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Chapter 18

Chapter 18. Cost Behavior and Cost-Volume-Profit Analysis. Conceptual Learning Objectives. C1: Describe different types of cost behavior in relation to production and sales volume. C2: Identify assumptions in cost-volume profit analysis and explain their impact.

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Chapter 18

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  1. Chapter 18 Cost Behavior and Cost-Volume-Profit Analysis

  2. Conceptual Learning Objectives C1: Describe different types of cost behavior in relation to production and sales volume. C2: Identify assumptions in cost-volume profit analysis and explain their impact. C3: Describe several applications of cost-volume-profit analysis.

  3. Analytical Learning Objectives A1:Compare the scatter diagram, high-low, and regression methods of estimating costs. A2: Compute contribution margin and describe what it reveals about a company’s cost structure. A3:Analyze changes in sales using the degree of operating leverage.

  4. Procedural Learning Objectives P1:Determine cost estimates using three different methods. P2:Compute the break-even point for a single product company. P3:Graph costs and sales for a single product company. P4: Compute break-even point for a multiproduct company.

  5. Questions Addressed byCost-Volume-Profit Analysis CVP (BE) analysis is used to answer questions such as: • What sales volume is needed to break-even? • What sales volume is needed to earn a target income? • What is the change in income if selling prices decline and sales volume increases? • How much does income increase if we install a new machine to reduce labor costs? • What is the income effect if we change the sales mix of our products or services?

  6. Total Cost C1 Total Costs = Total fixed costs + Total variable Costs

  7. Total Fixed Cost(Exhibit 18.1, Page 757) C1 Total fixed costsremain unchangedwhen activity (units) changes. Monthly Basic Telephone Bill Your monthly basictelephone bill probablydoes not change whenyou make more local calls. Number of Local Calls

  8. Fixed Cost Per Unit C1 Fixed costs per unit declineas activity (units) increases. Monthly Basic Telephone Bill per Local Call Your average cost perlocal call decreases asmore local calls are made. Number of Local Calls

  9. Total Variable Cost(Exhibit 18.1, Page 757) C1 • Total variable costschangewhen activity (units) changes. Total Long DistanceTelephone Bill Your total long distancetelephone bill is basedon how many minutesyou talk. Minutes Talked

  10. Variable Cost Per Unit C1 Variable costs per unitdo not changeas activity (unit) increases. Per MinuteTelephone Charge The cost per long distanceminute talked is constant.For example, 7cents per minute. Minutes Talked

  11. Cost Behavior Summary C1

  12. Mixed Costs(Exhibit 18.1, Page 757) Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage. Example: monthly electric utility charge • Fixed service fee • Variable charge perkilowatt hour used

  13. Step-Wise Costs Exhibit 18.2 (page 758) Total cost remainsconstant within anarrow rangeofactivity. Cost Activity

  14. Curvilinear CostsExhibit 18.2 (page 758) 1. Increase at a non-constant rate as volume increases.2. Substantial gains in efficiency at low volume;Smaller gains in efficiency at higher volume. 3. When volume and costs are graphed, curvilinear costs appear as a curved line that starts at intersection point of cost axis and volume axis (total cost is zero when volume is zero) and increases at different rates.

  15. Cost Behavior Exercise 2

  16. The objectiveis to classify all costs as either fixed or variable. MeasuringCost Behavior P1

  17. Measuring Cost Behavior After establishing that cost data are reliable and useful in predicting future costs, three methods commonly used to analyze past cost behavior.-Scatter Diagrams -High-Low Method -Least-Squares Regression

  18. Δin costΔin units Unit Variable Cost = Slope = 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Diagram Exhibit 18.3: Data Vertical distance is the change in cost. Horizontal distance is the change in activity.

  19. Scatter Diagram Exercise 1

  20. The High-Low Method The following relationships between units produced and costs are observed: Using these two levels of activity, compute: • the variable cost per unit. • the total fixed cost.

  21. $8,500$50,000 Δin costΔin units • Unit variable cost = = = $0.17 /unit • Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per unit × 17,500)Fixed cost = $29,000 – $11,475 = $17,525 The High-Low Method

  22. High-Low Method Exercise 7

  23. Least-Squares Regression P1 • Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators. The objective of the cost analysis remains the same: determination oftotal fixed costand thevariable unit cost.

  24. Computing Break-Even Point P2 The break-even point (expressed in units of product or dollars of sales) is the sales level at which a company earns neither a profit nor incurs a loss. @ BEP => Total Sales = TC = TFC + TVC

  25. Computing Break-Even Point(Contribution Margin) P2 Contribution margin is amount by which revenueexceeds thevariable costsof producing the revenue.

  26. Computing Break-Even Point P2 How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $24,000

  27. Computing Break-Even Point P2 How manyunitsmust this company sell to cover its fixed costs (break even)? Answer: $24,000 ÷ $30 per unit = 800 units

  28. Fixed costs Break-even point in units = Contribution margin per unit Computing Break-Even Point P2 We have just seen one of the basic CVP relationships => the break-evencomputation. Unit sales price less unit variable cost($30 in previous example)

  29. Fixed costs Break-even point in dollars = Contribution marginratio Computing Break-Even Point P2 The break-even formula may also be expressed in sales dollars. Unit contribution margin Unit sales price

  30. CVP Analysis Exercise 9

  31. Total costs • Draw the total cost line with a slopeequal to the unit variable cost. Preparing a CVP Chart(Exhibit 18.14, Page 764) P3 • Plot total fixed costs on the vertical axis. Total fixed costs Costs and Revenuein Dollars Volume in Units

  32. Preparing a CVP Chart(Exhibit 18.14, Page 764) P3 • Starting at the origin, draw the sales line with a slope equal to the unit sales price. Sales Total fixed costs Costs and Revenuein Dollars Total costs Break-even Point Volume in Units

  33. CVP Chart Exercise 9

  34. Assumptions of CVP Analysis C2 • A limited range of activity called therelevant range, where CVP relationships are linear. • Unit selling price remains constant. • Unit variable costs remain constant. • Total fixed costs remain constant. • Production = sales (no inventory changes).

  35. Computing Income from Expected Sales C3 Income (pretax) = Sales – Variable costs – Fixed costs

  36. Computing Sales for a Target Income C3 Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income. Fixed costs +Target income Unit sales = Contribution margin per unit Fixed costs +Target income Dollar sales = Contribution margin ratio

  37. Exercise 10

  38. Target netincome is income after income tax. But we can use target income before tax in our calculations. Computing Sales (Dollars) for aTarget Net Income C3 Fixed Target income costs before tax + Dollar sales = Contribution margin ratio

  39. Computing Sales (Dollars) for a Target Net Income To convert target net income to before- tax income, use the following formula: Target net income Before-tax income = 1 - tax rate Net Income = Income before Tax - Tax Expense Tax Expense = Income before Tax * Tax Rate Therefore; Net Income = Income before Tax ( 1 - Tax Rate) => Income before Tax = Net Income / ( 1-Tax Rate)

  40. Exercise 11

  41. Margin of safety is the amount by which sales can drop before the company incurs a loss. Margin of safety equalsexcess of expected sales over sales at break-even sales level. Margin of safety may be expressed as a percentage of expected sales: Margin of safety Expected sales - Break-even sales percentage Expected sales = Computing the Margin of Safety Exhibit 18.24, page 768

  42. Contribution margin Income Statement Exhibit 18.19, page 767: Pretax Exhibit 18.20, page 767: After tax

  43. The basic CVP relationships may be used to analyze a number of situations such as: -changing sales price, -changing variable cost, or -changing fixed cost. Exercise 12 Sensitivity Analysis

  44. The CVP formulas may be modified for use when a company sells more than one product: The unit contribution margin is replaced with the contribution margin for acomposite unit. A composite unit is composed of specific numbers of each product in proportion to the productsales mix. Sales mix is the ratio of the volumes of the various products. Computing Multiproduct Break-Even Point

  45. Computing MultiproductBreak-Even Point P4 The resulting break-even formulafor composite unit sales is: Fixed costsContribution marginper composite unit Break-even pointin composite units =

  46. Computing Multiproduct Break-Even Point • To apply multiproduct CVP analysis, estimate break-even point by using a composite unit. • -Determine sales mix of various products. • -Using sales mix, determine the selling price of a composite unit by multiplying the sales mix ratio times the selling price of each product and then adding the totals for all of the products. • -Compute the variable price of a composite unit in the same manner, and then determine the CM per composite unit. • -Compute Break-even point in composite units; BEP equals total fixed costs divided by CM per composite unit. • -To determine how many units of each product must be sold to break even, multiply the number of units of each product in the composite unit by the break-even point in composite units.

  47. Exercises 15 & 17

  48. Contribution margin Pretax income = Degree of operating leverage Operating Leverage A measure of the extent to which fixed costs are being used in an organization. A measure of how a percentage change in sales will affect profits. Degree of operating leverage (DOL) is defined as total CM (in dollars) divided by pretax income.

  49. DOL is used to measure the effect of changes in the level of sales on pretax income by multiplying DOL by the percentage change in sales. A high DOL firm will experience a higher increase in pretax income due to increase in the level of sales. Exercises 19 3 Steps: -Prepare a CM Income Statement & calculate DOL for Co. A; -Prepare a CM Income Statement & calculate DOL for Co. B; -Analyze & interpret which company benefits more from a 20% sales increase;

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