1. COST-VOLUME-PROFIT ANALYSIS CHAPTER 7 Professor Garvin, JD; CPA – ACG2071

2. Cost-Volume-Profit (CVP) Analysis  Is a powerful tool that helps managers make important business decisions  Is a relationship among costs, volume, and profit or loss  Determines how much the company must sell each month just to cover costs or to break even  Helps managers decide how sales volume would need to change to achieve the same profit level 2

3. Components of CVP Analysis  CVP analysis relies on the interdependency of five components or pieces of information  Sales price per unit  Volume sold  Variable costs per unit  Fixed costs  Operating income  If you know or can estimate four of these five components, you can compute the remaining unknown amount 3

4. CVP Assumptions  Change in volume is only factor that affects total costs; No Volume discounts  Managers can classify each cost as either variable or fixed  These costs are linear throughout relevant range  Revenues are linear throughout relevant range  Inventory levels will not change  The sales mix of products will not change 4

5. CVP Example Facts: Kay’s Posters Kay has an Internet poster business. She currently sells each poster for $35, while each poster has a variable cost of $21. Kay has fixed costs of $7,000. Kay is currently selling 550 posters per month. 5

6. Contribution Margin Income Statement Kay’s Internet poster bsn. example from prior slide Sales revenue (550 posters)..................................... $ 19,250 Less: Variable expenses............................................ (11,550) Contribution margin................................................... 7,700 Less: Fixed expenses................................................... (7,000) Operating income........................................................ 700 6

7. Contribution Margin per Unit Sales price per unit $35 - Variable costs per unit (21) = Contribution margin per unit $14 What will profit be if can sell 650 units next month (increase of 100) Contribution margin (650 units x $14)$9,100 - Fixed Costs (7,000) Operating Income$2,100 $1,400 increase in op.inc. when sell extra 100 posters $14 CM/unit x 100 extra units = $1,400 increase in op.inc. 7

8. Contribution Margin Ratio Contribution margin ratio = Contribution margin/unit = $14 Sales price per unit $35 = 40% CMR Contribution margin ratio = Contribution margin = $ 7,700 Sales revenue $19,250 = 40% Contribution margin ratio = percentage of each sales dollar that is available for covering fixed expenses and generating a profit. (Numbers above are from the Kay’s Internet poster example on previous slides.) We can also compute CMR from Contribution Margin Income St. 8

9. Bay Cruiseline offers nightly dinner cruises off the coast of Miami, San Francisco, and Seattle. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210,000 per month. The company’s relevant range extends to 15,000 monthly passengers. a. What is the contribution margin per passenger? Sales revenue (1 passenger) $50 Less: Variable expenses (20) Contribution margin/unit 30 9

10. b. What is the contribution margin ratio? c. Use the contribution margin/unit to project operating income if monthly sales total 10,000 passengers. d. Use the contribution margin ratio to project operating income if monthly sales revenue totals $400,000. Contribution margin ( $400,000 sales X 60%)$ 240,000 Fixed cost (210,000) Operating Income$ 30,000 Contribution margin ratio = Contribution margin/unit = $ 30 Sales price per unit = $ 50 = 60% 10,000 x $30 = $300,000 CM (210,000) TFC = $90,000 Op Inc. 10

11. Bay Cruiseline offers nightly dinner cruises off the coast of Miami. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210,000 per month. The company’s relevant range extends to 15,000 monthly passengers. If Bay Cruiseline sells an additional 500 tickets, by what amount will its operating income increase (or operating loss decrease)? Contribution Margin per unit x additional tickets 500 extra tickets X $30 CM/unit = $15,000 incremental profit 11

12. Breakeven Point  Breakeven point:  Sales level at which operating income is zero  If sales above breakeven point, then profit  If sales below breakeven point, then loss  At Breakeven point:  Fixed expenses = total contribution margin  Total sales = total expenses at B/E point 12

13. Calculating Breakeven Point  Three approaches to calculating breakeven:  Income statement approach  Shortcut approach using contribution margin/unit  Shortcut approach using contribution margin ratio 13

14. CM Income Statement Approach Sales - Variable Expenses Contribution Margin - Fixed Expenses Operating Income 14 ($35) x units sold) – ($21 x units sold) - $7,000 = 0 = 500 posters

15. Cost-Volume-Profit Analysis  The Profit Equation  Profit = SP(x) – VC(x) – TFC  Equation Abbreviations  x = Quantity of units produced and sold  SP = Selling price per unit  VC = Variable cost per unit; TFC = Total fixed cost  $0 = $35(x) - $21(x) - $7,000  $0 = $14(x) - $7,000  X = 500 units 15

16. Short-Cut Approach to Calculating Breakeven Using CM/Unit Fixed expenses + Operating income Contribution margin per unit Units sold = $7,000 + $0 $14 Units sold = = 500 posters 16

17. Short-Cut Using Contribution Margin Ratio Fixed expenses + Operating income Contribution margin ratio Sales in $ = $7,000 + $0 0.40 Sales in $ = = $17,500 Dividing fixed costs by CM/unit gives breakeven in units Dividing fixed costs by CM Ratio gives breakeven in sales revenue dollars 17

18. Finding the Volume Needed for a Target Profit Using CM/Unit CVP analysis helps managers determine what they need to sell to earn a target amount of profit. Fixed expenses + Operating income Contribution margin per unit Units sold = $7,000 + $4,900 $14 Units sold = = 850 posters $11,900 $14 Check our calculations: Sales (850 units) x $35 = $29,750 Less: Variable Costs (850 x $21) ( 17,850) Fixed Costs (7,000) Profit $4,900 18 =

19. Finding the Sales Volume Needed for a Target Profit Using CM Ratio CVP analysis helps managers determine what amount of sales revenue needed to earn a target amount of profit. Fixed exp + Target profit (operating inc) Contribution margin ratio Sales $ = $7,000 + $4,900 0.40 Sales $ = = Sales = $29,750 to generate profit of $4,900 Check: $29,750 ÷ $35 = 850 posters $11,900 0.40 19

20. a. Use the income statement equation approach. ($50 x units) – ($20 x units) - $210,000 = $0 $30 x units= $210,000 units= $210,000/$30 units= 7,000 b. Profit Equation: (Profit) = SP(x) – VC(x) – TFC $0 = $50(x) - $20(x) - $210,000 x = 7,000 units Facts: SP/unit = $50; VC/unit = $20; TFC = $210,000 Relevant range up to 15,000 passengers 20 Use information from Bay Cruise Line Data to compute # of dinner cruise tickets it must sell to break even.

21. B. Use the shortcut contribution margin/unit approach, then perform a numerical proof to ensure that your answer is correct. Proof: 7000 tix x $50sp/unit $350,000 = 0 C. Use your answers from a and b to determine the sales revenue needed to break even. 7,000 units to break even X $50 sales price/unit = $350,000 Sales Revenue needed to break even Fixed expenses + Operating income Contribution margin per unit Units sold = $210,000 + $0 $30 Units sold = = 7,000 tickets 21

22. Fixed expenses + Operating income Contribution margin ratio Sales in $ = $210,000 + 0 0.60 (CM/unit ÷ SP/unit) Sales in $ = = $350,000 Sales Revenue to Break even $210,000 0.60 Sales in $ = 22 D. Use the contribution margin ratio approach to verify the sales revenue needed to break even.

23. Graphing the CVP Relationships Step 1:  Choose a sales volume (Units x $Price)  Plot point for total sales revenue  Draw sales revenue line from origin through the plotted point 23

24. Preparing a CVP Chart Co. sells units for $10 per unit.

25. Step 2: Draw the fixed cost line. Fixed Costs are $4,000 25 Preparing a CVP Chart

26. Step 3: Draw the total cost line (fixed plus variable) Variable cost/unit is $4

27. Step 4: Identify the breakeven point Preparing a CVP Chart Breakeven point 667

28. Preparing a CVP Chart Operating Loss Operating Income Breakeven point Step 5: Mark operating income and operating loss areas on the graph.

29. Sensitivity Analysis  Managers need to be prepared for increasing costs, pricing pressure from competitors, and other changing business conditions.  Sensitivity Analysis:  Conducts “What if” analysis  What if the sales price changes?  What if costs change?  What if the sales mix changes? 29

30. What if the Sales Price Changes?  Calculate a new contribution margin/unit using the new sales price  Use the new contribution margin/unit to compute breakeven sales in units  Use the new contribution margin/unit to compute breakeven sales to maintain target profit  Using the new breakeven numbers, decide if a change should be made to sales price 30

31. Kay want to know what sales price/unit needs to be to earn a profit of $10,000 next month?  Base Info: SP/unit - $35; VC/unit - $21; TFC - $7,000 Breakeven units – 500  Profit Equation: Profit=SP/unit(x) – VC/unit(x) - TFC $10,000 = SP(500 units) - $21(500 units) - $7,000 SP(500 units) = $27,500 ÷ 500 units SP = $55/unit  What if she can sell 700 posters? $10,000 = SP(700) - $21(700) - $7000; SP = $45.29 31

32. What if Fixed Costs Change?  Mgt. considering change in production process that will increase fixed costs/month by $2,000, but will decrease variable costs/unit to $16. Current InfoProposed VC/unit = 21 $16 TFC = $7,000 $9,000 Currently selling 850 posters so Current profit = $35(850) - $21(850) - $7,000 = $4,900 Proposed profit = $35(850) - $16(850) - $9,000 = $7,150  What if Variable Costs Change? Supplier raises price for Kay’s raw materials. Everything else stays same. What is breakeven point? Higher variable cost/unit has same effect as lower sales price/unit – both reduce product’s cm/unit, so increases B/E pt. 32

33. What if Fixed Costs & Volume Changes?  Sales Mgr thinks a $5,000 increase in advertising budget would increase sales by $12,250 to a total of 1200 units. Should advertising budget be increased?  Current: SP = $35/unit; Volume = 850 units  Incremental CM: $12,250 x 40% CM Ratio = $4,900 Increased CM  Less: incremental advertising expense (5,000)  Decreased profit $ (100) Proof:Current Proposed Difference Sales$29,750 $42,000 $12,250 (VC)(17,850) (25,200) (7,350) CM 11,900 16,800 4,900 TFC (7,000) (12,000) (5,000) Incr. Profit(Loss)$ 4,900 4,800 (100) 33

34. Information Technology and Sensitivity Analysis  Allows managers to perform a wide array of sensitivity analyses before committing to decisions.  Uses Excel spreadsheets to perform sensitivity analyses  Allows managers to estimate how one change (or several simultaneous changes) affects business operations  Uses spreadsheet software to create CVP graphs 34

35. Breakeven in Sales Revenue: Multiproduct Firm Kay has decided to start selling large posters in addition to regular posters. None of her original costs will change. Large poster sales price = $70; V.C./unit = $40 so CM/unit = $30. For every 5 regular posters sold, Kay expects to sell 3 large posters. (5/8 of sales will be reg. posters & 3/8 will be large posters, that is a 5:3 sales mix of posters). Kay estimates total sales of 800 posters. What is weighted-average CMR? 35

36. Breakeven in Sales Revenue: Multiproduct Firm Total expected contribution margin: Regular posters (500 x $14) $ 7,000 Large posters (300 x $30) $ 9,000 Total expected contribution margin $16,000 Divided by total expected sales revenue: Regular posters (500 x $35) $17,500 Large posters (300 x $70) 21,000 Total expected sales ÷ $38,500 Wtd. Avg. Contribution margin ratio = 41.558% 36

37. Breakeven in Sales Revenue: Kay’s Posters Fixed expenses + Operating income Wtd. Avg. Contribution margin ratio B/E-Sales $ = B/E - Sales $ = = = $16,844 (rounded) Sales Revenue $7,000 0.41558 $7,000 + 0 0.41558 For every 5 reg. posters, Kay expects to sell 3 lrg posters; 5:3 sales mix. $16,844 ÷ 8 posters = $2,106 x 5 reg. posters= $10,530 rev from sale of reg. posters, & $2,106 x 3 large posters = $ 6,318 rev from sale of lrg posters Now Kay wants to know what sales revenue needs to be to reach target monthly income of $10,000. (Just replace 0 above with $10,000) Sales $ = $7,000 +10,000 ÷.41558 = $40,907 Sales Revenue 37

38. Bay Cruise Line decides to offer 2 types of dinner cruises: regular & executive cruises. Exec. cruise includes free cocktails & a 5-course dinner on upper deck. Fixed expenses stay at $210,000/mo & ticket prices & variable expenses are as listed: Regular CruiseExecutive Cruise Sales price per ticket$50$130 Variable expense per passenger$20$40 Sales Mix Calculation Regular ExecutiveTotal Sales price per unit........................ $ 50 $130 Less: Variable cost per unit........... (20) (40) Contribution margin per unit........ $ 30 $ 90 Sales mix....................................... x 4 x 1 = 5 Contribution margin..................... $120 $ 90 =$210 Weighted-average contribution margin per unit ($210/5)........... $ 42 38 Assuming that Bay Cruise Line expects to sell four regular cruises for every executive cruise, compute the weighted-average contribution margin per unit.

39. Is this weighted avg. C/M/unit higher or lower than the old C/M/unit when they just sold regular cruises? (higher) Why? Will this new sales mix cause Bay Cruiseline’s breakeven point to increase or decrease its breakeven point? Sales Mix Calculation Regular ExecutiveTotal Sales price per unit $ 50 $130 Less: Variable cost per unit (20) (40) Contribution margin per unit $ 30 $ 90 Sales mix x 4 x 1 5 Contribution margin $120 $ 90 $210 Wtd-avg CM per unit ($210/5) $ 42 Same info as previous slide 39

40. Will this new sales mix cause Bay Cruise Line’s breakeven point to increase or decrease from what it was when it sold only regular cruises? Sales Mix Calculation Regular ExecutiveTotal Sales price per unit $ 50 $130 Less: Variable cost per unit (20) (40) Contribution margin per unit $ 30 $ 90 Sales mix x 4 x 1 5 Contribution margin $120 $ 90 $210 Wtd-avg CM per unit ($210/5) $42 Fixed expenses + Operating income Weighted Average Contribution margin per unit B/E Sales in $ = $210,000 + 0 – B/E $42 wtd avg CM/unit Sales in $ = = 5,000 tickets Decrease, down from 7,000 tickets before 40

41. What if the Sales Mix Changes? Must recalculate based on new Sales Mix Sales Mix Calculation Reg Product Large Product Total Sales price per unit $ 35 $ 70 Less: Variable cost per unit (21) (40) Contribution margin per unit $ 14 $ 30 Sales mix x 5 x 3 8 Contribution margin $ 70 $ 90 $160 Weighted-average contribution margin per unit ($160/8) $ 20 Sales Mix Calculation Regular Product Large Product Total Sales price per unit $ 35 $ 70 Less: Variable cost per unit (21) (40) Contribution margin per unit $ 14 $ 30 Sales mix x 6 x 2 8 Contribution margin $ 84 $ 60 $144 Weighted-average contribution margin per unit ($144/8) $ 18 41

42. Common Indicators of Risk  Margin of Safety  The excess of expected sales over breakeven sales  Operating Leverage  The relative amount of fixed and variable costs that make up a company’s total costs 42

43. Margin of Safety  Excess of expected sales over breakeven sales  Drop in sales that the company can absorb before incurring a loss  Used to evaluate the risk of current operations as well as the risk of new plans 43

44. Margin of Safety for Kay’s Poster Bsn Breakeven sales in units Margin of safety in units Expected sales in units = − Breakeven sales Margin of safety in dollars Expected sales = − = 950 units − 500 units = 450 units = $33,250 – $17,500 = $15,750 44

45. Margin of Safety as a Percentage Margin of safety as a percentage Margin of safety in units Expected sales in units = 450 Units 950 Units = 47.4% (rounded) = Margin of safety as a percentage Margin of safety in dollars Expected sales in dollars = = $15,750 $33,250 47.4% (rounded) = 45

46. High Operating Leverage  High operating leverage companies have:  Higher levels of fixed costs and lower levels of variable costs  Higher contribution margin ratios  For high operating leverage companies, changes in volume significantly affect operating income, so they face:  Higher risk  Higher potential for reward  Examples include golf courses, hotels, rental car agencies, theme parks, airlines, cruise lines 46

47. Low Operating Leverage  Low operating leverage companies have:  Higher levels of variable costs and lower levels of fixed costs  Lower contribution margin ratios  For low operating leverage companies, changes in volume do NOT have as significant an effect on operating income, so they face:  Lower risk  Lower potential for reward  Examples include merchandising companies. 47

48. Operating Leverage Factor  How responsive a Co.’s operating income is to changes in volume  Lowest value for Operating Leverage factor is 1, if Co. has no fixed costs Operating leverage factor = Contribution margin Operating income Operating leverage factor = $ 13,300 $6,300 If sales revenue increases by 10%, then operating income will increase by 10% x 2.11 (OL factor) = 21% increase in op. income 48 = 2.11 (rounded)

49. Using OLF to Measure Expected Change in Profit Taco King & Mexi Land are competitors & reported same sales revenue & before-tax profit during May: Taco King Mexi Land Sales $40,000 $40,000. Variable costs (22,000) (8,000) Contribution margin 18,000 32,000. Fixed costs (8,000)(22,000) Operating Income $10,000. 49 If sales drop by 20% for both, which company suffers more? Taco King Mexi Land Degree of operating leverage $18,000 CM $10,000 Op. Inc. = 1.8 OLF $32,000 CM $10,000 Op.Inc. = 3.2 OLF Decrease in profit 1.8 × 20% = 36% Decline in Profit 3.2 × 20% = 64% Decline in Profit Mexi Land’s higher operating leverage results in a larger profit decline.

50. END OF SEGMENT Professor Garvin, JD; CPA – ACG2071