Cost Classification & Behavior: Variable vs Fixed Costs

Core Concepts: Cost Classification

1. Definitions and Types of Costs

Costs are classified based on nature, traceability, and behavior. The primary classifications are:

A. By Nature (Element-wise)

classDiagram
    class MaterialCost {
        +Direct Material
        +Indirect Material
    }
    class LaborCost {
        +Direct Labor
        +Indirect Labor
    }
    class OverheadCost {
        +Production Overhead
        +Selling & Admin Overhead
    }
    MaterialCost --> LaborCost : "Combined into"
    LaborCost --> OverheadCost : "Combined into"
    OverheadCost --> TotalCost : "Forms"

B. By Traceability (Function-wise)

2. Cost Behavior: How Costs React to Activity Levels

Costs behave differently with changes in production/activity. The key classifications are:

A. Variable Costs (VC)

• Definition: Costs that vary directly with production volume.
• Per-unit cost remains constant; total cost changes proportionally.
• Formula: $$\text{Total VC}=\text{VC per unit}\times \text{Number of units}$$

B. Fixed Costs (FC)

• Definition: Costs that remain constant regardless of production volume (within a relevant range).
• Per-unit cost decreases as volume increases (spread over more units).
• Formula: $$\text{FC per unit}=\frac{\text{Total FC}}{\text{Number of units}}$$

C. Mixed Costs (Semi-Variable Costs)

• Definition: Costs with both fixed and variable components.
• Example: Electricity bill (fixed base charge + variable usage).
• Separation Method: Use High-Low Method or Least Squares Regression to split into FC and VC.

In the Real World

1. Daraz (Nepal’s Amazon)

   • Variable Cost: Delivery agent’s fuel cost per order (varies with number of deliveries).
   • Fixed Cost: Daraz’s warehouse rent in Kathmandu (same regardless of orders).
   • Mixed Cost: Electricity bill for Daraz’s data centers (fixed base + variable usage).

2. Ncell (Telecom)

   • Variable Cost: Cost of SMS per message sent (Rs. 0.50 per SMS).
   • Fixed Cost: Salary of Ncell’s customer service executives (same even if calls drop).
   • Mixed Cost: Internet data charges (fixed monthly plan + extra usage fees).

3. Kathmandu Traffic Routes (Public Sector)

   • Fixed Cost: Maintenance of a flyover (same cost whether 100 or 10,000 vehicles pass).
   • Variable Cost: Fuel cost for a bus service (increases with more passengers).
   • Application: Helps NTC decide if expanding bus routes is profitable.

Visualizing Cost Behavior

1. Graphical Representation

graph LR
    A["Total Cost"] --> B["Fixed Cost (FC)"]
    A --> C["Variable Cost (VC)"]

• FC: Horizontal line (constant).
• VC: Diagonal line (steepens with volume).
• Total Cost (TC): Sum of FC + VC.

2. T-Account for Cost Classification

Caption: Allocation of indirect costs to products in a Pokhara textile mill.

Worked Example: Kathmandu Retail Shop

Scenario: Shree Ram Trading House in Kathmandu sells traditional sweaters. For January 2024, the shop recorded:

• Sales: 500 sweaters at Rs. 2,000 each.
• Variable Costs:
  • Direct Material (wool): Rs. 800 per sweater.
  • Direct Labor: Rs. 300 per sweater.
  • Variable Overhead (packaging): Rs. 50 per sweater.
• Fixed Costs:
  • Shop Rent: Rs. 100,000.
  • Salary of Manager: Rs. 50,000.
  • Utilities: Rs. 20,000.

Tasks:

1. Calculate Total Cost (TC), Variable Cost (VC), and Fixed Cost (FC).
2. Determine Contribution Margin (CM) and Profit.
3. Find Break-Even Point (BEP) in units.

Step 1: Calculate Costs

Step 2: Contribution Margin and Profit

• Contribution Margin (CM): $$\text{CM per unit}=\text{Sales Price}-\text{VC per unit}=2,000-1,150=\text{Rs. 850}$$ $$\text{Total CM}=500\times 850=\text{Rs. 425,000}$$
• Profit: $$\text{Profit}=\text{Total CM}-\text{Total FC}=425,000-170,000=\text{Rs. 255,000}$$

Step 3: Break-Even Point (BEP)

Formula: $$\text{BEP (units)}=\frac{\text{Total FC}}{\text{CM per unit}}=\frac{170,000}{850}\approx 200\text{ sweaters}$$ Verification:

• At 200 units:
  • Total VC = 200 × 1,150 = Rs. 230,000
  • Total Revenue = 200 × 2,000 = Rs. 400,000
  • Profit = 400,000 - (230,000 + 170,000) = Rs. 0 (Break-Even).

Comparison Table: Variable vs Fixed Costs

Mixed Costs: High-Low Method Example

Scenario: Nepal Electricity Authority (NEA) provides electricity to a factory. Data for 5 months:

Task: Separate fixed and variable costs using the High-Low Method.

Step 1: Identify Highest and Lowest Points

• Highest: May (14,000 kWh, Rs. 90,000)
• Lowest: Apr (8,000 kWh, Rs. 75,000)

Step 2: Calculate Variable Cost per Unit (VC)

$$\text{VC per kWh}=\frac{\text{Change in Cost}}{\text{Change in Units}}=\frac{90,000-75,000}{14,000-8,000}=\frac{15,000}{6,000}=\text{Rs. 2.50 per kWh}$$

Step 3: Calculate Fixed Cost (FC)

Using the highest point: $$\text{Total Cost}=\text{FC}+(\text{VC per unit}\times \text{Units})$$ $$90,000=\text{FC}+(2.50\times 14,000)$$ $$\text{FC}=90,000-35,000=\text{Rs. 55,000}$$

Cost Equation: $$\text{Total Cost}=55,000+(2.50\times \text{Units})$$

Verification:

• For Jan (10,000 kWh): $$55,000+(2.50\times 10,000)=55,000+25,000=\text{Rs. 80,000}\text{(Matches)}$$

Exam Tip

1. Always classify costs correctly in exams. Use the nature, traceability, and behavior framework.
2. For mixed costs, prefer the High-Low Method (simpler) unless asked for Least Squares.
3. Break-Even Analysis is a high-scoring question. Memorize: $$\text{BEP (Rs.)}=\frac{\text{Total FC}}{\text{CM Ratio}}\text{where}\text{CM Ratio}=\frac{\text{CM}}{\text{Sales}}$$
4. Real-world examples (like Daraz, Ncell) can boost marks if tied to theory.
5. Watch for units:
   • BEP can be in units or Rs. (multiply units by selling price for Rs. BEP).
6. Common Pitfalls:
   • Forgetting to exclude fixed costs when calculating CM.
   • Misapplying variable cost per unit (e.g., using total VC instead of per-unit VC).
7. Diagrams save time: Draw TC = FC + VC graphs to visualize relationships.

Final Note: Mastering this unit is crucial for Unit 2 (CVP Analysis) and Unit 5 (ABC Costing). Practice numerical problems from past TU/PU exams to build speed and accuracy.

In the real world

• Daraz (Nepal’s e-commerce giant) uses variable costing to price delivery fees: Fuel cost per order (Rs. 150–Rs. 300) varies with the number of deliveries, while warehouse rent (fixed cost) remains constant regardless of order volume. This helps Daraz set dynamic delivery charges based on demand.

• NTC (Nepal Telecom) applies fixed cost analysis for its bus routes: The cost of maintaining a bus depot in Kathmandu (e.g., Rs. 500,000/month) does not change with passenger numbers, but fuel costs (variable) increase with more passengers. This helps NTC decide whether to expand routes profitably.

• Nepal Rastra Bank (NRB) uses mixed cost separation for ATM transaction fees: Banks incur a fixed cost for ATM maintenance (e.g., Rs. 200,000/month) plus a variable cost per transaction (e.g., Rs. 20 per withdrawal). The high-low method helps NRB allocate these costs fairly to commercial banks.