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Learning Objectives

Learning Objectives. Determine the number of units that must be sold to break even or to earn a targeted profit. Determine the amount of revenue required to break even or to earn a targeted profit. Apply cost-volume-profit analysis in a multiple-product setting. Learning Objectives (continued).

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Learning Objectives

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  1. Learning Objectives • Determine the number of units that must be sold to break even or to earn a targeted profit. • Determine the amount of revenue required to break even or to earn a targeted profit. • Apply cost-volume-profit analysis in a multiple-product setting.

  2. Learning Objectives (continued) • Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each. • Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis. • Discuss the impact of activity-based costing on cost-volume-profit analysis.

  3. Sample Questions Raised and Answered by CVP Analysis (continued) 1. How many units must be sold (or how much sales revenue must be generated) in order to break even? 2. How many units must be sold to earn a before-tax profit equal to $60,000? A before-tax profit equal to 15 percent of revenues? An after-tax profit of $48,750? 3. Will total profits increase if the unit price is increased by $2 and units sold decrease 15 percent? 4. What is the effect on total profit if advertising expenditures increase by $8,000 and sales increase from 1,600 to 1,750 units?

  4. Sample Questions Raised and Answered by CVP Analysis (continued) 5. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit and sales increase from 1,600 units to 1,900 units? 6. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit, advertising expenditures are increased by $8,000, and sales increased from 1,600 units to 2,300 units? 7. What is the effect on total profit if the sales mix is changed?

  5. CVP: A Short-Term Planning and Analysis Tool Benefits of CVP: • Assists in establishing prices of products. • Assists in analyzing the impact that volume has on short-term profits. • Assists in focusing on the impact that changes in costs (variable and fixed) have on profits. • Assists in analyzing how the mix of products affects profits.

  6. Cost-Volume-Profit Graph Total Revenue Revenue Profit Total Cost Y Loss X Units sold X = Break-even point in units Y = Break-even point in revenue

  7. Simple CVP Example Fixed costs (F) = $40,000 Selling price per unit (P) = $10 Variable cost per unit (V) = $6 Tax rate = 40% 1. What is the break-even point in units? 2. What is the break-even point in dollars?

  8. Simple CVP Example: BEP 1. Let X = break-even point in units Operating income = Sales revenue -Variable expenses - Fixed expenses 0 = $10X -$6X - $40,000 $10X - $6X = $40,000 $4X = $40,000 X = 10,000 units 2. Break-even point in sales dollars is: 10,000 x $10 or $100,000 This can be shown with a variable-costing income statement.

  9. Variable-Costing Income Statement Sales (10,000 x $10) $100,000 Less: Variable costs (10,000 x $6) 60,000 Contribution margin $ 40,000 Less: Fixed costs 40,000 Profit before taxes $0 Less: Income taxes 0 Profit after taxes $ 0 =====

  10. Sales Revenue Approach Alternative approach to solving break-even point in sales dollars: Let X equal break-even sales in dollars Operating income = Sales revenue - Variable expenses - Fixed expenses 0 = X - 0.6X - $40,000 X - 0.6X = $40,000 0.4X = $40,000 X = $100,000 Note: V is the variable cost percentage which is found by: Variable Cost per Unit 6 Selling Price per Unit 10 = 0.6

  11. CVP Example: Targeted Pretax Income What sales in units and dollars are needed to obtain a targeted profit before taxes of $20,000? Let X = break-even point in units Sales $ = $10X Less: Variable costs = 6X Contribution margin $60,000 = $ 4X Less: Fixed costs 40,000 Profit before taxes $20,000 ==== Therefore, $60,000 = $4X 15,000 units = X Sales in dollars is (15,000 x $10) = $150,000. Check this by completing the variable-costing income statement.

  12. CVP Example: Targeted Pretax Income (continued) Sales $150,000 = 15,000 x $10 Less: Variable costs 90,000 = 15,000 x $6 Contribution margin $ 60,000 Less: Fixed costs 40,000 Profit before taxes $ 20,000 ======= It checks!

  13. CVP Analysis: Targeted After-Tax Income What sales in units and dollars are needed to obtain a targeted profit after taxes of $24,000? Let X = break-even point in units Sales $ = $10X Less: Variable costs = 6X Contribution margin $ = $ 4X Less: Fixed costs 40,000 Profit before taxes $ Less income taxes Profit after taxes $24,000 ====== We have the same problem as PPT 9-13 assuming we are able to find the profit before taxes.

  14. CVP Analysis:Targeted After-Tax Income (continued) The Approach: AFTER = Profit after taxes BEFORE = Profit before taxes AFTER = (1 - tax rate) x BEFORE $24,000 = (1 - .4) x BEFORE $24,000/.6 = BEFORE $40,000 = BEFORE

  15. CVP Analysis:Targeted After-Tax Income (continued) Therefore, Sales $ = $10X Less: Variable costs = $ 6X Contribution margin $80,000 = $ 4X Less: Fixed costs 40,000 Profit before taxes $40,000 Less: Income taxes 16,000 = 40% ($40,000) Profit after taxes $24,000 ====== $4X = $80,000 X = $80,000/$4 X = 20,000 units Sales in dollars is (20,000 x $10) or $200,000

  16. CVP Analysis:Targeted After-Tax Income (continued) The income statement below illustrates that $200,000 in sales will give you an after-tax profit of $24,000. Sales $200,000 Less: Variable costs 120,000 Contribution margin $ 80,000 Less: Fixed costs 40,000 Profit before taxes $ 40,000 Less: Income taxes 16,000 Profit after taxes $ 24,000 ======

  17. CVP Analysis: Targeted Pretax Income What sales in dollars is needed to obtain a targeted profit before taxes equal to 20 percent of sales? Let X = sales in dollars Sales $ = 1.0X Less: Variable costs = 0.6X Contribution margin $40,000 + .2X = 0.4X Less: Fixed costs $40,000 Profit before taxes .2X .4X = $40,000 + .2X .2X = $40,000 X = $40,000/.2 X = $200,000

  18. CVP Analysis: Targeted Pretax Income (continued) The following variable-costing income statement can be used to check the solution. Sales $200,000 Less: Variable costs 120,000 = .6 ($200,000) Contribution margin $ 80,000 = .4 ($200,000) Less: Fixed costs 40,000 Profit before taxes $ 40,000 ======= $40,000 is 20% of $200,000. It checks!

  19. CVP Analysis: Targeted After-Tax Income What sales in dollars is needed to obtain a targeted profit after taxes equal to 6 percent of sales? Let X = sales in dollars Sales $ = 1.0X Less: Variable costs = 0.6X Contribution margin $ = 0.4X Less: Fixed costs 40,000 Profit before taxes $ Less: Income taxes Profit after taxes $ .06X =====

  20. CVP Analysis: Targeted After-Tax Income (continued) Use the method from PPT 9-16 AFTER = (1- tax rate) x BEFORE 0.06X = (1 - .4) x BEFORE 0.06X / 0.6 = BEFORE 0.1X = BEFORE Therefore, Sales $ = 1.0X Less: Variable costs = 0.6X Contribution margin $ 40,000 + .1X = 0.4X Less: Fixed costs 40,000 Profit before taxes 0.10X Less: Income taxes 0.04X Profit after taxes 0.06X ====== .4X = 40,000 + .1X .3X = 40,000 X = $40,000/.3 X = $133,333

  21. CVP Analysis:Targeted After-Tax Income(continued) The following income statement checks the solution: Sales $133,333 Less: Variable costs 80,000 = .6 x $133,333 Contribution margin $ 53,333 Less: Fixed costs 40,000 Profit before taxes $ 13,333 Less: Income taxes 5,333 = .4 x $13,333 Profit after taxes $ 8,000 ======= $8,000 is 6% of $133,333. It Checks!

  22. Multiple-Product Example Product P - V = CM x Mix = Total CM A $10 - $6 = $4 x 3 = $12 B 8 - 5 = 3 x 2 = 6 Total CM per package $18 === Total fixed expenses = $180,000

  23. Multiple-Product Example (continued) Break-even point: X = Fixed cost / Unit contribution margin = $180,000 / $18 = 10,000 packages to break even Each package contains 3 units of A and 2 units of B. Therefore, to break even, we need to sell the following units of A and B: A: 3 x 10,000 = 30,000 units B: 2 x 10,000 = 20,000 units

  24. Another Multiple-Product Example Assume the following: Regular Deluxe Total Percent Units sold 400 200 600 ---- Sales price per unit $ 500 $750 ---- ---- Sales $200,000 $150,000 $350,000 100.0% Less: Variable expenses 120,000 60,000 180,000 51.4 Contribution margin $ 80,000 $ 90,000 $170,000 48.6% Less: Fixed expenses 130,000 Net income $ 40,000 ======= 1. What is the break-even point? 2. How much sales-revenue of each product must be generated to earn a before tax profit of $50,000?

  25. Another Multiple-Product Example:BEP BEP = Fixed cost / CM ratio for sales mix = $130,000 / 0.486 = $267,490 for the firm BEP for Regular Model: (400/600) x $267,490 = $178,327 BEP for Deluxe Model: (200/600) x $267,490 = $89,163

  26. Another Multiple-Product Example: Targeted Revenue BEP = (Fixed Costs + Targeted income) / CM ratio per sales mix = ($130,000 + $50,000) / 0.486 = $370,370 for the firm BEP for Regular Model: (400/600) x $370,370 = $246,913 BEP for Deluxe Model: (200/600) x 370,370 = $123,457

  27. Profit-Volume Graph Profit I = (P-V)X-F Slope = P-V Profit loss break-even point UNITS in units -F

  28. The Limitations of CVP Analysis A number of limitations are commonly mentioned with respect to CVP analysis: 1. The analysis assumes a linear revenue function and a linear cost function. 2. The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range. 3. The analysis assumes that what is produced is sold. 4. For multiple-product analysis, the sales mix is assumed to be known. 5. The selling prices and costs are assumed to be known with certainty.

  29. Margin of Safety Assume that a company has the following projected income statement: Sales $100,000 Less: Variable expenses 60,000 Contribution margin $ 40,000 Less: Fixed expenses 30,000 Income before taxes $ 10,000 ======= Break-even point in dollars (R): R = $30,000/.4 = $75,000 Safety margin = $100,000 - $75,000 = $25,000

  30. Degree of Operating Leverage (DOL) DOL = $40,000/$10,000 = 4.0 Now suppose that sales are 25% higher than projected. What is the percentage change in profits? Percentage change in profits = DOL x percentage change in sales Percentage change in profits = 4.0 x 25% = 100%

  31. DOL (continued) Proof: Sales $125,000 Less: Variable expenses 75,000 Contribution margin $ 50,000 Less: Fixed expenses 30,000 Income before taxes $ 20,000 ======

  32. CVP and ABC Assume the following: Sales price per unit $15 Variable cost 5 Fixed costs (conventional) $180,000 Fixed costs (ABC) 100,000 with $80,000 subject to ABC analysis Other Data: Unit Level of Variable Activity Activity Driver Costs Driver Setups $500 100 Inspections 50 600 1. What is the BEP under conventional analysis? 2. What is the BEP under ABC analysis? 3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40?

  33. CVP and ABC (continued) 1. Break-even units (conventional analysis) BEP = $180,000/$10 = 18,000 units 2. Break-even units (ABC analysis) BEP = [$100,000 + (100 x $500) + (600 x $50)]/$10 = 18,000 units 3. BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10 = 16,900 units What implications does ABC have for improving performance?

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