Fill-in-the-Blank Equations
1. __________ = Difference in Total Cost ÷ Difference in Units Produced
2. Contribution Margin = Sales – __________
3. Contribution Margin Ratio = __________ ÷ Sales
4. __________ = Fixed Costs ÷ Unit Contribution Margin
5. Sales (units) = (__________ + Target Profit) ÷ Unit Contribution Margin
6. Operating Leverage = Contribution Margin ÷ __________
7. Margin of Safety (percent of current sales) = (Sales – Sales at Break-Even Point) ÷__________
8. Margin of Safety (SAR) = Sales (SAR) – __________
Break-Even Sales (SAR)
9. The total cost of production for the last four quarters for Moore’s Mowers is as follows. Use the high-low method to determine the variable cost per unit and the fixed cost.
Total Cost Units Produced
Quarter 1 51,000 SAR 2,000
Quarter 2 56,400 SAR 2,300
Quarter 3 49,200 SAR 1,900
Quarter 4 53,700 SAR 2,150
Variable Cost
= ____________
_
Fixed Cost = ____________
10. During 2023, Caps by Huely sold 50,000 finished products with a contribution margin of 55%. The variable costs totaled 40,500 SAR for the year. Determine the sales, contribution margin, and unit contribution margin.
Sales = ____________
Sales price per unit = ____________
Variable cost per unit = ____________
Contribution margin per unit= ____________
Contribution margin= ____________
11. If a manufacturing company had a contribution margin of $65,700 for 20Y5 from selling 25,000 products at 6 SAR each, determine the variable cost per unit, contribution margin ratio, and unit contribution margin. Round unit answers to two decimal places and percentages to the nearest whole percent.
Sales (SAR) = ____________
Contribution margin = ____________
Total variable cost= ____________
Variable cost per unit= ____________
Unit contribution margin= ____________
Contribution margin ratio = ____________
12. Determine the change in operating income for each situation for a company that has an increase in total sales of $52,000.
a. Unit contribution margin of $4.50 and each product selling for $8.
= ____________
b. Contribution margin ratio of 24% and each product selling for $10.
= ____________
c. Unit contribution margin of $6, with total variable costs of $25,000 at $5 per unit.
= ____________
13. After incurring an operating loss of $(6,000) in 20Y5, the production manager would like to know the break-even point in sales and units for the company. During 2023, the company sold 6,000 at $3 each. Variable costs for the year totaled $10,800. Determine the sales and units sold that were needed to break even.
Sales = ____________
Variable costs = ____________
Contribution margin = ____________
Fixed costs= ____________
Operating income = ____________
14. A tire manufacturer sells its finished goods for 80 SAR each. The variable cost to manufacture each product is 20 SAR, while fixed costs equal 20,700 SAR. In 2022, the company earned operating income of 32,100SAR. In 2023, the CEO would like to increase operating income by 5%. Determine the sales in dollars and units needed to achieve the CEO’s goal. Round answers to the nearest whole number.
Target Profit = ____________
Chapter 6
Cost-Volume-Profit
Analysis
Learning Objectives
• Obj. 1: Classify costs as variable costs, fixed costs, or mixed costs.
• Obj. 2: Compute the contribution margin, the contribution margin
ratio, and the unit contribution margin.
• Obj. 3: Determine the break-even point and sales necessary to
achieve a target profit.
• Obj. 4: Using a cost-volume-profit chart and a profit-volume chart,
determine the break-even point and sales necessary to achieve a
target profit.
• Obj. 5: Compute the break-even point for a company selling more
than one product, the operating leverage, and the margin of safety.
• Obj. 6: Describe and illustrate the use of cost-volume-profit analysis
for decision making in a service business.
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Cost Behavior
(slide 1 of 2)
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Cost Behavior
(slide 2 of 2)
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Variable Costs
(slide 1 of 2)
• Variable costs are costs that vary in proportion to
changes in the activity base.
• When the activity base is units produced, direct materials
and direct labor costs are normally classified as variable
costs.
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Variable Costs
(slide 2 of 2)
• Assume that Jason Sound Inc. produces stereo systems. The parts
for the stereo systems are purchased from suppliers for $10 per unit
and are assembled by Jason Sound. For Model JS-12, the direct
materials costs for the relevant range of 5,000 to 30,000 units of
production are as follows:
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 units
$10
$100,000
15,000 units
$10
$150,000
20,000 units
$10
$200,000
25,000 units
$10
$250,000
30,000 units
$10
$300,000
• As shown, variable costs have the following characteristics:
o
Cost per unit remains the same regardless of changes in the activity
base.
o
Total cost changes in proportion to changes in the activity base.
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Variable Cost Graphs
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Variable Costs and Their Activity Bases
Type of Business
Cost
Activity Base
University
Instructor salaries
Number of classes
Passenger airline
Fuel
Number of miles flown
Manufacturing
Direct materials
Number of units produced
Hospital
Nurse wages
Number of patients
Hotel
Housekeeping wages
Number of guests
Bank
Teller wages
Number of banking transactions
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Fixed Costs
(slide 1 of 2)
• Fixed costs are costs that remain the same in total
dollar amount as the activity base changes.
• When the activity base is units produced, many
factory overhead costs such as straight-line
depreciation are classified as fixed costs.
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Fixed Costs
(slide 2 of 2)
• Assume that Minton Inc. manufactures, bottles, and distributes perfume. The
production supervisor is Jane Sovissi, who is paid $75,000 per year. For the
relevant range of 50,000 to 300,000 bottles of perfume, the total fixed cost of
$75,000 does not vary as production increases. As a result, the fixed cost
per bottle decreases as the units produced increase. This is because the
fixed cost is spread over a larger number of bottles, as follows:
Number of bottles of perfume
produced
Total salary for
Jane Sovissi
Salary per bottle of
perfume produced
50,000 bottles
$75,000
$1,500
100,000 bottles
$75,000
$0.750
150,000 bottles
$75,000
$0.500
200,000 bottles
$75,000
$0.375
250,000 bottles
$75,000
$0.300
300,000 bottles
$75,000
$0.250
• As shown, fixed costs have the following characteristics:
Cost per unit decreases as the activity level increases and increases as the
activity level decreases.
o Total cost remains the same regardless of changes in the activity base.
o
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Fixed Cost Graphs
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Fixed Costs and Their Activity Bases
Type of Business
Fixed Cost
Activity Base
University
Building (straight-line)
depreciation
Number of students
Passenger airline
Airplane (straight-line)
depreciation
Number of miles flown
Manufacturing
Plant manager salary
Number of units produced
Hospital
Property insurance
Number of patients
Hotel
Property taxes
Number of guests
Bank
Branch manager salary
Number of customer accounts
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Mixed Costs
(slide 1 of 8)
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Mixed Costs
(slide 2 of 8)
• Assume that Simpson Inc. manufactures sails,
using rented machinery. The rental charges are
as follows:
Rental charge = $15,000 per year + $1 for each hour used in excess
of 10,000 hours
• The rental charges for various hours used within
the relevant range of 8,000 hours to 40,000
hours are as follows:
Hours Used
Rental Charge
8,000 hours $15,000
12,000 hours $17,000 {$15,000 + [(12,000 hrs. – 10,000 hrs.) × $1]}
20,000 hours $25,000 {$15,000 + [(20,000 hrs. – 10,000 hrs.) × $1]}
40,000 hours $45,000 {$15,000 + [(40,000 hrs. – 10,000 hrs.) × $1]}
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Mixed Costs
(slide 3 of 8)
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Mixed Costs
(slide 4 of 8)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Mixed Costs
(slide 5 of 8)
• Assume that the Equipment Maintenance
Department of Kason Inc. incurred the following
costs during the past five months:
Months
Units Produced
Total Cost
June
1,000 units
$45,550
July
1,500 units
$52,000
August
2,100 units
$61,500
September
1,800 units
$57,500
October
750 units
$41,250
• The number of units produced is the activity
base, and the relevant range is the units
produced between June and October.
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Mixed Costs
(slide 6 of 8)
• For Kason, the difference between the units produced and the total
costs at the highest and lowest levels of production are as follows:
Units Produced
Total Cost
Highest level
2,100 units
$61,500
Lowest level
(750) units
(41,250)
Difference
1,350 units
$20,250
• The total fixed cost does not change with changes in production.
o
Thus, the $20,250 difference in the total cost is the change in the total
variable cost.
▪ Dividing this difference of $20,250 by the difference in production is an
estimate of the variable cost per unit. For Kason, this estimate is computed
as follows:
Difference in total cost
Variable cost per unit =
Difference in units produced
$20,250
=
= $15 per unit
1,350 units
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Mixed Costs
(slide 7 of 8)
• The fixed cost is estimated by subtracting the total variable costs
from the total costs for the units produced, as follows:
Fixed cost = Total costs – (Variable cost per unit × Units produced)
• The fixed cost is the same at the highest and the lowest levels of
production, as follows for Kason:
Highest level (2,100 units) :
Fixed cost = Total costs – (Variable cost per unit × Units produced)
= $61,500 – ($15 × 2,100 units)
= $61,500 – $31,500
= $30,000
Lowest level (750 units) :
Fixed cost = Total costs – (Variable cost per unit × Units produced)
= $41,250 – ($15 × 750 units)
= $41,250 – $11,250
= $30,000
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Mixed Costs
(slide 8 of 8)
• Using the variable cost per unit and the fixed
cost, the total equipment maintenance cost for
Kason can be computed for various levels of
production as follows:
Total costs = (Variable cost per unit × Units produced) + Fixed costs
= ($15 × Units produced) + $30,000
o For example, the estimated cost of 2,000 units of
production is $60,000, computed as follows:
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Variable and Fixed Cost Behavior
Effect of Changing Activity Level
Cost
Total Amount
Per-Unit Amount
Variable
Increases and decreases
proportionately with activity level.
Remains the same
regardless of activity level.
Fixed
Remains the same regardless of
activity level.
Increases and decreases
Inversely with activity level.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Variable, Fixed, and Mixed Costs
Variable Costs
Fixed Costs
Mixed Costs
Direct materials
Straight-line depreciation
Quality Control
Department salaries
Direct labor
Property taxes
Purchasing Department
salaries
Electricity expense
Production supervisor
salaries
Maintenance expenses
Supplies
Insurance expense
Warehouse expenses
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Check Up Corner
Cost Behavior
(slide 1 of 2)
•
O&W Metal Company makes designer emblems for luxury vehicles. Each emblem
is handcrafted out of titanium to the customer’s design specifications. O&W’s
artisans are paid an hourly wage and work between 30 and 60 hours a week. O&W
uses the straight-line method of depreciation. To ensure that each emblem
conforms to the customer’s specifications, O&W has each emblem inspected by an
independent company. The inspection company charges a set price per month,
plus an additional amount for each item inspected. After inspection, each emblem
is shipped in a crush-resistant shipping container.
a.
Which of O&W’s costs (titanium, artisan wages, equipment depreciation, inspection,
shipping containers) is a mixed cost?
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Check Up Corner
Cost Behavior
(slide 2 of 2)
b.
Data on total mixed costs and total production for O&W’s five months of
operations are as follows:
Units produced
Total cost
August
1,000 units
$ 80,000
September
1,200 units
$ 86,000
October
1,600
$ 98,000
November
2,500
$125,000
December
2,200
$116,000
Using the high-low method, determine the (1) variable cost per unit and (2) total
fixed costs.
c.
O&W estimates that it will produce 2,000 units during January. Using your
answer to (b), estimate the (1) total variable costs and (2) fixed cost per unit
for January.
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Check Up Corner
Cost Behavior Solution
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Cost-Volume-Profit Relationships
• Cost-volume-profit analysis is the examination of the
relationships among selling prices, sales and production
volume, costs, expenses, and profits.
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Contribution Margin
(slide 1 of 2)
• Contribution margin is the excess of sales over
variable costs, computed as follows:
• Contribution margin covers fixed costs. Once the
fixed costs are covered, any additional
contribution margin increases operating income.
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Contribution Margin
(slide 2 of 2)
• Assume the following data for Lambert Inc.:
Sales
50,000 units
Sales price per unit
$20 per unit
Variable cost per unit
$12 per unit
Fixed costs
$300,000
Contribution Margin Income Statement Format
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Contribution Margin Ratio
(slide 1 of 3)
• The contribution margin ratio, sometimes
called the profit-volume ratio, indicates the
percentage of each sales dollar available to
cover fixed costs and to provide operating
income.
• The contribution margin ratio is computed as
follows:
Contribution margin ratio =
o
Contribution margin
Sales
The contribution margin for Lambert Inc. is computed as
follows:
Contribution margin ratio =
$400,000
= 40%
$1,000,000
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Contribution Margin Ratio
(slide 2 of 3)
• The contribution margin ratio is most useful
when the increase or decrease in sales volume
is measured in sales dollars. In this case, the
change in sales dollars multiplied by the
contribution margin ratio equals the change in
operating income, computed as follows:
Change in operating income = Change in sales dollars × Contribution margin ratio
o For example, if Lambert adds $80,000 in sales from
the sale of an additional 4,000 units, its operating
income will increase by $32,000, computed as
follows:
Change in operating income = Change in sales dollars × Contribution margin ratio
Change in operating income = $80,000 × 40% = $32,000
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Contribution Margin Ratio
(slide 3 of 3)
• The preceding analysis is confirmed by the
contribution margin income statement of
Lambert that follows:
Sales (54,000 units × $20)
Variable costs (54,000 units × $12)
Contribution margin (54,000 units × $8)
Fixed costs
Operating income
$1,080,000
(648,000)*
$ 432,000**
(300,000)
$ 132,000
*$1,080,000 × 60%
**$1,080,000 × 40%
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Unit Contribution Margin
(slide 1 of 3)
• The unit contribution margin is useful for
analyzing the profit potential of proposed
decisions.
• The unit contribution margin is computed as:
Unit contribution margin = Sales price per unit – Variable cost per unit
o If Lambert Inc.’s unit selling price is $20 and its
variable cost per unit is $12, the unit contribution
margin is computed as follows:
Unit contribution margin = Sales price per unit – Variable cost per unit
Unit contribution margin = $20 – $12 = $8
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Unit Contribution Margin
(slide 2 of 3)
• The unit contribution margin is most useful when the
increase or decrease in sales volume is measured in
sales units (quantities). In this case, the change in
sales volume (units) multiplied by the unit
contribution margin equals the change in operating
income, computed as follows:
Change in operating income = Change in sales units × Unit contribution margin
o Assume that Lambert’s sales could be increased by
15,000 units, from 50,000 units to 65,000 units. The
increase in Lambert’s operating income is computed
as follows:
Change in operating income = Change in sales units × Unit contribution margin
Change in operating income = 15,000 units × $8 = $120,000
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Unit Contribution Margin
(slide 3 of 3)
• The preceding analysis is confirmed by the
contribution margin income statement of
Lambert that follows:
Sales (65,000 units × $20)
Variable costs (65,000 units × $12)
Contribution margin (65,000 units × $8)
Fixed costs
Operating income
$1,300,000
(780,000)
$ 520,000
(300,000)
$ 220,000
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Check Up Corner
•
Contribution Margin
Toussant Company sells 20,000 units at $120 per unit. Variable costs are $90 per
unit, and fixed costs are $250,000.
a.
b.
c.
Prepare an income statement for Toussant in contribution margin format.
Determine Toussant’s (1) contribution margin ratio and (2) unit contribution margin.
How much would operating income change if Toussant’s sales increased by 3,000
units?
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Check Up Corner
Contribution Margin Solution
(Slide 1 of 2)
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Check Up Corner
Contribution Margin Solution
(Slide 2 of 2)
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Break-Even Point
(slide 1 of 6)
• The break-even point is the level of operations
at which a company’s revenues and expenses
are equal.
• At break-even, a company reports neither an
operating income nor an operating loss.
• The break-even point in sales units is computed
as follows:
Fixed costs
Break – even sales (units) =
Unit contribution margin
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Break-Even Point
(slide 2 of 6)
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Break-Even Point
(slide 3 of 6)
• Assume the following data for Baker
Corporation:
$90,000
Fixed costs
Unit selling price
$ 25
Unit variable cost
(15)
Unit contribution margin
$ 10
• The break-even point for Baker is computed as
follows:
Break – even sales (units) =
Fixed costs
$90,000
=
= 9,000 units
Unit contribution margin
$10
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Break-Even Point
(slide 4 of 6)
• The following income statement for Baker
verifies the break-even point of 9,000 units:
Sales (9,000 units × $25)
$225,000
Variable costs (9,000 units × $15)
(135,000)
Contribution margin
$ 90,000
Fixed costs
Operating income
(90,000)
$
0
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Break-Even Point
(slide 5 of 6)
• The break-even point in sales dollars can be
determined directly as follows:
Break – even sales (dollars) =
Fixed costs
Contribution margin ratio
o The contribution margin ratio can be computed using
the unit contribution margin and unit selling price as
follows:
Unit contribution margin
Contribution Margin Ratio =
Unit selling price
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Break-Even Point
(slide 6 of 6)
• The contribution margin ratio for Baker is
computed as follows:
Contribution Margin Ratio =
Unit contribution margin $10
=
= 40%
Unit selling price
$25
• Thus, the break-even sales dollars for Baker can
be computed directly as follows:
Break – even sales (units) =
Fixed costs
$90,000
=
= $225,000
Contribution margin ratio
40%
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Changes in Fixed Costs
(Slide 1 of 3)
• Fixed costs do not change in total with changes
in the level of activity. However, fixed costs may
change because of other factors such as
advertising campaigns, changes in property tax
rates, or changes in factory supervisors’
salaries.
• Changes in fixed costs affect the break-even
point as follows:
o
Increases in fixed costs increase the break-even point.
o
Decreases in fixed costs decrease the break-even point.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Change in Fixed Costs on Break-Even
Point
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Effect of Changes in Fixed Costs
(slide 2 of 3)
• Assume that Bishop Co. is evaluating a proposal
to budget an additional $100,000 for advertising.
The data for Bishop Co. follow:
Current
Proposed
Unit selling price
$ 90
$ 90
Unit variable cost
(70)
(70)
$ 20
$ 20
$600,000
$700,000
Unit contribution margin
Fixed costs
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Changes in Fixed Costs
(slide 3 of 3)
• Bishop’s break-even point before the additional
advertising expense of $100,000 is computed as
follows:
Break – even sales (units) =
Fixed costs
$600,000
=
= 30,000 units
Unit contribution margin
$20
• Bishop’s break-even point after the additional
advertising expense of $100,000 is computed as
follows:
Break – even sales (units) =
Fixed costs
$700,000
=
= 35,000 units
Unit contribution margin
$20
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Changes in Unit Variable Costs
(slide 1 of 3)
• Unit variable costs do not change with changes in the
level of activity. However, unit variable costs may be
affected by other factors such as changes in the cost per
unit of direct materials, changes in the wage rate for
direct labor, or changes in the sales commission paid to
salespeople.
• Changes in unit variable costs affect the break-even
point as follows:
o
Increases in unit variable costs increase the break-even point.
o
Decreases in unit variable costs decrease the break-even point.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Change in Unit Variable
Cost on Break-Even Point
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Effect of Changes in Unit Variable Costs
(slide 2 of 3)
• Assume that Park Co. is evaluating a proposal to
pay an additional 2% commission on sales to its
salespeople as an incentive to increase sales.
The data for Park follow:
Current
Proposed
Unit selling price
$ 250
$ 250
Unit variable cost
(145)
Unit contribution margin
$ 105
$ 100
$840,000
$840,000
Fixed costs
(150)*
*$150 = $145 + (2% × $250 unit selling price)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Changes in Unit Variable Costs
(slide 3 of 3)
• Park’s break-even point before the additional 2%
commission is computed as follows:
Break – even sales (units) =
Fixed costs
$840,000
=
= 8,000 units
Unit contribution margin
$105
• Bishop’s break-even point after the additional
2% commission is computed as follows:
Break – even sales (units) =
Fixed costs
$840,000
=
= 8,400 units
Unit contribution margin
$100
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Effect of Changes in Unit Selling Price
(slide 1 of 3)
• Changes in the unit selling price affect the
break-even point as follows:
o Increases in the unit selling price decrease the break-
even point.
o Decreases in the unit selling price increase the break-
even point.
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Effect of Change in Unit Selling Price on BreakEven Point
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Changes in Unit Selling Price
(slide 2 of 3)
• Assume that Graham Co. is evaluating a
proposal to increase the unit selling price of a
product from $50 to $60. The data for Graham
follow:
Current
Proposed
Unit selling price
$ 50
$ 60
Unit variable cost
(30)
(30)
Unit contribution margin
$ 20
$ 30
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Effect of Changes in Unit Selling Price
(slide 3 of 3)
• Graham’s break-even point before price
increase is computed as follows:
Break – even sales (units) =
Fixed costs
$600,000
=
= 30,000 units
Unit contribution margin
$20
• Graham’s break-even point after price increase
is computed as follows:
Break – even sales (units) =
Fixed costs
$600,000
=
= 20,000 units
Unit contribution margin
$30
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effects of Changes in Selling Price and Costs
on Break-Even Point
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Target Profit
(slide 1 of 4)
• The sales required to earn a target or desired
amount of profit is determined by modifying the
break-even equation as follows:
Sales (units) =
Fixed costs + Target profit
Unit contribution margin
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Target Profit
(slide 2 of 4)
• Assume the following data for Waltham Co.:
Fixed costs
$200,000
Target profit
100,000
Unit selling price
$ 75
Unit variable cost
(45)
Unit contribution margin
$ 30
• The sales necessary for Waltham to earn the
target profit of $100,000 is computed as follows:
Sales (units) =
Fixed costs + Target profit $200,000 + $100,000
=
= 10,000 units
Unit contribution margin
$30
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Target Profit
(slide 3 of 4)
• The following income statement for Waltham
verifies the computation on Slide 59:
Sales (10,000 units × $75)
$ 750,000
Variable costs (10,000 units × $45)
(450,000)
Contribution margin (10,000 units × $30)
$ 300,000
Fixed costs
(200,000)
Operating income
$ 100,000 = Target profit
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Target Profit
(slide 4 of 4)
• As shown on the income statement for Waltham,
sales of $750,000 are necessary to earn a target
profit of $100,000. The sales of $750,000
needed to earn a target profit of $100,000 can
be computed directly using the contribution
margin ratio as follows:
Unit contribution margin $30
=
= 40%
Unit selling price
$75
Fixed costs + Target profit
Sales (dollars) =
Contribution margin ratio
$200,000 + $100,000 $300,000
=
=
= $750,000
40%
40%
Contribution Margin Ratio =
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit (Break-Even) Chart
(slide 1 of 5)
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Cost-Volume-Profit (Break-Even) Chart
(slide 2 of 5)
• The cost-volume-profit chart is constructed using the following steps:
o
Step 1: Volume in units of sales is indicated along the horizontal axis. The range
of volume shown is the relevant range in which the company expects to operate.
Dollar amounts of total sales and total costs are indicated along the vertical axis.
o
Step 2: A total sales line is plotted by connecting the point at zero on the left
corner of the graph to a second point on the chart. The second point is
determined by multiplying the maximum number of units in the relevant range,
which is found on the far right of the horizontal axis, by the unit sales price. A line
is then drawn through both of these points. This is the total sales line.
o
Step 3: A total cost line is plotted by beginning with total fixed costs on the vertical
axis. A second point is determined by multiplying the maximum number of units in
the relevant range, which is found on the far right of the horizontal axis by the unit
variable costs and adding the total fixed costs. A line is then drawn through both
of these points. This is the total cost line.
o
Step 4: The break-even point is the intersection point of the total sales and total
cost lines. A vertical dotted line drawn downward at the intersection point
indicates the units of sales at the break-even point. A horizontal dotted line drawn
to the left at the intersection point indicates the sales dollars and costs at the
break-even point.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit (Break-Even) Chart
(slide 3 of 5)
• Assume the following data for Munoz Co.:
Total fixed costs
$100,000
Unit selling price
$ 50
Unit variable cost
(30)
Unit contribution margin
$ 20
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Chart
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit (Break-Even) Chart
(slide 4 of 5)
• The break-even point for Munoz is $250,000 of
sales, which represents sales of 5,000 units.
o Operating profits will be earned when sales levels are
to the right of the break-even point.
o Operating losses will be incurred when sales levels
are to the left of the break-even point.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit (Break-Even) Chart
(slide 5 of 5)
• Assume that Munoz is evaluating a proposal to
reduce fixed costs by $20,000. In this case, the
total fixed costs would be $80,000 ($100,000 –
$20,000).
o Under this scenario, the total sales line on the cost-
volume-profit will not change, but the total cost line will
change.
o Also, the break-even point for Munoz will decrease to
$200,000 and 4,000 units of sales.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Revised Cost-Volume-Profit Chart
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 1 of 7)
• Another graphic approach to cost-volume-profit
analysis is the profit-volume chart, which plots
only the difference between total sales and total
costs (or profits).
o In this way, the profit-volume chart allows managers to
determine the operating profit (or loss) for various
levels of units sold.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 2 of 7)
• The profit-volume chart is constructed using the following steps:
o
Step 1: Volume in units of sales is indicated along the horizontal axis.
The range of volume shown is the relevant range in which the company
expects to operate. Dollar amounts indicating operating profits and
losses are shown along the vertical axis.
o
Step 2: A point representing the maximum operating loss is plotted on
the vertical axis at the left. This loss is equal to the total fixed costs at the
zero level of sales.
o
Step 3: A point representing the maximum operating profit within the
relevant range is plotted on the right.
o
Step 4: A diagonal profit line is drawn connecting the maximum
operating loss point with the maximum operating profit point.
o
Step 5: The profit line intersects the horizontal zero operating profit line
at the break-even point in units of sales. The area indicating an operating
profit is identified to the right of the intersection, and the area indicating
an operating loss is identified to the left of the intersection.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 3 of 7)
• Assume the following data for Munoz Co.:
Total fixed costs
$100,000
Unit selling price
$ 50
Unit variable cost
(30)
Unit contribution margin
$ 20
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 4 of 7)
• The maximum operating loss is equal to the
fixed costs of $100,000. Assuming that the
maximum units that can be sold within the
relevant range is 10,000 units, the maximum
operating profit is $100,000, computed as
follows:
Sales (10,000 units × $50)
$ 500,000
Variable costs (10,000 units × $30)
(300,000)
Contribution margin (10,000 units × $20)
$ 200,000
Fixed costs
(100,000)
Operating income
$ 100,000 = Maximum profit
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 5 of 7)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 6 of 7)
• The break-even point for Munoz is 5,000 units of
sales, which is equal to total sales of $250,000.
o Operating profits will be earned when sales levels are
to the right of the break-even point (operating profit
area).
o Operating losses will be incurred when sales levels
are to the left of the break-even point (operating loss
area).
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Profit-Volume Chart
(slide 7 of 7)
• Assume that Munoz is evaluating a proposal to increase fixed
costs by $20,000. In this case, the total fixed costs will
increase to $120,000 ($100,000 + $20,000), and the maximum
operating loss will also increase to $120,000. At the maximum
sales of 10,000 units, the maximum operating profit would be
computed as follows:
Sales (10,000 units × $50)
$ 500,000
Variable costs (10,000 units × $30)
(300,000)
Contribution margin (10,000 units × $20)
$ 200,000
Fixed costs
(120,000)
Operating income
$ 80,000 = Revised maximum profit
o
Under this scenario, the break-even point for Munoz will increase
to $300,000 and 6,000 units of sales.
o
The operating loss area will increase, while the operating profit
area will decrease.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Original Profit-Volume Chart and
Revised Profit-Volume Chart
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Assumptions of Cost-Volume-Profit Analysis
• Cost-volume-profit analysis depends on several
assumptions. The primary assumptions are as
follows:
o Total sales and total costs can be represented by straight
lines.
o Within the relevant range of operating activity, the
efficiency of operations does not change.
o Costs can be divided into fixed and variable components.
o The sales mix is constant.
o There is no change in the inventory quantities during the
period.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Check Up Corner
Break-Even Sales and Target Profit
• DeHan Company, a sporting goods manufacturer, sells binoculars for $140
per unit. The variable cost is $100 per unit, while the fixed costs are
$1,200,000.
a.
Compute:
▪ 1. The anticipated break-even sales (units) for binoculars.
▪ 2. The sales (units) for binoculars required to realize target operating income of
$400,000.
b.
Construct a cost-volume-profit chart for the anticipated break-even sales for
binoculars.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Check Up Corner
Break-Even Sales and Target Profit
Solution (slide 1 of 2)
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Check Up Corner
Break-Even Sales and Target Profit
Solution (slide 2 of 2)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sales Mix Considerations
(slide 1 of 5)
• Many companies sell more than one product at
different selling prices. In addition, the products
normally have different unit variable costs and,
thus, different unit contribution margins.
• In such cases, break-even analysis can still be
performed by considering the sales mix.
o The sales mix is the relative distribution of sales
among the products sold by a company.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sales Mix Considerations
(slide 2 of 5)
• Assume that Cascade Company sold Products A and B
during the past year, as follows:
Total fixed costs
$ 200,000
Product A Product B
Unit selling price
$ 90
$140
Unit variable cost
(70)
(95)
Unit contribution margin
$ 20
$ 45
Units sold
8,000
2,000
Sales mix
80%
20%
• A total of 10,000 (8,000 + 2,000) units were sold during
the year. Therefore, the sales mix is 80% (8,000 ÷
10,000) for Product A and 20% (2,000 ÷ 10,000) for
Product B.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Multiple Product Sales Mix
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sales Mix Considerations
(slide 3 of 5)
• For break-even analysis, it is useful to think of the
individual products as components of one overall
enterprise product.
• The unit selling price of the overall enterprise
product equals the sum of the unit selling prices of
each product multiplied by its sales mix percentage.
• Likewise, the unit variable cost and unit contribution
margin of the overall enterprise product equal the
sum of the unit variable costs and unit contribution
margins of each product multiplied by its sales mix
percentage.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sales Mix Considerations
(slide 4 of 5)
• For Cascade, Products A and B are components
of one overall enterprise product called E. The
unit selling price, unit variable cost, and unit
contribution margin for E are computed as
follows:
Product E
Product A
Product B
Unit selling price of E
$100 =
($90 × 0.8)
+
($140 × 0.2)
Unit variable cost of E
(75) =
($70 × 0.8)
+
($95 × 0.2)
Unit contribution margin of E
$ 25 =
($20 × 0.8)
+
($45 × 0.2)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sales Mix Considerations
(slide 5 of 5)
• Cascade has total fixed costs of $200,000. The
break-even point of E can be determined as
follows using the unit selling price, unit variable
cost, and unit contribution margin of E:
Break – even sales (units) for E =
Fixed costs
$200,000
=
= 8,000 units
Unit contribution margin
$25
• Because the sales mix for Products A and B is
80% and 20%, respectively, the break-even
quantity of A is 6,400 units (8,000 units × 80%)
and B is 1,600 units (8,000 units × 20%).
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Break-Even Sales: Multiple Products
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Operating Leverage
(slide 1 of 6)
• A company’s operating leverage is computed as
follows:
Contribution margin
Operating leverage =
Operating income
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Operating Leverage
(slide 2 of 6)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Operating Leverage
(slide 3 of 6)
• Assume the following data for Jones Inc. and Wilson Inc.:
Jones Inc.
Wilson Inc.
Sales
$ 400,000
$ 400,000
Variable costs
(300,000)
(300,000)
Contribution margin
$ 100,000
$ 100,000
(80,000)
(50,000)
$ 20,000
$ 50,000
Fixed costs
Operating income
• As shown, Jones and Wilson have the same sales, the same
variable costs, and the same contribution margin. However, Jones
has larger fixed costs and, thus, a higher operating leverage than
Wilson.
Jones Inc.
Operating leverage =
Contribution margin $100,000
=
=5
Operating income
$20,000
Wilson Inc.
Operating leverage =
Contribution margin $100,000
=
=2
Operating income
$50,000
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Operating Leverage
(slide 4 of 6)
• Operating leverage can be used to measure the impact
of changes in sales on operating income.
• Using operating leverage, the effect of changes in sales
on operating income is computed as follows:
Percent change in operating income = Percent change Operating
in sales
leverage
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Operating Leverage
(slide 5 of 6)
• Assume that sales increased by 10%, or $40,000
($400,000 × 10%), for Jones and Wilson. The percent
increase in operating income for Jones and Wilson is
computed as follows:
Jones Inc.
Percent change in operating income = Percent change Operating
in sales
leverage
= 10% 5% = 50%
Wilson Inc.
Percent change in operating income = Percent change Operating
in sales
leverage
= 10% 2% = 20%
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Operating Leverage
(slide 6 of 6)
• The validity of this analysis is shown in the following
income statements for Jones and Wilson based on the
10% increase in sales:
Jones Inc.
Wilson Inc.
Sales
$ 440,000
$ 440,000
Variable costs
(330,000)
(330,000)
Contribution margin
$ 110,000
$ 110,000
(80,000)
(50,000)
$ 30,000
$ 60,000
Fixed costs
Operating income
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Effect of Operating Leverage
on operating income
Operating Leverage
Percentage Impact on Operating
Income from a Change in Sales
High
Large
Low
Small
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Margin of Safety
(slide 1 of 3)
• The margin of safety indicates the possible
decrease in sales that may occur before an
operating loss results.
o Thus, if the margin of safety is low, even a small
decline in sales revenue may result in an operating
loss.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Margin of Safety
(slide 2 of 3)
• The margin of safety may be expressed in the following
ways:
Dollars of sales
o Units of sales
o Percent of current sales
o
▪ The margin of safety expressed as a percent of current sales is
computed as follows:
Sales − Sales at break – even point
Margin of safety =
Sales
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Margin of Safety
(slide 3 of 3)
• Assume the following data:
Sales
$250,000
Sales at the break-even point
200,000
Unit selling price
25
• The margin of safety in dollars of sales is $50,000
($250,000 – $200,000).
• The margin of safety in units is 2,000 units ($50,000 ÷
$25).
• The margin of safety expressed as a percent of current
sales is 20% ($50,000 ÷ $250,000).
Therefore, the current sales may decline $50,000, 2,000
units, or 20% before an operating loss occurs.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Check Up Corner
•
Blueberry Inc., a consumer electronics company, manufactures and sells two
products, smartphones and tablet computers. The unit selling price, unit variable
cost, and sales mix for each product are as follows:
Products
•
Special Cost-Volume-Profit
Relationships Solution (Slide 1 of 2)
Unit Selling Price Unit Variable Cost
Sales Mix
Smartphone
$650
$560
60%
Tablet
$550
$475
40%
The company’s fixed costs are $4,200,000.
a. How many units of each product would be sold at the break-even point?
b. Assume Blueberry sells 37,500 smartphones and 25,000 tablets during a
recent year.
▪ Compute the company’s (1) operating leverage and (2) margin of safety.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Check Up Corner
Special Cost-Volume-Profit
Relationships Solution (Slide 1 of 2)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Check Up Corner
Special Cost-Volume-Profit
Relationships Solution (Slide 2 of 2)
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Analysis for Service
Companies (slide 1 of 6)
• Cost-volume-profit relationships in a service company
are measured with respect to customers and activities,
rather than units of product. Examples are as follows:
Service
Break-Even Analysis
Education
Break-even number of students per course
Air transportation
Break-even number of passengers per flight
Health care
Break-even number of patients per outpatient facility
Hotel
Break-even number of guests per time period (day, month, etc.)
Freight transportation
Break-even number of tons per train
Theme park
Break-even number of guests per time period (day, month, etc.)
Financial services
Break-even number of invested funds (dollars) under
management
Subscription services
Break-even number of subscribers
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Analysis for Service
Companies (slide 2 of 6)
• Break-even analysis for a service company
involves identifying the correct unit of analysis
and the correct measure of activity for that unit.
• For example, the unit of analysis for an
educational institution could be a course, a
major, a college, or the university as a whole.
o For a specific course, the measure of activity would
be the number of students enrolled in the course.
Each student is the same in his or her demand for
course-level services. Thus, a break-even analysis
would discover the number of students required for
the course to break even.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Analysis for Service
Companies (slide 3 of 6)
• At other units of analysis, the measure of activity
may change.
o For example, the break-even for a college would likely
be measured in number of student credit hours, not
number of students. Not all students are equal in their
demand for college services, because some students
are part-time and some are full-time. However, each
student credit hour is nearly the same.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Analysis for Service
Companies (slide 4 of 6)
• The unit of analysis can influence whether costs
are defined as fixed or variable.
o For example, the instructor’s salary is a fixed cost for
a specific course, but can be a variable cost to the
number of sections taught at the college level.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Analysis for Service
Companies (slide 5 of 6)
• To illustrate, consider the break-even number of
students for a noncredit course in pottery.
o The course tuition is $500. The costs consist of the
following:
Variable costs per student:
Pottery supplies
$300
Enrollment costs
20
Fixed costs for the course:
Instructor’s salary
$3,000
Rental cost of the classroom
1,500
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Cost-Volume-Profit Analysis for Service
Companies (slide 6 of 6)
Fixed costs
Break – Even Sales (units) =
Unit contribution margin
$4,500
Break – Even Sales (units) =
= 25 students
$500 – $320
o Thus, the course would need to enroll 25 students to
break even.
© 2020 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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