chap 05 - study guide

8/18/2019 Chap 05 - Study Guide

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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%.


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.


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......... .... ........

..

...........

...

........

$ ==

69


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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


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


Unitssoldto _Fixedexpenses+Targetprofit_ $48,000+ 12,000 - 5000 t

.

i

-

-

ums

attamtargetpro It Unitcontributionmargin $12perunit

74


11/14

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

75


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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.

76


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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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chap 05 - study guide

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