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# Cost-Volume-Profit Analysis

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1. Cost-Volume-Profit Analysis Chapter6 Main Concepts: 1. Basics of CVP Analysis 2. Contribution Approach 3. Break-Even Analysis a. Equation Method b. Contribution Margin Method 4. The Concept of Sales Mix

2. Assumptions of CVP Analysis • Selling price is constant throughout the entire relevant range. • Costs are linear throughout the entire relevant range. • In multi-product companies, the sales mix is constant.

3. The Basics of Cost-Volume-Profit (CVP) Analysis Contribution Margin (CM) is the amount remaining from sales revenue after variable cost have been deducted.

4. The Basics of Cost-Volume-Profit (CVP) Analysis CM goes to cover fixed costs.

5. The Basics of Cost-Volume-Profit (CVP) Analysis After covering fixed costs, any remaining CM contributes to income.

6. The Contribution Approach Consider the following information developed by the accountant at Sakuraba Co.:

7. The Contribution Approach For each additional unit Sakuraba sells, \$200 more in contribution margin will help to cover fixed costs and profit.

8. The Contribution Approach Each month Sakuraba must generate at least \$80,000 in CM to break even for the month.

9. The Contribution Approach If Sakuraba sells 400 units in a month, it will be operating at the break-even point.

10. The Contribution Approach If Sakuraba sells one additional unit (401 bikes), net income will increase by \$200.

11. The Contribution Approach • The break-even point can be defined either as: • The point where total sales revenue equals total costs (variable and fixed). • The point where total contribution margin equals total fixed costs.

12. Contribution margin Sales = CM Ratio Contribution Margin Ratio • The contribution margin ratio is defined as follows:

13. Contribution margin Sales = CM Ratio \$200 \$500 = 40% Contribution Margin Ratio • The contribution margin ratio is defined as follows: • For Sakuraba, the contribution margin ratio is:

14. Contribution Margin Ratio At Sakuraba, each \$1.00 increase in sales revenue results in a total contribution margin increase of 40¢. If sales increase by \$50,000, what will be the increase in total contribution margin? \$20,000 = \$.40 x \$50,000

15. Contribution Margin Ratio A \$50,000 increase in sales revenue

16. Contribution Margin Ratio A \$50,000 increase in sales revenue results in a \$20,000 increase in CM. (\$50,000 × 40% = \$20,000)

17. Break-Even Analysis • The break-even point is the point where • Total sales revenue = total costs or • Total contribution margin = total fixed costs. • Break-even analysis can be approached in two ways: • Equation method • Contribution margin method.

18. Equation Method Sales – (Variable costs + Fixed costs) = Profits OR Sales = Variable costs + Fixed costs + Profits OR S/uX = VC/uX + Fixed costs + Profits At the break-even point profits equal zero.

19. Equation Method Here is the information from the Sakuraba Co.:

20. Equation Method • We calculate the break-even point as follows: S/uX = VC/uX + Fixed costs + Profits

21. Equation Method • We calculate the break-even point as follows: S/uX = VC/uX + Fixed costs + Profits \$500X = \$300X + \$80,000 + 0 Where: X = Number of bikes sold \$500 = Unit sales price \$300 = Unit variable cost \$80,000 = Total fixed costs

22. Equation Method • We calculate the break-even point as follows: S/uX = VC/uX + Fixed costs + Profits \$500X = \$300X + \$80,000 + 0 \$200X = \$80,000

23. Equation Method • We calculate the break-even point as follows: S/uX = VC/uX + Fixed costs + Profits \$500X = \$300X + \$80,000 + 0 \$200X = \$80,000 X = 400 units

24. Contribution Margin Method The contribution margin method is a variation of the equation method.

25. Fixed costs Unit contribution margin Break-even point in units sold = Contribution Margin Method The contribution margin method is a variation of the equation method.

26. Fixed costs Unit contribution margin Break-even point in units sold = \$80,000 \$200 = 400 bikes Contribution Margin Method The contribution margin method is a variation of the equation method.

27. Contribution Margin Method We can calculate the break-even point in total sales dollars as follows:

28. Fixed costs CM ratio Break-even point in total sales dollars = Contribution Margin Method We can calculate the break-even point in total sales dollars as follows:

29. Fixed costs CM ratio Break-even point in total sales dollars = \$80,000 40% = \$200,000 sales Contribution Margin Method We can calculate the break-even point in total sales dollars as follows:

30. CVP Relationships in Graphic Form • Viewing CVP relationships in a graph gives managers a perspective that can be obtained in no other way. • Consider the following information for Sakuraba Co.:

31. CVP Graph Dollars Fixed costs \$80,000 Units

32. CVP Graph Dollars Variable costs \$300/unit X \$90,000/300 units Units

33. CVP Graph Total costs Dollars \$80,000 + \$300X Units

34. CVP Graph \$150,000/300 units \$500/unit X Total Sales Dollars Units

35. CVP Graph Price X Dollars Break-even point Y = a + bX a + bX = Price X Units

36. CVP Graph Price X Dollars Y = a + bX \$80,000 + \$300/unit (400 units) = \$500/unit (400 units) = \$200,000 Units

37. CVP Graph Price X Dollars Break-even point 400 units or \$200,000 sales. Y = a + bX Units

39. Basics of CVP Analysis 1. What does CVP stand for? 2. Compare the Traditional and Contribution Income Statement. Cost-Volume-Profit Sales Sales -CGS -VarExp GM CM -S&A -Fixed Exp NI NI

40. Break-Even Analysis Total CM/Sales or CM per unit/Price 1. The Contribution Ratio = ________________________________. 2. At Break-Even, fixed costs = ________________________. 3. At Break-Even, sales = ________________________________. 4. Units at Break-Even = ________________________. 5. Sales at Break-Even = ________________________. Sales - Var Exp. = CM Total Exp = Fixed Exp. + Var. Exp Fixed Exp./CM per unit Fixed Exp./CM%

41. Exercise 1 Pringle Company manufactures and sells a single product. The company’s sales and costs for a recent month follow: 1. What is the monthly break-even point in units sold and in sales dollars? 2. Without resorting to computations, what is the total contribution margin at the break-even point. 3. What is the company’s CM ratio? If monthly sales increase by \$80,000 and there is no change in fixed costs, by how much would you expect monthly net income to increase.

42. Exercises 1 1. What is the monthly break-even point in units sold and in sales dollars? S/uX = VC/uX + Fixed costs + Profits \$40X = \$28X + \$150,000 + \$0 \$12X = \$150,000 X = \$150,000/\$12 X = 12,500 units 12,500 units x \$40/u = \$500,000 2. Without resorting to computations, what is the total contribution margin at the break-even point. The fixed cost of \$150,000, which would yield a profit of zero. 3a. Determine the CM ratio? CM ratio = CM/Sales = \$180,000/\$600,000 = 30% 3b. If monthly sales increase by \$80,000, by how much would you expect monthly net income to increase CM ratio X Sales = 30% X \$80,000 = \$24,000

43. Exercise 2 Super Sales Company is the exclusive distribution for a new product. The product sells for \$60 per unit and has a CM ratio of 40%. The company’s fixed costs are \$360,000 per year. 1. What are the contribution margin & variable costs per unit? 2. Using the equation method: a. What is the break-even point in units and in sales dollars? CM per unit = \$60 x 40% = \$24 Variable exp. per unit : \$60 x (100% - 40%) = \$36 S/uX = VC/uX + Fixed costs + Profits \$60X = \$36X + \$360,000 + \$0 X = 15,000 units or Fixed costs/CM per unit = \$360,000/\$24 per unit = 15,000 units Sales@BE = PriceX = \$60/unit (15,000 units) = \$900,000 or Sales@BE = Fixed costs/CM ratio = \$360,000/40%= \$900,000

44. Target Net Profit Analysis Suppose Sakuraba Co. wants to know how many bikes must be sold to earn a profit of \$100,000. We can use our CVP formula to determine the sales volume needed to achieve a target net profit figure.

45. The CVP Equation S/uX = VC/uX + Fixed costs + Profits

46. The CVP Equation S/uX = VC/uX + Fixed costs + Profits \$500X = \$300X + \$80,000 + \$100,000 Where: X = Number of bikes sold \$500 = Unit sales price \$300 = Unit variable cost \$80,000 = Total fixed costs \$100,000 = Target net income

47. The CVP Equation S/uX = VC/uX + Fixed costs + Profits \$500X = \$300X + \$80,000 + \$100,000 \$200X = \$180,000

48. The CVP Equation S/uX = VC/uX + Fixed costs + Profits \$500X = \$300X + \$80,000 + \$100,000 \$200X = \$180,000 X = 900 bikes

49. The Contribution Margin Approach We can determine the number of bikes that must be sold to earn a profit of \$100,000 using the contribution margin approach.

50. Fixed costs + Target profit Unit contribution margin Units sold to attain the target profit = The Contribution Margin Approach We can determine the number of bikes that must be sold to earn a profit of \$100,000 using the contribution margin approach.