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# Cost-Volume-Profit Analysis

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1. Cost-Volume-Profit Analysis Chapter 3

2. Understand the assumptions underlying cost-volume-profit (CVP) analysis.

3. Cost-Volume-Profit Assumptionsand Terminology Cost volume profit analysis examines the behavior of total costs and operating income as changes occur in the output level, the selling price, the variable cost per unit, and /or the fixed costs of a product.

4. Explain the features of CVP analysis.

5. 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.

6. 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)

7. 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

8. 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%

9. 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.

10. Determine the breakeven point and output level needed to achieve a target operating income using the equation, contribution margin, and graph methods.

11. Breakeven PointEquation Method Variable expenses Fixed expenses Sales – = Total revenues = Total costs

12. Abbreviations SP = Selling price VCU = Variable cost per unit CMU = Contribution margin per unit = SP - VCU CM% = Contribution margin percentage FC = Fixed costs

13. Abbreviations Q = Quantity of output units sold (and manufactured) OI = Operating income TOI = Target operating income TNI = Target net income

14. Equation Method Total revenues = Total costs (Selling price × Quantity sold) = (Variable unit cost × Quantity sold) + Fixed costs Let Q = number of units to be sold to break even \$70Q – \$42Q – \$84,000 = 0 \$28Q = \$84,000 Q = \$84,000 ÷ \$28 = 3,000 units

15. Contribution Margin Method PE in units = FC / CMU \$84,000 ÷ \$28 = 3,000 units \$84,000 ÷ 40% = \$210,000

16. Graph Method Breakeven Revenue Total costs Fixed costs

17. Target Operating Income (Fixed costs + Target operating income) / Contribution margin (per unit or ratio)

18. 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

19. Understand how income taxes affect CVP analysis.

20. Target Net Incomeand 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

21. Target Net Incomeand 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

22. Target Net Incomeand 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

23. Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty.

24. Sensitivity Analysis andUncertainty 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.

25. Sensitivity Analysis andUncertainty 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

26. Sensitivity Analysis andUncertainty 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

27. Sensitivity Analysis andUncertainty 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

28. Use CVP analysis to plan fixed and variable costs.

29. 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.

30. 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

31. 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

32. 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.

33. Apply CVP analysis to a company producing different products.

34. 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.

35. Effects of Sales Mix on Income Contribution margin per shirt: \$20 – \$9 = \$11 What is the contribution margin of the mix? \$28 + (2 × \$11) = \$28 + \$22 = \$50

36. 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

37. 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

38. Effects of Sales Mix on Income What is the weighted-average budgeted contribution margin? Pants: 1 × \$28 + Shirts: 2 × \$11 = \$50 ÷ 3 = \$16.667

39. 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

40. Effects of Sales Mix on Income Sales mix can be stated in sales dollars: PantsShirts Sales price \$70 \$40 Variable costs 42 18 Contribution margin \$28 \$22 Contribution margin ratio 40% 55%

41. 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%

42. 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

43. End of Chapter 3