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## Chapter 22

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**Chapter 22**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 C3: Describe several applications of cost-volume-profit analysis**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**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**Questions Addressed byCost-Volume-Profit Analysis**C2 CVP analysis is used to answer questions such as: • 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?**Total Fixed Cost**C1 Total fixed costsremain unchangedwhen activity changes. Your monthly basictelephone bill probablydoes not change whenyou make more local calls. Monthly Basic Telephone Bill Number of Local Calls**Fixed Cost Per Unit**C1 Fixed costs per unit declineas activity increases. Your average cost perlocal call decreases asmore local calls are made. 1- Economic of scale 2- Learning curve Monthly Basic Telephone Bill per Local Call Number of Local Calls**Total Variable Cost**C1 • Total variable costschangewhen activity changes. Your total long distancetelephone bill is basedon how many minutesyou talk. Total Long DistanceTelephone Bill Minutes Talked**Variable Cost Per Unit**C1 Variable costs per unitdo not changeas activity increases. The cost per long distanceminute talked is constant.For example, 7cents per minute. Per MinuteTelephone Charge Minutes Talked**Mixed Costs**C1 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**Mixed Costs**C1 Total mixed cost Variable Utility Charge Total Utility Cost Fixed MonthlyUtility Charge Activity (Kilowatt Hours)**Step-Wise Costs**C1 Total cost remainsconstant within anarrow rangeofactivity. Cost Activity**Step-Wise Costs**C1 Total cost increases to a new higher cost for the next higher range of activity. Cost Activity**Curvilinear Costs**C1 Costs that increase when activity increases, but in a nonlinearmanner. Total Cost Activity**Scatter Diagram**P1 A scatter diagram of past cost behavior may be helpful in analyzing mixed costs.**20*** * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Diagram P1 Plot the data points on a graph (total cost vs. activity).**20*** * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Diagram P1 Draw a line through the plotted data points so that about equal numbers of points fall above and below the line. Estimated fixed cost = 10,000**Δin costΔin 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 P1 Vertical distance is the change in cost. Horizontal distance is the change in activity.**The High-Low Method**P1 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.**$8,500$50,000**Δin costΔin units • Unit variable cost = = = $0.17/ unit The High-Low Method P1 Exh. 22-6**$8,500$50,000**Δin costΔin units • Unit variable cost = = = $0.17/unit • Fixed cost = Total cost – Total variable The High-Low Method P1 Exh. 22-6**$8,500$50,000**Δin costΔin units • Unit variable cost = = = $0.17 /unit • Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per unit × $67,500) Fixed cost = $29,000 – $11,475 = $17,525 The High-Low Method P1 Exh. 22-6**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.**Break-Even Analysis**P2 Let’s extend ourknowledge ofcost behavior to break-even analysis.**Computing Break-Even Point**P2 The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company earns neither a profit nor incurs a loss.**Computing Break-Even Point**P2 Contribution margin is amount by which revenueexceeds thevariable costsof producing the revenue.**Computing Break-Even Point**P2 How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $24,000**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**Fixed costs**Break-even point in units = Contribution margin per unit Computing Break-Even Point P2 Exh. 22-8 We have just seen one of the basic CVP relationships – the break-evencomputation. Unit sales price less unit variable cost($30 in previous example)**Fixed costs**Break-even point in dollars = Contribution marginratio Computing Break-Even Point P2 Exh. 22-9 The break-even formula may also be expressed in sales dollars. Unit contribution margin Unit sales price**Computing Break-Even Point**P2 ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units**Unit contribution = $5.00 - $3.00 = $2.00**Fixed costsUnit contribution $200,000$2.00 per unit = = 100,000 units Computing Break-Even Point P2 ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units**Computing Break-Even Point**P2 Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000**Computing Break-Even Point**P2 Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Unit contribution = $5.00 - $3.00 = $2.00 Contribution margin ratio = $2.00 ÷ $5.00 = .40 Break-even revenue = $200,000 ÷ .4 = $500,000**Total costs**• Draw the total cost line with a slopeequal to the unit variable cost. Preparing a CVP Chart P3 • Plot total fixed costs on the vertical axis. Total fixed costs Costs and Revenuein Dollars Volume in Units**Preparing a CVP Chart**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**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).**Computing Income from Expected Sales**C3 Exh. 22-12 Income (pretax) = Sales – Variable costs – Fixed costs**Computing Income from Expected Sales**C3 Exh. 22-13 Rydell expects to sell 1,500 units at $100 each next month. Fixed costs are $24,000 per month and the unit variable cost is $70. What amount of income should Rydell expect? Income (pretax) = Sales – Variable costs – Fixed costs = [1,500 units × $100]– [1,500 units × $70] – $24,000 = $21,000**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**Computing Sales for a Target Income**C3 ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units**Unit contribution = $5.00 - $3.00 = $2.00**Fixed costs + Target income Unit contribution $200,000 + $40,000 $2.00 per unit = 120,000 units Computing Sales for a Target Income C3 ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units**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 Exh. 22-14 Fixed Target income costs before tax + Dollar sales = Contribution margin ratio**Computing Sales (Dollars) for aTarget Net Income**C3 To convert target net income to before-tax income, use the following formula: Target net income Before-tax income = 1 - tax rate**Computing Sales (Dollars) for aTarget Net Income**C3 Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. • What is Rydell’s before-tax income andincome tax expense?**Target net income**Before-tax income = 1 - tax rate $18,000 Before-tax income = = $24,000 1 - .25 Computing Sales (Dollars) for aTarget Net Income C3 Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. • What is Rydell’s before-tax income andincome tax expense? Income tax = .25 × $24,000 = $6,000**Computing Sales (Dollars) for aTarget Net Income**C3 Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. • What monthly sales revenue will Rydellneed to earn the target net income?**Fixed Target net income costs before**tax + Dollar sales = Contribution margin ratio $24,000 + $24,000 Dollar sales = = $160,000 30% Computing Sales (Dollars) for aTarget Net Income C3 Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent. • What monthly sales revenue will Rydellneed to earn the target net income?**The formula for computing dollar sales may be used to**compute unit sales by substituting contribution per unit in the denominator. Fixed Target net income taxes before taxes + + Unit sales = Contribution margin per unit $24,000 + $24,000 Unit sales = = 1,600 units $30 per unit Formula for Computing Sales (Units) for a Target Net Income C3 Exh. 22-16