Cost Behavior and CostVolumeProfit Analysis

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Cost Behavior and Cost-Volume-Profit Analysis
Revised by Judy Beebe, Western Oregon University

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Cost Behavior
Cost behavior refers to the manner in which a
cost changes as a related activity changes. Such
activities are called activity base (or activity
drivers). The range of activity over which the
changes in the cost are of interest is called the
relevant range.
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Variable Costs
Variable costs are costs that vary in proportion
to changes in the level of activity.
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Jason Inc.s Waterloo Plant
Jason Inc. produces stereo sound systems under
the brand name of J-Sound. The parts for the
J-Sound stereos are purchased from outside
suppliers for 10 per unit (a variable cost) and
assembled in Jason Inc.s Waterloo plant.
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Variable Cost Graphs (Contd)
Total Variable Cost Graph
300,000 250,000 200,000 150,000 100,000
50,000
Total Direct Materials Cost
0
10 20 30
Total Units (Model JS-12) Produced (thousands)
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Variable Cost Graphs
Unit Variable Cost Graph
20 15 10 5
Direct Materials Cost per Unit
0
10 20 30
Total Units (Model JS-12) Produced (thousands)
(Concluded)
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Unit Cost Compared to Total Cost
300,000 250,000 200,000 150,000 100,000
50,000
20 15 10 5
Cost per Unit
Total Costs
0
10 20 30
Units Produced (000)
0
10 20 30
Units Produced (000)
Number of Units of Model JS-12 Produced
Direct Materials Cost per Unit
Total Direct Materials Cost
5,000 units 10 50,000 10,000 10 l00,000
15,000 10 150,000 20,000 10 200,000 25,000 1
0 250,000 30,000 10 300,000
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Fixed Costs
Fixed costs are costs that remain the same in
total dollar amount as the level of activity
changes.
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Minton Inc.s Los Angeles Plant
The production supervisor for Minton Inc.s Los
Angeles plant is Jane Sovissi. She is paid
75,000 per year. The plant produces from 50,000
to 300,000 bottles of La Fleur Perfume.
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Fixed Versus Variable Cost of Jane Sovissis
Salary
Salary per Bottle of Perfume Produced
Number of Bottles of Perfume Produced
Total Salary for Jane Sovissi
50,000 bottles 75,000 1.500 100,000 75,000
0.750 150,000 75,000 0.500 200,000 75,000 0.3
75 250,000 75,000 0.300 300,000 75,000 0.250
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150,000 125,000 100,000 75,000 50,000
25,000
1.50 1.25 1.00 .75 .50 .25
Total Costs
Unit Cost
100 200 300
0
100 200 300
0
Bottles Produced (000)
Units Produced (000)
Salary per Bottle of Perfume Produced
Number of Bottles of Perfume Produced
Total Salary for Jane Sovissi
50,000 bottles 75,000 1.500 100,000 75,000
0.750 150,000 75,000 0.500 200,000 75,000 0.37
5
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Mixed Costs
A mixed cost has characteristics of both a
variable and a fixed cost. Over one range of
activity, the total mixed cost may remain the
same. Over another range of activity, the mixed
cost may change in proportion to changes in level
of activity.
Mixed costs are sometimes called semivariable or
semifixed costs.
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Simpson Inc. Example
Simpson Inc. manufactures sails using rented
equipment. The rental charges are 15,000 per
year, plus 1 for each machine hour used over
10,000 hours.
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Mixed Cost Graph for Simpson Inc.s Equipment
Rental Charges
45,000 40,000 35,000 30,000 25,000 20,000
15,000 10,000 5,000
Mixed costs are usually separated into their
fixed and variable components for management
analysis.
Total Costs
0
10 20 30 40
Total Machine Hours (000)
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High-Low Method
The high-low method is a simple cost estimate
technique that may be used for separating mixed
costs into their fixed and variable components.
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Estimating Variable Cost Using High-Low
Production Total (Units) Cost
First, select the highest and lowest levels of
activity.
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
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Estimating Variable Cost Using High-Low
Production Total (Units) Cost
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
Then, fill in the formula.
61,500
41,250
20,250
20,250
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Estimating Variable Cost Using High-Low
Production Total (Units) Cost
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
Then, fill in the formula.
2,100
750
1,350
20,250
1,350
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Estimating Variable Cost Using High-Low
Production Total (Units) Cost
Variable cost per unit is 15
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
20,250
15
Variable Cost per Unit
1,350
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Estimating Fixed Cost Using High-Low
Production Total (Units) Cost
First, insert the variable cost of 15 into the
formula.
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
Total cost (Variable Cost per Unit x Units of
Production) Fixed Cost
Total cost (15 x Units of Production) Fixed
Cost
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Estimating Fixed Cost Using High-Low
Production Total (Units) Cost
Using the highest level of production, we insert
the total cost and units produced in the formula.
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
June 1,000 45,550 July 1,500 52,000 August 2,100
61,500 September 1,800 57,500 October 750 41,250
Total cost (Variable Cost per Unit x Units of
Production) Fixed cost
61,500
Total cost (15 x Units of Production) Fixed
Cost
2,100 units)
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Estimating Fixed Cost Using High-Low
61,500 (15 x 2,100 units) Fixed cost
61,500 31,500 Fixed cost 61,500 31,500
Fixed cost 30,000 Fixed cost
If the lowest level had been chosen, the results
of the formula would provide the same fixed cost
of 30,000.
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The manufacturing cost of Alex Industries for the
first three months of the year are provided below
Total Cost Production
January 80,000 1,000 units February 125,000 2,
500 March 100,000 1,800
Using the high-low method, determine the (a)
variable cost per unit, and (b) the total fixed
cost.
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b. 50,000 125,000 (30 x 2,500) or 80,000
(30 x 1,000)
For Practice PE19-1A, PE19-1B
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Summary of Cost Behavior Concepts
Total Variable Costs
Total Costs
Total Units Produced
Unit Variable Costs
Per Unit Cost
Total Units Produced
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Summary of Cost Behavior Concepts
Total Fixed Costs
Total Costs
Total Units Produced
Unit Fixed Costs
Per Unit Cost
Total Units Produced
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Cost-Volume-Profit Relationships
Cost-volume-profit analysis is the systematic
examination of the relationships among selling
prices, sales and production volume, costs,
expenses, and profits.
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The contribution margin is the excess of sales
revenues over variable costs. It contributes
first toward covering fixed costs, then
contributes to profit.
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Contribution Margin Income Statement
Sales (50,000 units) 1,000,000 Variable costs
600,000 Contribution margin 400,000
Fixed costs 300,000 Income from
operations 100,000
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Contribution Margin Ratio
100 60
Sales (50,000 units) 1,000,000 Variable costs
600,000 Contribution margin 400,000
Fixed costs 300,000 Income from
operations 100,000
40
30 10
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Unit Contribution Margin
The unit contribution margin is also useful for
analyzing the profit potential of proposed
projects. The unit contribution margin is the
sales price less the variable cost per unit.
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Using Contribution Margin per Unit as a Shortcut
50,000 units
1,300,000 780,000 520,000
300,000
Sales (20) 1,000,000 Variable costs (12)
600,000 Contribution margin (8) 400,000
Fixed costs 300,000 Income from
operations 100,000
220,000
The increase in income from operations of
120,000 could have been determined quickly by
multiplying the increase in unit sales (15,000)
by the contribution margin per unit (8).
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100 60 40 30 10
20 12 8
Sales (50,000 units) 1,000,000 Variable costs
600,000 Contribution margin 400,000
Fixed costs 300,000 Income from
operations 100,000
Unit contribution margin analyses can provide
useful information for managers.
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Review
100 60 40 30 10
20 12 8
Sales (50,000 units) 1,000,000 Variable costs
600,000 Contribution margin 400,000
Fixed costs 300,000 Income from
operations 100,000
The contribution margin can be expressed three
ways
1. Total contribution margin in dollars.
2. Contribution margin ratio (percentage).
3. Unit contribution margin (dollars per unit).
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Molly Company sells 20,000 units at 12 per unit.
Variable costs are 9 per unit, and fixed costs
are 25,000. Determine the (a) contrib-ution
margin ratio, (b) unit contribution margin, and
(c) income from operations.
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a. 25 (12 9)/12 or (240,000
180,000)/240,000

• 3 per unit 12 9

• Sales 240,000 (20,000 x 12)
• Variable costs 180,000 (20,000 x 9)
• Contribution margin 60,000 20,000 x
  12 9)
• Fixed costs 25,000
• Income from operations 35,000

For Practice PE19-2A, PE19-2B
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Break-Even Point
The break-even point is the level of operations
at which a businesss revenues and expired costs
are exactly equal.
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Barker Corporations fixed costs are estimated to
be 90,000. The unit contribution margin is
calculated as follows
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The break-even point is calculated using the
following equation
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Proof of the Preceding Computation
Income from operations is zero when 9,000 units
are soldhence, break-even is 9,000 units.
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Bishop Co. is evaluating a proposal to budget an
additional 100,000 for advertising. Fixed costs
before the additional advertising are estimated
at 600,000, and the unit contribution margin is
20.
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Without additional advertising
With additional advertising
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Park Co. is evaluating a proposal to pay an
additional 2 commission on sales to its
salespeople (a variable cost) as an incentive to
increase sales. Fixed costs are estimated at
840,000. The unit contribution margin before
the additional 2 commission is determined as
follows
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Without additional 2 commission
With additional 2 commission
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Graham Co. is evaluating a proposal to increase
the unit selling price of a product from 50 to
60. The following data have been gathered
Total fixed costs 600,000 600,000
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Without price increase
With price increase
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Nicholas Enterprises sells a product for 60 per
unit. The variable cost is 35 per unit, while
fixed costs are 80,000. Determine the (a)
break-even point in sales units, and (b)
break-even point if the selling price were
increased to 67 per unit.
a. 3,200 units 80,000/(60 35)
b. 2,500 units 80,000/(67 35)
For Practice PE19-3A, PE19-3B
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Target Profit
The sales volume required to earn a target profit
is determined by modifying the break-even
equation.
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Units Required for Target Profit
Fixed costs are estimated at 200,000, and the
desired profit is 100,000. Unit contribution
margin is 30.
100,000
200,000
30
Sales (units) 10,000 units
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Sales (10,000 units x 75) 750,000 Variable
costs (10,000 x 45) 450,000 Contribution
margin (10,000 x 30) 300,000 Fixed costs
200,000 Income from operations 100,000
Proof that sales of 10,000 units will provide a
profit of 100,000.
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The Forest Company sells a product for 140 per
unit. The variable cost is 60 per unit, and
fixed costs are 240,000. Determine the (a)
break-even point in sales units, and (b)
break-even point in sales units if the company
desires a target profit of 50,000.
a. 3,000 units 240,000/(140 60)
b. 3,625 units (240,000 50,000)/(140 60)
For Practice PE19-4A, PE19-4B
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Cost-Volume-Profit (Break-Even) Chart
A cost-volume-profit chart, sometimes called a
break-even chart, may assist management in
understanding relationships among costs, sales,
and operating profit or loss.
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The cost-volume-profit chart in Exhibit 5 (Slides
55-63) is based on the following data
Unit selling price 50 Unit variable cost
30 Unit contribution margin 20 Total fixed
costs 100,000
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Cost-Volume-Profit Chart
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Volume is shown on the horizontal axis.
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
A sales line is plotted by determining one value
(500,000 in sales divided by the 50 selling
price equals 10,000 units).
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Now, beginning at zero on the left corner of the
graph, connect a straight line to the dot.
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Fixed cost of 100,00 is a horizontal line.
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Similar to the sales line, a point is determined
on the cost line (10,000 _at_ 30 300,000
100,000 400,000)
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Beginning with the total fixed cost at the
vertical axis (100,000), draw a line to the red
dot. This is the total cost line.
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Horizontal and vertical lines are drawn at the
intersection point of the sales and cost lines,
which is the break-even point.
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Cost-Volume-Profit Chart (Continued)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
Break-even is sales of 5,000 units or 250,000.
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Cost-Volume-Profit Chart (Concluded)
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
Profit area
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
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Revised Cost-Volume-Profit Chart
Using the data from Slide 54, assume that a
proposal to reduced fixed cost by 20,000 is to
be evaluated. A cost-volume-profit chart can be
created to assist in this evaluation.
Click this button to go to Slide 54. Return to
this slide by typing 64 and striking Enter.
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Revised Cost-Volume- Profit Chart
500 450 400 350 300 250 200 150 100 50
Sales and Costs (in thousands)
80,000
1 2 3 4 5 6 7 8 9 10
0
Units of Sales (in thousands)
If fixed costs can be reduced to 80,000, the new
break-even point is sales of 200,000 or 4,000
units.
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Profit-Volume Chart
Another graphic approach to cost-volume-profit
analysis, the profit-volume chart, plots only the
difference between total sales and total costs
(or profits). Again, the data from Slide 54
(shown below) will be used.
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The maximum operating loss is equal to the fixed
costs of 100,000. Assuming that the maximum
unit sales within the relevant range is 10,000
units, the maximum operating profit is 100,000,
computed as follows
Sales (10,000 units x 50) 500,000 Variable
costs (10,000 units x 30) 300,000
Contribution margin (10,000 units x
20) 200,000 Fixed costs 100,000 Operating
profit 100,000
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Assumptions of Cost-Volume-Profit Analysis
The primary assumptions are

• Total sales and total costs can be represented by
  a straight line.
• Within the relevant range of operating activity,
  the efficiency of operations does not change.
• Costs can be accurately divided into fixed and
  variable components.
• The sales mix is constant.
• There is no change in the inventory quantities
  during the period.

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Sales Mix Considerations
The sales volume necessary to break even or to
earn a target profit for a business selling two
or more products depends upon the sales mix. The
sales mix is the relative distribution of sales
among the various products sold by a business.
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Cascade Company sold 8,000 units of Product A and
2,000 units of Product B during the past year.
Cascade Companys fixed costs are 200,000.
Other relevant data are as follows
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Cascade Company Example
For Cascade Company, the overall enterprise
product is called E.
Unit selling price of E (90 x 0.8) (140 x
0.2) 100 Unit variable cost of E (70 x
0.8) ( 95 x 0.2) 75 Unit contribution
margin of E (20 x .08) (45 x .02) 25
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Break-Even Point of 8,000 Units of E
Fixed Costs Unit Contribution Margin
Break-Even Sales (units)
Break-Even Sales (units) 8,000 units
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Verification of Analysis
Break-even point
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Megan Company has fixed cost of 180,000. The
unit selling price, variable cost per unit, and
contribution margin per unit for the companys
two products are provided below
Variable Contribution Sales Selling Cost
per Margin per Mix Product Price Unit Unit
Q 160 100 20 75 Z 140 95 45 25
Determine the break-even point in units of Q and
Z.
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Unit selling price of E (160 x .75) (100 x
.25) 145 Unit variable cost of E (100 x
.75) (80 x .25) 95 Unit contribution
margin of E (60 x .75) (20 x .25), or
145 95 50
Break-even sales (units) 3,600 units
180,000/50
For Practice PE19-5A, PE19-5B
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Operating Leverage
The relative mix of a businesss variable costs
and fixed costs is measured by the operating
leverage. It is computed as follows
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Operating Leverage Example
Jones
Inc. Wilson Inc.
Sales 400,000 400,000 Variable costs 300,000
300,000 Contribution margin 100,000 100,000 Fix
ed costs 80,000 50,000 Income from
operations 20,000 50,000 Operating
leverage ? ?
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Jones
Inc. Wilson Inc.
Sales 400,000 400,000 Variable costs 300,000
300,000 Contribution margin 100,000 100,000 Fix
ed costs 80,000 50,000 Income from
operations 20,000 50,000 Operating
leverage ? ?
5
Contribution Margin Income from Operations
100,000
5
Jones Inc.
20,000
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Jones
Inc. Wilson Inc.
Sales 400,000 400,000 Variable costs 300,000
300,000 Contribution margin 100,000 100,000 Fix
ed costs 80,000 50,000 Income from
operations 20,000 50,000 Operating
leverage ? ?
2
5
Contribution Margin Income from Operations
100,000
2
Wilson Inc.
50,000
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High Versus Low Operating Leverage
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The Tucker Company reports the following data.
Sales 750,000 Variable costs 500,000 Fixed
costs 187,500
Determine Tucker Companys operating leverage.
4.0 (750,000 500,000)/(750,000 500,000
187,500) 250,000/62,500
For Practice PE19-6A, PE19-6B
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Margin of Safety
The difference between the current sales revenue
and the sales revenue at the break-even point is
called the margin of safety.
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If sales are 250,000, the unit selling price is
25, and the sales at the break-even point are
200,000, the margin of safety is 20, computed
as follows
Margin of Safety 20
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The Rachel Company has sales of 400,000, and the
break-even point in sales dollars is 300,000.
Determine the companys margin of safety.
25 (400,000 300,000)/400,000
For Practice PE19-7A, PE19-7B
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Preparing a Variable Costing Income Statement
Number Unit Total Cost of Units Cost
Manufacturing costs Variable 375,000 15,000 25
Fixed 150,000 15,000 10
Total 525,000 35 Selling and
administrative expenses Variable (5 per unit
sold) 75,000 Fixed 50,000
Total 125,000