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## Cost-Volume-Profit Analysis

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**Cost-Volume-Profit Analysis**Chapter 22**Learning objectives**• Purpose of C-V-P Analysis • Identifying Cost Behavior • Measuring Cost Behavior • Using Break-Even Analysis • Applying C-V-P Analysis • Decision Analysis: • Degree of Operating Leverage**Questions Addressed by Cost-Volume-Profit Analysis**CVP analysis is used to answer questionssuch as: • How much must I sell to earn my desired income? • How will income be affectedif I reduce selling prices toincrease sales volume? • How will income be affectedif I change the sales mixof my products?**2. Identifying Cost Behavior - Total Fixed Cost**Total fixed costs remain unchangedwhen activity changes. Monthly Basic Telephone Bill Your monthly basictelephone bill probablydoes not change whenyou make more local calls. Number of Local Calls**Fixed Cost Per Unit**Fixed costs per unit declineas activity increases. Monthly Basic Telephone Bill per Local Call Your average cost perlocal call decreases asmore local calls are made. Number of Local Calls**Total Variable Cost**• Total variable costs changewhen activity changes. Total Long DistanceTelephone Bill Your total long distancetelephone bill is basedon how many minutesyou talk. Minutes Talked**Variable Cost Per Unit**Variable costs per unit do not changeas activity increases. Per MinuteTelephone Charge The cost per long distanceminute talked is constant.For example, 7cents per minute. Minutes Talked**Mixed Costs**Mixed costs contain a fixed portion that is incurred even when 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**Total mixed cost Variable Utility Charge Total Utility Cost Fixed MonthlyUtility Charge Activity (Kilowatt Hours)**Step-Wise Costs**Total cost remainsconstant within anarrow rangeofactivity. Cost Activity**Step-Wise Costs**Total cost increases to a new higher cost for the next higher range of activity. Cost Activity**Curvilinear Costs**Costs that increase when activity increases, but in a nonlinearmanner. Total Cost Activity**The objectiveis to classify all costs as either fixed or**variable. 3. Measuring Cost Behavior**Scatter Diagram**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 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 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**in costin 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 Vertical distance is the change in cost. Horizontal distance is the change in activity.**The High-Low Method**Exh. 22-6 The following relationships between salesand costs are observed: Using these two levels of activity, compute: • the variable cost per unit. • the total fixed cost.**$8,500$50,000**in costin units • Unit variable cost = = = $0.17 per $ The High-Low Method Exh. 22-6**$8,500$50,000**in costin units • Unit variable cost = = = $0.17 per $ • Fixed cost = Total cost – Total variable The High-Low Method Exh. 22-6**$8,500$50,000**in costin units • Unit variable cost = = = $0.17 per $ • Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per sales $ × $67,500) Fixed cost = $29,000 – $11,475 = $17,525 The High-Low Method Exh. 22-6**Least-Squares Regression**• Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with computer software because of the large number of calculations required. The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost.**4. Break-Even Analysis**Let’s extend ourknowledge ofcost behavior to break-even analysis.**Computing Break-Even Point**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**Contribution margin is amount by which revenue exceeds thevariable costsof producing the revenue.**Computing Break-Even Point**How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $30,000**Computing Break-Even Point**How manyunits must this company sell to cover its fixed costs (break even)? Answer: $30,000 ÷ $20 per unit = 1,500 units**Fixed costs**Break-even point in units = Contribution margin per unit Computing Break-Even Point Exh. 22-8 We have just seen one of the basic CVP relationships – the break-evencomputation. Unit sales price less unit variable cost($20 in previous example)**Fixed costs**Break-even point in dollars = Contribution margin ratio Computing Break-Even Point Exh. 22-9 The break-even formula may also be expressed in sales dollars. Unit contribution margin Unit sales price**Computing Break-Even Point**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 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**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**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 • Plot total fixed costs on the vertical axis. Total fixed costs Costs and Revenuein Dollars Volume in Units**Preparing a CVP Chart**• 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**• 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).**5. Applying C-V-P Analysis - Computing Income from**Expected Sales Exh. 22-12 Income (pretax) = Sales – Variable costs – Fixed costs**Computing Income from Expected Sales**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**5. Applying C-V-P Analysis - Computing Sales for a Target**Income Break-even formulas may be adjusted to show the sales volume needed to earnany 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**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 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.**Computing Sales (Dollars) for aTarget Net Income Exh. 22-14 Fixed Target net Incomecosts income taxes + + Dollar sales = Contribution margin ratio**Computing Sales (Dollars) for aTarget Net Income**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**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 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**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 Incomecosts income**taxes + + Dollar sales = Contribution margin ratio $24,000 + $18,000 + $6,000 Dollar sales = = $160,000 30% Computing Sales (Dollars) for aTarget Net Income 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 Incomecosts income taxes + + Unit sales = Contribution margin per unit $24,000 + $18,000 + $6,000 Unit sales = = 1,600 units $30 per unit Formula for Computing Sales (Units)for a Target Net Income Exh. 22-16**Margin of safety is the amount by which sales may decline**before reaching break-even sales. Margin of safety may be expressed as a percentage of expected sales. Margin of safety Expected sales - Break-even sales percentage Expected sales = 5. Applying C-V-P Analysis - Computing the Margin of Safety Exh. 22-17