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Chapter 18 Cost Behavior and Cost-Volume-Profit Analysis

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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.

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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. Analytical Learning Objectives

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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. Procedural Learning Objectives

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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? 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? Questions Addressed by Cost-Volume-Profit Analysis

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

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Number of Local Calls Monthly Basic Telephone Bill Total fixed costs remain unchanged when activity (units) changes. Your monthly basic telephone bill probably does not change when you make more local calls. Total Fixed Cost (Exhibit 18.1, Page 757) C1

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

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Minutes Talked Total Long Distance Telephone Bill Total variable costs change when activity (units) changes. Your total long distance telephone bill is based on how many minutes you talk. Total Variable Cost (Exhibit 18.1, Page 757) C1

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Minutes Talked Per Minute Telephone Charge Variable costs per unit do not change as activity (unit) increases. The cost per long distance minute talked is constant. For example, 7 cents per minute. Variable Cost Per Unit C1

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Cost Behavior Summary C1

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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 per kilowatt hour used Mixed Costs (Exhibit 18.1, Page 757)

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Activity Cost Total cost remains constant within a narrow range of activity. Step-Wise Costs Exhibit 18.2 (page 758)

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Curvilinear Costs Exhibit 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.

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Cost Behavior Exercise 2

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The objective is to classify all costs as either fixed or variable. Measuring Cost Behavior P1

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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

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

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Scatter Diagram Exercise 1

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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. The High-Low Method

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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 Δ in cost Δ in units $8,500 $50,000 The High-Low Method

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High-Low Method Exercise 7

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

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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 Computing Break-Even Point P2

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Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue. Computing Break-Even Point (Contribution Margin) P2

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

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

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

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

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CVP Analysis Exercise 9

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

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

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CVP Chart Exercise 9

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A limited range of activity called the relevant range, where CVP relationships are linear. 4 Unit selling price remains constant. 4 Unit variable costs remain constant. 4 Total fixed costs remain constant. Production = sales (no inventory changes). Assumptions of CVP Analysis C2

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

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

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Exercise 10

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

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To convert target net income to before- tax income, use the following formula: Before-tax income = Target net income 1 - tax rate Computing Sales (Dollars) for a Target Net Income 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)

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Exercise 11

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

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18-42 Contribution margin Income Statement Exhibit 18.19, page 767: Pretax Exhibit 18.20, page 767: After tax

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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 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

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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 a composite unit. A composite unit is composed of specific numbers of each product in proportion to the product sales mix. Sales mix is the ratio of the volumes of the various products. Computing Multiproduct Break-Even Point

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The resulting break-even formula for composite unit sales is: Break-even point in composite units Fixed costs Contribution margin per composite unit = P4 Computing Multiproduct Break-Even Point

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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.

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Exercises 15 & 17

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

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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; 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.

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