Cost-Volume-Profit Analysis Chapter 4

Chapter 4: Cost-Volume-Profit Relationships

• Cost-volume-profit (CVP) analysis is a powerful tool used by managers to understand the relationship between cost, volume, and profit. It focuses on the interplay of five key elements: product prices, activity level, per-unit variable costs, total fixed costs, and product mix.

Learning Objectives Part 1

• Explain how changes in activity affect contribution margin and operating income.
• Prepare and interpret a cost-volume-profit graph.
• Calculate the contribution margin ratio and variable expense ratio. Use the contribution margin ratio to calculate changes in contribution margin and operating income resulting from changes in sales volume.
• Show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume.

Learning Objectives Part 2

• Compute the break-even point in unit sales and sales dollars.
• Determine the level of sales needed to achieve a desired target profit.
• Compute the margin of safety and explain its significance.
• Explain cost structure, compute the degree of operating leverage at a particular sales level, and explain how operating leverage can be used to predict changes in operating income.

Learning Objectives Part 3

• Compute the break-even point for a multi-product company and explain the effect of changes in sales mix on contribution margin and the break-even point.
• Conduct a cost-volume-profit analysis with uncertainty (Online Appendix 4A).

Cost-Volume-Profit Relationship Interactions

• CVP analysis helps managers understand the interaction between cost, volume, and profit.
• The key elements are product prices, activity level, per-unit variable costs, total fixed costs, and product mix.

Basics of Cost-Volume-Profit Analysis

• The contribution income statement helps managers assess the impact of changes in selling price, cost, or volume on profits.
• Contribution margin (CM) is the amount remaining from sales revenue after variable expenses are deducted.

Contribution Margin (CM)

• Sales, variable expenses, and contribution margin can be expressed on a per-unit basis.
• If an additional unit is sold, $200 additional CM would be generated.

Contribution Margin Ratio

• The contribution margin ratio is calculated by dividing the total contribution margin by total sales.

  • CM ratio = Total contribution margin / total sales

• For Example Company, the ratio is 40%.

• Each $1.00 increase in sales results in a $0.40 increase in total contribution margin.

The Contribution Approach

• Each month, $80,000 in total contribution margin must be generated to break even.
• Any additional contribution margin becomes operating income.

The Contribution Approach 2

• If 400 units are sold, the company is operating at the break-even point.

The Contribution Approach 3

• Selling one more unit beyond the break-even point increases net operating income by $200.

The Contribution Approach 4

• It is not necessary to prepare an income statement for every sales level.
• Simply multiply the number of units sold above break-even by the contribution margin per unit to estimate profits at different sales levels.

CVP Relationships in Graphic Form

• Relationships among revenue, cost, profit, and volume can be expressed graphically using a Cost-Volume-Profit graph.

CVP Graph 1

• In a CVP graph, unit volume is shown on the horizontal (X) axis and dollars are shown on the vertical (Y) axis.

CVP Graph 2

• A CVP graph shows total sales, total expenses, and fixed expenses.

CVP Graph 3

• The CVP graph shows the break-even point, profit area, and the loss area.

Contribution Margin Ratio 1

• The contribution margin ratio is calculated by dividing the total contribution margin by the total sales.
• For Example Company, the ratio is 40%

Contribution Margin Ratio 2

• In terms of units, the contribution margin ratio is the unit contribution margin divided by the unit selling price.
• Example Company's ratio is 40%

Contribution Margin Ratio 3

• A $50,000 increase in sales leads to a $20,000 increase in contribution margin. [The formula is: (Change in CM) = (CM ratio) x (Change in Sales)]

Contribution Margin Ratio 4

• Changes in sales revenue can be calculated using the formula (Change in CM) = (CM Ratio) x (Change in Sales)

Quick Check (Example Questions)

• Questions focusing on calculating CM ratios, break-even points, and margins of safety.

Break-Even Analysis 1

• Break-even analysis is a way to determine if a company will lose money or make a profit at varying sales levels.

Break-Even Analysis 2

• The contribution format income statement can be expressed mathematically in equation form.
  • Profit = (Sales - Variable Expenses) - Fixed Expenses

Break-Even Analysis 3

• The above formula can be simplified to Profit = (Contribution Margin x Units Sold) - Fixed Expenses

Break-Even Analysis 4

• Break-even units sold = (Fixed Expenses) / (Unit CM)
• Break-even sales in dollars = (Fixed Expenses) / (CM ratio)

Break-Even Analysis 5

• Example Company's income statement at 500 units shows operating income of $20,000,
• Calculating break-even point in units and dollars using provided data for the company.

Break-Even Analysis 6

• Break-even point (units) = (Fixed Expenses) / (Unit CM)
• Break-even point (dollars) = (Fixed Expenses) / (CM Ratio)

Target Operating Profit Analysis 1

• CVP formulas can determine the sales volume or dollars needed to achieve a target operating profit.
• Assume that Example Company wants to earn a profit of $100,000 by knowing the unit sales needed.

Target Operating Profit Analysis 2

• Calculating the number of units needed to be sold to achieve a target operating profit.
• [Units to achieve target profit] = [Fixed Costs + Target Profit] / [Unit Contribution Margin]

Target Operating Profit Analysis 3

• Calculating target sales dollars to achieve a target profit using the formula [Target Sales Dollars] = [Fixed Costs + Target Profit]/[CM Ratio]

After-Tax Analysis 1

• For-profit companies pay corporate income tax on profits.
• In general, operating profit after tax can be computed as a fixed percentage of income before tax.

After-Tax Analysis 2

• Profit after tax = Before tax profit – Tax.
• Before tax profit = Profit after tax / (1 − tax rate)

The Margin of Safety 1

• Margin of safety is the excess of budgeted (or actual) sales over the break-even sales.
• Margin of safety = Total sales – Break-even sales.

The Margin of Safety 2

• Margin of safety percentage = Margin of safety / Total sales

The Margin of Safety 3

• Expressing margin of safety as a percentage from the relationship ($50,000 / $250,000 = 20%)

The Margin of Safety 4

• Determining margin of safety in terms of units sold, given a sales price per unit and total margin of safety in dollars

Cost Structure and Profit Stability 1

• Cost structure refers to the proportion of fixed and variable costs.
• Managers have choices in determining cost structure.

Cost Structure and Profit Stability 2

• High fixed costs lead to higher income in good years but lower in bad years.
• Low fixed costs lead to more income stability in good and bad years.

Operating Leverage 1

• Operating leverage measures the sensitivity of net operating income to percentage changes in sales.
• Degree of operating leverage = Contribution Margin / Operating Income
• % change in operating income = Degree of operating leverage x % change in sales

Operating Leverage 2

• Example calculation of operating leverage for Example Company. [Example: $100,000 (Operating income) / $20,000 (Net operating income)= 5 ]

Operating Leverage 3

• If sales increase by 10%, net operating income will increase by 50% (at 5 times operating leverage).

Operating Leverage 4

• Showing the impact of a sales increase on the net operating income. For 10% increase in sales, Net Operating Income increases by 50% (at 5 times operating leverage).

Assumptions of CVP Analysis

• Selling prices are constant.
• Costs are linear.
• Variable costs per unit are constant.
• Fixed costs are constant in total.
• Sales mix is constant.
• In manufacturing companies, inventories do not change.

End of Chapter Summary Part 1

• Cost-volume-profit (CVP) analysis is based on a simple model of how contribution margin (CM) and operating income respond to changes in selling prices, costs, and volume.
• A CVP graph graphically displays the relationships between sales volume in units and fixed/variable expenses, total expenses, total sales, and profits.

End of Chapter Summary Part 2

• The CM ratio (contribution margin ratio) is used to estimate the effect of a change in total sales on operating income.
• The break-even point is the level of sales at which zero profits occur.
• The margin of safety is the amount by which current sales exceed break-even sales.

End of Chapter Summary Part 3

• The degree of operating leverage measures how much a percentage change in sales affects the company's operating income.
• Companies with a higher degree of operating leverage are more sensitive to sales changes.
• Profits of multiproduct companies are influenced by their sales mix.

Cost-Volume-Profit Analysis with Uncertainty (Appendix 4A)

• Cost-volume-profit analysis is used to assess future possibilities under various alternatives and management can use data for various alternatives and relevant decision trees in the analysis.
• Subjective probabilities can be used to model what a manager believes will occur, determining the probability for different possible alternatives.
• This information can be used to estimate expected future profits.

Explore the essential concepts of Cost-Volume-Profit (CVP) relationships in this quiz. Learn how changes in activity levels affect contribution margins and operating incomes, and master the calculations necessary for effective financial decision-making. This quiz will also cover graph interpretations and break-even analysis.