Cost-Volume-Profit Analysis Study Notes

Managerial Accounting: Cost-Volume-Profit Analysis

Chapter Objectives

  • By the end of this chapter, you should be able to:

    • Obj. 1: Classify costs as variable costs, fixed costs, or mixed costs.

    • Obj. 2: Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.

    • Obj. 3: Determine the break-even point and sales necessary to achieve a target profit.

    • Obj. 4: Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit.

    • Obj. 5: Compute the break-even point for a company selling more than one product, the operating leverage, and the margin of safety.

    • Obj. 6: Use cost-volume-profit analysis for decision making in a service business.

Cost Behavior (LO1)

  • Cost behavior refers to how a cost changes as a related activity changes.

  • Understanding cost behavior involves:

    • Identifying the activities that cause costs to change, known as activity bases (or activity drivers).

    • Specifying the relevant range of activity over which the changes in cost are of interest.

  • Costs are generally classified as:

    • Variable Costs: Costs that vary in proportion to changes in the activity base.

    • Fixed Costs: Costs that remain the same in total dollar amount as the activity base changes.

    • Mixed Costs: Costs that have characteristics of both variable and fixed costs.

Variable Costs

  • For example, consider Jason Sound Inc. produces stereo systems:

    • Model JS-12 production relevant range: 5,000 to 30,000 units.

    • Direct Materials Costs:

    • 5,000 units: $10/unit, Total: $50,000

    • 10,000 units: $10/unit, Total: $100,000

    • 15,000 units: $10/unit, Total: $150,000

    • 20,000 units: $10/unit, Total: $200,000

    • 25,000 units: $10/unit, Total: $250,000

    • 30,000 units: $10/unit, Total: $300,000

  • Key Characteristics:

    • Cost per unit remains constant despite changes in activity base.

    • Total cost changes in proportion to changes in activity base.

  • Exhibit 1 - Variable Cost Graphs:

    • Total Variable Cost varies with units produced.

    • Unit Variable Cost remains constant across production levels.

Fixed Costs

  • Fixed costs are costs that remain the same in total dollar amount despite changes in the activity base.

  • Example of Minton Inc., producing perfume:

    • Relevant range: 50,000 to 300,000 bottles.

    • Total Salary for Jane Sovissi:

    • 50,000 bottles: $75,000, $1.50/bottle

    • 100,000 bottles: $75,000, $0.75/bottle

    • 150,000 bottles: $75,000, $0.50/bottle

    • 200,000 bottles: $75,000, $0.375/bottle

    • 250,000 bottles: $75,000, $0.300/bottle

    • 300,000 bottles: $75,000, $0.250/bottle

  • Key Characteristics:

    • Fixed cost per unit decreases as units produced increase due to spreading fixed costs over more units.

  • Exhibit 3 - Fixed Cost Graphs:

    • Total Fixed Cost remains constant while Unit Fixed Cost varies inversely with the production level.

Mixed Costs

  • Mixed Costs possess characteristics of both variable and fixed costs, sometimes referred to as semi-variable or semi-fixed costs.

  • Example from Simpson Inc., which manufactures sails:

    • Rental Charge: $15,000 per year + $1 for each hour used beyond 10,000 hours.

    • Rental charges:

    • 8,000 hours: $15,000

    • 12,000 hours: $17,000

    • 20,000 hours: $25,000

    • 40,000 hours: $45,000

  • Exhibit 5 - Mixed Costs illustrates total rental costs and their behavior based on hours used.

The High-Low Method

  • The High-Low Method is a cost estimation technique that separates mixed costs into their fixed and variable components using the highest and lowest activity levels.

  • For example, Kason Inc. maintenance costs for units produced:

    • Data:

    • June: 1,000 units, $45,550

    • July: 1,500 units, $52,000

    • August: 2,100 units, $61,500

    • September: 1,800 units, $57,500

    • October: 750 units, $41,250

  • Identifying High and Low:

    • Highest: 2,100 units - $61,500

    • Lowest: 750 units - $41,250

    • Calculate total cost difference: $20,250.

    • Variable cost per unit estimate:
      extVariableCostperUnit=rac20,2501,350=15ext{Variable Cost per Unit} = rac{20,250}{1,350} = 15

  • Estimate Fixed Costs:

    • Use formula: extFixedCost=extTotalCosts−(extVariableCostperUnitimesextUnitsProduced)ext{Fixed Cost} = ext{Total Costs} - ( ext{Variable Cost per Unit} imes ext{Units Produced})

    • Total Cost formula links variable and fixed costs to total output:

    • extTotalCost=(extVariableCostperUnitimesextUnitsProduced)+extFixedCostsext{Total Cost} = ( ext{Variable Cost per Unit} imes ext{Units Produced}) + ext{Fixed Costs} note that at the highest or lowest levels, fixed costs remain constant.

Cost-Volume-Profit Relationships (LO2)

  • Cost-Volume-Profit (CVP) analysis is a management tool for evaluating the relationships among selling prices, sales and production volumes, costs, expenses, and profits, serving as a basis for decision making.

  • Uses of CVP analysis include:

    • Analyzing effects of selling price changes on profits.

    • Analyzing effects of cost changes on profits.

    • Analyzing effects of changes in volume on profits.

    • Setting selling prices, selecting product mixes, and determining marketing strategies.

Contribution Margin

  • The Contribution Margin is calculated as:
    extContributionMargin=extSales−extVariableCostsext{Contribution Margin} = ext{Sales} - ext{Variable Costs}

  • It represents the revenue available to cover fixed costs and generate profit.

  • Example from Lambert Inc.:

    • Sales: 50,000 units at $20/unit, variable costs at $12/unit, and fixed costs of $300,000.

  • Contribution margin using sales data:

    • ext{Sales (50,000 units × $20)} = 1,000,000

    • ext{Variable costs (50,000 units × $12)} = 600,000

    • Resulting contribution margin: 400,000400,000

Contribution Margin Ratio

  • The Contribution Margin Ratio indicates the percentage of each sales dollar contributing to fixed costs and income.

  • extContributionMarginRatio=racextContributionMarginextSalesext{Contribution Margin Ratio} = rac{ ext{Contribution Margin}}{ ext{Sales}}

  • Example calculation from Lambert Inc. shows a ratio of 40%:

    • With sales increasing from $1,000,000 to $1,080,000, operating income increases aligned with the contribution margin ratio.

Unit Contribution Margin

  • The Unit Contribution Margin is calculated as:
    extUnitContributionMargin=extSalesPriceperUnit−extVariableCostperUnitext{Unit Contribution Margin} = ext{Sales Price per Unit} - ext{Variable Cost per Unit}

  • Can be utilized to determine changes in operating income from unit sales changes. For Lambert Inc.:

    • At 50,000 units sold, profit is $100,000, increasing to $220,000 upon selling 65,000 units.

Mathematical Approach to CVP Analysis (LO3)

  • The mathematical approach determines required sales for break-even or target profits using equations.

  • The break-even point is identified where revenues equal expenses:

    • extRevenues=extCostsext{Revenues} = ext{Costs}

  • Example of Baker Corporation:

    • Fixed costs: $90,000

    • Unit selling price: $25

    • Unit variable cost: $15, yielding a contribution margin of $10.

    • Break-even point calculation as follows: (extBreak−evenpointinunits=rac90,00010=9,000units).( ext{Break-even point in units} = rac{90,000}{10} = 9,000 units).

Effect of Changes in Costs

  • Fixed costs, variable costs, and selling prices impact the break-even point:

    • Increases in fixed costs raise the break-even point while reductions lower it.

    • Example of Bishop Co. evaluates a $100,000 advertising budget:

    • Pre-advertising break-even: 30,000 units;

    • Post-advertising break-even: 35,000 units.

Effect of Changes in Selling Price

  • An increase in the selling price impacts the contribution margin, thus affecting the break-even volume.

  • For Graham Co., shifting price from $50 to $60 changes break-even from 30,000 to 20,000 units.

Target Profit Analysis

  • To calculate sales to achieve a target profit, modify the break-even equation:

    • Example from Waltham Co. with a target profit of $100,000 indicating sales of 10,000 units to meet both fixed costs and target profit.

Cost-Volume-Profit Chart

  • A Cost-Volume-Profit chart displays sales, costs, and profits for varying sales volumes.

  • Chart construction involves:

    • Establishing sales volume and dollar amounts for total sales and costs.

    • Identifying the break-even point via the intersection of total sales and total cost lines.

    • Analyzing changes via adjustments in unit selling prices or costs through graphical representations.

Profit-Volume Chart

  • The profit-volume chart illustrates the difference between total sales and total costs to reflect profits or losses at different sales levels.

  • Constructing involves plotting maximum losses and profits, showing overall performance at various unit sales levels.

Special Cost-Volume-Profit Relationships (LO5)

  • Companies with multiple products can perform CVP analysis considering the sales mix.

  • Example from Cascade Company with products A and B exhibiting a sales mix of 80-20%, affecting break-even quantities and product profitability.

Operating Leverage

  • Operating leverage assesses the impact of contribution margin on operating income, especially for companies with high fixed costs. The operating leverage effect can be measured by:

    • extPercentageChangeinOperatingIncome=extPercentageChangeinSalesimesextOperatingLeverageext{Percentage Change in Operating Income} = ext{Percentage Change in Sales} imes ext{Operating Leverage}

Margin of Safety

  • Margin of Safety (MOS) is the potential drop in sales before incurring losses, expressed in dollars, units, or percentages:

    • Example calculation shows MOS for a sales of $250,000 against a break-even of $200,000, yielding a margin of safety of $50,000 or 20%.

Analysis for Decision Making: CVP Analysis for Service Companies (LO6)

  • The break-even analysis is as crucial for service companies as for manufacturers, regulated by customer metrics.

  • Sample applications: evaluating break-even for courses, flights, healthcare, and services reflecting customer dynamics.

Summary

  • Skills learned:

    • Classifying costs as variable, fixed, or mixed.

    • Computing contribution margin metrics.

    • Identifying break-even points and target profit sales.

    • Utilizing charts for visualizing cost-volume relationships and their implications for decision-making.