Estimating Cost Behaviour

• Accounting Analysis – Method for analyzing cost behaviour in which each account under consideration is classified as either variable or fixed based on analyst’s prior knowledge of how the cost in the account behaves.
• i.e. direct materials are variable because they vary in direct proportion with number of units produced.
• To identify fixed – Take sum of cists for fixed accounts.
• To identify variable – Divide t he sum of the costs for the variable accounts.
• Engineering Approach – A detailed analysis of cost behaviour based on an industrial engineer’s evaluation of the physical inputs required to produce a unit of output and of the costs of those outputs.
• Very time consuming and used where no past experience on activity and costs is available.
• Used only for direct materials as it is too time consuming to identify indirect materials. (i.e. salt used in Pizza Hut)
• Scattergraph Plots
• Applying the high-low cost method involves diagnosing cost behaviour with a scatter-graph plot.
• It reveals non-linearities and other problems

#### Two Things to Note:

• Dependent Variable – The cost is plotted on the vertical axis, it depends on the level of activity.
• Independent Variable – The activity is plotted on the horizontal axis.

Linear Cost Behaviour – Cost behaviour where the relationship between cost and activity can be reasonably approximated by a straight line.

• If there is more than 1 relevant range, we can use more than one straight line to identify the different ranges. • Using the High-Low Method
• A method of separating a mixed cost into its fixed and variable elements by analyzing the change in cost between the high and low levels of activity.
• Graph is a straight line - The slope of the straight line is equal to the variable cost per unit of activity.
• Variable Cost = Slope of the line = Rise/Run = ΔY/ΔX
• To analyze mixed costs, identify the period with the lowest activity level and highest activity level.
• Variable Cost = ΔY/ΔX = (Cost at highest activity – Cost at lowest activity) / (Highest Activity – Lowest Activity)
• Fixed Cost = Total Cost (Take the cost from either highest/lowest)– Variable Cost Element (Multiply the variable cost by activity at highest/lowest)
• Due to possibility of misrepresentation with only extremes, other methods of cost analysis may be used, such as least-squares regression.

### 3) Prepare an income statement using the contribution format.

#### Contribution Format

• Contribution Approach – An income statement format where costs are separated into variable and fixed categories.
• Distinguishing these categories has limitations for internal processes.
• Contribution Margin – Amount remaining from sales revenues after all variable expenses have been deducted.
• This value contributes towards covering fixed expenses and then towards profit.
• Common Assumption – Variable production expenses assume production = sales in terms of units.
• Expenses for production use sales volume as the driver.
• A more complete income statement must show beginning/ending inventory levels so that variable production costs use production volume activity as the cost driver.
• The emphasis on cost facilitates cost-volume-profit analysis, budgeting, pricing, use of scarce resources, and make or buy analysis. 