# CHAPTER 22 COST-VOLUME-PROFIT ANALYSIS

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1 CHAPTER 22 COST-VOLUME-PROFIT ANALYSIS Related Assignment Materials Student Learning Objectives Conceptual objectives: C1. Describe different types of cost behavior in relation to production and sales volume. C2. Describe several applications of cost-volume-profit analysis. Discussion Questions 2, 3, 4, 5, 10, 12, 19 Quick Studies* 22-1, 22-2, 22-2, 22-3, , 9, 11, , , 22-12, 22-13, 22-14, 22-15, Exercises* Problems* Beyond the Numbers 22-4, 22-5, 22-6, , 22-5, , 22-4, 22-5, 22-6, 22-9 Analytical objectives: A1. Compute contribution margin and describe what it reveals about a company s cost structure. A2. Analyze changes in sales using the degree of operating leverage. Procedural objectives: P1. Determine cost estimates using the scatter diagram, high-low, and regression methods of estimating costs. P2. Compute 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. 6, 7, , , , , , 22-8 A , , 22-8, , 22-4, 22-5, , , , 22-18, 22-19, *See additional information on next page that pertains to these quick studies, exercises and problems

2 Additional Information on Related Assignment Material Connect (Available on the instructor s course-specific website) repeats all numerical Quick Studies, all Exercises and Problems Set A. Connect provides new numbers each time the Quick Study, Exercise or Problem is worked. It allows instructors to monitor, promote, and assess student learning. It can be used in practice, homework, or exam mode. Corresponding problems in set B also relate to learning objectives identified in grid on previous page. Problems 22-2A and 22-6A can be completed using EXCEL. The Serial Problem for Business Solutions starts in this chapter and continues throughout many chapters of the text. It is most readily solved manually if you use the working papers that accompany text. Narrated PowerPoint Correlation Guide Learning Objective Slides C1 3-7 P A P P C P A Synopsis of Chapter Revision Johnny Cupcakes NEW opener with new entrepreneurial assignment Streamlined learning objectives Revised cost exhibits for added clarity and learning New discussion on global use of contribution margin 22-2

3 I. Identifying Cost Behavior (CVP analysis) Cost-volume-profit analysis is a tool to predict how changes in costs and sales levels affect income; conventional CVP analysis requires that all costs must be classified as either fixed or variable with respect to production or sales volume before CVP analysis can be used. A. Fixed Costs 1. A total fixed cost remains unchanged in amount when volume of activity varies from period to period within a relevant range. 2. The fixed cost per unit of output decreases as volume increases (and vice versa). 3. When production volume and cost are graphed, units of product are usually plotted on the horizontal axis and dollars of cost are plotted on the vertical axis. (Exhibit 22.1) a. Fixed cost is represented by a horizontal line with no slope (cost remains constant at all levels of volume within the relevant range). b. Intersection point of line on cost (vertical) axis is at fixed cost amount. 4. Likely that amount of fixed cost will change when outside of relevant range. B. Variable Costs 1. A total variable cost changes in proportion to changes in volume of activity 2. Variable cost per unit remains constant but the total amount of variable cost changes with the level of production. 3. When production volume and cost are graphed, (Exhibit 22.1) a. Variable cost is represented by a straight line starting at the zero cost level. b. The straight line is upward (positive) sloping. The line rises as volume increases. C. Mixed Costs 1. Include both fixed and variable cost components. 2. When volume and cost are graphed, a. Mixed cost is represented by a straight line with an upward (positive) slope. b. Start of line is at fixed cost point (or amount of total cost when volume is zero) on cost (vertical) axis. As activity level increases, mixed cost line increases at an amount equal to the variable cost per unit. 3. Mixed costs are often separated into fixed and variable components when included in a CVP analysis. 22-3

4 D. Step-wise Costs 1. Fixed within a relevant range of the current production volume. If production volume expands significantly, total costs go up by a lump-sum amount (stair-step cost). 2. Treated as either fixed or variable cost in conventional CVP analysis; depends on width of range, and requires judgment. E. Curvilinear (or Nonlinear) Costs 1. Increase at a non-constant rate as volume increases. 2. 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. II. Measuring Cost Behavior After establishing that cost data are reliable and useful in predicting future costs, three methods are commonly used to analyze past cost behavior. A. Scatter Diagrams 1. Display past cost and unit data in graphical form. 2. Units are plotted on horizontal axis, cost on the vertical axis. 3. Each point reflects the number of units for a prior period. 4. Estimated line of cost behavior drawn with a line that best fits the points visually. a. Intersection point of line on cost axis is at fixed cost amount. b. The variable cost per unit of volume equals the slope of the line. i. Select any two points on horizontal axis. ii. Draw a vertical line from each of these points to intersect the estimated line of cost behavior. iii. The slope of the line, or variable cost per unit is computed as follows: Change in Costs Change in volume (units) = variable cost per unit c. Cost equation. i. Fixed cost + Variable cost per unit x number of units Total Costs ii. Useful to predict future cost levels at different volumes. 5. Deficiency of scatter diagram method estimates are based on visual fit of cost line, subject to interpretation. 22-4

5 B. High-low Method 1. Estimate the cost equation by graphically connecting the two cost amounts at the highest and lowest unit volumes. a. Intersection point of line on cost axis is at fixed cost amount. b. Variable cost per unit is the slope of the line is computed as the change in cost divided by the change in units: Variable cost = high volume costs low volume costs per unit high volume units low volumes units 2. To compute the estimated fixed costs, use the cost equation at the low or high volumes and total costs 3. Cost equation may differ slightly from that determined using the scatter diagram method. 4. Deficiency of high-low method ignores all cost points except the highest and lowest resulting in less precision. C. Least-Squares Regression computation details covered in advanced cost accounting courses. 5. Statistical method of identifying cost behavior. 6. Cost equation readily calculated using most spreadsheet programs. Illustrated in Appendix 22A using Excel 7. Cost equation may differ slightly from those determined using the scatter diagram and high-low methods; superior due to use of all data points available. III. Break-Even Analysis special case of CVP analysis. A. Contribution Margin 1. Requires separating costs and expenses by behavior (fixed or variable). 2. Definition the amount by which a product s unit selling prices exceeds its total unit variable costs. (This excess amount contributes to covering fixed costs and generating profits on a per unit basis). 3. Contribution margin per unit (CM per unit) is computed as: Selling price per unit minus Variable cost per unit 4. Users often use contribution margin in the form of a contribution margin ratio the proportion of a unit s selling price that exceeds total unit variable cost. (Interpreted as what proportion of each sales dollars remains after deducting total unit variable costs). 5. Contribution margin ratio (CM %) is computed as: contribution margin per unit divided by sales price per unit. 22-5

6 B. Computing Break-Even Point 1. Break-even point a. Sales level at which company neither earns a profit nor incurs a loss. b. Can be expressed either in units or dollars of sales. 2. Computation of break-even point a. Break-even units = Fixed costs CM per unit b. Break-even sales dollars = Fixed costs CM% c. Contribution Margin Income Statement Revenues - Variable Costs Contribution Margin - Fixed Costs Net Income. d. Differs from a conventional income statement in two ways: i. Classifies costs and expenses as variable and fixed ii. Reports contribution margin C. Preparing a Cost-Volume-Profit Chart (also called a break-even graph or chart) 1. Horizontal axis number of units produced and sold (volume) 2. Vertical axis dollars of sales and costs. 3. Three steps: a. Plot fixed costs on vertical axis; draw horizontal line at this level to show that FC remains unchanged regardless of output volume. b. Draw line reflecting total costs (variable costs plus fixed costs) for a relevant range of volume levels. i. Line starts at fixed costs on vertical axis. ii. Slope equals variable cost per unit; compute total costs for any volume level, and connect this point with the vertical axis intercept. iii. Stop line at productive capacity for the planning period. c. Draw sales line. i. Line starts at origin (zero units and zero dollars of sales). ii. Slope of line is equal to selling price per unit; compute total revenues for any volume level, and connect this point with the origin. iii. Stop line at productive capacity for the planning period. 22-6

7 4. The break-even point is at the intersection of total cost line and sales line. 5. On either side of break-even point, the vertical distance between sales line and total cost line at any specific sales volume reflects the profit or loss expected at that point. a. Volume levels to left of break-even point vertical distance is amount of loss expected because the total costs line is above the total sales line. b. Volume levels to right of break-even point vertical distance is amount of profit expected because the total sales line is above the total costs line. D. Assumptions of Cost-Volume-Profit Analysis 1. Usefulness depends on validity of three assumptions. a. Constant selling price per unit. b. Constant variable costs per unit. c. Constant total fixed costs. 2. If expected cost and revenue behavior is different from three assumptions stated above, CVP analysis may still be useful. a. Summing of costs can offset individual deviations Individual variable cost items may not be perfectly variable, but when summed, individual deviations can offset each other. The same can be said for fixed costs. b. Relevant range of operations Assumes a specific cost is variable or fixed is more likely valid when operations are within the relevant range. (If normal range of activity changes, some costs may need reclassification.) c. Estimates from CVP analysis Managers need to understand that CVP analysis provides approximate estimates about future, not precise answers, and that other qualitative factors should also be considered. 3. Output Measures - level of production often expressed in terms of sales volume (in dollars or units), or units produced. Assume production level coincides with sales level. (Inventory levels do not change). IV. Applying Cost-Volume-Profit Analysis Useful in helping managers evaluate likely effects of strategies considered in planning business operations. A. Computing Income from Sales and Costs 1. Sales (# units sold x unit selling price) - Variable Costs (# units sold x unit variable cost) Contribution Margin - Fixed Costs Income (pretax) 22-7

8 B. Computing Sales for a Target Income 1. Sales (in dollars) required for target pretax income equals: fixed costs + target pretax income CM% 2. Sales (in units) required for target income equals fixed costs + target pretax income CM C. Margin of safety can be expressed in units, dollars, or as a percent of predicted level of sales 1. Expected Unit Sales Expected Sales Dollars - Break-even Unit sales - Break-even Sales Dollars Margin of safety (units) Margin of Safety (dollars) 2. Margin of Safety Rate (%) = Margin of Safety Expected Sales D. Sensitivity Analysis Knowing the effects of changing some estimates used in CVP analysis by substituting new estimated amounts (in total or per unit as appropriate) in the related formula can be helpful in making predictions. E. Computing Multiproduct Break-Even Point Modify basic CVP analysis when company produces and sells several products. 1. Important assumption Sales mix of the different products is known and remains constant. 2. Sales mix is the ratio (proportion) of the sales volumes for various products. 3. To apply multiproduct CVP analysis, estimate break-even point by using a composite unit. a. Determine sales mix of various products. b. Composite Unit a specific number of units of each product in proportion to their expected sales mix. c. 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. d. Compute the variable price of a composite unit in the same manner, e. Determine the CM per composite unit by subtracting the total variable price from the total selling price of the composite unit. 22-8

9 f. In break-even analysis, a composite unit is treated as a unit of a single product. g. Break-even point in composite units is computed as: Fixed Costs _ CM per composite unit h. 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. 3. To apply multiproduct CVP analysis, estimate break-even point by using a weighted average contribution margin. a. Determine sales mix of various products. b. Using the sale mix, determine the percent contribution of each individual product. If there is a 2:2:1 product mix, then the percent contribution of the first product would be 2/5 or 40%. c. Compute the contribution margin per unit of each product. (sales price per unit less variable cost per unit d. Multiply the contribution margin per unit for each unit x the respective percentage of the sales mix. e. Total the individual amounts to compute the weighted average contribution margin. f. Divide fixed costs by the weighted average contribution margin to compute the break-even point in units. V. Decision Analysis--Degree of Operating Leverage Useful tool in assessing the effect of changes in the level of sales on income. A. Operating leverage is the extent, or relative size, of fixed costs in the total cost structure. B. Degree of operating leverage (DOL) is computed as: Total Contribution margin (dollars) pretax income C. Use DOL to measure the effect of changes in the level of sales on pretax income by multiplying DOL by the percentage change in sales. 22-9

10 Alternate Demo Problem Twenty-Two Trimble Company sells an electronic toy for \$40. The variable cost is \$24 per unit and the fixed cost is \$32,000 per year. Management is considering the following changes: Alternative #1 Lease a new packaging machine for \$4,000 per year, which will reduce variable cost by \$1 per unit. Alternative #2 Increase selling price 10 percent to counteract an expected 25 percent increase in fixed cost. Alternative #3 Reduce fixed cost by 25 percent by moving to a lower rent location. This would have the effect of increasing variable costs by 10 percent. Required: Consider and answer each of the following questions independently: Round calculations to the nearest unit (a) Determine the current break-even point in units and dollars. (b) Determine the expected profit assuming alternative #1 and sales of 3,200 units. (c) Determine the break-even point in units and dollars assuming alternative #2. (d) Determine the break-even point required in units and dollars assuming alternative #3. (e) Determine the volume of sales required to earn \$23,600 assuming alternative #

11 Solution: Alternate Demo Problem Twenty-Two (a) Break-even point (in units) = Fixed costs/cm per unit \$32,000/(\$40 per unit - \$24 per unit) = 2,000 units 2,000 units x \$40 per unit = \$80,000 dollars (or) Break-even point (in dollars) = Fixed costs/cm ratio \$32,000/[(\$40 per unit \$16 per unit)/\$40 per unit] = \$80,000 \$80,000 dollars/\$40 per unit = 2,000 units (b) Net income = (CM per unit x number of units sold) - Fixed costs New fixed costs = \$32,000 + \$4,000 = \$36,000 New CM = \$40 per unit - \$23 per unit = \$17 per unit (\$17 per unit x 3,200 units) - \$36,000 = \$18,400 (c) Break-even point (in units) = Fixed costs/cm per unit New fixed costs = \$32,000 + \$8,000 = \$40,000 New CM = \$44 per unit - \$24 per unit = \$20 per unit \$40,000/\$20 per unit = 2,000 units 2,000 units x \$44 per unit = \$88,000 (d) Break-even point (in units) = Fixed costs/cm per unit New fixed costs = \$32,000 - \$8,000 = \$24,000 New CM = \$40 per unit - \$26.40 per unit = \$13.60 per unit \$24,000/\$13.60 per unit = 1,765 units 1,765 units x \$40 per unit = \$70,600 (e) Required sales (in units) = (Fixed costs + Target NI)/CM per unit (\$24,000 + \$23,600)/\$13.60 per unit = 3,500 units 22-11

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