Cost-Volume-Profit Analysis
Learning Objective 1 <ul><li>Understand the assumptions </li></ul><ul><li>underlying cost-volume-profit </li></ul><ul><li>...
Cost-Volume-Profit Assumptions and Terminology 1. Changes in the level of revenues and costs arise only because of changes...
Cost-Volume-Profit Assumptions and Terminology 3. When graphed, the behavior of total revenues and total costs is linear (...
Cost-Volume-Profit Assumptions and Terminology 5. The analysis either covers a single product or assumes that the sales mi...
Cost-Volume-Profit Assumptions and Terminology Operating income = Total revenues from operations –  Cost of goods sold and...
Learning Objective 2 <ul><li>Explain the features </li></ul><ul><li>of CVP analysis. </li></ul>
Essentials of Cost-Volume-Profit (CVP) Analysis Example Assume that the Pants Shop can purchase pants for $32 from a local...
Essentials of Cost-Volume-Profit (CVP) Analysis Example How much revenue will the business receive if 2,500 units are sold...
Essentials of Cost-Volume-Profit (CVP) Analysis Example What is the contribution margin per unit? $70 – $42 = $28 contribu...
Essentials of Cost-Volume-Profit (CVP) Analysis Example Contribution margin percentage (contribution margin ratio) is the ...
Essentials of Cost-Volume-Profit (CVP) Analysis Example If the business sells 3,000 pairs of pants, revenues will be $210,...
Learning Objective 3 <ul><li>Determine the breakeven point </li></ul><ul><li>and output level needed to achieve </li></ul>...
Breakeven Point Sales Variable expenses Fixed expenses – = Total revenues = Total costs
Abbreviations SP =  Selling  price VCU = Variable cost per unit CMU = Contribution margin per unit CM% = Contribution marg...
Abbreviations Q = Quantity of output units sold (and manufactured) OI = Operating income TOI = Target operating income TNI...
Equation Method $70Q – $42Q – $84,000 = 0 $28Q = $84,000 Q = $84,000 ÷ $28 = 3,000 units Let Q = number of units to be sol...
Contribution Margin Method $84,000 ÷ $28 = 3,000 units $84,000 ÷ 40% = $210,000
Graph Method Revenue Total costs Breakeven Fixed costs
Target Operating Income (Fixed costs + Target operating income) divided either by Contribution margin percentage or Contri...
Target Operating Income Assume that management wants to have an operating income of $14,000. How many pairs of pants must ...
Learning Objective 4 <ul><li>Understand how income </li></ul><ul><li>taxes affect CVP analysis. </li></ul>
Target Net Income and Income Taxes Example Management would like to earn an after tax income of $35,711. The tax rate is 3...
Target Net Income and Income Taxes Example How many units must be sold? Revenues – Variable costs – Fixed costs = Target n...
Target Net Income and Income Taxes Example Proof: Revenues: 4,822  ×  $70 $337,540 Variable costs: 4,822  ×  $42   202,524...
Learning Objective 5 <ul><li>Explain CVP analysis </li></ul><ul><li>in decision making and </li></ul><ul><li>how sensitivi...
Using CVP Analysis Example Suppose the management anticipates selling 3,200 pairs of pants. Management is considering an a...
Using CVP Analysis Example 3,200 pairs of pants sold with no advertising: Contribution margin $89,600 Fixed costs   84,000...
Using CVP Analysis Example Instead of advertising, management is considering reducing the selling price to $61 per pair of...
Using CVP Analysis Example 3,200 pairs of pants sold with no change in the selling price: Operating income = $5,600 4,500 ...
Sensitivity Analysis and Uncertainty Example Assume that the Pants Shop can sell 4,000 pairs of pants. Fixed costs are $84...
Sensitivity Analysis and Uncertainty Example To satisfy a demand for 4,000 pairs, management must acquire additional space...
Sensitivity Analysis and Uncertainty Example Operating income at $245,000 revenues with existing space = ($245,000  ×  .40...
Sensitivity Analysis and Uncertainty Example Operating income at $280,000 revenues with additional space = ($280,000  ×  ....
Learning Objective 6 <ul><li>Use CVP analysis to plan  </li></ul><ul><li>fixed and variable costs. </li></ul>
Alternative Fixed/Variable Cost Structures Example What is the new contribution margin? Decrease the price they charge fro...
Alternative Fixed/Variable Cost Structures Example $70 – ($25 + $10) = $35 Contribution margin increases from $28 to $35. ...
Alternative Fixed/Variable Cost Structures Example Management questions what sales volume would yield an identical operati...
Alternative Fixed/Variable Cost Structures Example Cost with existing arrangement = Cost with new arrangement .60x + 84,00...
Operating Leverage Operating leverage describes the effects that fixed costs have on changes in operating income as change...
Operating Leverage Example Degree of operating leverage = Contribution margin ÷ Operating income What is the degree of ope...
Operating Leverage Example $98,000 contribution margin – $84,000 fixed costs = $14,000 operating income $98,000 ÷ $14,000 ...
Operating Leverage Example $122,500 contribution margin –  $114,000 fixed costs = $8,500 $122,500 ÷ $8,500 = 14.4 The degr...
Learning Objective 7 <ul><li>Apply CVP analysis to a company </li></ul><ul><li>producing different products. </li></ul>
Effects of Sales Mix on Income Pants Shop Example  Management expects to sell 2 shirts at $20 each for every pair of pants...
Effects of Sales Mix on Income What is the contribution margin of the mix? Contribution margin per shirt: $20 – $9 = $11 $...
Effects of Sales Mix on Income $84,000 fixed costs ÷ $50 = 1,680 packages 1,680  ×  2  = 3,360 shirts 1,680  ×  1  =  1,68...
Effects of Sales Mix on Income What is the breakeven in dollars? 3,360 shirts  ×  $20 = $  67,200 1,680 pairs of pants  × ...
Effects of Sales Mix on Income What is the weighted-average budgeted  contribution margin? Pants: 1  ×  $28 + Shirts: 2  ×...
Effects of Sales Mix on Income The breakeven point for the two products is: $84,000 ÷ $16.667 = 5,040 units   5,040  ×  1/...
Effects of Sales Mix on Income Sales mix can be stated in sales dollars:   Pants   Shirts Sales price $70 $40 Variable cos...
Effects of Sales Mix on Income Assume the sales mix in dollars is 63.6% pants and 36.4% shirts. Weighted contribution woul...
Effects of Sales Mix on Income Breakeven sales dollars is $84,000 ÷ 45.46% = $184,778 (rounding). $184,778  ×  63.6% = $11...
Learning Objective 8 <ul><li>Adapt CVP analysis to situations  </li></ul><ul><li>in which a product has more </li></ul><ul...
Multiple Cost Drivers Example Suppose that the business will incur an additional cost of $10 for preparing documents assoc...
Multiple Cost Drivers Example Revenues: 3,500  ×  $70 $245,000 Variable costs: Pants: 3,500  ×  $42 147,000 Documents: 100...
Multiple Cost Drivers Would the operating income of the Pants Shop be lower or higher if the business sells pants to more ...
Learning Objective 9 <ul><li>Distinguish between </li></ul><ul><li>contribution margin </li></ul><ul><li>and gross margin....
Contribution Margin versus Gross Margin Contribution income statement emphasizes contribution margin. Financial accounting...
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Cost volume-profit analysis

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Cost volume-profit analysis

  1. 1. Cost-Volume-Profit Analysis
  2. 2. Learning Objective 1 <ul><li>Understand the assumptions </li></ul><ul><li>underlying cost-volume-profit </li></ul><ul><li>(CVP) analysis. </li></ul>
  3. 3. Cost-Volume-Profit Assumptions and Terminology 1. Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold. 2. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.
  4. 4. Cost-Volume-Profit Assumptions and Terminology 3. When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range (and time period). 4. The unit selling price, unit variable costs, and fixed costs are known and constant.
  5. 5. Cost-Volume-Profit Assumptions and Terminology 5. The analysis either covers a single product or assumes that the sales mix when multiple products are sold will remain constant as the level of total units sold changes. 6. All revenues and costs can be added and compared without taking into account the time value of money.
  6. 6. Cost-Volume-Profit Assumptions and Terminology Operating income = Total revenues from operations – Cost of goods sold and operating costs (excluding income taxes) Net income = Operating income – Income taxes
  7. 7. Learning Objective 2 <ul><li>Explain the features </li></ul><ul><li>of CVP analysis. </li></ul>
  8. 8. Essentials of Cost-Volume-Profit (CVP) Analysis Example Assume that the Pants Shop can purchase pants for $32 from a local factory; other variable costs amount to $10 per unit. The local factory allows the Pants Shop to return all unsold pants and receive a full $32 refund per pair of pants within one year. The average selling price per pair of pants is $70 and total fixed costs amount to $84,000.
  9. 9. Essentials of Cost-Volume-Profit (CVP) Analysis Example How much revenue will the business receive if 2,500 units are sold? 2,500 × $70 = $175,000 How much variable costs will the business incur? 2,500 × $42 = $105,000 $175,000 – 105,000 – 84,000 = ($14,000)
  10. 10. Essentials of Cost-Volume-Profit (CVP) Analysis Example What is the contribution margin per unit? $70 – $42 = $28 contribution margin per unit What is the total contribution margin when 2,500 pairs of pants are sold? 2,500 × $28 = $70,000
  11. 11. Essentials of Cost-Volume-Profit (CVP) Analysis Example Contribution margin percentage (contribution margin ratio) is the contribution margin per unit divided by the selling price. What is the contribution margin percentage? $28 ÷ $70 = 40%
  12. 12. Essentials of Cost-Volume-Profit (CVP) Analysis Example If the business sells 3,000 pairs of pants, revenues will be $210,000 and contribution margin would equal 40% × $210,000 = $84,000.
  13. 13. Learning Objective 3 <ul><li>Determine the breakeven point </li></ul><ul><li>and output level needed to achieve </li></ul><ul><li>a target operating income using </li></ul><ul><li>the equation, contribution margin, </li></ul><ul><li>and graph methods. </li></ul>
  14. 14. Breakeven Point Sales Variable expenses Fixed expenses – = Total revenues = Total costs
  15. 15. Abbreviations SP = Selling price VCU = Variable cost per unit CMU = Contribution margin per unit CM% = Contribution margin percentage FC = Fixed costs
  16. 16. Abbreviations Q = Quantity of output units sold (and manufactured) OI = Operating income TOI = Target operating income TNI = Target net income
  17. 17. Equation Method $70Q – $42Q – $84,000 = 0 $28Q = $84,000 Q = $84,000 ÷ $28 = 3,000 units Let Q = number of units to be sold to break even (Selling price × Quantity sold) – (Variable unit cost × Quantity sold) – Fixed costs = Operating income
  18. 18. Contribution Margin Method $84,000 ÷ $28 = 3,000 units $84,000 ÷ 40% = $210,000
  19. 19. Graph Method Revenue Total costs Breakeven Fixed costs
  20. 20. Target Operating Income (Fixed costs + Target operating income) divided either by Contribution margin percentage or Contribution margin per unit
  21. 21. Target Operating Income Assume that management wants to have an operating income of $14,000. How many pairs of pants must be sold? ($84,000 + $14,000) ÷ $28 = 3,500 What dollar sales are needed to achieve this income? ($84,000 + $14,000) ÷ 40% = $245,000
  22. 22. Learning Objective 4 <ul><li>Understand how income </li></ul><ul><li>taxes affect CVP analysis. </li></ul>
  23. 23. Target Net Income and Income Taxes Example Management would like to earn an after tax income of $35,711. The tax rate is 30%. What is the target operating income? Target operating income = Target net income ÷ (1 – tax rate) TOI = $35,711 ÷ (1 – 0.30) = $51,016
  24. 24. Target Net Income and Income Taxes Example How many units must be sold? Revenues – Variable costs – Fixed costs = Target net income ÷ (1 – tax rate) $70Q – $42Q – $84,000 = $35,711 ÷ 0.70 $28Q = $51,016 + $84,000 Q = $135,016 ÷ $28 = 4,822 pairs of pants
  25. 25. Target Net Income and Income Taxes Example Proof: Revenues: 4,822 × $70 $337,540 Variable costs: 4,822 × $42 202,524 Contribution margin $135,016 Fixed costs 84,000 Operating income 51,016 Income taxes: $51,016 × 30% 15,305 Net income $ 35,711
  26. 26. Learning Objective 5 <ul><li>Explain CVP analysis </li></ul><ul><li>in decision making and </li></ul><ul><li>how sensitivity analysis helps </li></ul><ul><li>managers cope with uncertainty. </li></ul>
  27. 27. Using CVP Analysis Example Suppose the management anticipates selling 3,200 pairs of pants. Management is considering an advertising campaign that would cost $10,000. It is anticipated that the advertising will increase sales to 4,000 units. Should the business advertise?
  28. 28. Using CVP Analysis Example 3,200 pairs of pants sold with no advertising: Contribution margin $89,600 Fixed costs 84,000 Operating income $ 5,600 4,000 pairs of pants sold with advertising: Contribution margin $112,000 Fixed costs 94,000 Operating income $ 18,000
  29. 29. Using CVP Analysis Example Instead of advertising, management is considering reducing the selling price to $61 per pair of pants. It is anticipated that this will increase sales to 4,500 units. Should management decrease the selling price per pair of pants to $61?
  30. 30. Using CVP Analysis Example 3,200 pairs of pants sold with no change in the selling price: Operating income = $5,600 4,500 pairs of pants sold at a reduced selling price: Contribution margin: (4,500 × $19) $85,500 Fixed costs 84,000 Operating income $ 1,500
  31. 31. Sensitivity Analysis and Uncertainty Example Assume that the Pants Shop can sell 4,000 pairs of pants. Fixed costs are $84,000. Contribution margin ratio is 40%. At the present time the business cannot handle more than 3,500 pairs of pants.
  32. 32. Sensitivity Analysis and Uncertainty Example To satisfy a demand for 4,000 pairs, management must acquire additional space for $6,000. Should the additional space be acquired? Revenues at breakeven with existing space are $84,000 ÷ .40 = $210,000. Revenues at breakeven with additional space are $90,000 ÷ .40 = $225,000
  33. 33. Sensitivity Analysis and Uncertainty Example Operating income at $245,000 revenues with existing space = ($245,000 × .40) – $84,000 = $14,000. (3,500 pairs of pants × $28) – $84,000 = $14,000
  34. 34. Sensitivity Analysis and Uncertainty Example Operating income at $280,000 revenues with additional space = ($280,000 × .40) – $90,000 = $22,000. (4,000 pairs of pants × $28 contribution margin) – $90,000 = $22,000
  35. 35. Learning Objective 6 <ul><li>Use CVP analysis to plan </li></ul><ul><li>fixed and variable costs. </li></ul>
  36. 36. Alternative Fixed/Variable Cost Structures Example What is the new contribution margin? Decrease the price they charge from $32 to $25 and charge an annual administrative fee of $30,000. Suppose that the factory the Pants Shop is using to obtain the merchandise offers the following:
  37. 37. Alternative Fixed/Variable Cost Structures Example $70 – ($25 + $10) = $35 Contribution margin increases from $28 to $35. What is the contribution margin percentage? $35 ÷ $70 = 50% What are the new fixed costs? $84,000 + $30,000 = $114,000
  38. 38. Alternative Fixed/Variable Cost Structures Example Management questions what sales volume would yield an identical operating income regardless of the arrangement. 28x – 84,000 = 35x – 114,000 114,000 – 84,000 = 35x – 28x 7x = 30,000 x = 4,286 pairs of pants
  39. 39. Alternative Fixed/Variable Cost Structures Example Cost with existing arrangement = Cost with new arrangement .60x + 84,000 = .50x + 114,000 .10x = $30,000  x = $300,000 ($300,000 × .40) – $ 84,000 = $36,000 ($300,000 × .50) – $114,000 = $36,000
  40. 40. Operating Leverage Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold. Organizations with a high proportion of fixed costs have high operating leverage.
  41. 41. Operating Leverage Example Degree of operating leverage = Contribution margin ÷ Operating income What is the degree of operating leverage of the Pants Shop at the 3,500 sales level under both arrangements? Existing arrangement: 3,500 × $28 = $98,000 contribution margin
  42. 42. Operating Leverage Example $98,000 contribution margin – $84,000 fixed costs = $14,000 operating income $98,000 ÷ $14,000 = 7.0 New arrangement: 3,500 × $35 = $122,500 contribution margin
  43. 43. Operating Leverage Example $122,500 contribution margin – $114,000 fixed costs = $8,500 $122,500 ÷ $8,500 = 14.4 The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating income.
  44. 44. Learning Objective 7 <ul><li>Apply CVP analysis to a company </li></ul><ul><li>producing different products. </li></ul>
  45. 45. Effects of Sales Mix on Income Pants Shop Example Management expects to sell 2 shirts at $20 each for every pair of pants it sells. This will not require any additional fixed costs.
  46. 46. Effects of Sales Mix on Income What is the contribution margin of the mix? Contribution margin per shirt: $20 – $9 = $11 $28 + (2 × $11) = $28 + $22 = $50
  47. 47. Effects of Sales Mix on Income $84,000 fixed costs ÷ $50 = 1,680 packages 1,680 × 2 = 3,360 shirts 1,680 × 1 = 1,680 pairs of pants Total units = 5,040
  48. 48. Effects of Sales Mix on Income What is the breakeven in dollars? 3,360 shirts × $20 = $ 67,200 1,680 pairs of pants × $70 = 117,600 $184,800
  49. 49. Effects of Sales Mix on Income What is the weighted-average budgeted contribution margin? Pants: 1 × $28 + Shirts: 2 × $11 = $50 ÷ 3 = $16.667
  50. 50. Effects of Sales Mix on Income The breakeven point for the two products is: $84,000 ÷ $16.667 = 5,040 units 5,040 × 1/3 = 1,680 pairs of pants 5,040 × 2/3 = 3,360 shirts
  51. 51. Effects of Sales Mix on Income Sales mix can be stated in sales dollars: Pants Shirts Sales price $70 $40 Variable costs 42 18 Contribution margin $28 $22 Contribution margin ratio 40% 55%
  52. 52. Effects of Sales Mix on Income Assume the sales mix in dollars is 63.6% pants and 36.4% shirts. Weighted contribution would be: 40% × 63.6% = 25.44% pants 55% × 36.4% = 20.02% shirts 45.46%
  53. 53. Effects of Sales Mix on Income Breakeven sales dollars is $84,000 ÷ 45.46% = $184,778 (rounding). $184,778 × 63.6% = $117,519 pants sales $184,778 × 36.4% = $ 67,259 shirt sales
  54. 54. Learning Objective 8 <ul><li>Adapt CVP analysis to situations </li></ul><ul><li>in which a product has more </li></ul><ul><li>than one cost driver. </li></ul>
  55. 55. Multiple Cost Drivers Example Suppose that the business will incur an additional cost of $10 for preparing documents associated with the sale of pants to various customers. Assume that the business sells 3,500 pants to 100 different customers. What is the operating income from this sale?
  56. 56. Multiple Cost Drivers Example Revenues: 3,500 × $70 $245,000 Variable costs: Pants: 3,500 × $42 147,000 Documents: 100 × $10 1,000 Total 148,000 Contribution margin 97,000 Fixed costs 84,000 Operating income $ 13,000
  57. 57. Multiple Cost Drivers Would the operating income of the Pants Shop be lower or higher if the business sells pants to more customers? The cost structure depends on two cost drivers: 1. Number of units 2. Number of customers
  58. 58. Learning Objective 9 <ul><li>Distinguish between </li></ul><ul><li>contribution margin </li></ul><ul><li>and gross margin. </li></ul>
  59. 59. Contribution Margin versus Gross Margin Contribution income statement emphasizes contribution margin. Financial accounting income statement emphasizes gross margin.
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