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Chapter
CHAPTER HIGHLIGHTS
A
The contribution margin is a key concept. The
contribution margin
is the difference between total
salesandtotalvariableexpenses.The
unit contribution
margin
isthedifferencebetween theunit
and
the
unitvariableexpense.
L
Net
vlJ',-,.a.Ull.)e,
incomeisequaltothecontribu
tion expenses.
Sales...............................
.
Variableexpenses...........
..
Contributionmargin.........
xxx
Fixedexpenses.................
Net income.....
.
2. The
break-even point
is the level
of
sales at
which iszero.Thisisalsothepointatwhichthe
totalcontribution equalsfixedexpenses.
3.
Therelationbetweencontributionmarginand
net operating income a very powerful
ning tooL It themanagerthe ability to predict
whatprofitswillbe atvariousactivitylevelswithout
the detailedincomestatements.
a. The contribution must first c over
fixed Ifitdoesn't, the company has aloss.
Below break-even every unit s old r educes
thelossbytheamountof theunitcontribution
b. Oncethe break-evenpointis net
VI-""'U;'.'HJ'F, incomewill increaseby the amountof the
unitcontribution foreachadditionalunitsold.
B. The contribution ratio (CM which
expresses the contribution margin
as
a percentage
of
isanothervery concept.
1. Thecontributionmarginratioisdefinedasfol
lows:
. Contribution
CM
ratlo= = -
Sales
with a product, the
CM ratiocanalso
vVJIJlIJ ' ' ' 'U
computedasfollows:
2
Ina
Unitcontribution
CM
Unitsellingprice
3.
The contribution
dietthe intotal
resultfromagivenchange
in
dollarsales:
' - ' H > " l ~ , ' - '
indollarsales.................
xxx
x CM ratio................. .................. ....
' - ' l " ' L a ~ ' - ' incontributionmargin
.. ..
66
4 thatfixedexpensesarenotatt1cct,cO.
an increase (
or
decrease) in contribution
will be reflected dollar for dollar in increased (or
netooeraLtlnl1! income.
5, The CM ratio is
useful when
a
company has multiple
such
volume is most
in tenns
of
totaldollarsalesratherthanin
C. Cost-volume-profit (CVP) can b e used
inmanyday-to-daydecisions. Carefullystudythe ex
amples under the h eading Some
of
CVP inthe
of
the
1.
Notice that each solutionmakesuse of either
theunitcontribution
or
theCM ratio,Thisun
derscoresthe twol'".,l'P t
2. Also notice that severalof the
incremental analysis.
An
incremental is
on thosecosts and revenues that
differ
between
alternatives.
D. Two examples of CVP called
break-even
and
target prolit analysis
are
often used. Break-even analysis is a special case
of
analysis, so profit is con-
below.
1. profitanalysis is used to find outhow
haveto besoldto attaina ' v v ,uv
isbasedonthefollowingequation:
Profits Sales Variableexpenses Fixedexpenses
In CVP thisequationisoftenrewrittenas:
Sales= Variableexpenses Fixedexpenses Profits
All
of
the problems can beworked
this basic
AmIM,A, . ,
and
fonnu
some
of
the more
common formulas are discussed
below.
2
is used in two basic
variations. In the first the q uestion is how
many
units
wouldhaveto besoldto attainthe
In
the second the is how
muchtotal dollarsaleswould havetobe to attainthe
targetprofit.Thefonnulasare:
Unitsalesto
Fixedext)em;es-t-Ta
attaintargetprofit
Dollar sales
to
~ ~ i x ~ e ~ d ~ ~ ~ ~ ~ ~ ~ ~
attaintargetprofit
CM ratio
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hapte
r
E. Break-even occurs when
profit is
zero. Thus,
break even analysis is really just a special case of tar
get profit analysis
n
which tlle target profit is zero .
Therefore, the break-even formulas can be stated as
follows:
Break-even point _ Fixed expenses
in units sold - Unit contribution margin
Break-even point _ Fixed expenses
in total sales dollars - CM ratio
F. CVP and break-even analysis can also be done
graphically. Exhibits 6-1 and 6-2 show how a CVP
graph is prepared and interpreted . A cost-volume
profit graph depicts the relations among sales, costs,
and volume.
G The margin ofsafety
is
the excess of budgeted (or
actual) sales over the break-even volume of sales.
t
is
the amount by which sales can drop before losses be
gin to be incurred. The margin of safety can be stated
in terms
of
either dollars or as a percentage
of
sales:
Total budgeted (or actual) sales .. ..
Less break-even sales .... .. .... ........ .
Margin of safety ...... ............
..
......
..
Margin
of
safety = Margin of safety
percentage Total budgeted (or actual) sales
H Cost structure the relative proportion of fixed
and variable costs- has an impact on how sensitive a
company's profits are to changes in sales. A company
with low fixed costs and high variable costs will tend
to have a lower CM ratio than a company with a
greater proportion
of
fixed costs. Such a company will
tend to have less volatile profits, but at the risk of los
ing substantial profits if sales trend sharply upward.
I Operating leverage
refers to the effect a given
percentage increase in sales will have on net operating
income.
1. The degree of operating leverage
is
defined as:
Degree
of
operating
=
Contribution margin
leverage Net operating income
2. To estimate the percentage change in net op
erating income that would occur as the result of a
given percentage change in dollar sales; mUltiply the
change in sales by the degree of operating leverage.
67
Percentage change in dollar sales .. ... .
x Degree of operating leverage .. .. ...... ..
Percentage change in net operating
income .......................................... .
3. The degree
of
operating leverage is not con
~ t a n t
It changes as sales increase or decrease. In gen
eral, the degree of operating leverage decreases the
further a company moves away from its break-even
point.
1. When a company has more than one product , the
sales mix can be crucial. The sales mix refers to the
relative proportions in which the company's products
are sold.
I. When CVP analysis involves more than one
product, the analysis is normally based on the overall
contribution margin ratio
This is computed exactly
like the CM ratio
is
computed in a single product com
pany except that overall figures are used for both the
contribution margin and sales:
. Overall contribution margin
O
vera
CM
ratro = =: -
Overall sales
2
When the company has more than one prod
uct, the
overall
CM ratio is used in the target profit
and break-even formulas instead of the CM ratio.
3. As the sales mix changes,
the overall ratio
will also change f the shift
is
toward less profitable
products, then the overall CM ratio will fall; if the
shift
is
toward more profitable products, then the over
all CM ratio will rise.
K
CVP analysis ordinarily relies on the following
assumptions :
I. The selling price is constant; it does not
change as unit sales change.
2. Costs are linear. Costs can be accurately di
vided into variable and fixed elements. The variable
cost per unit is constant and the total fixed cost is con
stant.
3. In multi-product situations, the sales mix is
constant.
4. In manufacturing companies, inventories do
not change.
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Chapter
REVIEW AND SELF-TEST
Questions and Exercises
True or False
Enter a T
r
an F in the blank to indicate whether the
statement is true or false.
1.
If
product has a higher unit contribution
margin than product
B,
then product
A
will also have a
higher CM ratio than product
B.
2. The break-even point occurs where the
contribution margin
is
equal to total variable expenses.
3. The break-even point can be expressed ei
ther in terms of units sold or in terms
of
total sales dol
lars.
4.
If
the sales mix changes, the break-even
point may change.
5. For a given increase in sales dollars, a high
CM ratio will result in a greater increase in profits
than will a low CM ratio.
6.
If
sales increase by 8%, and the degree
of
operating leverage
is
4, then profits can be expected to
increase by 12%.
7.
The degree of operating leverage remains
the same at all levels of sales.
8. Once the break-even point has been
reached, net operating income wiIl increase by the lmit
contribution margin for each additional unit sold.
9. A shift in sales mix toward less profitable
products will cause the overall break-even point to
fall.
_
10
. Incremental analysis focuses on the differ
ences in costs and revenues between alternatives.
_ 11.
If
a company's cost structure shifts toward
higher fixed costs and lower variable costs, the com
pany' s CM ratio will fall.
_
12
. One way to compute the break-even point
is to divide total sales by the CM ratio.
_
l3
. When a company has more than one prod
uct, a key assumption in break-even analysis is that the
sales mix will not change.
Multiple Choices
Choose the best answer or response by placing the
identifying letter in the space provided.
1.
Lester Company has a single product. The
selling price is $50 and the variable cost is $30 per
unit. The company's fixed expense
is
$200,000 per
68
month. What is the company
s
unit contribution mar
gin? a) $50; b) $30; c) $20; d) $80.
2. Refer to the data for Lester Company in
question 1 above. What
is
the company's contribution
margin ratio? a) 60%;
b
40%; c) 167%; d 20%.
3. Refer to the data for Lester Company in
question 1 above. What is the company's break-even
in sales dollars? a) $500,000; b $33,333;
c
$200,000 ;
d) $400,000.
4. Refer to the data for Lester Company in
question 1 above . How many units would the company
have to sell to attain target profits
of
$50,000?
a) 10,000; b
12
,500; c)
15
,000; d 13,333.
5. Parker Company has provided the follow
ing data for the most recent year: net operating in
come, $30,000; fixed expense, $90,000; sales,
$200,000; and CM ratio, 60%. The company's margin
of
safety in dollars
is:
a) $150,000;
b)
$30,000;
c) $50,000; d $80,000.
6. Refer
to
the data in question for Parker
Company in 5 above. The margin of safety in percent
age form is: a) 60%; b) 75%; c) 40%; d 25%.
7.
Refer to the data for Parker Company in
question 5 above. What is the company's total contri
bution margin? a) $110,000; b) $120,000;
c $170,000; d $200,000.
8. Refer to the data for Parker Company in
question 5 above. What
is
the company's degree
of
operating leverage? a) 0.25; b) 0.60; c) 1.25; d 4.00.
9. f
sales increase from $400,000 to
$450,000, and
if
the degree of operating leverage is 6,
net operating income should increase by: a) 12.5%;
b) 75%; c) 67%; d) 50%.
_ 10. In mUltiple product companies, a shift in
the sales mix from less profitable products to more
profitable products will cause the company's break
even point to: a) increase; b) decrease; c) there will be
no change in the break-even point; d) none
of
these.
_ 11. Herman Corp. has two products, A and B,
with the following total sales and total variable costs :
Product Product B
Sales ... ... ..
..
....... ..... ... . $10,000 $30,000
Variable expenses .... .
$4,000 $24,000
What is the overall contribution margin ratio? a) 70%;
b) 50%; c 30%; d 40%.
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hapter
Exercises
Exercise
-1. Hardee
Company
sells a single product. The selling price is 30
per
unit
and
the variable
expense
is$1&
per unit. The company's most recent annual contribution fonnat income statement is given below:
Sales ............................. .
$135,000
Variable expenses ........ . 81,000
Contribution margin ..... . 54,000
Fixed expenses ............. 48,000
Net operating income
....
$ 6.000
a. Compute the contribution margin per unit. $_____
b.
Compute the CM ratio.
____%
c. Compute the break-even point in sales dollars. $
____
_
d.
Compute the break-even point in units sold.
_____
units
e.
How many units must be sold next year
to
double the company's profits?
_____
Ullits
f. Compute the company's degree of operating leverage. _____
g.
Sales for next year (in units) are expected
to
increase by 5%. Using the degree
of
operating leverage,
compute the expected percentage increase in net operating income.
%
h. Verify your answer to part g above by preparing a contribution fonnat income statement showing a 5%
increase in sales.
Sales........
..
..................................................
.. ...
......
$_______
Variable expenses .........................................
...
....
..
Contribution margin .......
..
.................. ....... ..........
.
Fixed expenses ..................................................... .
Net operating income......... .... ........
..
...........
...
........
$ ==
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hapter
Exercise -2. Using the data below, construct a cost-volume-profit graph like the one in Exhibit 6-1 in the text:
Sales:
15
,000 units at 10 each.
Variable expense: 6 per unit.
Fixed expense: 40,000 total.
200
180
160
140
Iii'
120
Q
Q
Q
100
.
'0
C 80
60
40
20
0
o
2 4
6
8
10 12
14
nits
0005)
What is the break-even point in units? _ _ _
What is the break-even point in total sales dollars? _
16 18
70
20
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hapter
Exercise -3. Seaver Company produces and sells two products, X and Y. Data concerning the products fol
low:
Product X
Product Y
Selling price per unit.. ............
.
$10 $12
Variable expense per unit ...... ..
...2
Contribution margin per unit ..
.$..A
U
In the
mo
st recent month, the company sold 400 units
of
Product X and 600 units
of
Product
Y.
Fixed expense
is
$5,000 per month.
a. Complete the following contribution format income statement for the most recent month (carry percentages
to one decimal point):
Product
mount
%
Product Y
mount
%
Total
mount
%
Sales ............... .....
..
...
..
.... .
Variable expenses .......... .
_ -
_ - _ -
Contribution margin ...... .
Fixed expenses .......... .... ..
Net operating income ....
$= = =
===
===
b. Compute the company's overall monthly break-even point in sales dollars.
$____
c. f the company continues
to
sell 1,000 units, in total, each month, but the sales mix shifts so that an equal
number
of
units of each product is being sold, would you expect monthly net operating income to rise or
fall? Explain.
d. Refer to the data in part c above.
f
the sales mix shifts as explained, would you expect the company's
monthly break-even point
to
rise or fall? Explain.
71
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hapter
Exercise -4. ritical thought writing exercise: Able Company and Baker Company are competing COlTIo:a·
nies that
s ll
a product at the
same
Both above the break-even and have
lar total Able costs are Baker
Company's costs are fixed.
In
a
time of sales, which company will tend t realize the most rapid increase in net Ex-
plain your answer.
-
_ __
72
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hapter
nswers to Questions and Exercises
True
r
False
1. F
The
eM
ratiois the unitcontributionmar
gin divided by the unit selling price. One
product mighthave ahigher unit contribu
tion than another, butits sellingprice may
belower.
2. F Thebreak-evenoccurswhereprofitis zero.
3. T Thebreak-evencanbecomputedintermsof
unitssoldorsalesdollars.
4. T A change in sales mix often results in a
change in theoveralleM ratio.
f
theover
all CM ratio changes, the break-even will
alsochange.
5.
T TheCM ratiomeasureshowmuch of asales
dollar is translated into increasedcontribu
tionmargin.
6.
F Profitsshouldincreaseby32%
=
4x 8%.
7. F The degreeof operatingleveragedecreases
as a company moves further and further
fromitsbreak-even.
8.
T
At the break-even all fixed costs are cov
ered. All contribution margins generated
from thatpoint forward increasesnetoper
atingincome.
9. F
Thereverse is true the overallbreak-even
will rise becausetheaverage
eM
ratiowill
belowerasaresultof sellinglessprofitable
products.
10. T
By
definition, incremental analysis deals
onlywithdifferencesbetweenalternatives.
11. F The reverse is true one would expectthe
company'sCM ratioto rise. Variablecosts
would be lower and hence the eM ratio
wouldbehigher.
12. F Thebreak-even is computedbydividingto
tal
fIXed expenses
bytheeM ratio.
13. T Thisis akey assumptionbecausea change
inthesalesmixwillchangethebreak-even.
Multiple hoices
1.
c
Unitsellingprice................
$50
Lessunitvariableexpenses. 2.Q
Unitcontributionmargin.....
$2.Q
b
Unitcontributionmargin..... $20
Unitsellingprice..........
..
...... $50
Contributionmarginratio
....
40%
3.
a
Breakevenpoint _Fixedexpenses
intotalsalesdollars- CMratio
$200,000 $500,000
0.40
4. b
Unitsalesto _Fixedexpenses+Targetprofit
attaintargetprofit- Unitcontributionmargin
$200,000+$50,000
$20perunit
= 12,500units
5. c
Break-evenpoint_Fixedexpenses
indollarsales - eM ratio
= $90,000= $150 000
0.60 '
Marginof safety
=
$200,000- $150,000
= $50,000
6. d
$50,000-7- $200,000= 25%
7.
b
Sales.
..
.............
..
............ $200,000
CMratio..................
..
..
..
x 0.60
Contributionmargin...
..
$120,000
8. d
Contributionmargin....
..
$120,000
Net operatingincome
...
; $30,000
Operatingleverage........ 4.0
9. b Thecomputationsare:
e r c e ~ t a g e
=
$450,000- $400,000
=
12.5%
change
n
sales $400,000
Percentagechangeindollarsales
..
. 12.5%
Degree
of
operatingleverage.......
.
x 6.0
Percentage change in net operat
ingincome................................
.
75.0%
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Chapter
1O.b
Ashift tomoreprofitableproductswouldresult
11.c
in
anincreaseintheoverallCMratio.Thus, Product A Product B Total
fewer sales wouldbe needed to cover the
Sales
..
......
$\0,000
$30,000
4G,GGG
fixed costsand the break-evenwould there
Variable
foredecrease.
expenses"
4,000 24,000
28,000
Contribution
margin.....
6,000
$12000
OverallCMratio
=
$12,000
$40,000
30%
Exercises
Exercise -1.
a.
er
Unit
Sellingprice........................... $30
100%
Variableexpenses............... ..
60%
Unitcontributionmargin........
l2
~
b.
CMratio== Contributionmargin =$54,000 == 40%
Sales $135,000
c. Sales Variableexpenses+Fixedexpenses+Profits
X= 0.60X+$48,000+$0
O OX
= $48,000
X
=
$48,000
+-
O O
X== $120,000
Alternativesolution:
. Breakevenpoint =Fixedexpenses == $48,000 $120 000
III totalsalesdollars CMratio O O
d.
Sales
=
Variableexpenses
+
Fixedexpenses+Profits
$30Q=$18Q+$48,000+$0
$12Q= $48,000
Q
=
$48,000 -7 $12perunit
Q= 4,000units
Alternativesolution:
Breakevenpoint_ Fixedexpenses _ $48,000_4000 .
. . ld - - - units
III units so Unitcontributionmargin $12
e.
Sales
=
Variableexpenses+Fixedexpenses+Profits
$30Q=$18Q+$48,000+$12,000
$12Q= $60,000
Q
=
$60,000
-7
$12perunit
Q= 5,000units
Alternativesolution:
Unitssoldto _Fixedexpenses+Targetprofit_ $48,000+ 12,000 - 5000 t
.
i
-
-
ums
attamtargetpro It Unitcontributionmargin $12perunit
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hapter
f.
g.
Degree of operating _ Contribution margin
leverage - Net income
$54,000 9.0
$6,000
Percentage change in dollar sales ....... .. ...... , 5%
Degree of operating leverage .................. ....... x 9.0
Percentage change in net operating income;... 45%
h.
New sales volume: 4,500 units x 105% = 4,725 units
Sales (4,725 units @ $30 per unit) ... .. .................. .
Variable expenses (4,725 wilts @ $18 per unit) ... .
Contribution margin ........... .................................. .
Fixed expenses ............. ............................. ........... .
Net operating income ................... ....... ................. .
$141,750
85,050
56,700
48,000
$ 8.700
Current net operating income ................................
Expected increase: $6,000 x 45% ........................ .
Expected net operating income (as above) ........... .
$ 6,000
2,700
$ 87
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hapter
Exercise -2.
200
180
160
140
'Vi' 120
o
o
o
100
.
0
Q
80
60
40
20
0
The completed CVP graph:
til eak
/
V
V
V
V
V
T ]
tal a t e ~
V
[Y
/
i-
V
otal
x p n s ~
b?'
F
xed Ex
~ n s s
o
2
4 6
8 10 12 14
16
18
20
nits
OOOs)
The break-even point is 10,000 units or 100,000 in sales.
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Chapter
Exercise -3.
a. The completed income statement
Product X
Product Y
Total
mount
mount
%
mount
%
Sales......... ...................... .
4,000 100
7,200
100 11,200
100.0
Variableexpenses
..
........
.
2,400 1,800
..l2.
4,200 37.5
Contribution margin ...... .
a§ .A.Q
-.12
7,000
62.5
Fixed expenses ..............
.
5,000
Net operating income ....
..
2,QQ.Q
Breakeven point _ Fixed expenses _ 5,000 _ 8 000
b.
in total sales dollars - CM ratio - 0.625 - ,
c.
Monthly net operating income will fall. The shift in sales mix means that less of Product Y and more of
Product X are being sold. Because Product Y has a higher contribution margin per unit than Product X, less
contribution margin in total will be available and profits will therefore fall.
d.
The monthly break-even will rise. As explained above, the shift in sales
m x
will be toward the less profit
able Product X, which has a CM ratio
of
only 40% as compared to 75% for Product Y. Thus, the company's
overall
CM ratio will fall, and the break-even will rise because less contribution margin will be available
per
unit to cover the fixed costs.
Exercise -4. Baker Company will have a higher contribution margin ratio (and contribution margin per unit)
due to its lower variable costs. Thus, the company's contribution margin (and net operating income) will increase
more rapidly than Able Company's as sales increase. Therefore , Baker Company will realize the most rapid in
crease in net operating income. The impact on net operating income can also be viewed in tenns of operating lev
erage. Baker Company will have a higher degree of operating leverage than Able Company because of its higher
contribution margin. Therefore, as sales increase, Baker's net operating income will rise more rapidly than will
Able's.
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