Introduction to Cost Behavior and Inventory Costing Systems

Principles of Cost Behavior and Judgement

• Contextual Dependency: Cost behavior is not an inherent property of a cost itself but is dependent on the activity it is compared against. Different costs are used for different purposes, and a cost's classification as fixed or variable can change depending on the activity or the specific context of the problem.

• Judgment Criteria: To determine if a cost is fixed or variable, one must first identify the activity being compared. If there is no relationship between the cost and the activity, the cost is considered fixed relative to that activity.

Characteristics and Assumptions of Variable Costs

• Definition: A variable cost is a cost that changes in total as the activity level changes.

• Direct Positive Relationship: It is assumed that as activity increases, the cost increases, and as activity decreases, the cost decreases. Ideally, this link is causal, meaning the activity is a true cost driver, which provides the best predictive power for budgeting and forecasting. At a minimum, a reliable correlation or association over time is required for predictive purposes.

• Linear Relationship and Constant Slope: To simplify mathematical modeling, cost accounting assumes a linear relationship where the variable cost per unit remains constant. This constant slope allows for the use of linear algebra tools such as rise-over-run and least squares regression.

• Graphical Representation: On a graph where the x-axis represents activity and the y-axis represents total cost:

  • A purely variable cost starts at the origin $(0,0)$, meaning zero activity results in zero cost.

  • The line slopes upward to the right.

  • The slope is constant, representing the fixed dollar amount change in total cost for every unit change in activity ($x$).

  • The variable cost per unit could be as small as $0.02$ or as large as $\$20,000,000$ per unit, but the slope remains constant over the relevant range.

The Relevant Range and Economic Realities

• Definition of Relevant Range: This is the range of activity within which the firm expects to operate and for which existing cost relationships are valid.

• Linear vs. Curvilinear: In reality, cost functions are often curvilinear. At very low levels of production, costs may curve at a decreasing rate. Within the "sweet spot" or relevant range—where workers have learned their jobs and machines are calibrated—the relationship approximates a linear function.

• Diseconomies of Scale: Once production exceeds the relevant range or physical capacity, costs often increase at an increasing rate. This is known as diminishing returns or diseconomies of scale.

• Illustrations of Capacity Overload:

  • Lucy and Ethel Metaphor: When a conveyor belt (production process) speeds up beyond the workers' ability to keep pace, efficiency collapses, mistakes occur, and the cost per unit (e.g., a box of chocolates) begins to soar.

  • Mechanical Failure: Operating machines faster than physically intended leads to breakdowns and accidents, driving up costs significantly outside the stable relevant range.

Fixed Costs and the Per-Unit Trap

• Total Fixed Cost: Remains constant in total regardless of activity levels within the relevant range.

• The Inverse Relationship of Per-Unit Fixed Cost: The fixed cost per unit is "tricky" because it changes inversely with activity. As activity increases, the fixed cost per unit decreases because the same total cost is spread over more units.

• Per-Unit Calculation Formula:     $\text{Fixed Cost per Unit} = \frac{\text{Total Fixed Cost}}{\text{Total Units}}$

• Numerical Example:

  • Total Fixed Cost = $\$10,000$ per month.

  • Scenario A (10,000 units): \frac{\10,000}{10,000\,\text{units}} = \$1.00\,\text{per unit}$.

  • Scenario B (20,000 units): \frac{\10,000}{20,000\,\text{units}} = \$0.50\,\text{per unit}$.

• Decision-Making Dangers: Although it appears the product is getting cheaper to produce as volume increases, the economic cost ($\$10,000$) remains unchanged. Relying on per-unit fixed costs can lead to poor production decisions or financial manipulation.

• Ethical and Financial Implications: Managers can manipulate operating income by overproducing inventory. Under GAAP, fixed manufacturing overhead is a product cost treated as inventory. By producing more than is sold, some fixed costs are "trapped" on the balance sheet rather than being expensed on the income statement, making profit look artificially high.

Case Study: Cooper Furniture (Potomac, Maryland)

• Operations: Cooper Furniture assembles two types of chairs—recliners and rockers—on separate assembly lines.

• Cost Object: The total cost of producing the total number of recliners assembled.

• Classification Examples:

  • Fabric/Leather for Recliners: Direct (traceable to recliners) and Variable (more recliners require more material).

  • Public Relations Manager Salary: Indirect (represents the whole company) and Fixed (salary does not vary with recliner volume).

  • Lubricant for Recliner Assembly Line: Direct (traceable to that specific line). Usually classified as Variable as usage increases with volume, though it could be Fixed if part of a routine, time-based maintenance schedule.

  • Freight Cost of Recliner Frames: Direct and Variable.

  • Electricity (Entire Plant on One Bill): Indirect (must be allocated between rockers and recliners). Primarily Variable (as machine usage increases with production), though it contains Fixed components (lighting and HVAC based on building size).

  • Temporary Assembly Line Workers (Hourly): Direct and Variable.

  • Annual Fire Insurance for the Plant: Indirect and Fixed (based on building size/location risk, not unit volume).

Case Study: Gummy Land Jawbreaker Production

• Operational Parameters:

  • Current capacity: $5,000\,\text{units/month}$.

  • Machine Cost: $\$6,500$; Straight-line depreciation over $10$ years; $\$0$ residual value.

  • Rent/Other: $\$1,200/month$.

  • Material Cost (Variable): $\$0.40/unit$.

  • Current Sales: $3,900\,\text{units/month}$.

• Current Annual Financials:

  • Annual Depreciation: \frac{\6,500}{10\,\text{years}} = \$650/year$.

  • Annual Fixed Cost: (\1,200 \times 12) + \$650 = \$15,050$.

  • Annual Variable Cost: $3,900\,\text{units/month} \times 12\,\text{months} \times \$0.40 = \$18,720$.

• Expansion Planning (Next Year):

  • Expect to double demand to $7,800\,\text{units/month}$.

  • Requirement: Must buy an identical second machine to increase capacity (as current limit is $5,000$).

  • Benefit: $10\%$ bulk discount on materials (\0.40 \times 0.90 = \$0.36/unit$).

• Projected Annual Financials for Expansion:

  • New Annual Fixed Cost: Rent stays constant ($\$14,400$), but depreciation doubles (\650 \times 2 = \$1,300$). Total = $\$15,700$.

  • New Annual Variable Cost: $(7,800 \times 12) \times \$0.36 = \$33,696$.

  • New Relevant Range: Capacity increases from $0\text{--}60,000$ units annually to $0\text{--}120,000$ units annually.

Product Costs vs. Period Costs

• Product Costs (Inventoriable Costs): These are costs incurred to produce or purchase inventory. They are accumulated on the balance sheet as an asset and are only matched against revenue (expensed as Cost of Goods Sold) when the inventory is sold. This is described metaphorically as the cost "crossing the River Styx" to the income statement.

• Period Costs: Non-manufacturing costs such as Selling, Administrative, and Research & Development (R&D). Under GAAP, these must be expensed in the period they are incurred and cannot be treated as inventory.

• Sector-Specific Treatment:

  • Service Businesses (Accounting/Law Firms): For financial reporting, they have no saleable inventory; all costs are period costs. For internal decision-making, they may track "inventory" of customer representation costs.

  • Merchandising Businesses (Walmart/Amazon): Product costs include the purchase price of inventory, freight-in, and tariffs/taxes. Freight-out (shipping to customers) is a selling/period cost.

  • Manufacturing Businesses: Direct materials, direct labor, and manufacturing overhead are all product costs.