1. McGraw-Hill/IrwinCopyright ©2008 The McGraw-Hill Companies, Inc. All rights reserved. Fundamentals of Cost-Volume-Profit Analysis Chapter 3

2. 3-2 Learning Objectives: 2.Understand the effect of cost structure on decisions. 3.Use Microsoft Excel to perform CVP analysis. 1.Use cost-volume-profit (CVP) analysis to analyze decisions. 4.Incorporate taxes, multiple products, and alternative cost structures into the CVP analysis. 5.Understand the assumptions and limitations of CVP analysis.

3. 3-3 Cost-Volume-Profit Analysis LO1Use cost-volume-profit (CVP) analysis to analyze decisions. What is CVP? COST VOLUME PROFIT CVP studies the relationship between revenue, cost, and volume and their effect on profits. #

4. 3-4 The Profit Equation The Income Statement Total Revenue - Total Costs = Operating Profit Operating Profit equals Total Revenue less Total Costs! The Income Statement written horizontally: Operating Profit  = = Total Revenue - TC Total Cost -TR

5. 3-5 Profit Equation, Continued… Total Revenue (TR) = Price (P) x Units of output produced and sold (X) TR=PX Total Cost (TC) = [Variable Costs per unit (V) x Units of Output (X)] + Fixed Cost (F) TC= VX + F

6. 3-6 Profit Equation, Continued…  =TR-TC  =PX-VX+F  =P-VX-F

7. 3-7 U-Develop: An Example U-Develop Income Statement For the Month Ending March 200X Total Per Unit Sales$ 7,200$ 0.60 Less: Variable Cost of Goods Sold3,6000.30 Less: Variable Selling Costs720.06 Contribution Margin2,8800.24 Less: Fixed Costs1,500 Operating Profit$ 1,380 Developed 12,000 prints in March

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10. 3-10 Contribution Margin Contribution Margin:The difference between price and variable cost. It is what is leftover to cover fixed costs and then add to operating profit. AKA: “CM” Contribution Margin Per Unit: Price Per Unit-Variable Cost Per Unit=CM Per Unit P unit -V unit =CM unit

11. 3-11 Contribution Margin (Total) Total Contribution Margin: (Price x Quantity)-(Variable Cost x Quantity=Total CM P-VX= or PX-VX=Total CM

12. 3-12 Example: U-Develop CM Using the data from U-Develop Sold 12,000 units Total Per Unit Sales$ 7,200$ 0.60 Less: Variable Cost of Goods Sold3,6000.30 Less: Variable Selling Costs720.06 Contribution Margin2,8800.24 Less: Fixed Costs1,500 Operating Profit$ 1,380 1.What is CM per unit?$0.60 – $0.36 = $0.24 2.What is total CM?($0.60 - $0.36)(12,000) = $2,880

13. 3-13 Contribution Margin, cont… Contribution Margin, why do I care? U-Develop: Cm unit = $0.24 For every $1.00 in sales, U-Develop has $0.24 available to cover fixed costs. Once fixed costs are covered, $0.24 for each dollar sales will increase profits!

14. 3-14 Contribution Margin Ratio Contribution Margin Ratio: Contribution margin as a percentage of sales revenue. Total Contribution Margin Ratio: Total contribution margin as a percent of total sales revenue. It describes how much the contribution margin is for each dollar in sales. Unit Contribution Margin Ratio: Contribution margin per unit as a percentage of sales price per unit. This calculates the contribution margin provided for each dollar of revenue. P -VX PX P-V P CM Per Sales Dollar

15. 3-15 Example: Contribution Margin Ratio (CMR) CMR PVX PX U-Develop $.60$.3612,000.6012,000 CMR $2,880 $7,200.40 CMR unit $.24 $.60.40

16. 3-16 Break-Even Break-even:The point at which profits equal zero. At break-even, all fixed costs are covered, but the firm is not producing any operating profit. Equations: TR – TC = π Break-even is where π = 0 TR = TC + π TR = PX and TC = VX + F) PX = VX + F + π PX – VX = F + π X(P-V) = F + π Break-Even= F XP-V + π = F XP-V

17. 3-17 Break-Even, continued… Since, sales – variable cost = contribution margin, then: Break-Even = Fixed Costs Contribution Margin Unit Contribution Margin: If unit CM is used, then the calculation provides the number of units necessary to break-even. Contribution Margin Ratio: If unit CM Ratio is used, then the calculation provides the sales dollars necessary to break-even.

18. 3-18 Example: Break-Even in Units F X  CM unit X $.24 $0$1,500 X6,250 prints

19. 3-19 Example: Break-Even in Sales Dollars The total sales dollars at which profits equal zero. Break-even: Total revenues = Total costs F TR $0 CMR  = $0 TR.40 $1500 = $3,750 6,250 prints X $.60 = $3,750

20. 3-20 Target Volume in Units Target Profit =P-VX-F Target Volume (units) = Fixed Cost + Target Profit Unit Contribution Margin X = F+  P-V

21. 3-21 Example: Target Volume in Units U-DevelopTarget Profit = $ 1,800 Formula: = F +  CM unit X = $ 1,500 + $ 1,800 $ 0.24 X = 13,750 units

22. 3-22 Target Volume in Sales Dollars = Fixed costs+Target profit Contribution margin ratio Target volume sales dollars TR F  + CMR =

23. 3-23 Example: Target Volume in Sales Dollars U-Develop: F TR  + CMR = TR.40 $1,800$1,500 TR$8,250 13,750 x $.60 = $8,250 Given: Target  $1,800

24. 3-24 CVP Summary: Break-Even Break-even volume (units) = Fixed costs Unit contribution margin Break-even volume (sales dollars) = Fixed costs Contribution margin ratio

25. 3-25 CVP Summary: Target Volume Target volume (units) = Fixed costs + Target profit Unit contribution margin Target volume sales dollars = Fixed costs+Target profit Contribution margin ratio

26. 3-26 Graphic Presentation: U-Develop Break-Even Total revenue Total cost $3,750 6,250 prints

27. 3-27 CVP and the Effects of Different Cost Structures LO2Understand the effect of cost structure on decisions. Cost Structure: The proportion of fixed and variable costs to total costs. Operating Leverage: The extent to which the cost structure is comprised of fixed cost. Operating Leverage = Contribution Margin Fixed Costs The higher the organization’s operating leverage, the higher the break-even point.

28. 3-28 Comparison of Cost Structures Lo-Level CompanyHigh-Level Company (1,000,000 units) AmountPercentageAmountPercentage Sales$1,000,000100%$1,000,000100% Variable Cost$750,00075%$250,0025% Contribution Margin$250,00025%$750,00075% Fixed Costs$50,0005%$550,00055% Operating Profit$200,00020%$200,00020% Break-Even200,000 units733,334 units CM per Unit$0.25$0.75 Degree of Operating Leverage1.253.75

29. 3-29 Example: Operating Leverage Why do I care?Suppose Low Level & High- Level both increase sales 10% or $100,000 Low-LevelHigh-Level C Sales$100,000 CMR.25.75 Increase in Profit$25,000$75,000 Prior NI$200,000 NI with Sales increase of 10%$225,000$275,000

30. 3-30 Operating Leverage, Continued... Low-LevelHigh-Level Percent Increase in sales Degree of Operating Leverage Percent increase in NI Prior NI Percent increase in NI NI with sales increase of 10% 10% 1.25 12.5% $200,000 12.5% $225,000 10% 1.75 17.5% $200,000 17.5% $235,000

31. 3-31 Margin of Safety The excess of projected or actual sales volume over break-even volume. or The excess of projected or actual sales revenue over break-even revenue. Suppose U-Develop sells 8,000 prints 8,0006,2501,750 prints $4,800$3,750$1,050 1750 x $.60 = $1,050

32. 3-32 Using Spreadsheets for CVP Analysis LO3Using Microsoft Excel to perform CVP analysis. Using Excel, combined with an analysis tool such as Goal Seek, CVP analysis is simplified. Steps: 1.In the “Set cell” edit field, enter the cell address for the target profit calculation. 2.In the “To value” edit field, enter the target profit. 3.In the “By changing cell” edit field, enter the cell address of the volume variable. 4.Click “OK” and the program will find the break-even volume.

33. 3-33 Extending CVP: Taxes LO4 Incorporate taxes, multiple products, and alternative cost structures into the CVP analysis. What if U-Develop is in the 25% tax bracket and wants profit after taxes of $1,800? Target Volume CM unit F 1 - t  target.75 X $1,500 $1,800 $.24 = 16,250

34. 3-34 CVP and Taxes, Continued... To Prove it Works: 16,250$.60$9,750Sales VC16,250$.365,850 CM$3,900 FC1,500 NIBT$2,400 Taxes6002,40025% Net Income$1,800

35. 3-35 Extending CV P: Multiple Products What if: U-Develop does prints and enlargements? PrintsEnlargements Selling price$.60$1.00 Variable cost.36.56 Contribution margin$. 24$. 44 Total Fixed Costs$1,820

36. 3-36 Example: Product Mix For every 9 prints sold U- Develop sells 1 enlargement. U-Develop’s product mix: Weighted Average Contribution Margin 9/10$.241/10$.44$.26 Breakeven $1,820 $.26 7,000 6,300 prints 9/10 700 enlargements 1/10

37. 3-37 Alternative Cost Structures Given:Fixed costs of $1,500 are sufficient for monthly volumes less than or equal to 5,000 prints. For every additional 5,000 prints U-Develop must rent a machine for $480 per month. Remember, original break-even was 6,250 units. (CM x X) – FC = π ($0.24 x 6,250) – ($1,500 + $480) = ($480) Recalculate break-even using new fixed cost containing the rental of the additional machine. Break-even Units = F new CM units = $1,500 +$480 $0.24 = 8,250

38. 3-38 Assumptions and Limitations of CVP LO5Understand the assumptions and limitations of CVP analysis. Assumptions & Limitations: 1.Although the CVP model is a very strong tool, the output is dependent upon the assumptions made by cost analyst. These assumptions include which costs are fixed vs. variable. 2.With the aid of software programs, many of the limitations have been eliminated. Complicated cost structures are easily incorporated in CVP analysis when software tools are used.

39. 3-39 The Power Tool Division of ABC Hardware sells one product, Jig Saw, and has the following data for the second quarter: Units of output: 1,200 units Price per unit: $150 Variable cost per unit: 90 Total fixed costs: 48,000 Required: Determine Quarterly operating profit when 1,200 units are sold. Break-even volume in units and sales dollars. Contribution margin ratio. Sales dollars and units needed to generate an operating profit of $57,000. Number of units sold that would produce an operating profit of 15% of sales dollars. Problem 1

40. 3-40 The Power Tool Division of ABC Hardware introduces a second product, Circular Saw, whose unit price and unit variable cost are $200 and $120, respectively. The total fixed cost is increased to $68,000. The manager of ABC Hardware estimates that Jig Saws and Circular Saws will sell in a 3:2 ratio. Required: Calculate the break-even volume in units using fixed product mix method, and weighted-average contribution margin method. Problem 2 (cont. from problem 1)