P12-9. DOL
LG 2; Intermediate
a.
$380,000 8,000 units
( ) $63.50 $16.00
FC
QP VC
= = =
– –
9,000 Units 10,000 Units 11,000 Units
b.
c.
50%
d.
% change in sales
e.
´ –
=´ – –
[ ( )]
DOL [ ( )]
Q P VC
Q P VC FC
´ –
=´ – –
[10,000 ($63.50 $16.00)]
DOL [10,000 ($63.50 $16.00) $380,000]
= =
$475,000
DOL 5.00
$95,000
P12-10. DOL—graphical
LG 2; Intermediate
a.
$72,000 24,000 units
( ) $9.75 $6.75
FC
QP VC
= = =
– –
b.
´ –
=´ – –
[ ( )]
DOL [ ( )]
Q P VC
Q P VC FC
´ –
= =
´ – –
[25,000 ($9.75 $6.75)]
DOL 25.0
[25,000 ($9.75 $6.75)] $72,000
´ –
= =
´ – –
[30,000 ($9.75 $6.75)]
DOL 5.0
[30,000 ($9.75 $6.75)] $72,000
´ –
= =
´ – –
[40,000 ($9.75 $6.75)]
DOL 2.5
[40,000 ($9.75 $6.75)] $72,000
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2 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition
c.
d.
´ –
= =¥
´ – –
[24,000 ($9.75 $6.75)]
DOL [24,000 ($9.75 $6.75)] $72,000
At the operating breakeven point, the DOL is infinite.
e. DOL decreases as the firm expands beyond the operating breakeven point.
P12-11. EPS calculations
LG 2; Intermediate
(a) (b) (c)
EBIT $24,600 $30,600 $35,000
Less: Interest 9,600 9,600 9,600
P12-12. Degree of financial leverage
LG 2; Intermediate
a.
EBIT $80,000 $120,000
Less: Interest 40,000 40,000
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Chapter 3: Financial Statements and Ratio Analysis 3
b.
EBIT
DFL 1
EBIT (1 )
I PD T
=é ù
æ ö
– – ´
ê ú
ç ÷
–
è ø
ë û
= =
– –
$80,000
DFL 2
[$80,000 $40,000 0]
c.
EBIT $80,000 $120,000
Less: Interest 16,000 16,000
4 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition
P12-14. DFL and graphic display of financing plans
LG 2, 5; Challenge
a.
=é ù
æ ö
– – ´
ê ú
ç ÷
–
è ø
ë û
EBIT
DFL 1
EBIT (1 )
I PD T
= =
– –
$67,500
DFL 1.5
[$67,500 $22,500 0]
b.
c.
= =
é ù
– –
ê ú
ë û
$67,500
DFL 1.93
$6,000
$67,500 $22,500 0.6
d. See graph, which is based on the following equation and data points.
Financing EBIT EPS
Original
financing
plan
$67,500
($67,000 $22,500)(1 0.4) $1.80
15,000
– – =
$17,500
($17,500 $22,500)(1 0.4) $0.20
15,000
– – =–
Revised
financing
plan
$67,500
($67,000 $22,500)(1 0.4) 6,000 $1.40
15,000
– – – =
$17,500
($17,500 $22,500)(1 0.4) 6,000 $0.60
15,000
– – – =–
e. The lines representing the two financing plans are parallel because the number of shares of common stock
outstanding is the same in each case. The financing plan, including the preferred stock, results in a higher
financial breakeven point and a lower EPS at any EBIT level.
P12-15. Integrative—multiple leverage measures
LG 1, 2; Intermediate
a.
$28,000
Operating breakeven 175,000 units
$0.16
= =
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Chapter 3: Financial Statements and Ratio Analysis 5
b.
´ –
=´ – –
[ ( )]
DOL [ ( )]
Q P VC
Q P VC FC
´ –
= = =
´ – –
[400,000 ($1.00 $0.84)] $64,000
DOL 1.78
[400,000 ($1.00 $0.84)] $28,000 $36,000
c. EBIT (P Q) FC (Q VC)
=é ù
æ ö
– – ´
ê ú
ç ÷
–
è ø
ë û
EBIT
DFL 1
EBIT (1 )
I PD T
= =
é ù
æ ö
– –
ê ú
ç ÷
–
è ø
ë û
$36,000
DFL 1.35
$2,000
$36,000 $6,000 (1 0.4)
d.
*[ ( )]
DTL
( ) (1 )
Q P VC
PD
Q P VC FC I T
´ –
=é ù
æ ö
´ – – – –
ê ú
ç ÷
–
è ø
ë û
´ –
=é ù
æ ö
´ – – – –
ê ú
ç ÷
–
è ø
ë û
[400,000 ($1.00 $0.84)]
DTL $2,000
400,000 ($1.00 $0.84) $28,000 $6,000 (1 0.4)
= = =
– –
$64,000 $64,000
DTL 2.40
[$64,000 $28,000 $9,333] $26,667
DTL DOL DFL
*Degree of total leverage.
P12-16. Integrative—leverage and risk
LG 2; Intermediate
a.
´ –
= = =
´ – –
[100,000 ($2.00 $1.70)] $30,000
DOL 1.25
[100,000 ($2.00 $1.70)] $6,000 $24,000
R
= =
–
$24,000
DFL 1.71
[$24,000 $10,000]
R
= ´ =DTL 1.25 1.71 2.14
R
b.
´ –
= = =
´ – –
[100,000 ($2.50 $1.00)] $150,000
DOL 1.71
[100,000 ($2.50 $1.00)] $62,500 $87,500
W
= =
–
$87,500
DFL 1.25
[$87,500 $17,500]
W
= ´ =DTL 1.71 1.25 2.14
R
d. Two firms with differing operating and financial structures may be equally leveraged. Because total leverage is
6 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition
P12-17. Integrative—multiple leverage measures and prediction
LG 1, 2; Challenge
a. Q FC (P VC) Q $50,000 ($6 $3.50) 20,000 latches
b. Sales ($6 30,000) $180,000
Less:
Fixed costs 50,000
c.
´ –
=´ – –
[ ( )]
DOL [ ( )]
Q P VC
Q P VC FC
´ –
= = =
´ – –
[30,000 ($6.00 $3.50)] $75,000
DOL 3.0
[30,000 ($6.00 $3.50)] $50,000 $25,000
d.
=é ù
æ ö
– – ´
ê ú
ç ÷
–
è ø
ë û
EBIT
DFL 1
EBIT (1 )
I PD T
= = =
– – ´ ¸
$25,000 $25,000
DFL 75.00
$25,000 $13,000 [$7,000 (1 0.6)] $333.33
f.
15,000
Change in sales 50%
30,000
= =
Percentage change in EBIT % change in sales DOL 50% 3 150%
P12-18. Personal finance: Capital structures
LG 3; Intermediate
Kirsten’s ratio is less than the bank maximum of 37.0%. Because Kirsten’s debt-related expenses as a percentage
of her monthly gross income are less than bank-specified maximums, her loan application should be accepted.
P12-19. Various capital structures
LG 3; Basic
Debt Ratio Debt Equity
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Chapter 3: Financial Statements and Ratio Analysis 7
10% $100,000 $900,000
20% $200,000 $800,000
Theoretically, the debt ratio cannot exceed 100%. Practically, few creditors would extend loans to companies with
exceedingly high debt ratios (70%).
P12-20. Debt and financial risk
LG 3; Challenge
a. EBIT Calculation
Probability 0.20 0.60 0.20
Sales $200,000 $300,000 $400,000
Less: Variable costs (70%) 140,000 210,000 280,000
b. EPS
Earnings after taxes $(16,200) $ 1,800 $ 19,800
=
= ´
å
1
Expected EPS EPS Pr
n
j j
i
s
=
= – ´
å2
EPS
1
(EPS EPS) Pr
n
i i
i
s= – – ´ + – ´ + – ´
222
EPS [( $1.62 $0.18) 0.20] [($0.18 $0.18) 0.60] [($1.98 $0.18) 0.20]
s= ´ + + ´EPS ($3.24 0.20) 0 ($3.24 0.20)
s= +EPS $0.648 $0.648
s= =EPS $1.296 $1.138
s
= = =
EPS
EPS 1.138 6.32
Expected EPS 0.18
CV
c.
EBIT *$(15,000) $15,000 $45,000
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8 Gitman/Zutter Principles of Managerial Finance, Brief, Seventh Edition
Less: Interest 0 0 0
Net profit before taxes $(15,000) $15,000 $45,000
*From part a
Expected EPS ($0.60 0.20) ($0.60 0.60) ($1.80 0.20) $0.60
2 2 2
EPS [( $0.60 $0.60) 0.20] [($0.60 $0.60) 0.60] [($1.80 $0.60) 0.20]s= – – ´ + – ´ + – ´
s= ´ + + ´EPS ($1.44 0.20) 0 ($1.44 0.20)
s= =EPS $0.576 $0.759
= =EPS $0.759 1.265
0.60
CV
d. Summary statistics
With Debt All Equity
Expected EPS $0.180 $0.600
Including debt in Tower Interiors’ capital structure results in a lower expected EPS, a higher standard deviation,
P12-21. EPS and optimal debt ratio
LG 4; Intermediate
a.
Maximum EPS appears to be at 60% debt ratio, with $3.95 per share earnings.
b.
s
=EPS
EPS EPS
CV
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Chapter 3: Financial Statements and Ratio Analysis 9
Debt Ratio CV
0% 0.5
20 0.6
40 0.8
60 1.0
80 1.5
© 2015 Pearson Education, Inc.