Cost Behavior and Cost-Volume-Profit Analysis

Overview of Cost Behavior Analysis

• Definition: Cost behavior analysis is the internal study of how specific costs respond to changes in the level of business activity. Understanding these responses is critical for effective management.

• General Principle: Some costs vary directly with activity, while others remain constant regardless of the volume.

• Purpose for Management:

  • Helps in planning operations.

  • Assists in deciding between alternative courses of action.

  • Applies to all types of businesses and entities (retail, service, manufacturing, etc.).

• Activity Index: The starting point for analysis is measuring key business activities. This index identifies the activity that causes changes in cost behavior and allows costs to be categorized as variable, fixed, or mixed.

  • Examples of Activity Bases:

    • Retail: Sales dollars.

    • Trucking: Miles driven.

    • Hotel: Room occupancy.

    • Dance Studio: Number of classes taught.

  • Volume Index: Changes in the level or volume of activity must be correlated with changes in costs to be a valid index.

Variable Costs

• Definition: Costs that vary in total directly and proportionately with changes in the activity level.

  • Total Behavior: If activity level increases by $10\%$, total variable costs increase by $10\%$. If activity decreases by $25\%$, total variable costs decrease by $25\%$.

  • Unit Behavior: Variable costs remain the same per unit at every level of activity.

• Illustration (Damon Company):

  • Example: Manufacturing tablet computers using a camera that costs $10$ per unit.

  • Total Cost Behavior: At $2,000$ tablets, total cost is $20,000$ ($2,000 \times 10$). At $10,000$ tablets, total cost is $100,000$ ($10,000 \times 10$).

  • Unit Cost Behavior: The camera cost remains exactly $10$ per unit whether producing $2,000$ or $10,000$ tablets.

Fixed Costs

• Definition: Costs that remain the same in total regardless of changes in the activity level, provided the activity remains within a relevant range.

  • Total Behavior: Fixed costs are constant in total regardless of volume increases or decreases.

  • Unit Behavior: Fixed cost per unit varies inversely with activity. As volume increases, the fixed cost per unit declines. As volume decreases, the fixed cost per unit increases.

• Examples:

  • Property taxes.

  • Insurance.

  • Rent.

  • Depreciation on buildings and equipment.

• Illustration (Damon Company Facility Lease):

  • Example: Damon Company leases facility for $10,000$ per month.

  • Total Cost: Remains exactly $10,000$ every month whether they produce $0$ or $10,000$ tablets.

  • Unit Cost: At $2,000$ units, rent per unit is $5$ ($10,000 \div 2,000$). At $10,000$ units, rent per unit drops to $1$ ($10,000 \div 10,000$).

Cost-Volume-Profit (CVP) Analysis

• Definition: The study of the effects of changes in costs and volume on a company’s profits.

• Management Relevance: It is a critical factor for:

  • Setting selling prices.

  • Determining the best product mix.

  • Maximizing the use of production facilities.

• Basic Components:

  • Sales volume or level of activity.

  • Unit selling prices.

  • Variable costs per unit (e.g., raw materials, labor).

  • Total fixed costs (e.g., utilities, taxes, depreciation).

  • Sales mix (the relative percentage of each product sold if multiple products exist).

• CVP Assumptions:

  • Cost and revenue behavior is linear throughout the relevant range.

  • Costs can be accurately classified as either variable or fixed.

  • Changes in activity are the only factors that affect costs.

  • All units produced are sold (no inventory fluctuation).

  • When multiple products are sold, the sales mix remains constant.

The CVP Income Statement

• Purpose: An internal statement that classifies costs and expenses as fixed or variable.

• Net Income: It reports the same net income as a traditional income statement but provides more detail for decision-making.

• Contribution Margin (CM): The amount of revenue remaining after deducting variable costs. It is available to cover fixed costs and contribute to net income.

• Vargo Video Case Data:

  • Selling price per unit: $500$

  • Variable cost per unit: $300$

  • Total monthly fixed costs: $200,000$

  • Units sold: $1,600$

• Vargo Video Income Statement Components:

  • Total Sales ($1,600 \times 500$): $800,000$

  • Total Variable Costs ($1,600 \times 300$): $480,000$

  • Total Contribution Margin: $320,000$

  • Total Fixed Costs: $200,000$

  • Net Income: $120,000$

• Contribution Margin Formulas:

  • Unit Contribution Margin: $\text{Unit Selling Price} - \text{Unit Variable Costs}$

    • Vargo Video Example: $500 - 300 = 200$

  • Contribution Margin Ratio: $\text{Unit Contribution Margin} \div \text{Unit Selling Price}$

    • Vargo Video Example: $200 \div 500 = 40\%$

  • Effect of Sales Increases: If Vargo Video increases sales by $100,000$ ($200$ units), net income increases by $40,000$ ($100,000 \times 40\%$ ).

Break-Even Analysis

• Definition: The level of activity at which total revenues equal total costs (Variable + Fixed), resulting in zero net income.

• CVP Mathematical Equation:

  • $\text{Sales} = \text{Variable Costs} + \text{Fixed Costs} + \text{Net Income}$

  • Example (Lombardi Company): Unit Price = $400$, Unit Variable Cost = $240$, Fixed Costs = $180,000$.

  • Equation: $400Q - 240Q - 180,000 = 0$

  • $160Q = 180,000$

  • $Q = 1,125 \text{ units}$

• Contribution Margin Technique:

  • Break-Even Point in Units: $\frac{\text{Fixed Costs}}{\text{Unit Contribution Margin}}$

    • Vargo Video: $200,000 \div 200 = 1,000 \text{ units}$

  • Break-Even Point in Dollars: $\frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}}$

    • Vargo Video: $200,000 \div 0.40 = 500,000$

Target Net Income and Margin of Safety

• Target Net Income: The level of sales necessary to achieve a specific profit goal.

  • Required Sales in Units: $\frac{\text{Fixed Costs} + \text{Target Net Income}}{\text{Unit Contribution Margin}}$

  • Required Sales in Dollars: $\frac{\text{Fixed Costs} + \text{Target Net Income}}{\text{Contribution Margin Ratio}}$

• Margin of Safety: Measures the "cushion" provided by actual sales relative to break-even sales.

  • Margin of Safety in Dollars: $\text{Actual (Expected) Sales} - \text{Break-even Sales}$

  • Margin of Safety Ratio: $\frac{\text{Margin of Safety in Dollars}}{\text{Actual (Expected) Sales}}$

  • Management Interpretation: The higher the dollars or percentage, the lower the risk of falling into a net loss.

Questions & Discussion

• Question: What are variable costs?

  • Answer: Costs that vary in total directly and proportionately with activity changes and remain the same per unit at every level.

• Question: Which of the following is not involved in CVP analysis? (Sales mix, unit selling prices, fixed costs per unit, or volume).

  • Answer: Fixed costs per unit (because total fixed costs are used, and they remain constant in total, not per unit).

• Question: Gossen Company plans to sell $200,000$ units at $4$ each with a CM ratio of $25\%$. If they break even at this level, what are the fixed costs?

  • Answer: $200,000$ ($200,000 \times 4 = 800,000$ total sales; $800,000 \times 0.25 = 200,000$ Contribution Margin, which must equal Fixed Costs at break-even).

• Question: Marshall Company had actual sales of $600,000$ and break-even sales of $420,000$. What is the margin of safety ratio?

  • Answer: $30\%$ ($600,000 - 420,000 = 180,000$; $180,000 \div 600,000 = 0.30$).

Comprehensive Practice: Zootsuit Inc.

• Scenario Data: Bag Sale Price = $56$, Variable Cost = $42$, Fixed Costs = $320,000$, Actual Sales = $1,382,400$.

• a) Break-even in dollars:

  • Unit CM = $56 - 42 = 14$

  • CM Ratio = $14 \div 56 = 25\%$

  • BE Dollars = $320,000 \div 0.25 = 1,280,000$

• b) Margin of Safety:

  • Dollars = $1,382,400 - 1,280,000 = 102,400$

  • Ratio = $102,400 \div 1,382,400 = 7.4\%$

• c) Sales for Target Net Income of $410,000$:

  • Required Dollars = $(320,000 + 410,000) \div 0.25 = 730,000 \div 0.25 = 2,920,000$