Solution manual financial management 10e by keown chapter 15

Contribution margin analysis 1 Unit selling price - unit variable cost = contribution margin2 Fixed cost divided by the contribution margin per unit equals the break-even quantity in uni

CHAPTER 15

Analysis and Impact

of Leverage

I Business risk and financial risk

A Risk is defined as the likely variability associated with expected revenue

streams

1 The variations in the income stream can be attributed to

a The firm's exposure to business risk

b The firm's decision to incur financial risk

B Business risk is defined as the variability of the firm's expected earnings

before interest and taxes

1 Business risk is measured by the firm's corresponding expected

coefficient of variation

2 Dispersion in operating income does not cause business risk It is the

result of several influences, such as the company’s cost structure,product demand characteristics, and intra-industry competition

C Financial risk is a direct result of the firm's financing decision It refers to

the additional variability in earnings available to the firm’s commonstockholders and the additional chance of insolvency borne by the commonshareholder when financial leverage is used

1 Financial leverage is the financing of a portion of the firm's assets

with securities bearing a fixed rate of return in hopes of increasingthe return to the common shareholders

2 Financial risk is passed on to the common shareholders who must

bear most of the inconsistencies of returns to the firm after thededuction of fixed payments

II Break-even Analysis

A The objective of break-even analysis is to determine the break-even quantity

of output by studying the relationships among the firm’s cost structure,volume of output, and operating profit

1 The break-even quantity of output results in an EBIT level equal to

zero

B Use of the model enables the financial officer to

1 Determine the quantity of output that must be sold to cover all

operating costs

2 Calculate the EBIT achieved at various output levels

C Some potential applications include

1 Capital expenditure analysis as a complementary technique to

discounted cash flow evaluation models

2 Pricing policy

3 Labor contract negotiations

4 Evaluation of cost structure

5 Financial decision making

D Essential elements of the break-even model

1 Production costs must be separated into fixed costs and variable

costs Fixed costs do not vary as the sales volume or the quantity ofoutput changes Examples include

2 Variable costs vary in total as output changes Variable costs are

fixed per unit of output Examples include

3 In order to implement the break-even model, it is necessary for the

financial manager to

a Identify the most relevant output range for planning purposes

b Approximate all costs in the semifixed and semivariable

range and allocate them to the fixed and variable costcategories

4 Total revenue and volume of output

a Total revenue (sales dollars) is equal to the selling price per

unit multiplied by the quantity sold

b Volume of output refers to the firm’s level of operations and

is expressed as a unit quantity or sales dollars

E Finding the break-even point

1 The break-even model is just an adaptation of the firm's income

statement expressed assales - (total variable costs + total fixed costs) = profit

2 Three ways to find the break-even point are explained

a Trial and error

(1) Select an arbitrary output level

(2) Calculate the corresponding EBIT amount

(3) When EBIT equals zero, the break-even point has

been found

b Contribution margin analysis

(1) Unit selling price - unit variable cost = contribution

margin(2) Fixed cost divided by the contribution margin per unit

equals the break-even quantity in units

c Algebraic analysis

(l) QB = the break-even level of units sold,

P = the unit sales price,

F = the total fixed cost for the period,

V = unit variable cost

(2) Then,

QB =

VPF

−

F The break-even point in sales dollars

1 It is convenient to calculate the break-even point in terms of sales

dollars if the firm deals with more than one product It can becomputed by using data from the firm's annual report

2 Since variable cost and selling price per unit are assumed constant,

the ratio of total variable costs to total sales is a constant for anylevel of sales

G Limitations of break-even analysis

1 Assumes linear cost-volume-profit relationship

2 The total revenue curve is presumed to increase linearly with the

volume of output

3 Assumes constant production and sales mix

4 This is a static form of analysis

III Operating Leverage

A Operating leverage is the responsiveness of a firm's EBIT to fluctuations in

sales Operating leverage results when fixed operating costs are present inthe firm's cost structure

B This responsiveness can be measured as follows:

levelsalesbase

thefromleverage

operatingof

degree

= DOLs = %%changechangein in EBITsales

C If unit costs are available, the DOL can be measured by

DOLs = Q(PQ(P−V)−V)−F

D If an analytical income statement is the only information available, the

following formula is used:

DOLs =

EBIT

costsfixedbeforerevenue =

FVCS

VCS

−

−

−

Note: All three formulas provide the same results

E Implications of operating leverage

1 At each point above the break-even level, the degree of operating

leverage decreases

2 At the break-even level of sales, the degree of operating leverage is

undefined

3 Operating leverage is present when the percentage change in EBIT

divided by the percentage change in sales is greater than one

4 The degree of operating leverage is attributed to the business risk

that a firm faces

IV Financial Leverage

A To see if financial leverage has been used to benefit the common

shareholder, the focus will be on the responsiveness of the company'searnings per share (EPS) to changes in its EBIT

B The firm is using financial leverage and is exposing its owners to financial

risk when

EBIT

in change

%

EPS

in change

%

is greater than 1.00

C A measure of the firm's use of financial leverage is as follows:

levelEBITbase

thefromleverageoffinancial

degree

= DFLEBIT =

EBIT

in change

%

EPS

in change

EBIT

−

where I is the sum of all fixed financing costs

V Combining operating and financial leverage

A Changes in sales revenues cause greater changes in EBIT If the firm

chooses to use financial leverage, changes in EBIT turn into largervariations in both EPS and EAC Combining operating and financialleverage causes rather large variations in EPS

B One way to measure the combined leverage can be expressed as

levelsalesbase from theleverage

combinedof

degree

= DCLs = %%changechangein in salesEPS

If the DCL is equal to 5.0 times, then a 1% change in sales will result in a5% change in EPS

C The degree of combined leverage is the product of the two independent

leverage measures Thus:

DCLS = (DOLS ) x (DFLEBIT)

D Another way to compute DCLs is with the following equation:

DCLs = Q(PQ(P−V)−−V)F−I

E Implications of combining operating and financial leverage

1 Total risk can be managed by combining operating and financial

leverage in different degrees

2 Knowledge of the various leverage measures helps to determine the

proper level of overall risk that should be accepted

ANSWERS TO END-OF-CHAPTER QUESTIONS

15-1 Business risk is the uncertainty that envelops the firm's stream of earnings before

interest and taxes (EBIT) One possible measure of business risk is the coefficient

of variation in the firm's expected level of EBIT Business risk is the residual effect

of the: (1) company's cost structure, (2) product demand characteristics, (3) industry competitive position The firm's asset structure is the primary determinant

intra-of its business risk Financial risk can be identified by its two key attributes: (1)the added risk of insolvency assumed by the common stockholder when the firmchooses to use financial leverage; (2) the increased variability in the stream ofearnings available to the firm's common stockholders

15-2 Financial leverage is financing a portion of the firm's assets with securities bearing

a fixed (limited) rate of return Anytime the firm uses preferred stock to financeassets, financial leverage is employed

15-3 Operating leverage is the use of fixed operating costs in the firm's cost structure

When operating leverage is present, any percentage fluctuation in sales will result

in a greater percentage fluctuation in EBIT

15-4 Break-even analysis, as it is typically presented, categorizes all operating costs as

being either fixed or variable Based upon this division of costs, the break-evenpoint is computed The computation procedure for the cash break-even point omitsany noncash expenses that the firm might incur Typical examples of noncashexpenses include depreciation and prepaid expenses The ordinary break-even pointwill always exceed the cash break-even point, provided some noncash charges arepresent

15-5 The most important shortcomings of break-even analysis are:

(1) The cost-volume-profit relationship is assumed to be linear over the entire

(4) The level of total fixed costs and the variable cost to sales ratio is held

constant over all output and sales ranges

15-6 Total risk exposure is the result of the firm's use of both operating leverage and

financial leverage Business risk and financial risk produce this total risk Acompany that is normally exposed to a high degree of business risk may manage itsfinancial structure in such a way as to minimize financial risk A firm that enjoys astable pattern in its earnings before interest and taxes might reasonably elect to use

a high degree of financial leverage This would increase both its earnings per shareand its rate of return on the common equity investment

15-7 By taking the degree of combined leverage times the sales change of a negative 15

percent, the earnings available to the firm's common shareholders will decline by 45percent

15-8 As the sales of a firm increase, two things occur that bias the cost and revenue

functions toward a curvilinear shape First, sales will increase at a decreasing rate

As the market approaches saturation, the firm must cut its price to generate salesrevenue Second, as production approaches capacity, inefficiencies occur that result

in higher labor and material costs Furthermore, the firm's operating system mayhave to bear higher administrative and fixed costs The result is higher per unitcosts as production output increases

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Solutions To Problem Set A

F = 

50,000

= 450,000

= 125,000

15-2A Break-even Quantity = QB

QB =

V)(P

F

−

QB =

(.70)($30) -

$30

$360,000

QB = 40,000 bottles15-3A Degree of Operating Leverage = DOLS

DOLS =

F]

V)[Q(P

V)Q(P

$)21

$30($

000,50[

)21

$30($

000,50

−

−

−

DOLS = 5 times15-4A

(a)

Jake's Sarasota JeffersonLawn Chairs Sky Lights WholesaleSales $600,640.00 $2,450,000 $1,075,470Variable Costs $326,222 60 $1,120,000 $957,000Revenue before

fixed costs $274,417.40 $1,330,000 $118,470Fixed costs $120,350 00 $850,000 $89,500EBIT $ 154,067 40 $ 480,000 $ 28,970(b)

Jake's Lawn Chairs: QB = P−FV = $32 $17.38

350,120

$

−

=

62.14

$

350,120

$

= 8,232Sarasota Skylights: QB = $875$850−,000$400 = $475

000,850

$ = 1,789

Jefferson Wholesale: QB = $97$.8977,500−$87 = $10.77

500,89

$ = 8,310(c)

Jake's Sarasota JeffersonLawn Chairs Skylights WholesaleEBIT

CostsFixed Before

Revenue

=

40.067,154

$

40.417,274

$

$480,000

$1,330,000

970,28

$

470,118

=

000,750,13

$

000,950,22

$

= 1.67 times

(b)

IEBIT

EBIT

− = $13,750,000 1,350,000

000,750,13

$

− = $12,400,000

000,750,13

$

= 1.11 times(c) DCL45,750,000 = (1.67) (1.11) = 1.85 times

(d) S* =

S

VC1

F

000,750,45

$

000,800,22

$1

000,200,9

− = 91,200−.498,000

=

502

000,200,9

= $18,326,693.23 (e) (25%) × (1.85) = 46.25%

15-6A

(a) QB =

VP

F

− = $85 $58

000,170

$

− = $27

000,170

000,170

$

− = $1170−.682,000 = $170.318,000 = $534,591.20

(c)

7,000 9,000 15,000Pairs of Shoes Pairs of Shoes Pairs of ShoesSales $595,000 $765,000 $1,275,000Variable Costs 406,000 522,000 870,000Revenue before

fixed costs $189,000 $243,000 $405,000Fixed costs 170,000 170,000 170,000EBIT $ 19,000 $ 73,000 $ 235,000

7,000 9,000 15,000 Pairs of Shoes Pairs of Shoes Pairs of Shoes

000,19

$

000,189

$

000,73

$

000,243

$

000,235

$

000,405

$

= 9.95 times 3.33 times 1.72 timesNotice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point

15-7A

(a) QB =

VP

F

− = $180 $110

000,630

$

− = $70

000,630

$

= 9000 Units(b) S* = 9000 units × $180 = $1,620,000

Alternatively,

S* =

S

VC1

000,630

$

−

=

6111.01

000,630

$

− = 3889

000,630

$

= $1,619,954 Note: $1,619,954 differs from $1,620,000 due to rounding

(c) 12,000 15,000 20,000

units units unitsSales $2,160,000 $2,700,000 $3,600,000Variable Costs 1,320,000 1,650,000 2,200,000Revenue before

fixed costs 840,000 1,050,000 1,400,000Fixed costs 630,000 630,000 630,000EBIT $ 210,000 $ 420,000 $ 770,000(d) 12,000 units 15,000 units 20,000 units

000,210

$

000,840

$

000,420

$

000,050,1

000,770

$

000,400,1

= 4 times = 2.5 times = 1.82 timesNotice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point

15-8A (a)

Blacksburg Lexington WilliamsburgFurniture Cabinets ColonialsSales $1,125,000 $1,600,000 $520,000Variable costs 926,250 880,000 188,500Revenue before

fixed costs $198,750 $720,000 $331,500Fixed costs 35,000 100,000 70,000EBIT $163,750 $620,000 $261,500(b)

:Furniture

Blacksburg

QB =

VP

F

− = $15.00 $12.35

000,35

$

− = 2.65

000,35

$

= 13,208 units

:Cabinets

Lexington

QB = $400$100−,000$220 = $180

000,100

$

= 556 units

:Colonials

rgWilliamsbu Q

B =

50.14

$00.40

$

000,70

$

− = $25.50

000,70

CostsFixed Before

Revenue

750,163

$

750,198

$

000,620

$

000,720

$

500,261

$

500,331

$

= 1.21 times 1.16 times 1.27 times

(d) Williamsburg Colonials, since its degree of operating leverage

exceeds that of the other two companies

15-9A

(a) {S- (VC + F)} (1-T) = $50,000

(1 T)

FS

VCS

{$375,000 - $206,250 – F} (0.6) = $50,000($168,750 - F) (0.6) = $50,000

F = $85,416.67

(b) QB = P−FV = $27.00 $14.85

67.416,85

$

− = $12.15

67.416,85

$ = 7,030 units

S* =

S

VC1

F

− = 1 .55

67.416,85

S

VC

= 0.5,

so, VC = (0.5) $3,250,000 = $1,625,000Now, solve for total fixed costs:

000,780

=

000,500,8

000,500,16

$

= 1.94 times

(b)

IEBIT

EBIT

− = 7,500,000

000,500,8

= 1.13 times(c) DCL$30,000,000= (1.94) × (1.13) = 2.19 times

(d) S* =

S

VC1

$

5.13

$1

000,000,8

− = 81,000−0.,45000 = 8,0000.55,000 =

$14,545,455(e) (25%) × (2.19) = 54.75%

15-12A.Given the data for this problem, several approaches are possible for finding the

break-even point in units The approach below seems to work well with students

Step (1) Compute the operating profit margin:

Operating Profit Margin x Operating Asset Turnover = Return

on operating assets(M) x (5) = 0.25

M = 05Step (2) Compute the sales level associated with the given output

Step (3) Compute EBIT:

(.05) ($100,000,000) = $5,000,000Step (4) Compute revenue before fixed costs Since the degree of

operating leverage is 4 times, revenue before fixed costs(RBF) is 4 times EBIT as follows:

RBF = (4) × ($5,000,000) = $20,000,000Step (5) Compute total variable costs:

(Sales) - (Total variable costs) = $20,000,000

$100,000,000 - (Total variable costs) = $20,000,000Total variable costs = $80,000,000

Step (6) Compute total fixed costs:

RBF - Fixed costs = $5,000,000

$20,000,000 - fixed costs = $5,000,000Fixed costs = $15,000,000

Step (7) Find the selling price per unit, and the variable cost per unit:

P =

000,000,10

000,000,100

$

= $10.00

V =

000,000,10

000,000,80

$

= $8.00Step (8) Compute the break-even point:

QB =

VP

F

− = ($10) ($8)

000,000,15

$

000,000,15

$ = 7,500,000 units

(a) QB =

VP

F

− = $180 $126

000,540

$

− = $54

000,540

$ = 10,000 units

(b) S* =

S

VC1

000,540

$

− = 1 0.7

000,540

$

− = 3

000,540

$

= $1,800,000

(c) 12,000 15,000 20,000

Units Units UnitsSales $2,160,000 $2,700,000 $3,600,000Variable costs 1,512,000 1,890,000 2,520,000Revenue before fixed costs $ 648,000 $ 810,000 $1,080,000Fixed costs 540,000 540,000 540,000EBIT $ 108,000 $ 270,000 $ 540,000(d) 12,000 units 15,000 units 20,000 units

000,108

$

000,648

$

= 6 times

000,270

$

000,810

$

= 3 times

000,540

$

000,080,1

= 2 times

Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point

15-14A

(a) Oviedo Gainesville Athens

Seeds Sod PeachesSales $1,400,000 $2,000,000 $1,200,000Variable costs 1,120,000 1,300,000 840,000Revenue before fixed costs $280,000 $ 700,000 $ 360,000Fixed costs 25,000 100,000 35,000EBIT $ 255,000 $ 600,000 $ 325,000

(b) Oviedo Seeds: QB =

VP

F

− = $14.00 $11.20

000,25

$

− = 2.80

000,25

$

000,100

$

− = $70

000,100

$

= 1,429 units

Athens Peaches: QB =

50.17

$00.25

$

000,35

$

− = 7.50

000,35

$

= 4,667 units

Oviedo Gainesville

000,255

$

000,280

$

= 1.098 times

000,600

$

000,700

$

= 1.167 times

AthensPeaches000,325

$

000,360

$

= 1.108 times

(d) Gainesville Sod, since its degree of operating leverage exceeds that of the

other two companies

15-15A

(a) {S - [VC + F]} (1 - T) = $40,000

(1 T)

FS

VCS

F = $173,333.33

(b) QB =

VP

F

− = $12

33.333,173

$ = 14,444 units

S* =

S

VC1

F

− = 1 0.40

33.333,173

VCS

$360,000 - 6F = $80,000

F = $466,666.67

(b) QB =

VP

F

− = $24

67.666,466

$ = 19,444 units

S* =

S

VC1

F

− = 1 .7

67.666,466

$

− = 3

67.666,466

$

= $1,555,555.5715-17A

(a) S (1 - 0.75) - $300,000 = $240,000

0.25S = $540,000

S = $2,160,000 = (P × Q)Now, solve the above relationship for P:

(a) First, find the EBIT level at the forecast sales volume:

= 0.28So: EBIT = (0.28) $3,750,000 = $1,050,000

Next, find total variable costs:

= 0.5So: VC = (0.50) $3,750,000 = $1,875,000

Then, solve for total fixed costs:

000,825

F

− = $150

000,180

F

− = $1180−0,.00070 = $600,000

(c) DOL$2,500,000 =

000,180

$)350

$500($

000,5

)350

$500($

000,5

−

−

−

000,570

$

000,750

$

= 1.316 times

(d) (20%) x (1.316) = 26.32% Increase

(a) QB = P−FV = $25 $15

000,50

$

− = $10

000,50

$ = 5,000 units

(b) S* =

S

VC1

000,50

$

− = 1 0.6

000,50

$

− = 4

000,50

$

= $125,000

(c) 4000 units 6000 units 8000 units

Sales $100,000 $150,000 $200,000Variable costs 60,000 90,000 120,000Revenue before fixed costs $ 40,000 $ 60,000 $ 80,000Fixed costs 50,000 50,000 50,000EBIT $-10,000 $ 10,000 $ 30,000

(d) 4000 units 6000 units 8000 units

000,10

$

000,40

$

− = -4X $10,000

000,60

$

= 6X

000,30

$

000,80

$

= 2.67X

(e) The degree of operating leverage decreases as the firm's sales level rises

above the break-even point

15-22A Compute the present level of break-even output:

QB = P−FV =

712

$

000,120

$

− = 24,000 units

Compute the new level of fixed costs at the break-even output:

S – V – F = 0($12) (24,000) - ($5) (24,000) - F = 0

$288,000 - $120,000 - F = 0

$168,000 = FCompute the addition to fixed costs:

$168,000 - $120,000 = $48,000 addition

15-23A DOL$360,000 =

000,120

$)712($

000,30

)712($

000,30

$

000,150

$

= 5 times Any percentage change in sales will magnify EBIT by a factor of 5

15-24A

(a) DOL$480,000 =

000,120)712($

000,40

)712($

000,40

$

000,200

$

= 2.5 times

(b) DFL$80,000 =

000,30

$000,80

$

000,80

$

− = 1.6 times

(c) DCL$480,000 =

000,30

$000,120

$)712($

000,40

)712($

000,40

$

000,200

$

= 4 times Alternatively:

(DOLS) x (DFLEBIT) = DCLS

(2.5) x (1.6) = 4 times

15-25A The task is to find the break-even point in units for the firm Several

approaches are possible, but the one presented below makes intuitive sense

to students

Step (1) Compute the operating profit margin:

(Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets

(M) x (5) = 0.15

M = 0.03Step (2) Compute the sales level associated with the given output level: