1 click to edit master title style 1 1 1 cost behavior and cost- volume-profit analysis 4
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Cost Cost Behavior Behavior and Cost-and Cost-Volume-Volume-
Profit Profit AnalysisAnalysis
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Classify costs by their behavior as variable costs, fixed costs, or
mixed costs.
Objective 1Objective 1Objective 1Objective 1
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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.
Jason Inc.’s Waterloo Plant 4-1
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Total Variable Cost GraphT
otal
Dir
ect
Mat
eria
ls C
ost $300,000
$250,000$200,000$150,000$100,000 $50,000
10 20 300Total Units (Model JS-12)
Produced (thousands)
Variable Cost Graphs (Cont’d) 4-1
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Unit Variable Cost Graph
$20
$15
$10
$5
0
Dir
ect
Mat
eria
ls
Cos
t p
er U
nit
10 20 30Total Units (Model JS-
12) Produced (thousands)
Variable Cost Graphs
(Concluded)
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Tot
al C
osts
$300,000$250,000$200,000$150,000$100,000 $50,000
10 20 300
$20$15$10
$5
0
Cos
t per
Uni
t
10 20 30
Number ofUnits of Model JS-12 Produced
Units Produced (000)
Units Produced (000)
Direct Materials Cost
per UnitTotal Direct
Materials Cost
5,000 units $10 $ 50,00010,000 10 l00,00015,000 10 150,00020,000 10 200,00025,000 10 250,00030,000 10 300,000
Unit Cost Compared to Total Cost 4-1
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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.
Minton Inc.’s Los Angeles Plant 4-1
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Number ofBottles of Perfume
ProducedTotal Salary
for Jane Sovissi
50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375
250,000 75,000 0.300300,000 75,000 0.250
Salary per Bottle of Perfume Produced
Fixed Versus Variable Cost of Jane Sovissi’s Salary
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Tot
al C
osts
$150,000$125,000$100,000$75,000$50,000
$25,000
100 200 3000Bottles Produced (000)
Number ofBottles of Perfume
Produced
Un
it C
ost
$1.50$1.25$1.00
$.75$.50
$.25
100 200 3000Units Produced (000)
Total Salary for Jane Sovissi
50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375
Salary per Bottle of Perfume Produced
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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.
Simpson Inc. Example 4-1
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Tot
al C
osts
0Total Machine Hours (000)
$45,000$40,000 $35,000$30,000$25,000$20,000$15,000$10,000 $5,000
10 20 30 40
Mixed costs are usually separated into
their fixed and variable components
for management analysis.
Mixed Cost Graph for Simpson Inc.’s Equipment Rental Charges
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The high-low method is a simple cost estimate
technique that may be used for separating mixed costs into their fixed and
variable components.
High-Low Method 4-1
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Example Exercise 4-1
4-1
The manufacturing cost of Alex Industries for the first three months of the year are provided below:
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Total Cost ProductionJanuary $80,000 1,000 unitsFebruary $125,000 2,500March $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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For Practice: PE4-1A, PE4-1B
Follow My Example 4-1
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4-1
b. $50,000 = $125,000 – ($30 x 2,500) or $80,000 – ($30 x 1,000)
a. $30 per unit =$125,000 – $80,000
(2,500 – 1,000)
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Total Variable
Costs
Total Units Produced
Unit Variable
Costs
Total Units Produced
Tot
al C
osts
Per
Uni
t Cos
t
Total costs increase and
decrease proportionately
with activity level.
Summary of Cost Behavior Concepts
Unit costs remain the same per unit
regardless of activity.
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Total Units Produced
Tot
al C
osts
Total Units Produced
Per
Uni
t Cos
t
Unit costs remain the same
regardless of activity.
Total costs increase and
decrease with activity
level.
Summary of Cost Behavior Concepts
Total Fixed Costs
Unit Fixed Costs
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Compute the contribution margin, the contribution margin ratio,
and the unit contribution margin, and explain how they may be
useful to managers.
Objective 2Objective 2Objective 2Objective 2
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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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Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000
Contribution Margin Income Statement
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Contribution Margin Ratio 4-2
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100% 60%
Contribution Margin Ratio = 40%
Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000
Contribution Margin Ratio =Sales – Variable Costs
Sales$1,000,000 – $600,000
$1,000,000 Contribution Margin Ratio =
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
Sales ($20) $1,000,000Variable costs ($12) 600,000Contribution margin ($8) $ 400,000 Fixed costs 300,000Income from operations $ 100,000
50,000 units
65,000 units
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).
$1,300,000 780,000$ 520,000 300,000
$220,000
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100% 60%
40% 30%
10%
$20 12$ 8
Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000
Unit contribution margin analyses can provide useful information for managers.
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100% 60%
40% 30%
10%
1. Total contribution margin in dollars.
$20 12$ 8
Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000
2. Contribution margin ratio (percentage).
The contribution margin can be expressed three ways:
3. Unit contribution margin (dollars per unit).
Review 4-2
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Example Exercise 4-2
4-2
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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For Practice: PE4-2A, PE4-2B
Follow My Example 4-2
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4-2
a. 25% = ($12 – $9)/$12 or ($240,000 – $180,000)/$240,000b. $3 per unit = $12 – $9
c. 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 25,000Income from operations $ 35,000
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Using the unit contribution margin, determine the break-even point and the volume necessary to
achieve a target profit.
Objective 3Objective 3Objective 3Objective 3
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Break-Even Point
The break-even point is the level of operations at
which a business’s revenues and expired costs
are exactly equal.
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Barker Corporation’s fixed costs are estimated to be $90,000. The unit contribution margin is calculated as follows:
Unit selling price $25Unit variable cost 15Unit contribution margin $10
4-3
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The break-even point is calculated using the following equation:
Break-Even Sales (units) =Fixed Costs
Unit Contribution Margin
Break-Even Sales (units) =$90,000
$10
Break-Even Sales (units) = 9,000 units
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Proof of the Preceding Computation
Sales ($25 x 9,000) $225,000Variable costs ($15 x 9,000) 135,000Contribution margin $ 90,000Fixed costs 90,000Income from operations $ 0
Income from operations is zero when 9,000 units are sold—hence, break-
even is 9,000 units.
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Effect of Changes in Fixed Costs
Fixed Fixed CostsCosts
Fixed Fixed CostsCostsIf
Break-Break-EvenEven
Break-Break-EvenEvenThen
Fixed Fixed CostsCosts
Fixed Fixed CostsCostsIf Then Break-Break-
EvenEven
Break-Break-EvenEven
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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:
4-3
Break-Even in Sales (units) =Fixed Costs
Unit Contribution Margin
Break-Even in Sales (units) =$600,000
$20=
30,000 units
With additional advertising:
Break-Even in Sales (units) =$700,000
$20=
35,000 units
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Effect of Changes in Unit Variable Costs
Unit Unit Variable Variable
CostCost
Unit Unit Variable Variable
CostCostIf Break-Break-
EvenEven
Break-Break-EvenEven
Then
Unit Unit Variable Variable
CostsCosts
Unit Unit Variable Variable
CostsCosts
If Then Break-Break-EvenEven
Break-Break-EvenEven
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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:
Unit selling price $250Unit variable cost 145Unit contribution margin $105
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Without additional 2% commission:
Break-Even in Sales (units) =Fixed Costs
Unit Contribution Margin
Break-Even in Sales (units) =$840,000
$105=
8,000 units
With additional 2% commission:
Break-Even in Sales (units) =$840,000
$100=
8,400 units
$250 – [$145 + ($250 x 2%)] = $100
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Effect of Changes in the Unit Selling Price
Unit Unit Selling Selling PricePrice
Unit Unit Selling Selling PricePrice
If
Break-Break-EvenEven
Break-Break-EvenEven
Then
Unit Unit Selling Selling
PricePrice
Unit Unit Selling Selling
PricePriceIf Then
Break-Break-EvenEven
Break-Break-EvenEven
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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:
Unit selling price $50 $60Unit variable cost 30 30Unit contribution margin $20 $30
Current Proposed
Total fixed costs $600,000 $600,000
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Without price increase:
Break-Even in Sales (units) =Fixed Costs
Unit Contribution Margin
Break-Even in Sales (units) =$600,000
$20=
30,000 units
With price increase:
Break-Even in Sales (units) =$600,000
$30=
20,000 units
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Summary of Effects of Changes on Break-Even Point
Effect of ChangeDirection of on Break-Even
Change Sales (Units)Type of Change
Fixed cost Increase IncreaseDecrease Decrease
Variable cost per unit Increase IncreaseDecreaseDecrease
Unit sales price Increase DecreaseIncreaseDecrease
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Example Exercise 4-3
4-3
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.
57For Practice: PE4-3A, PE4-3B
Follow My Example 4-3
a. 3,200 units = $80,000/($60 – $35)
b. 2,500 units = $80,000/($67 – $35)
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Target Profit
The sales volume required to earn a target profit is determined by modifying the break-even equation.
Sales (units) =Fixed Costs + Target ProfitUnit Contribution Margin
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Fixed costs are estimated at $200,000, and the desired profit is $100,000. Unit contribution margin is $30.
Unit selling price $75Unit variable cost 45Unit contribution margin $30
Sales (units) =Fixed Costs + Target ProfitUnit Contribution Margin$30
Sales (units) = 10,000 units
Units Required for Target Profit 4-3
$200,000 $100,000
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Sales (10,000 units x $75) $750,000Variable costs (10,000 x $45) 450,000Contribution margin (10,000
x $30) $300,000Fixed costs 200,000Income from operations $100,000
Proof that sales of 10,000 units will Proof that sales of 10,000 units will provide a profit of $100,000.provide a profit of $100,000.
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Example Exercise 4-4
4-3
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.
61For Practice: PE4-4A, PE4-4B
Follow My Example 4-4
a. 3,000 units = $240,000/($140 – $60)
b. 3,625 units = ($240,000 + $50,000)/($140 – $60)
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Using a cost-volume-profit chart and a profit-volume chart,
determine the break-even point and the volume necessary to
achieve a target profit.
Objective 4Objective 4Objective 4Objective 4
4-4
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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.
4-4
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Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20
Total fixed costs $100,000
The cost-volume-profit chart in Exhibit 5 (Slides 65-73) is based on the following data:
4-4
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
Cost-Volume-Profit Chart
Volume is shown on the horizontal axis.Volume is shown on the horizontal axis.
Dollar amounts
are indicated along the vertical
axis.
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4-4
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Cost-Volume-Profit Chart (Continued)
Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
1 2 3 4 5 6 7 8 9 10
A sales line is plotted by determining one value ($500,000 in sales divided by the $50 selling price equals 10,000 units).
4-4
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
1 2 3 4 5 6 7 8 9 10
Now, beginning at zero on the left corner of the graph, connect a straight line to the dot.
Cost-Volume-Profit Chart (Continued)
4-4
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
Fixed cost of $100,00 is a horizontal line.
1 2 3 4 5 6 7 8 9 10
Cost-Volume-Profit Chart (Continued)
4-4
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
Similar to the sales line, a point is determined on the cost line (10,000 @ $30 = $300,000 + $100,000 = $400,000)
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Cost-Volume-Profit Chart (Continued)
4-4
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
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)
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
Horizontal and vertical lines are drawn at the intersection point of the sales and cost lines, which is the break-even point.
1 2 3 4 5 6 7 8 9 10
Cost-Volume-Profit Chart (Continued)
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
Break-even is sales of 5,000 units or $250,000.
1 2 3 4 5 6 7 8 9 10
Cost-Volume-Profit Chart (Continued)
4-4
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
1 2 3 4 5 6 7 8 9 10
Profit area
Loss area
Cost-Volume-Profit Chart (Concluded)
4-4
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Revised Cost-Volume-Profit Chart
Using the data from Slide 64, 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.
4-4
Click this button to go to Slide 64. Return to this slide by typing “74” and striking “Enter.”
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Sale
s an
d C
osts
(in
th
ousa
nds)
0Units of Sales (in thousands)
$500$450$400$350$300$250$200$150$100$ 50
1 2 3 4 5 6 7 8 9 10
$80,000
If fixed costs can be reduced to $80,000, the new break-even point is sales of $200,000 or 4,000 units.
Revised Cost-Volume-Profit Chart
4-4
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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 64 (shown below) will be used.
Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20
Total fixed costs $100,000
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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
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:
4-4
Maximum profit
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Units of Sales (in thousands)
1 2 3 4 5 6 7 8 9 10
Profit Line
Operating Operating lossloss
Operating Operating profitprofit
$100,000$75,000$50,000$25,000
$ 0$(25,000)$(50,000)$(75,000)
$(100,000)
Op
erat
ing
Pro
fit
(Los
s)
Maximum loss is $100,000, the fixed costs.
Profit-Volume Chart
Break-Even Point
4-4
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Assumptions of Cost-Volume-Profit Analysis
The primary assumptions are:
1. Total sales and total costs can be represented by a straight line.
2. Within the relevant range of operating activity, the efficiency of operations does not change.
3. Costs can be accurately divided into fixed and variable components.
4. The sales mix is constant.5. There is no change in the inventory quantities
during the period.
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Compute the break-even point for a business selling more than one
product, the operating leverage, and the margin of safety, and explain how
managers use these concepts.
Objective 5Objective 5Objective 5Objective 5
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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.
4-5
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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 Company’s fixed costs are $200,000. Other relevant data are as follows:
Unit Unit Unit SalesSelling Variable Contribution Mix
Product Price Cost Margin %
A $ 90 $70 $20 20%B 140 95 45 80%
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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
4-5Cascade Company Example
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4-5Break-Even Point of 8,000 Units of E
Break-Even Sales (units) =Fixed Costs
Unit Contribution Margin
Break-Even Sales (units) =$200,000
$25
Break-Even Sales (units) = 8,000 units
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Verification of Analysis
Break-even point
4-5
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Example Exercise 4-5
4-5
Megan Company has fixed cost of $180,000. The unit selling price, variable cost per unit, and contribution margin per unit for the company’s two products are provided below:
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Variable Contribution SalesSelling 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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For Practice: PE4-5A, PE4-5B
Follow My Example 4-5
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4-5
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 marginof E: ($60 x .75) + ($20 x .25), or $145 – $95 = $50
Break-even sales (units) = 3,600 units = $180,000/$50
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The relative mix of a business’s variable costs and fixed costs is measured by the operating leverage. It is computed as follows:
4-5Operating Leverage
Operating Leverage =Contribution Margin
Income from Operations
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Both companies have the same contribution margin.
Jones Inc. Wilson Inc.
Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Operating leverage ? ?
4-5Operating Leverage Example
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Contribution Margin
Income from Operations
$100,000
$20,000= 5 Jones Inc.:
Jones Inc. Wilson Inc.
Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Operating leverage ? ? 5
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Contribution Margin
Income from Operations
$100,000
$50,000= 2 Wilson Inc.:
Jones Inc. Wilson Inc.
Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Operating leverage ? ? 25
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High Versus Low Operating Leverage 4-5
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Example Exercise 4-6
4-5
The Tucker Company reports the following data.
93For Practice: PE4-6A, PE4-6B
Follow My Example 4-6
4.0 = ($750,000 – $500,000)/($750,000 – $500,000 – $187,500) = $250,000/$62,500
Sales $750,000Variable costs $500,000Fixed costs $187,500
Determine Tucker Company’s operating leverage.
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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:
4-5
Margin of Safety =Sales – Sales at Break-Even Point
Sales
Margin of Safety = 20%
Margin of Safety =$250,000 – $200,000
$250,000
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Example Exercise 4-7
4-5
The Rachel Company has sales of $400,000, and the break-even point in sales dollars is $300,000. Determine the company’s margin of safety.
96For Practice: PE4-7A, PE4-7B
Follow My Example 4-7
25% = ($400,000 – $300,000)/$400,000
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Preparing a Variable Costing Income Statement
Number UnitTotal Cost of Units Cost
Manufacturing costs:Variable $375,000 15,000 $25Fixed 150,000 15,000 10 Total $525,000 $35
Selling and administrativeexpenses:
Variable ($5 per unit sold) $ 75,000Fixed 50,000 Total $125,000
4-5