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Chapter FourCost-Volume-Profit Analysis: A Managerial Planning Tool
Chapter FourCost-Volume-Profit Analysis: A Managerial Planning Tool
COPYRIGHT © 2012 Nelson Education Ltd.
Learning ObjectivesLearning Objectives
1. Determine the break-even point in units and sales dollars
2. Determine the number of units that must be sold, and the amount of revenue required to earn a targeted profit
3. Prepare a profit-volume graph and a cost-volume-profit graph and explain the meaning of each
4. Apply cost-volume-profit analysis in a multiple product setting
5. Explain the impact of risk, uncertainty and changing variables on cost-volume-profit analysis
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Determine the break-even point in units and sales dollars
OBJECTIVE OBJECTIVE 11
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Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis
A powerful tool for planning and decision making It can be used to calculate:
The number of units that must be sold to
break-even
The impact of a given reduction in fixed
costs on the break-even point
The impact of an increase in price on
profit
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Break-Even PointBreak-Even Point
Total Revenue = Total Cost
Or put it another way:
Total Revenue- Total Costs Zero Profit
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Using Operating Income in Cost-Volume-Profit AnalysisUsing Operating Income in Cost-Volume-Profit Analysis
Contribution Margin
Sales - Variable Expense
=
Contribution Margin is then used to cover Fixed Costs and Operating Income
Contribution
Margin
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Contribution Margin Income StatementContribution Margin Income Statement
• Divides costs based on behaviour• Costs are divided into variable and fixed
components• Important subtotal is contribution margin
– Sales revenue minus variable expenses
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Using Operating Income in Cost-Volume-Profit AnalysisUsing Operating Income in Cost-Volume-Profit Analysis
Contribution Margin
Sales - Variable Costs
= Contribution
Margin
Break-even point is when Operating Income = 0
Contribution Margin
Fixed Costs
Operating Income
- =
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Cornerstone 4-1Cornerstone 4-1
How to Prepare a Contribution Margin Income Statement
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• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year. Product costs include:– Direct materials per mower $180– Direct labour per mower $100– Variable overhead per mower $25– Total fixed factory overhead $15,000
• Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000
Information:
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ExampleExample
• Calculate the total variable cost per unit• Calculate the total fixed expense for the year• Prepare a contribution margin income statement
for Whittier Co. for the coming year
Required:
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+
Variable CostVariable Cost
Variable Cost Per
unit=
Direct Materials +
Direct Labour
Variable Overhead
Variable Selling
Expense+ +
Variable Cost Per
unit= $180 + $100 $25 $20+
Variable Cost Per
unit= $325
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Fixed ExpensesFixed Expenses
Total Fixed Expenses =
Fixed Overhead +
Fixed Selling & Administrative
Expense
Total Fixed Expenses = $15,000 + $30,000
Total Fixed Expenses = $45,000
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Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Total Per Unit
Sales ($400 × 1,000 mowers) $400,000 $400
Total variable expense ($325 × 1,000) 325,000 325
Total contribution margin $ 75,000 $ 75
Total fixed expense 45,000
$ 30,000Operating income
Each unit contributes $75 to cover fixed costs
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Cornerstone 4-2Cornerstone 4-2
How to Solve for the Break-Even Point in Units
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• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year. Product costs include:– Direct materials per mower $180– Direct labour per mower $100– Variable overhead per mower $25– Total fixed factory overhead $15,000
• Variable selling expense is a commission of $20 per mower; fixed selling and administrative expense totals $30,000
Information:
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ExampleExample
• Calculate the total variable cost per unit• Calculate the total fixed expense for the year• Calculate the number of mowers that Whittier Co. must
sell to break-even• Check the answer by preparing a contribution margin
income statement based on the break-even point
Required:
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Variable & Fixed CostsVariable & Fixed Costs
Variable Cost Per
unit= $180 + $100 $25 $20+ +
Total Fixed Expenses = $15,000 + $30,000
These were computed in Cornerstone 4-1
= $325
= $45,000
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Break-Even Number of MowersBreak-Even Number of Mowers
Break-even units =
Total Fixed Cost
Contribution Margin per unit
Formula can be simplified down to:
Selling Price – Variable cost per unit
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Break-even units =
$45,000
($400 – $325)
Break-even units = 600 mowers
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Whittier CompanyContribution Margin Income Statement
For the Coming Year based on sales of 600 mowers
Whittier CompanyContribution Margin Income Statement
For the Coming Year based on sales of 600 mowers
Total Per Unit
Sales ($400 × 600 mowers) $240,000 $400
Total Variable Expense ($325 × 600) 195,000 325
Total Contribution Margin $ 45,000 $ 75
Total Fixed Expense 45,000
$ 0Operating Income
Operating income is zero when 600 units are sold. The break-even calculation is correct!
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Cornerstone 4-3Cornerstone 4-3
How to Calculate the Variable Cost Ratio and the Contribution Margin Ratio
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• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year
• Variable cost per unit is $325
• Total fixed cost is $45,000
Information:
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ExampleExample
• Calculate the variable cost ratio• Calculate the contribution margin ratio using unit
figures• Prepare a contribution margin income statement
based on the budgeted figures for next year– In a column next to the income statement, show the
percentages based on sales for:• Sales• Total variable costs• Total contribution margin
Required:
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Variable Cost RatioVariable Cost Ratio
Variable Cost Ratio =
Variable Cost
Sales
Variable Cost Ratio
=$325$400
Variable Cost Ratio = 81.25%
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Contribution Margin RatioContribution Margin Ratio
Contribution Margin per unit = Sales Variable Cost-
Contribution Margin per unit
= $75 per unit
Sales
Contribution Margin
18.75%Contribution Margin Ratio
Contribution Margin Ratio
=
$75$400= =
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Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Total% of Sales
Sales ($400 ×1,000 mowers) $400,000 100.00
Total Variable Exp. (0.8125 × $400,000) 325,000 81.25
Total Contribution Margin $ 75,000 18.75
Total Fixed Expense 45,000
$ 30,000Operating Income
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Cornerstone 4-4Cornerstone 4-4
How to Solve for the Break-Even Point in Sales Dollars
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• Whittier Co. plans to sell 1,000 mowers at $400 each in the coming year
• Variable cost per unit is $325• Total fixed cost is $45,000
Information:
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ExampleExample
• Calculate the contribution margin ratio• Calculate the sales revenue that Whittier Co. must make
to break-even by using the break-even point in sales equation
• Prepare a contribution margin income statement based on the break-even point in sales dollars
Required:
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Contribution Margin RatioContribution Margin Ratio
Contribution Margin per unit = $400 $75 per unit–
18.75%Contribution Margin Ratio
$75$400
= =
$325 =
These were computed in Cornerstone 4-1
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Break-Even Point in Sales DollarsBreak-Even Point in Sales Dollars
Break-even sales =
Total fixed expenses
Contribution margin ratio
Break-even sales = $45,000
0.1875
Break-even sales = $240,000
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Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Sales $240,000
Total Variable Exp. (0.8125 × $240,000) 195,000
Total Contribution Margin $ 45,000
Total Fixed Expense 45,000
Operating Income
Operating Income is zero when sales are $240,000 The break-even calculation is correct!
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$ 0
OBJECTIVE OBJECTIVE 22
Determine the number of units that must be sold and the
amount of revenue required to earn a targeted profit
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Units to Be Sold to Achieve a Target IncomeUnits to Be Sold to Achieve a Target Income
1. Using Operating Income equation
2. Using the Basic Break-even equation
Two Ways:
Cornerstone 4-5 will walk us through these computations
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Cornerstone 4-5Cornerstone 4-5
How to Solve for the Number of Units to Be Sold to Earn a Target Operating Income
COPYRIGHT © 2012 Nelson Education Ltd.
• Whittier Co. sells mulching mowers at $400 each • Variable cost per unit is $325 and total fixed cost is $45,000
Information:
• Calculate the number of units that Whittier Co. must sell to earn operating income of $37,500
• Prepare a contribution margin income statement based on the number of units calculated
Required:
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Units to Be Sold to Achieve a Target IncomeUnits to Be Sold to Achieve a Target Income
Number of units to earn
target income=
Total fixed expense + Target income
Price – Variable cost per unit
Number of units to earn
target income= $45,000 + $37,500
$400 - $325
Number of units to earn
target income= 1,100
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Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Sales ($400 ×1,100) $440,000
Total variable expense ($325 × 1,100) 357,500
Total contribution margin $ 82,500
Total fixed expense 45,000
$ 37,500Operating income
The calculation is correct! The operating income is $37,500
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Cornerstone 4-6Cornerstone 4-6
How to Solve for the Sales Needed to Earn a Target Operating Income
COPYRIGHT © 2012 Nelson Education Ltd.
• Whittier Co. sells mulching mowers at $400 each • Variable cost per unit is $325 and Total fixed cost is $45,000
Information:
• Calculate the contribution margin ratio• Calculate the sales that Whittier Co. must make to earn an
operating income of $37,500• Prepare a contribution margin income statement based on
the sales dollars calculated
Required:
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Sales Revenue to Achieve a Target IncomeSales Revenue to Achieve a Target Income
Sales dollars to earn target
income=
Fixed Cost + Target Income
Contribution margin ratio
Sales dollars to earn target
income= $45,000 + $37,500
0.1875
Sales dollars to earn target
income= $440,000
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Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Sales $440,000
Total variable exp. (0.8125 × $440,000) 357,500
Total contribution margin $ 82,500
Total fixed expense 45,000
$ 37,500Operating income
The calculation is correct! The operating income is $37,500
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Prepare a profit-volume graph and a cost-volume-profit graph
and explain the meaning of each
OBJECTIVE OBJECTIVE 33
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Profit-Volume GraphProfit-Volume Graph
• Visually portrays the relationship between profits and units sold
• Operating Income is the dependent variable• Units sold is the independent variable
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Cost-Volume-Profit GraphCost-Volume-Profit Graph
• Depicts relationship among cost volume and profits
• Graph two separate lines:– Total revenue– Total cost
• Vertical axis: measured in dollars• Horizontal axis: measured in units sold
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Assumptions of Cost-Volume-Profit AnalysisAssumptions of Cost-Volume-Profit Analysis
• Revenue and cost functions are linear• Price, total fixed costs, and unit variable costs
can be identified and remain constant over relevant range
• All units produced are sold –no changes in inventory levels
• Sales mix is constant• Selling prices and costs are known with certainty
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Linear Cost and Revenue FunctionsLinear Cost and Revenue Functions
Cost-Volume-Profit assumes that cost and revenue functions are linear
In other words they are straight lines
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Production Equal to SalesProduction Equal to Sales
• Cost-Volume-Profit assumes that what is produced is actually sold
• Inventory levels do not change over period• CVP focuses on current costs by excluding
inventory costs of previous periods
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Constant Sales MixConstant Sales Mix
Multiple product break-even analysis requires a constant sales mix
Relative combination of products being sold by a firm
Sales mix is difficult to predict with certainty
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Linear Cost and Revenue FunctionsLinear Cost and Revenue Functions
Firms seldom know prices, variable costs, and fixed costs with certainty
There are formal ways of explicitly building uncertainty into the Cost-Volume-Profit model
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Apply cost-volume-profit analysis in a multiple-product setting
OBJECTIVE OBJECTIVE 44
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Multiple-Product AnalysisMultiple-Product Analysis
Cost-Volume-Profit analysis becomes more complex with multiple products
We need to adapt the single-product formulas
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Direct & Common Fixed ExpensesDirect & Common Fixed Expenses
Fixed costs that can be traced to each
segment and would be avoided if the
segment did not exist
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Direct Fixed Expenses
Fixed costs that are not traceable to the
segments and would remain even if one of
the segments was eliminated
Common Fixed Expenses
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Multiple-Product AnalysisMultiple-Product Analysis
Break-even point in units
Key: identify expected sales mix
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• Measured in units sold• Reduced to the smallest possible whole numbers• Required in order to determine break-even point in
units
Sales Mix:
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Cornerstone 4-7Cornerstone 4-7
How to Calculate the Break-Even Units for a Multiple-Product Firm
COPYRIGHT © 2012 Nelson Education Ltd.
• Whittier Co. sells two products:– Mulching mowers priced at $400– Riding mowers priced at $800
• The variable costs per unit are:– $325 per mulching mower– $600 per riding mower
• Total fixed expense is $96,250• Whittier’s expected sales mix is three mulching mowers to
two riding mowers
Information:
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ExampleExample
• Form a package of mulching and riding mowers, based on the sales mix, and calculate the package contribution margin
• Calculate the break-even point in units for mulching mowers and for riding mowers
• Check calculations by preparing a contribution margin income statement
Required:
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Package Contribution MarginPackage Contribution Margin
Product
Riding
Price
200
Unit Variable
Cost
Sales Mix
Pkg. Unit Contrib. Margin
Mulching
800
$400 $ 75 3 $225
Package Total $625
Unit Contrib. Margin
$325
600 2 400
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Break-Even Point in UnitsBreak-Even Point in Units
Break-even packages =
Fixed Cost
Package contribution margin
Break-even packages = $96,250
$625
Break-even packages
= 154
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Break-Even Point in UnitsBreak-Even Point in Units
154 Break-even packages
Each package contains:3 mulching mowers, 2 riding mowers
Mulching mowers break-even units
Riding mowers break-even units
= 154 × 3 = 462
= 154 × 2 = 308
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462 × $325
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Sales
Riding TotalMulching
$184,800 $246,400
Total Variable Expense 150,150
$431,200
184,800 334,950
Total Contribution Margin $ 34,650 $ 61,600 $ 96,250
Total Fixed Expense $ 96,250
Operating Income $ 0
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308 × $800
462 × $400
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Cornerstone 4-8Cornerstone 4-8
How to Calculate the Break-Even Sales Dollars for a Multiple-Product Firm
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• Whittier Co. sells two products that are expected to produce:– Total revenue next year of $1,120,000– Total variable costs of $870,000
• Total fixed costs are expected to equal $96,250
Information:
• The break-even point in sales dollars for Whittier Co.• Check calculations by preparing a contribution margin
income statement
Required:
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CVP AnalysisCVP Analysis
Contribution Margin Ratio
=Expected Contribution Margin
Total Sales Revenue
Contribution Margin Ratio
= $250,000
$1,120,000
Contribution Margin Ratio
= 0.22*
Break-even point in sales dollars
*RoundedCOPYRIGHT © 2012 Nelson Education Ltd.
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CVP AnalysisCVP Analysis
Break-Even Sales =
Fixed Cost
Contribution Margin Ratio
Break-Even Sales = $96,250
0.22
Break-Even Sales
= $437,500
Break-even sales
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Whittier CompanyContribution Margin Income Statement
For the Coming Year
Whittier CompanyContribution Margin Income Statement
For the Coming Year
Sales $437,500
Total Variable Exp. (0.78 × 437,500) 341,250
Total Contribution Margin $ 96,250
Total Fixed Expense 96,250
$ 0Operating Income
Operating income is zero when sales are $437,500 The break-even calculation is correct!
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Explain the impact of risk, uncertainty, and changing variables
on cost-volume-profit analysis
OBJECTIVE OBJECTIVE 55
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CVP Analysis: Risk and UncertaintyCVP Analysis: Risk and Uncertainty
• The break-even point can be affected by changes in:– Price– Unit Contribution Margin– Fixed Cost
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Changes in any of the above will affect the sales mix
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Risk and Uncertainty Effects on ManagersRisk and Uncertainty Effects on Managers
• Must realize the uncertain nature of future prices, costs, and quantities
• Move from consideration of a break-even point to what might be called a “break-even band”
• May engage in sensitivity or what-if analysis
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Margin of SafetyMargin of Safety
• Units sold or revenue earned above break-even volume
• Crude measure of risk– When there is a downturn in sales, the risk of
suffering losses will be less if the firm’s margin of safety is large than if the margin of safety is small
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Cornerstone 4-9Cornerstone 4-9
How to Compute the Margin of Safety
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• This year, Whittier Co. plans to sell 1,000 mowers at $400 ea.• Variable costs are $325• Fixed costs are $45,000• Break-even units were previously calculated as 600
Information:
• Calculate the margin of safety for Whittier Co. in units• Calculate the margin of safety for Whittier Co. in sales
revenue
Required:
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Margin of Safety in UnitsMargin of Safety in Units
Margin of safety in units =
Sales in units
- Break-even units
Margin of safety in units = 1,000 600
Margin of safety in units = 400
-
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Margin of Safety in Sales RevenueMargin of Safety in Sales Revenue
Margin of safety in sales revenue = Sales - Break-even
units
Margin of safety in sales revenue = $400(1,000) $400(600)
Margin of safety in sales revenue = $160,000
-
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Operating LeverageOperating Leverage
• Relative mix of fixed costs to variable costs• Higher proportions of fixed costs to the amount of
variable costs create higher operating leverage• The greater the degree of operating leverage, the
larger the effect on operating income when sales change
Degree of operating leverage
=Contribution margin
Operating income
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Cornerstone 4-10Cornerstone 4-10
How to Compute the Degree of Operating Leverage
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• This year, Whittier Co. plans to sell 1,000 mowers at $400 ea.• Variable costs are $325• Fixed costs are $45,000• Operating Income at 1,000 units is $30,000
Information:
Required:• Calculate the degree of operating leverage for Whittier Co.
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Operating LeverageOperating Leverage
Degree of operating leverage
=Contribution Margin
Operating Income
Degree of operating leverage = ($400 - $325)(1,000 units)
$30,000
Degree of operating leverage = 2.5
Degree of operating leverage (DOL) can be measured for a given level of sales
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Cornerstone 4-11Cornerstone 4-11
How to Compute the Impact of Increased Sales on Operating Income Using the DOL
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• Whittier Co. plans to sell 1,000 mowers and earn operating income equal to $30,000 next year
• Whittier’s degree of operating leverage is equal to 2.5• Now, the company plans to increase sales by 20 percent
next year
Information:
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ExampleExample
• Calculate the percent change in operating income expected by Whittier Co. for the next year using the degree of operating leverage
• Calculate the operating income expected by Whittier Co. next year using the percent change in operating income calculated in the above requirement
Required:
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Percentage Change in Operating LeveragePercentage Change in Operating Leverage
Percent change in operating leverage = DOL × Percent change
in sales
Percent change in operating leverage = 2.5 20%
Percent change in operating leverage = 50%
×
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Expected Operating IncomeExpected Operating Income
Expected operating income
=Original
operating income
+ (percent change × original operating income)
Expected operating income
= $30,000 (0.50 × $30,000)
Expected operating income
= $45,000
+
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