Chapter 6 Cost-Volume-Profit Relationships
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This document provides an overview of cost-volume-profit (CVP) analysis concepts including contribution margin, break-even point, CVP graphs, contribution margin ratio, and how changes in variables like sales price, costs, and volume affect profits. It discusses the equation method and contribution margin method for calculating break-even point in units and dollars. Formulas and examples from a sample company called Racing Bicycle are provided to illustrate key CVP terms and calculations.
Chapter 6 Cost-Volume-Profit Relationships
- 1. CChhaapptteerr 66 Cost-Volume-Profit Relationships
- 2. Basics of Cost-Volume-Profit Analysis Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.
- 3. Basics of Cost-Volume-Profit Analysis CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.
- 4. Learning Objective LLOO11 To explain how changes in activity affect contribution margin and net operating income.
- 5. The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.
- 6. The Contribution Approach Each month, Racing must generate at least $80,000 in total CM to break even.
- 7. The Contribution Approach If Racing sells 440000 uunniittss in a month, it will be operating at the break-even point.
- 8. The Contribution Approach If Racing sells one more bike (440011 bbiikkeess), net operating income will increase by $200.
- 9. The Contribution Approach We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. IIff RRaacciinngg sseellllss 443300 bbiikkeess,, iittss nneett iinnccoommee wwiillll bbee $$66,,000000..
- 10. Learning Objective LLOO22 To prepare and interpret a cost-volume-profit (CVP) graph.
- 11. CVP Relationships in Graphic Form The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Racing developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph. Income 300 units Income 400 units Income 500 units Sales $ 150,000 $ 200,000 $ 250,000 Less: variable expenses 90,000 120,000 150,000 Contribution margin $ 60,000 $ 80,000 $ 100,000 Less: fixed expenses 80,000 80,000 80,000 Net operating income $ (20,000) $ - $ 20,000
- 12. CVP Graph IInn aa CCVVPP ggrraapphh,, uunniitt vvoolluummee iiss uussuuaallllyy rreepprreesseenntteedd oonn tthhee hhoorriizzoonnttaall ((XX)) aaxxiiss aanndd ddoollllaarrss oonn tthhee vveerrttiiccaall ((YY)) aaxxiiss.. Units Dollars IInn aa CCVVPP ggrraapphh,, uunniitt vvoolluummee iiss uussuuaallllyy rreepprreesseenntteedd oonn tthhee hhoorriizzoonnttaall ((XX)) aaxxiiss aanndd ddoollllaarrss oonn tthhee vveerrttiiccaall ((YY)) aaxxiiss..
- 13. Dollars CVP Graph Units Fixed Expenses
- 14. CVP Graph Dollars Units Fixed Expenses Total Expenses
- 15. CVP Graph Total Sales Fixed Expenses DollarsTotal Expenses Units
- 16. CVP Graph Dollars Units ssaalleess)) BBrreeaakk-eevveenn ppooiinntt ((440000 uunniittss oorr $$220000,,000000 iinn ssaalleess)) Profit Area Loss Area
- 17. Learning Objective LLOO33 To use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume.
- 18. Contribution Margin Ratio The contribution margin ratio is: Total CM CM Ratio = Total sales For Racing Bicycle Company the ratio is: $80,000 = 40% $200,000 Each $1.00 increase in sales results in a total contribution margin increase of 40¢.
- 19. Contribution Margin Ratio Or, in terms of units, the contribution margin ratio is: Unit CM CM Ratio = Unit selling price For Racing Bicycle Company the ratio is: $200 $500 = 40%
- 20. Contribution Margin Ratio 400 Bikes 500 Bikes Sales $ 200,000 $ 250,000 Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net operating income $ - $ 20,000 AA $$5500,,000000 iinnccrreeaassee iinn ssaalleess rreevveennuuee rreessuullttss iinn aa $$2200,,000000 iinnccrreeaassee iinn CCMM.. (($$5500,,000000 ×× 4400%% = $$2200,,000000))
- 21. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average, 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139
- 22. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average, 2,100 cups are sold each month. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139 Unit contribution margin CM Ratio = Unit selling price = ($1.49-$0.36) $1.49 = $1.13 $1.49 = 0.758
- 23. Learning Objective LLOO44 To show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume.
- 24. Changes in Fixed Costs and Sales Volume What is the profit impact if Racing can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?
- 25. Changes in Fixed Costs and Sales Volume $80,000 + $10,000 advertising $$$888000,,,000000000 +++ $$$111000,,,000000000 aaadddvvveeerrrtttiiisssiiinnnggg ==== $$$$99990000,,,,000000000000 SSaalleess iinnccrreeaasseedd bbyy $$2200,,000000,, bbuutt nneett ooppeerraattiinngg iinnccoommee ddeeccrreeaasseedd bbyy $$22,,000000..
- 26. Changes in Fixed Costs and Sales Volume The Shortcut Solution Increase in CM (40 units X $200) $ 8,000 Increase in advertising expenses 10,000 Decrease in net operating income $ (2,000)
- 27. Change in Variable Costs and Sales Volume What is the profit impact if Racing can use higher quality raw materials, thus, increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580?
- 28. Change in Variable Costs and Sales Volume 555588880000 uuuunnnniiiittttssss ×××× $$$$333311110000 vvvvaaaarrrriiiiaaaabbbblllleeee ccccoooosssstttt////uuuunnnniiiitttt ==== $$$$111177779999,,,,888800000000 SSaalleess iinnccrreeaassee bbyy $$4400,,000000,, aanndd nneett ooppeerraattiinngg iinnccoommee iinnccrreeaasseess bbyy $$1100,,220000..
- 29. Change in Fixed Cost, Sales Price and Volume What is the profit impact if Racing (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month?
- 30. Change in Fixed Cost, Sales Price and Volume SSaalleess iinnccrreeaassee bbyy $$6622,,000000,, ffiixxeedd ccoossttss iinnccrreeaassee bbyy $$1155,,000000,, aanndd nneett ooppeerraattiinngg iinnccoommee iinnccrreeaasseess bbyy $$22,,000000..
- 31. Change in Variable Cost, Fixed Cost and Sales Volume What is the profit impact if Racing (1) pays a $15 sales commission per bike sold, instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes?
- 32. Change in Variable Cost, Fixed Cost and Sales Volume Increase in CM (75 units X $85) $ 6,375 Reduced fixed costs 6,000 Increase in net operating income $ 12,375 SSaalleess iinnccrreeaassee bbyy $$3377,,550000,, vvaarriiaabbllee ccoossttss iinnccrreeaassee bbyy $$3311,,112255,, bbuutt ffiixxeedd eexxppeennsseess ddeeccrreeaassee bbyy $$66,,000000..
- 33. Change in Regular Sales Price If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by $3,000?
- 34. Change in Regular Sales Price $ 3,000 ÷ 150 bikes = $ 20 per bike Variable cost per bike = 300 per bike Selling price required = $ 320 per bike 150 bikes × $320 per bike = $ 48,000 Total variable costs = 45,000 Increase in net income = $ 3,000
- 35. Learning Objective LLOO55 To compute the breakeven point in unit sales and dollar sales.
- 36. Break-Even Analysis BBrreeaakk--eevveenn aannaallyyssiiss ccaann bbee aapppprrooaacchheedd iinn ttwwoo wwaayyss:: 11.. EEqquuaattiioonn mmeetthhoodd 22.. CCoonnttrriibbuuttiioonn mmaarrggiinn mmeetthhoodd
- 37. Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits AAtt tthhee bbrreeaakk--eevveenn ppooiinntt pprrooffiittss eeqquuaall zzeerroo
- 38. Break-Even Analysis Here is the information from Racing Bicycle Company: Total Per Unit Percent Sales (500 bikes) $ 250,000 $ 500 100% Less: variable expenses 150,000 300 60% Contribution margin $ 100,000 $ 200 40% Less: fixed expenses 80,000 Net operating income $ 20,000
- 39. Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed eexxppeennsseess ++ PPrrooffiittss $500Q = $300Q + $80,000 + $0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense
- 40. Equation Method We calculate the break-even point as follows: SSaalleess == VVaarriiaabbllee eexxppeennsseess ++ FFiixxeedd eexxppeennsseess ++ PPrrooffiittss $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 440000 bbiikkeess
- 41. Equation Method The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses ++ FFiixxeedd eexxppeennsseess ++ PPrrooffiittss XX == 00..6600XX ++ $$8800,,000000 ++ $$00 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses
- 42. Equation Method The equation can be modified to calculate the break-even point in sales dollars. SSaalleess == VVaarriiaabbllee eexxppeennsseess ++ FFiixxeedd eexxppeennsseess ++ PPrrooffiittss X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $$220000,,000000
- 43. Contribution Margin Method The contribution margin method has two key equations. Break-even point = Fixed expenses in units sold Unit contribution margin Fixed expenses CM ratio = Break-even point in total sales dollars
- 44. Contribution Margin Method Let’s use the contribution margin method to calculate the break-even point in total sales dollars at Racing. Break-even point in total sales dollars = Fixed expenses CM ratio $$8800,,000000 4400% == $$220000,,000000 bbrreeaakk--eevveenn ssaalleess
- 45. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average 2,100 cups are sold each month. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups
- 46. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable Break-even = Fixed expenses expense per cup is $0.36. The average Unit CM fixed expense per month is $1,300. On $1,300 average 2,100 cups are sold each month. = $1.49/What cup is - $the 0.36/break-cup even sales in units? $1,300 a. 872 cups = $1.13/cup b. 3,611 cups = 1,150 cups c. 1,200 cups d. 1,150 cups
- 47. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average 2,100 cups are sold each month. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129
- 48. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average 2,100 cups are sold each month. What is the break-even sales in dollars? a. $1,300 Break-even Fixed expenses b. $1,715 sales = CM Ratio c. $1,788 = $1,300 0.758 d. $3,129 = $1,715
- 49. Learning Objective LLOO66 To determine the level of sales needed to achieve a desired target profit.
- 50. Target Profit Analysis The equation and contribution margin methods can be used to determine the sales volume needed to achieve a target profit. Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of $100,000.
- 51. The CVP Equation Method Sales = Variable expenses ++ FFiixxeedd eexxppeennsseess ++ PPrrooffiittss $500Q = $300Q + $80,000 + $100,000 $200Q = $180,000 Q = 900 bikes
- 52. The Contribution Margin Approach The contribution margin method can be used to determine that 900 bikes must be sold to earn the target profit of $100,000. Unit = contribution margin Unit sales to attain the target profit $80,000 + $100,000 Fixed expenses + Target profit $200/bike = 900 bikes
- 53. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups
- 54. Quick Check Fixed expenses + Target profit Unit CM Unit sales to attain target profit = Coffee Klatch is an espresso stand in a downtown office building. The average = $1,300 selling + $2,500 price of a cup of coffee is $1.49 and the $1.49 average - $0.36 variable expense per cup is $0.36. The average fixed expense per month = is $$1,300. 3,800 How many cups of coffee would have to be $sold 1.13 to attain target profits of $2,500 per month? = 3,363 cups a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups
- 55. Learning Objective LLOO77 To compute the margin of safety and explain its significance.
- 56. The Margin of Safety The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales. Margin of safety = TToottaall ssaalleess -- BBrreeaakk--eevveenn ssaalleess Let’s look at Racing Bicycle Company and determine the margin of safety.
- 57. The Margin of Safety If we assume that Racing Bicycle Company has actual sales of $250,000, given that we have already determined the break-even sales to be $200,000, the margin of safety is $50,000 as shown Break-even sales 400 units Actual sales 500 units Sales $ 200,000 $ 250,000 Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net operating income $ - $ 20,000
- 58. The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000) Break-even sales 400 units Actual sales 500 units Sales $ 200,000 $ 250,000 Less: variable expenses 120,000 150,000 Contribution margin 80,000 100,000 Less: fixed expenses 80,000 80,000 Net operating income $ - $ 20,000
- 59. The Margin of Safety The margin of safety can be expressed in terms of the number of units sold. The margin of safety at Racing is $50,000, and each bike sells for $500. MMaarrggiinn ooff SSaaffeettyy iinn uunniittss == == 110000 bbiikkeess $$5500,,000000 $$550000
- 60. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average 2,100 cups are sold each month. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups
- 61. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average 2,100 cups are sold each month. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups Margin of safety = Total sales – Break-even sales = 2,100 cups – 1,150 cups = 950 cups or 950 cups 2,100 cups Margin of safety percentage = = 45%
- 62. Cost Structure and Profit Stability Cost structure refers to the relative proportion of fixed and variable costs in an organization. Managers often have some latitude in determining their organization’s cost structure.
- 63. Cost Structure and Profit Stability There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures. AAnn An aaddvvaannttaaggee advantage ooff aa hhiigghh ffiixxeedd ccoosstt ssttrruuccttuurree iiss tthhaatt iinnccoommee wwiillll bbee hhiigghheerr iinn ggoooodd yyeeaarrss ccoommppaarreedd ttoo ccoommppaanniieess wwiitthh lloowweerr pprrooppoorrttiioonn ooff ffiixxeedd ccoossttss.. AA ddiissaaddvvaannttaaggee ooff aa hhiigghh ffiixxeedd ccoosstt ssttrruuccttuurree iiss tthhaatt iinnccoommee wwiillll bbee lloowweerr iinn bbaadd yyeeaarrss ccoommppaarreedd ttoo ccoommppaanniieess wwiitthh lloowweerr pprrooppoorrttiioonn ooff ffiixxeedd ccoossttss..
- 64. Learning Objective LLOO88 To compute the degree of operating leverage at a particular level of sales and explain how it can be used to predict changes in net operating income.
- 65. Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. Contribution margin Net operating income Degree of operating leverage =
- 66. Operating Leverage At Racing, the degree of operating leverage is 5. Actual sales 500 Bikes Sales $ 250,000 Less: variable expenses 150,000 Contribution margin 100,000 Less: fixed expenses 80,000 Net income $ 20,000 $100,000 $20,000 = 55
- 67. Operating Leverage With an operating leverage ooff 55,, iiff RRaacciinngg iinnccrreeaasseess iittss ssaalleess bbyy 1100%,, nneett ooppeerraattiinngg iinnccoommee wwoouulldd iinnccrreeaassee bbyy 5500%.. Percent increase in sales 10% Degree of operating leverage × 5 Percent increase in profits 50% Here’s the verification!
- 68. Operating Leverage 10% increase in sales from $250,000 to $275,000 . . . . . . results in a 50% increase in income from $20,000 to $30,000.
- 69. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average 2,100 cups are sold each month on. What is the operating leverage? a. 2.21 b. 0.45 c. 0.34 d. 2.92
- 70. Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. On average2,100 cups are sold each month. What is the operating leverage? a. 2.21 b. 0.45 c. 0.34 d. 2.92 Contribution margin Net operating income Operating leverage = $2,373 = $1,073 = 2.21 Actual sales 2,100 cups Sales $ 3,129 Less: Variable expenses 756 Contribution margin 2,373 Less: Fixed expenses 1,300 Net operating income $ 1,073
- 71. Quick Check AAtt At CCooffffeeee Coffee KKllaattcchh Klatch tthhee aavveerraaggee sseelllliinngg pprriiccee ooff aa ccuupp ooff ccooffffeeee iiss $$11..4499,, tthhee aavveerraaggee vvaarriiaabbllee eexxppeennssee ppeerr ccuupp iiss $$00..3366,, aanndd tthhee aavveerraaggee ffiixxeedd eexxppeennssee ppeerr mmoonntthh iiss $$11,,330000.. OOnn aavveerraaggee 22,,110000 ccuuppss aarree ssoolldd eeaacchh mmoonntthh.. IIff ssaalleess iinnccrreeaassee bbyy 2200%,, bbyy hhooww mmuucchh sshhoouulldd nneett ooppeerraattiinngg iinnccoommee iinnccrreeaassee?? aa.. 3300..00% bb.. 2200..00% cc.. 2222..11% dd.. 4444..22%
- 72. Quick Check AAtt At CCooffffeeee Coffee KKllaattcchh Klatch tthhee aavveerraaggee sseelllliinngg pprriiccee ooff aa ccuupp ooff ccooffffeeee iiss $$11..4499,, tthhee aavveerraaggee vvaarriiaabbllee eexxppeennssee ppeerr ccuupp iiss $$00..3366,, aanndd tthhee aavveerraaggee ffiixxeedd eexxppeennssee ppeerr mmoonntthh iiss $$11,,330000.. OOnn aavveerraaggee 22,,110000 ccuuppss aarree ssoolldd eeaacchh mmoonntthh.. IIff ssaalleess iinnccrreeaassee bbyy 2200%,, bbyy hhooww mmuucchh sshhoouulldd nneett ooppeerraattiinngg iinnccoommee iinnccrreeaassee?? aa.. 3300..00% Percent increase in sales 20.0% bb.. 2200..00% × Degree of operating leverage 2.21 cc.. 2222..11% Percent increase in profit 44.20% dd.. 4444..22%
- 73. Verify Increase in Profit Actual sales Increased sales 2,100 cups 2,520 cups Sales $ 3,129 $ 3,755 Less: Variable expenses 756 907 Contribution margin 2,373 2,848 Less: Fixed expenses 1,300 1,300 Net operating income $ 1,073 $ 1,548 % change in sales 20.0% % change in net operating income 44.2%
- 74. Structuring Sales Commissions Companies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based on sales dollars can lead to lower profits in a company. Let’s llooookk aatt aann eexxaammppllee..
- 75. Structuring Sales Commissions Pipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution margin per unit of $25. The Turbo sells for $150 and earns a contribution margin per unit of $18. The sales force at Pipeline Unlimited is compensated based on sales commissions.
- 76. Structuring Sales Commissions If you were on the sales force at Pipeline, you would push hard to sell the Turbo even though the XR7 earns a higher contribution margin per unit. To eliminate this type of conflict, ccoommmmiissssiioonnss ccaann bbee bbaasseedd oonn ccoonnttrriibbuuttiioonn mmaarrggiinn rather than on selling price alone.
- 77. Learning Objective LLOO99 To compute the break-even point for a multiproduct company and explain the effects of shifts in the sales mix on contribution margin and the break-even point.
- 78. The Concept of Sales Mix Sales mix is the relative proportion in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. Let’s assume Racing Bicycle Company sells bikes and carts and that the sales mix between the two products remains the same.
- 79. Multi-product break-even analysis Racing Bicycle Co. provides the following information: $265,000 $550,000 = 48.2% (rounded)
- 80. Multi-product break-even analysis Fixed expenses CM Ratio Break-even sales = = $170,000 48.2% = $352,697
- 81. Key Assumptions of CVP Analysis SSeelllliinngg pprriiccee iiss ccoonnssttaanntt.. CCoossttss aarree lliinneeaarr.. IInn mmuullttii--pprroodduucctt ccoommppaanniieess,, tthhee ssaalleess mmiixx iiss ccoonnssttaanntt.. IInn mmaannuuffaaccttuurriinngg ccoommppaanniieess,, iinnvveennttoorriieess ddoo nnoott cchhaannggee ((uunniittss pprroodduucceedd == uunniittss ssoolldd))..
- 82. End of Chapter 6
Editor's Notes
- #2: Chapter 6: Cost-Volume-Profit Relationships. Cost-volume-profit (CVP) analysis helps managers understand the interrelationships among cost, volume, and profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions, such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.
- #3: The contribution income statement is helpful to managers in judging the impact of changes in selling price, cost, or volume on profits. For example, let's look at a hypothetical contribution income statement for Racing Bicycle Company (RBC). Contribution margin is defined as sales less variable expenses. In the case of Racing Bicycle Company, contribution margin is one hundred thousand dollars.
- #4: Contribution margin is used first to cover fixed expenses. Any remaining contribution margin contributes to net operating income.
- #5: Learning objective number 1 is to explain how changes in activity affect contribution margin and net income.
- #6: Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. For each additional unit Racing Bicycle Company sells, $200 more in contribution margin will help to cover fixed expenses and provide a profit.Each month Racing Bicycle must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero). If Racing sells 400 units a month, it will be operating at the break-even point. If Racing sells one more bike (401 bikes), net operating income will increase by $200.
- #7: Each month, Racing Bicycle must generate at least $80,000 in total contribution margin to break-even (which is the level of sales at which profit is zero).
- #8: If Racing sells 400 units a month, it will be operating at the break-even point. If Racing sells one more bike (401 bikes), net operating income will increase by $200.
- #9: You can see that the sale of one unit above the break-even point yields net income of $200 for Racing Bicycle.
- #10: <number> If we develop equations to calculate break-even and net income, we will not have to prepare an income statement to determine what net income will be at any level of sales. For example, we know that if Racing Bicycle sells 430 bikes, net income will be $6,000. The company will sell 30 bikes above the break-even unit sales and the contribution margin is $200 per bike. So, we multiply 30 bikes times $200 per bike and get net income of $6,000.
- #11: Learning objective number 2 is to prepare and interpret a cost-volume-profit graph.
- #12: The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a cost-volume-profit (CVP) graph. To illustrate, we will use contribution income statements for Racing Bicycle Company at 300, 400, and 500 units sold.
- #13: In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Once we understand this convention, we can prepare a CVP graph in three steps.
- #14: The first step begins by drawing a line parallel to the volume axis to represent total fixed expenses of $80,000.
- #15: <number> The second step is to choose some sales volume (for example, 500 units) and plot the point representing total expenses (e.g., fixed and variable) at that sales volume. Draw a line through the data point back to where the fixed expenses line intersects the dollar axis.
- #16: <number> The third step is to choose some sales volume (for example, 500 units) and plot the point representing total sales dollars at the chosen activity level. Draw a line through the data point back to the origin.
- #17: <number> The break-even point is where the total revenue and total expenses lines intersect. In the case of Racing Bicycle, break-even is 400 bikes sold, or sales revenue of $200,000. The profit or loss at any given sales level is measured by the vertical distance between the total revenue and the total expenses lines.
- #18: Learning objective number 3 is to use the contribution margin ratio, or CM ratio, to compute changes in contribution margin and net operating income resulting from changes in sales volume.
- #19: We can calculate the contribution margin ratio of Racing Bicycle by dividing total contribution margin by total sales. In the case of Racing Bicycle, the contribution margin ratio is 40%. This means that for each dollar increase in sales, the company will produce 40¢ in contribution margin.
- #20: We may also calculate the contribution margin ratio using per unit amounts, by dividing the contribution margin per unit by the selling price per unit.
- #21: Let’s see how we can use the contribution margin ratio to look at the contribution margin income statement of Racing Bicycle in a little different way. If Racing is able to increase its sales by $50,000, it will increase contribution margin by $20,000, that is, $50,000 times 40%.
- #22: Can you calculate the contribution margin ratio for Coffee Klatch? The calculation may take a minute or so to complete.
- #23: How did you do? The CM ratio is 75.8%.
- #24: Learning objective number 4 is to show the effects on contribution margin of changes in variable costs, fixed costs, selling price, and volume.
- #25: Let’s assume that the management of Racing Bicycle believes it can increase unit sales from 500 to 540, if it spends $10,000 on advertising. Would you recommend that the advertising campaign be undertaken? See if you can solve this problem before going to the next screen.
- #26: As you can see, even if sales revenue increases to two hundred seventy thousand dollars, Racing will experience a $12,000 increase in variable costs and a $10,000 increase in fixed costs (the new advertising campaign). As a result, net income will actually drop by $2,000. The advertising campaign would certainly not be a good idea. We can help management see the problem before any additional monies are spent.
- #27: Here is a shortcut approach to looking at the problem. You can see that an increase in contribution margin is more than offset by the increased advertising costs.
- #28: <number> Management at Racing Bicycle believes that using higher quality raw materials will result in an increase in sales from 500 to 580. The higher quality raw materials will lead to a $10 increase in variable costs per unit. Would you recommend the use of the higher quality raw materials?
- #29: <number> As you can see, revenues will increase by $40,000 (80 bikes times $500 per bike), and variable costs will increase by $29,800. Contribution margin will increase by $10,200. With no change in fixed costs, net income will also increase by $10,200.The use of higher quality raw materials appears to be a profitable idea.
- #30: <number> Here is a more complex situation because we will experience a change in selling price, advertising expense, and unit sales. Would you support this plan?
- #31: <number> Part I This appears to be a good plan because net income will increase by $2,000. Take a few minutes and analyze the change in sales revenue, variable expenses and fixed expenses. Part II Using the shortcut method, we see that variable costs per unit remain at $300, while sales price is decreased to $480 per unit, and we sell 150 additional units, so contribution margin increases by $17,000. At the same time, advertising expense, a fixed cost, increase by $15,000. The result is a $2,000 increase in net operating income.
- #32: <number> Here is another complex question involving cost-volume-profit relationships. In this question, we eliminate a fixed cost, and substitute a variable cost, while increasing the units sold. Be careful with your calculation of the profit impact of these changes.
- #33: <number> Part I Net income increases by $12,375. Notice that sales revenue and variable expenses increased, as well. Fixed expenses were decreased as a result of making sales commissions variable in nature.How did you do? We hope you are beginning to see the potential power of CVP analysis. Part II The shortcut approach shows that contribution margin will increase by $6,375. We will sell 75 more bikes but have a lower contribution. In addition, we reduce our fixed costs by $6,000 per month, so the net operating income is increased by $12,375.
- #34: <number> Suppose Racing Bicycle has a one-time opportunity to sell one hundred fifty bikes to a wholesaler. There would be no change in the cost structure as a result of this sale. Racing wants the one-time sale to produce a profit of $3,000. What selling price should Racing quote to the wholesaler?
- #35: <number> If we desire a profit of three thousand dollars on the sale of 150 bikes, we must have a profit of $20 per bike. The variable expenses associated with each bike are $300, so we would quote a selling price of $320. You can see the proof of the quote in the blue schedule.
- #36: Learning objective number 5 is to compute the breakeven point in unit sales and dollar sales.
- #37: We can accomplish break-even analysis in one of two ways. We can use the equation method or the contribution margin method. We get the same results regardless of the method selected. You may prefer one method over the other. It’s a personal choice, but be aware that there are problems associated with either method. Some are easier to solve using the equation method, while others can be quickly solved using the contribution margin method.
- #38: The equation method is based on the contribution approach income statement. The equation can be stated in one of two ways: Profits equal Sales less Variable expenses, less Fixed Expenses, or Sales equal Variable expenses plus Fixed expenses plus ProfitsRemember that at the break-even point, profits are equal to zero.
- #39: Here is some information provided for Racing Bicycle that we will use to solve some problems. We have the contribution margin income statement, the selling price and variable expenses per unit, and the contribution margin ratio.
- #40: The break-even point in units is determined by creating the equation as shown, where Q is the number of bikes sold, $500 is the unit selling price, $300 is the unit variable expense, and $80,000 is the total fixed expense.We need to solve for Q.
- #41: Solving this equation shows that the break-even point in units is 400 bikes. We want to be careful with the algebra when we group terms.
- #42: The equation can be modified, as shown, to calculate the break-even point in sales dollars. In this equation, X is total sales dollars, 0.60 (or 60%) is the variable expense as a percentage of sales, and $80,000 is the total fixed expense.We need to solve for X.
- #43: Solving this equation shows that the break-even point is sales dollars is $200,000. Once again, be careful when you combine the X values in the equation.
- #44: The contribution margin method has two key equations:Break-even point in units sold equals Fixed expenses divided by CM per unit, and Break-even point in sales dollars equals Fixed expenses divided by CM ratio.
- #45: Part ILet’s use the contribution margin method to calculate break-even in total sales dollars. Part IIThe break-even sales revenue is $200,000.
- #46: Now use the contribution margin approach to calculate the break-even point in cups of coffee sold.
- #47: The contribution margin per cup of coffee is $1.13. The number of cups to sell to reach break-even is 1,150.
- #48: Let’s calculate the break-even in sales dollars for Coffee Klatch.
- #49: With a contribution margin ratio of 75.8% rounded, break-even sales revenue is $1,715.
- #50: Learning objective number 6 is to determine the level of sales needed to achieve a desired target profit.
- #51: We can use either method to determine the revenue or units needed to achieve a target level of profits.Suppose Racing Bicycle wants to earn net income of $100,000. How many bikes must the company sell to achieve this profit level?
- #52: Instead of setting profit to zero, like we do in a break-even analysis, we set the profit level to $100,000. Solving for Q, we see that the company will have to sell 900 bikes to achieve the desired profit level.
- #53: A quicker way to solve this problem is to add the desired profits to the fixed cost and divide the total by the contribution margin per unit. Notice we get the same result of 900 bikes.
- #54: The Coffee Klatch wants to earn a monthly profit of $2,500. How many cups of coffee must the company sell to reach this profit goal?
- #55: We add the desired profit to the fixed cost and divide by the unit contribution of $1.13. The company must sell 3,363 cups of coffee to reach its profit goal.
- #56: Learning objective number 7 is to compute the margin of safety and explain its significance.
- #57: The margin of safety helps management assess how far above or below the break-even point the company is currently operating at. To calculate the margin of safety, we take total current sales and subtract break-even sales.Let’s calculate the margin of safety for Racing Bicycle.
- #58: Racing Bicycle is currently selling 500 bikes and producing total sales revenue of $250,000. Sales at the break-even point are $200,000, so the company’s margin of safety is $50,000.
- #59: We can express the margin of safety as a percent of sales. In the case of Racing Bicycle, the margin of safety is 20% ($50,000 divided by $200,000).
- #60: We can express the margin of safety in number of units. In the case of Racing Bicycle, the margin of safety is 100 bikes ($50,000 divided by $500).
- #61: Let’s see if you can calculate the margin of safety in cups of coffee for the Coffee Klatch.
- #62: The margin of safety is 950 cups, or we can calculate the margin of safety as 45%.
- #63: <number> A company’s cost structure refers to the relative proportion of fixed and variable expenses. Some companies have high fixed expenses relative to variable expenses. Do you remember our discussion about utility companies? Because of the heavy investment in property, plant and equipment, many utility companies have a high proportion of fixed costs.
- #64: <number> Generally, companies with a high fixed cost structure will show higher net income in good years than companies with lower fixed cost structures. Just the opposite is true in bad years. Companies with low fixed cost structures enjoy greater stability in income across good and bad years.
- #65: Learning objective number 8 is to compute the degree of operating leverage at a particular level of sales and explain how it can be used to predict changes in net operating income.
- #66: The degree of operating leverage is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. It is computed by dividing contribution margin by net operating income.Let’s look at Racing Bicycle.
- #67: Recall that Racing is currently selling 500 bikes and producing net income of $20,000. Contribution margin is $100,000. Operating leverage is 5. We determine this by dividing the $100,000 contribution by net income of $20,000. Now that we have calculated the degree of operating leverage for Racing, let’s see exactly what this means to management.
- #68: If Racing is able to increase sales by 10%, net income will increase by 50%. We multiply the percentage increase in sales by the degree of operating leverage. Let’s verify the 50% increase in profit.
- #69: A 10% increase in sales would increase bike sales from the current level of 500 to 550. Look at the contribution margin income statement; notice that income increased from $20,000 to $30,000, and a $10,000 increase in net income is a 50 percent increase.Operating leverage provides useful information to management.
- #70: See if you can calculate the degree of operating leverage for the Coffee Klatch.
- #71: The computations took a while to complete, didn’t they. You can see that operating leverage is 2.21.
- #72: If the Coffee Klatch is able to increase sales by 20%, what will be the increase in net income?
- #73: You are right. The increase in net income is 44.2%.
- #74: Here is our verification of the increase in net income. Take a few minutes and make sure you understand how we calculated all the numbers.
- #75: <number> You have probably heard that salespersons can be compensated on a commission basis. The commission is usually based on sales revenue generated. Some salespersons work on a salary plus commission.When salespersons are paid a commission based on sales dollars generated, the income statement impact may not be fully understood.Let’s look at an example.
- #76: <number> This company produces two surfboards. The XR7 model sells for $100 and has a contribution margin per unit of $25. The second surfboard, the Turbo model, sells for one $150 and has a contribution margin of $18 per unit sold. The sales force at Pipeline is paid on sales commissions.
- #77: <number> If you were on the sales force, you would try to sell all the Turbo models you could because it has a higher selling price per unit. The problem is that the XR7 model produces a higher contribution margin to the company.It might be a good idea for Pipeline to base its sales commissions on contribution margin rather than selling price alone.
- #78: Learning objective number 9 is to compute the break-even point for a multiproduct company and explain the effects of shifts in the sales mix on contribution margin and the break-even point.
- #79: When a company sells more than one product, break-even analyses become more complex because of the relative mix of the products sold. Different products will have different selling prices, cost structures and contribution margins.Let’s expand the product line at Racing Bicycle and see what impact this has on break-even. We are going to assume that the sales mix between the products remains the same in our example.
- #80: Racing Bicycle sells both bikes and carts. Look at the contribution margin for each product. Notice that we subtract fixed expenses from the total contribution margin. We do not allocate the fixed costs to each product.The sales mix shows that 45% of the company’s sales revenue comes from the sale of bikes and 55% comes from the sale of carts.The combined contribution margin ratio is 48.2% (rounded). Let’s look at break-even.
- #81: Part IBreak-even in sales dollars is $352,697. We calculate this amount in the normal way. We divide total fixed expenses of $170,000 by the combined contribution margin ratio. Part IIWe begin by allocating total break-even sales revenue to the two products. 45% of the total is assigned to the bikes and 55% to the carts.The variable costs-by-product are determined by multiplying the variable expense percent times the assigned revenue. The contribution margin is the difference between the assigned revenue and the variable expenses. Once again, we subtract fixed expenses from the combined total contribution margin for the two products. Because we used a rounded contribution margin percent, we have a rounding difference of $176.Obviously, the more products a company has, the more complex the break-even analysis becomes.
- #82: Here are the four key assumptions of cost-volume-profit analysis. Selling price is constant. Costs are linear and can be accurately divided into variable and fixed elements. The variable element is constant per unit, and the fixed element is constant in total over the entire relevant range. In multiproduct companies, the sales mix is constant. In manufacturing companies, inventories do not change. The number of units produced equals the number of units sold. You are probably familiar with the first three assumptions by now. The forth assumption tells us that there can be no change in inventory levels. That is, all units produced are sold in the current period.
- #83: End of Chapter 6.