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Cost-Volume-Profit Analysis Chapter 10

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Learning Objectives Determine the number of units that must be sold to break even or to earn a targeted profit. Determine the amount of revenue required to break even or to earn a targeted profit.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Learning Objectives (continued) Apply cost-volume-profit analysis in a multiple-product setting. Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Learning Objectives (continued) Explain the impact of risk, uncertainty, and changing variables on cost-volume- profit analysis. Discuss the impact of activity-based costing on cost-volume-profit analysis.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Sample Questions Raised and Answered by CVP Analysis 1.How many units must be sold (or how much sales revenue must be generated) in order to break even? 2.How many units must be sold to earn a before-tax profit equal to $60,000? A before-tax profit equal to 15 percent of revenues? An after-tax profit of $48,750? 3.Will total profits increase if the unit price is increased by $2 and units sold decrease 15 percent? 4.What is the effect on total profit if advertising expenditures increase by $8,000 and sales increase from 1,600 to 1,750 units?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Sample Questions Raised and Answered by CVP Analysis (continued) 5.What is the effect on total profit if the selling price is decreased from $400 to $375 per unit and sales increase from 1,600 units to 1,900 units? 6.What is the effect on total profit if the selling price is decreased from $400 to $375 per unit, advertising expenditures are increased by $8,000, and sales increased from 1,600 units to 2,300 units? 7.What is the effect on total profit if the sales mix is changed?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP: A Short-Term Planning and Analysis Tool Assists in establishing prices of products. Assists in analyzing the impact that volume has on short-term profits. Assists in focusing on the impact that changes in costs (variable and fixed) have on profits. Assists in analyzing how the mix of products affects profits. Benefits of CVP:

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Basics of Cost-Volume- Profit (CVP) Analysis Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Basics of Cost-Volume- Profit (CVP) Analysis CM goes to cover fixed expenses.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Basics of Cost-Volume- Profit (CVP) Analysis After covering fixed costs, any remaining CM contributes to income.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Approach For each additional unit Wind sells, $200 more in contribution margin will help to cover fixed expenses and profit.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Approach Each month Wind must generate at least $80,000 in total CM to break even.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Approach If Wind sells 400 units in a month, it will be operating at the break-even point.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Approach If Wind sells one more bike (401 bikes), net operating income will increase by $200.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP Relationships in Graphic Form Viewing CVP relationships in a graph is often helpful. Consider the following information for Wind Co.:

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP Graph Fixed expenses Units Dollars Total ExpensesTotal Sales

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Units Dollars CVP Graph Break-even point Profit Area Loss Area

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Cost-Volume-Profit Graph Revenue Total Revenue Total Cost Units sold X Y Loss Profit X = Break-even point in units Y = Break-even point in revenue

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Ratio The contribution margin ratio is: For Wind Bicycle Co. the ratio is: $ 80,000 $200,000 = 40% Total CM Total sales CM Ratio =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Ratio Or, in terms of units, the contribution margin ratio is: For Wind Bicycle Co. the ratio is: $200 $500 = 40% Unit CM Unit selling price CM Ratio =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Ratio At Wind, each $1.00 increase in sales revenue results in a total contribution margin increase of 40¢. If sales increase by $50,000, what will be the increase in total contribution margin?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Ratio A $50,000 increase in sales revenue

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Ratio A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000)

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a b c d

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a b c d Unit contribution margin Unit selling price CM Ratio = = ($1.49-$0.36) $1.49 = $1.13 $1.49 = 0.758

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Changes in Fixed Costs and Sales Volume Wind is currently selling 500 bikes per month. The company’s sales manager believes that an increase of $10,000 in the monthly advertising budget would increase bike sales to 540 units. Should we authorize the requested increase in the advertising budget?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Changes in Fixed Costs and Sales Volume. Sales increased by $20,000, but net operating income decreased by $2,000. $80,000 + $10,000 advertising = $90,000

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Changes in Fixed Costs and Sales Volume The Shortcut Solution

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Break-Even Analysis Break-even analysis can be approached in three ways: 1.Graphical analysis. 2.Equation method. 3.Contribution margin method.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Equation Method Profits = Sales – (Variable expenses + Fixed expenses) Sales = Variable expenses + Fixed expenses + Profits OR At the break-even point profits equal zero.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Break-Even Analysis Here is the information from Wind Bicycle Co.:

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Equation Method We can also use the following equation to compute the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Equation Method X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000 We can also use the following equation to compute the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Method The contribution margin method is a variation of the equation method. Fixed expenses Unit contribution margin = Break-even point in units sold Fixed expenses CM ratio = Break-even point in total sales dollars

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Fixed expenses Unit contribution margin Break-even = $1,300 $1.49 per cup - $0.36 per cup = $1,300 $1.13 per cup = 1,150 cups =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129 Fixed expenses CM Ratio Break-even sales = $1, = $1,715 =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Target Profit Analysis Suppose Wind Co. wants to know how many bikes must be sold to earn a profit of $100,000. We can use our CVP formula to determine the sales volume needed to achieve a target net profit figure.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The CVP Equation Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $100,000 $200Q = $180,000 Q = 900 bikes

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Margin Approach We can determine the number of bikes that must be sold to earn a profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Unit contribution margin = Unit sales to attain the target profit $80,000 + $100,000 $200 per bike = 900 bikes

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups Fixed expenses + Target profit Unit contribution margin Unit sales to attain target profit $1,300 + $2,500 $ $0.36 = $3,800 $1.13 = 3,363 cups = =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Variable-Costing Income Statement Sales (10,000 x $10)$100,000 Less: Variable costs (10,000 x $6) 60,000 Contribution margin$ 40,000 Less: Fixed costs 40,000 Profit before taxes$0 Less: Income taxes 0 Profit after taxes$ 0 =====

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP Analysis: Targeted After-Tax Income Let X = break-even point in units Sales$ = $10X Less: Variable costs$= 6X Contribution margin$ = $ 4X Less: Fixed costs 40,000 Profit before taxes $ Less income taxes Profit after taxes $24,000 ====== What sales in units and dollars are needed to obtain a targeted profit after taxes of $24,000?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP Analysis: Targeted After-Tax Income (continued) The Approach: AFTER=Profit after taxes BEFORE=Profit before taxes AFTER=(1 - tax rate) x BEFORE $24,000=(1 -.4) x BEFORE $24,000/.6=BEFORE $40,000=BEFORE

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Sales10X CV (6X) CM4 X FC(40,000) EBT? Income Tax(?) EAT 24,000 EAT = (1-Tax) EBT 24,000 = (1-0.4) EBT EBT = 40,000 EBT - Income Tax = EAT 40,000 – IT = 24,000 IT = 16,000 4X - 40,000 = 40,000 X = 20,000

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP Analysis: Targeted After-Tax Income (continued) The income statement below illustrates that $200,000 in sales will give you an after-tax profit of $24,000. Sales$200,000 Less: Variable costs 120,000 Contribution margin$ 80,000 Less: Fixed costs 40,000 Profit before taxes$ 40,000 Less: Income taxes 16,000 Profit after taxes$ 24,000 ======

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Margin of Safety Excess of budgeted (or actual) sales over the break-even volume of sales. The amount by which sales can drop before losses begin to be incurred. Margin of safety = Total sales - Break-even sales Let’s calculate the margin of safety for Wind.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Margin of Safety Wind has a break-even point of $200,000. If actual sales are $250,000, the margin of safety is $50,000 or 100 bikes.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000)

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups Margin of safety = Total sales – Break-even sales = 950 cups = 2,100 cups – 1,150 cups or 950 cups 2,100 cups Margin of safety percentage == 45%

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. With high leverage, a small percentage increase in sales can produce a much larger percentage increase in net operating income. Contribution margin Net operating income Degree of operating leverage =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Operating Leverage $100,000 $20,000 = 5

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Operating Leverage With a operating leverage of 5, if Wind increases its sales by 10%, net operating income would increase by 50%. Here’s the verification!

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Operating Leverage 10% increase in sales from $250,000 to $275, % increase in sales from $250,000 to $275, results in a 50% increase in income from $20,000 to $30, results in a 50% increase in income from $20,000 to $30,000.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage? a b c d. 2.92

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage? a b c d Contribution margin Net operating income Operating leverage = $2,373 $1,073 = = 2.21

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average. If sales increase by 20%, by how much should net operating income increase? a. 30.0% b. 20.0% c. 22.1% d. 44.2%

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average. If sales increase by 20%, by how much should net operating income increase? a. 30.0% b. 20.0% c. 22.1% d. 44.2%

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Verify increase in profit

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Concept of Sales Mix Sales mix is the relative proportions in which a company’s products are sold. Different products have different selling prices, cost structures, and contribution margins. Let’s assume Wind sells bikes and carts and see how we deal with break-even analysis.

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Multiple-Product Example ProductP-V=CMxMix= Total CM A$10-$6=$4x3=$12 B8-5= 3x2= 6 Total CM per package $18 === Total fixed expenses = $180,000

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Multiple-Product Example (continued) Break-even point: X = Fixed cost / Unit contribution margin = $180,000 / $18 = 10,000 packages to break even Each package contains 3 units of A and 2 units of B. Therefore, to break even, we need to sell the following units of A and B: A:3x10,000=30,000 units B:2x10,000=20,000 units

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Multi-product break-even analysis Wind Bicycle Co. provides the following information: $265,000 $550,000 = 48.2% (rounded)

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Multi-product break-even analysis Rounding error Fixed expenses CM Ratio Break-even sales = $170, = $352,697 =

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Assume the following: RegularDeluxeTotalPercent Units sold Sales price per unit $500 $ Sales $200,000$150,000$350, % Less: Variable expenses 120,000 60, , Contribution margin $ 80,000$ 90,000$170, % Less: Fixed expenses 130,000 Net income $ 40,000 ======= 1. What is the break-even point? 2. How much sales-revenue of each product must be generated to earn a before tax profit of $50,000? Another Multiple-Product Example

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Another Multiple-Product Example: BEP BEP = Fixed cost / CM ratio for sales mix = $130,000 / = $267,490 for the firm BEP for Regular Model: (400/600) x $267,490 = $178,327 BEP for Deluxe Model: (200/600) x $267,490 = $89,163

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Another Multiple-Product Example: Targeted Revenue BEP = (Fixed Costs + Targeted income) / CM ratio per sales mix = ($130,000 + $50,000) / = $370,370 for the firm BEP for Regular Model: (400/600) x $370,370 = $246,913 BEP for Deluxe Model: (200/600) x 370,370 = $123,457

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP and ABC Assume the following: Sales price per unit $15 Variable cost 5 Fixed costs (conventional)$180,000 Fixed costs (ABC) 100,000 with $80,000 subject to ABC analysis Other Data: UnitLevel of VariableActivity Activity DriverCostsDriver Setups$ Inspections What is the BEP under conventional analysis? 2. What is the BEP under ABC analysis? 3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin CVP and ABC (continued) 1.Break-even units (conventional analysis) BEP =$180,000/$10 =18,000 units 2. Break-even units (ABC analysis) BEP =[$100,000 + (100 x $500) + (600 x $50)]/$10 =18,000 units 3. BEP =[$100,000 + (100 x $450) + (600 x $40)]/$10 =16,900 units What implications does ABC have for improving performance?

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© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Assumptions of CVP Analysis Selling price is constant. Costs are linear. In multi-product companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold).

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