CHAPTER 13
CAPITAL STRUCTURE MANAGEMENT IN
PRACTICE
ANSWERS TO QUESTIONS:
1. Leverage is the use of assets and liabilities with fixed costs in order to increase the returns to
a firm's common stockholders.
2. a . Fixed costs are operating costs that are independent of sales levels in the short-run. These
costs are primarily related to the passage of time. Examples include depreciation, rent,
insurance, lighting and heating costs, property taxes, and the salaries of management.
b. Variable costs are operating costs that move in close relationship to changes in sales. Variable
costs are related to the output produced and sold, rather than the passage of time. Examples
include raw material costs, direct labor costs, and salespersons' commissions.
3. a. Operating leverage is the employment of assets with fixed operating costs in an attempt
to increase operating income (EBIT).
b. Financial leverage is the employment of funds having fixed capital costs in an attempt to
increase EPS.
4. The degree of combined leverage (DCL) is equal to the degree of operating leverage (DOL)
times the degree of financial leverage (DFL). This relationship shows that operating leverage
and financial leverage can be combined in many different ways to achieve a given degree of
combined leverage. High operating leverage can be offset with low financial leverage and
vice versa.
5. Yes. The level of business risk of a firm relates to the variability of that firm's operating
income. Even if a firm has a high degree of operating leverage, it is possible for it to have a
stable level of operating income if prices, sales quantities, and the variable costs of
production and marketing are stable over time.
6. Yes. If a firm has stable sales revenues and stable operating costs over time, the total risk of
the firm will be low. The degree of combined leverage relates changes in EPS to changes in
sales revenues. Thus, if sales revenues are relatively stable and variable operating costs are
also stable, then EPS also will be stable.
7. Use of EBIT-EPS analysis can determine which financing alternative maximizes EPS.
However, it is possible that maximizing EPS results in such a high risk level that the
weighted cost of capital is not minimized, and therefore the value of the firm is not
maximized.
185
186  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
8. A firm cannot tell exactly when it is at the optimal capital structure point. However, this is
not a great problem because the optimal capital structure, in practice, is best depicted as a
range. Many companies are able to conclude they are operating near the optimal range as a
result of borrowing nearly as much as they can at reasonable interest rates. Comparison with
other companies in the industry also should help the company determine whether it safely can
increase its proportion of "moderate" debt and reduce its weighted cost of capital. Other
techniques that can provide useful insight include EBIT-EPS analysis and cash insolvency
analysis.
9. A firm should use more debt if it traditionally has been more profitable than the average firm
in the industry, or if its operating income is more stable than the operating income of the
average firm in the industry. If the opposite factors (i.e., less profitable and less stable) are
true, the firm generally should use less debt. This answer assumes that the average firm in the
industry is operating at or near an optimal capital structure.
10. Public utilities typically incur more financial risk than major oil companies because public
utilities have less business risk than major oil companies. In general, the capital markets
permit low business risk firms to incur a larger percentage of debt in their capital structures
than high business risk firms.
11. Cash insolvency analysis is a tool that can be used to analyze the effects of a proposed capital
structure change. Cash insolvency analysis looks at the effects of a worst-case scenario of a
firm’s cash balances and net cash flows when a firm is faced with a major recession, or
downturn in its business. Cash insolvency analysis permits a manager to compute the
probability of the firm running out of cash in a recession, given the fixed financial charges
the firm faces with alternative capital structures.
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  187
SOLUTIONS TO PROBLEMS:
1. a.
Sales
$6,000,000
$6,600,000
Less: Variable operating costs
$4,500,000
$4,950,000
Fixed operating costs
800,000
800,000
Total operating costs
$5,300,000
$5,750,000
EBIT
$700,000
$850,000
Less: Interest expense
60,000
$60,000
Earnings before taxes
$640,000
$790,000
Less: Income taxes (40%)
256,000
316,000
Earnings after taxes
$384,000
$474,000
Less: Preferred stock dividends
60,000
60,000
$324,000
$414,000
$5.40
$6.90
Earnings available to common
stockholders
Earnings per share (60,000 shares)
b. i. DOL at "X" = (EBIT/EBIT)/(Sales/Sales)
DOL at $6,000,000 = [($850,000-$700,000) / $700,000] /[($6,600,000 $6,000,000)/$6,000,000] = 2.143
ii. DOL at "X" = (Sales - Variable cost)/EBIT
DOL at $6,000,000 = ($6,000,000 - $4,500,000)/$700,000
= 2.143
iii. From a base sales level of $6 million, each one percent change in sales results in a 2.143
percent change in EBIT, in the same direction as the sales change.
188  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
c. i. DFL at "X" = (EPS/EPS)/(EBIT/EBIT)
DFL at $700,000 = [($6.90 - $5.40)/$5.40]/[($850,000 - $700,000) / $700,000] = 1.2963
ii. DFL at "X" = EBIT/[EBIT - I - Dp/(1 - T)]
DFL at $700,000 = $700,000/[$700,000 - $60,000 - $60,000/(1-.4)]
= 1.2963
iii. From a base EBIT level of $700,000, each one percent change in EBIT results in a 1.2963
percent change in EPS, in the same direction as the EBIT change.
d. i. DCL = (EPS/EPS)/(Sales/Sales)
DCL = [($6.90-$5.40)/$5.40]/[($6,600,000 - $6,000,000) / $6,000,000]
= 2.778
ii. DCL = (Sales - Variable costs) / [EBIT - I - Dp/(1 - T)]
DCL = ($6,000,000-$4,500,000) / [($700,000 - $60,000
-$60,000)/(1-.4)] = 2.778
iii. DCL = DOL x DFL = 2.143 x 1.2963 = 2.778
iv. From a base sales level of $6,000,000, each 1 percent change in sales results in a 2.778
percent change in EPS, in the same direction as the sales change.
2. a. Fixed operating costs = Depreciation + .75(General, administrative, and selling expenses)
= $1,500,000 + .75($1,500,000) = $2,625,000
Variable operating costs = Total operating costs minus fixed operating costs
= $12,000,000 - $2,625,000 = $9,375,000
Variable cost ratio = $9,375,000 / $15,000,000 = 0.625
b. (i) DOL at $15 million = ($15,000,000 - $9,375,000) /
(ii) DFL at $3,000,000 = $3,000,000 / [($3,000,000
- $750,000 - $250,000) / (1 - .444444)] = 1.67
$3,000,000 = 1.875
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  189
(iii)
DCL = 1.875 x 1.67 = 3.13
c. DCL = 3.13, therefore a 15% increase in sales will yield a 15% x 3.13 = 47% increase in
Alexander's EPS next year. Next year's EPS is forecast to be (1 + .47) x $4 = $5.88.
d. Sales ($15,000,000 x 1.15) =
$17,250,000
Less: Variable operating costs
0.625 x $17,250,000 =
$10,781,250
Fixed operating costs
2,625,000
Total operating costs
$13,406,250
EBIT
$3,843,750
Less: Interest
Earnings before taxes
Less: Income taxes (T = .444444. . . )
Earnings after taxes
750,000
$3,093,750
1,375,000
$1,718,750
Less: Preferred dividends
Earnings available to common stockholders
250,000
$1,468,750
Earnings per share (250,000 shares)
e. No solution provided
3. a. Sales = $3,000,000
Variable costs = 0.5 x $3,000,000 = $1,500,000
EBIT = Sales - Variable costs - Fixed costs
= $3,000,000 - $1,500,000 - $900,000 = $600,000
Interest = .125($2,400,000) = $300,000
DCL = ($3,000,000 - $1,500,000) / ($600,000 - $300,000)
$5.88
190  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
= 5.0
b. Sales = 1.1 x $3,000,000 = $3,300,000
Variable costs = .475 x $3,300,000 = $1,567,500
EBIT = $3,300,000 - $1,567,500 - ($900,000 +$150,000)
= $682,500
Interest = $300,000 + .125($500,000) = $362,500
DCL = ($3,300,000 - $1,567,500) / ($682,500 - $362,500)
= 5.41
c. 5.0 = ($3,300,000 - $1,567,500) / ($682,500 - .125X)
X = $2,688,000
Gibson would have to reduce debt by ($2,900,000 - $2,688,000 or $212,000 in order to
maintain a DCL at 5.0 in 19x2.
4. Sales = P x Q
EBIT = P x Q - F - V x Q, where P = price/unit; F = fixed cost;
V = variable cost/unit
Sales = Sales2 - Sales1 = PQ2 - PQ1 = P(Q2 - Q1)
EBIT = EBIT2 - EBIT1
= (PQ2 - F - VQ2) - (PQ1 - F - VQ1) = (P - V)(Q2 - Q1)
DOL @ "Sales1" = (EBIT/EBIT1) / (Sales/Sales1)
= [(P - V)(Q2 - Q1) / (PQ1 - F - VQ1)] / [P(Q2 - Q1) / PQ1]
= (P - V)Q1 /(PQ1 - F - VQ1) = (PQ1 - VQ1)/(PQ1 - F - VQ1)
= (Sales1 - Variable cost1)/EBIT1
5. a. Sales = $8,000,000
Variable costs = .2($8,000,000) = $1,600,000
Fixed costs = $5,800,000
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  191
EBIT = $8,000,000 - $5,800,000 - $1,600,000 = $600,000
DOL @ $8,000,000 = ($8,000,000 - $1,600,000)/$600,000
= 10.67
b. DFL @ $600,000 = $600,000 / [($600,000 - $160,000
- $60,000)/(1 - .4)] = 1.765
c. DCL = DOL x DFL = 10.67 x 1.765 = 18.8
A DCL of 18.8 indicates that, from a base sales level of
(decrease) in sales will yield an 18.8%
$8,000,000, each 1% increase
increase (decrease) in EPS.
6. DCL @ $500,000 = [($1.56 - $1.00)/$1.00] / [($570,000 -
$500,000)/($500,000)] = 4.0
7. a. EBIT = $80,000,000 - .65($80,000,000) - $10,000,000
= $18,000,000
DOL @ $80 million = [($80,000,000 - .65($80,000,000)] / ($18,000,000) = 1.56
b. Interest = .1($20 million) + .12($6 million) = $2.72 million
DFL @ $18 million = $18,000,000 / [$18,000,000
- $2,720,000 - $5,000,000/(1-.4)] = 2.59
c. DCL = 1.56 x 2.59 = 4.04
A sales decline to $76 million represents a 5 percent sales decline. Earnings per share can be
expected to decline by 4.04 x 5% or 20.2%.
Current earnings per share are:
EPS = (Sales - Variable operating cost - Fixed operating cost - Interest
- Taxes - Preferred dividends) / Number of common shares
EPS = [($80,000,000 - $52,000,000 - $10,000,000
- $2,720,000)(1 - .4) - $5,000,000] / 2,000,000 = $2.08
Forecast EPS = $2.08 (1 - .202) = $1.66
192  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
8. DCL = DOL x DFL = 3.0 x 5.5 = 16.5
EPS can be expected to decline by 2% x 16.5 = 33%
Forecast EPS = $2.60 (1 - .33) = $1.74
9. Loss level of EBIT = Interest plus pretax preferred stock dividends
= $700,000 + $240,000/(1 - .4) = $1,100,000
The probability of negative earnings per share is the probability of having operating income less
than the loss level.
z = ($1,100,000 - $1,500,000)/$300,000
= -1.33 standard deviations
From Table V, p(z < -1.33) = 9.18%
10. a. DCL = (Sales - Variable cost)/[EBIT - Interest - Dp/(1-T)]
3.0 = ($10M - $5M) / ($2M - Interest)
Interest = $333,333
b. 2.5 = ($10M - $5M) / ($2M - Interest)
Interest = $0
11. DCL = DOL x DFL
6 = DOL x 2
DOL = 3
3 = %EBIT/+15%
%EBIT = +45%
12. Values in millions of dollars
a. VC = 0.4($30) = $12
EBIT = $30 - $12 - $10 = $8
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  193
DOL = ($30 - $12)/$8 = 2.25
b. Interest = [(0.1 x $2) + (0.12 x $10)] = $1.4
DFL = $8/ [$8 - $1.4 - ($0.96/(1 - 0.4)] = 1.6
c. DCL = DOL x DFL = 2.25 x 1.6 = 3.6
d. Current EPS:
EBIT
$8.00
Interest
1.40
EBT
$6.60
Tax
2.64
EAT and before preferred dividends
$3.96
Preferred dividends
Earnings available to C.S.
EPS
0.96
$3.00 (million)
$3.00
3.6 = %EPS/-5%
%EPS = -18%
New EPS = $3.00(1 - 0.18) = $2.46
13. Values in millions of dollars
a. VC = 0.65 ($40) = $26
DOL @ $40 = ($40 - $26)/($40 - $26 - $5)= 1.556
b. Interest expenses = (0.10 x $10) + (0.12 x $3) = $1.36
DFL = $9/[$9 - $1.36 - ($2.5/(1 - 0.35)] = 2.37
194  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
c. DCL = DOL x DFL = 3.69
Current EPS:
EBIT
$9.000
Interest
1.360
EBT
$7.640
Tax (@ 35%)
2.674
EAT and before preferred dividends
$4.966
Preferred dividends
Earnings available to C.S.
2.500
$2.466 (million)
EPS
$2.47
A sales decline to $38 is a 5 percent decline from $40
New EPS = $2.47 x (1 - (0.05 x 3.69)) = $2.01
Note: The use of the average tax rate in this solution assumes that this average rate does
not change with a change in sales and EBIT.
14. DCL = DOL x DFL
8.0 = 2.0 x DFL
DFL = 4.0 = %EPS/ +3%
%EPS = +12%
New EPS = $3.00 x 1.12 = $3.36
15. DOL = 2.5 = %EBIT/+5%
%EBIT = +12.5%
New EBIT = $450,000 x 1.125 = $506,250
Fixed financial charges = $200,000 + $60,000/(1 - 0.4) = $300,000
Therefore, EPS = $0 at an EBIT level of $300,000
z = ($300,000 - $506,250)/$300,000 = -0.69
From Table V, the probability of z<-0.69 24.51%
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  195
16. The probability that EPS will be less than $5 per share is equal to the probability that sales
will be less than $10,000,000:
z = ($10,000,000 - $11,000,000)/$500,000 = -2.0
p(z<-2.0) = 2.28% from Table V
17. Fixed financial charges to cover:
$1,000,000 + $600,000/(1 - 0.4) = $2,000,000
The probability of negative EPS is the probability of not covering fixed financial charges, or:
z = ($2,000,000 - $4,000,000)/$2,000,000 = -1.0
p(z<-1.0) = 15.87%
18. a. Emco Products
EPS (debt financing) = EPS (equity financing)
(EBIT - interest)(1 - tax rate)
(EBIT)(1 - tax rate)
=
(No. of common shares for debt
(No. of common shares for equity
alternative)
alternative)
[(EBIT - 5)(0.6)]/10 = [(EBIT)(0.6)]/15
9 EBIT - 45 = 6 EBIT
3 EBIT = 45
EBIT* = $15
b. Equity Financing:
EBIT = $10
EBIT = $15
EBIT = $25
EBIT
$10
$15
$25
I
0
0
0
EBT
10
15
25
T @ 40%
4
6
10
196  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
EAT
6
9
15
Shares Outstanding
15
15
15
EPS
$0.40
$0.60
$1.00
EBIT = $10
EBIT = $15
EBIT = $25
EBIT
$10
$15
$25
I
5
5
5
EBT
$5
$10
$20
T @ 40%
2
4
8
EAT
$3
$6
$12
Shares Outstanding
10
10
10
EPS
$0.30
$0.60
$1.20
Debt Financing:
Indifference point = $15 million
c. Indifference point moves to right, i.e., higher EBIT.
d. Indifference point moves to right, i.e., higher EBIT.
19. a Expansion:
Rock Island
Davenport
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  197
EBIT
$100
$100
I
32
8
EBT
$ 68
$ 92
T @ 40%
27.2
36.8
EAT
$ 40.8
$ 55.2
Shares outstanding
30
45
EPS
$1.36
$1.23
Rock Island
Davenport
EBIT
$ 60
$ 60
I
32
8
EBT
$ 28
$ 52
T @ 40%
11.2
20.8
EAT
$16.8
$31.2
Shares outstanding
30
45
EPS
$0.56
$0.69
Recession:
b. Rock Island is riskier because of its financial risk. The two stocks have identical business risk.
Rock Island would be expected to have a higher beta.
c. EPS (Rock Island) = EPS (Davenport)
[(EBIT - interest)(1 - T)]/No. of C.S. (Rock Island) =
[(EBIT - interest)(1 - T)]/No. of C.S. (Davenport)
198  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
[(EBIT - 32)(1 - .4)]/30 = [(EBIT - 8)(1- .4)]/45
EBIT* = $80 million
d. Price = (EPS)(P/E ratio)
Rock Island:
Price = (1.36)(9) = $12.24
Davenport:
Price = (1.23)(10) = $12.30
This example gives approximately equal stock prices for the two companies. Rock Island's
higher EPS is offset by its lower P/E ratio.
20. a. EPS (Plan 1) = EPS (Plan 2)
[(EBIT - 0)(1 - .4)]/2 = [(EBIT - 1.2)(1 - .4)]/1
EBIT* = $2.4 million
b.
Plan 1
Plan 2
EBIT
$6.0
$6.0
I
0
1.2
EBT
$6.0
$4.8
T @ 40%
2.4
1.92
EAT
$3.6
$2.88
Shares Outstanding
2.0
1.0
EPS
$1.80
$2.88
c. The factors the company should consider include the following:
1. The plan's effect on the company's stock price (difficult to determine in practice).
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  199
2. The capital structure of the parent company.
3. The probability distribution of expected EBIT.
d. Adopt plan 2 if the company can be reasonably sure that EBIT will not drop too much in a
recession. Otherwise, plan 1 appears better. (See Parts e and f below ).
e. T.I.E. = (EBIT/I) = (6.0/1.2) = 5 times
Note: This calculation assumes no short-term debt, either permanent or seasonal.
f. Required EBIT level = (Interest)(Required T.I.E.)
= (1.2)(3.5)
= $4.2 million
Therefore, EBIT could drop by $6.0 - $4.2 = $1.8 million, and the company would still be in
compliance with the loan agreement.
Note: In practice, the lenders also likely would require the parent company to guarantee the
loan.
g. z = (0 - $6,000,000)/$3,000,000 = -2.0
From Table V, the probability of a value greater than 2.0 standard deviations to the left of the
mean is 2.28%, i.e., small.
21. a. (EBIT - 60,000)(1 - .4) = (EBIT - 60,000 - 66,000)(1 - .4)
100,000 + 150,000
100,000
EBIT* = $170,000
b. Compute the probability that the actual EBIT will be greater than $170,000.
z = ($170,000 - $240,000)/$50,000 = -1.4
From Table V, the probability of a value less than 1.4 standard deviations to the left of the
mean is 8.08%. This is the probability that the equity alternative is superior to the debt
alternative. Thus, the probability that the debt alternative is superior is 91.92% (1.0 - .0808).
200  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
c. The probability of negative earnings is the probability that actual EBIT will fall below the loss
level ($126,000).
z = ($126,000 - $240,000)/$50,000 = -2.28
The probability of EBIT falling below the $126,000 loss level is 1.13% from Table V.
22. a.
[(EBIT - 46.2)(0.6)]/30 = [(EBIT - 37.5)(0.6)]/33
EBIT* = $133.2 million
b. The debt financing alternative should be selected because its average cost is 14.5% pretax,
compared to the 16% after-tax cost of the preferred stock alternative. In other words, the debt
financing alternative results in higher EPS values than the preferred stock financing
alternative at all EBIT levels. The two functions do not cross each other, and, as a result, no
indifference point exists.
23. a. The probability that the equity financing option will result in a higher EPS is equal to the
probability that the EBIT level will be less than $4.0 million. The probability that EBIT
will be less that $4.0 million is computed, as follows:
z = (4.0 - 4.5)/0.6 = -0.83
From Table V, the probability of a value less than 0.83 standard deviations to the left of the
mean is 20.33%.
b. The probability of losing money is the probability that the actual EBIT will fall below the $3
million level.
z = ($3.0 - $4.5)/$0.6 = -2.50
From Table V, the probability of EBIT falling below the $3.0
i.e., quite low.
24. a. [(EBIT - 6.3)(0.6)]/10 = [(EBIT - 5)(0.6)]/11
million level is 0.62%,
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  201
EBIT* = $19.3 million
b. [(EBIT - 5)(0.6) - 1.4]/10 = [(EBIT - 5)(0.6)]/11
EBIT* = $30.67 million
c. The debt financing alternative results in higher EPS values than the preferred stock alternative
for all EBIT levels. Thus, the two functions do not cross each other, and no indifference point
exists.
25. a. The probability that the equity financing option will result in a higher EPS is equal to the
probability that the EBIT level will be less than $500,000. The probability that EBIT will
be less than $500,000 is computed, as follows:
z = ($500,000 - $620,000)/$190,000 = -0.63
From Table V, the probability of a value less than 0.63 standard deviations to the left of the
mean is 26.43%. Thus, the probability that the equity alternative will be superior to the debt
alternative is about 26%.
b. The probability that the firm will incur losses is the probability that the actual EBIT will fall
below the $200,000 level.
z = ($200,000 - $620,000)/$190,000 = -2.21
From Table V, the probability of EBIT falling below the
$200,000 level is 1.36%.
26. a. Equity Alternative Debt Alternative
(EBIT - 1.2 - 2.8)(1-0.4) / 4.5 = (EBIT - 1.2 - 2.8 - 1.5)(1-0.4) / 4.0
EBIT* = $17.5 million
b. The probability that Alternative II will result in higher EPS than Alternative I is the
probability that EBIT will be above the indifference point, or:
202  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
z = (17.5 - 20)/ 5 = -0.5
p(z < - 0.5 ) = 30.85%
Hence the probability that Alternative II will yield higher EPS than Alternative I equals: 100%
- 30.85% = 69.15%
27. a
CB0 = $50 million; FCFR = $70 million; __= $60 million
CBR = $50 million + $70 million = $120 million
z = ($0 - $120) / $60 = -2.0
From Table V: p(z < - 2.0 ) = 2.28%
b. CBR = $50 million + $70 million - $60 million = $60 million
z = ($0 - $60) / $60 = -1.0
From Table V: p(z < - 1.0 ) = 15.87%
The expansion should not be undertaken because the risk of running out of cash (15.87%)
exceeds the level of risk the firm is willing to assume (10%).
28. a. EBIT = $8.0 million; _ = $5 million
z = ($1.5 - $8.0)/$5 = -1.30
From Table V: p(z < - 1.30) = 0.0968 or 9.68%
b. 1 - p(z < -1.30) = 1 - 0.0968 = 0.9032 or 90.32%
29. a
CB0 = $150 million; FCFR = $200 million; __= $200 million
CBR = $150 million + $200 million = $350 million
z = ($0 - $350)/$200 = -1.75
From Table V, p(z < - 1.75) = 4.01%
b. CBR = $150 million + $200 million - $50 million = $300 million
z = ($0 - $300)/$200 = -1.50
From Table V, p(z < - 1.50) = 6.68%
CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE  203
c. From Table V, p(z < zo) = 5.0% for zo = -1.65
-1.65 = (0 - CBR)/$200
CBR = $330 million
$330 million = $150 million + ($200 million - x)
x = $20 million
The company can incur additional fixed financial charges of $20
million.
30. a. [(EBIT - $26.0 - $30.0)(1 - 0.4) - $2.0]/10
= [(EBIT - $26.0)(1 - 0.4) - 2.0]/14
EBIT* = $134.33
b. z = ($134.33 - $150)/$20 = -0.78
From Table V: p(z < -0.78) = 21.77%
31. Debt = 0.6 ($20 million) = $12 million
Preferred = 0.1($20 million) = $2 million
Current interest = $12 million x 0.09 = $1.08 million
Current preferred dividends = $2 million x 0.12 = $0.24 million
Tax-adjusted preferred dividends = $0.24 million/(1 - 0.4) = $0.4 million
Current loss level = $1.08 million + $0.4 million = $1.48 million
z = ($1.48 million - $1.7 million)/$0.2 million = -1.1 standard deviations
From Table V, the probability of a value less than -1.1 standard deviations from the mean is about
13.57%.
New loss level = $1.48 million + $0.1 million = $1.58 million
z = ($1.58 million - $1.7 million)/$0.2 million = -0.6 standard deviations.
From Table V, the probability of a value less than -0.6 standard deviations from the mean is about
27.43%.
204  CHAPTER 13/CAPITAL STRUCTURE MANAGEMENT IN PRACTICE
Hence the increase in the probability of incurring a
loss is 27.43% - 13.57 % = 13.86%
32. a. Equity Alternative Debt Alternative
[(EBIT - $18)(1 - 0.4) - $5] / (4 + 1) = [(EBIT - $18 - $9.5)(1 - 0.4) - $5]/ 4
EBIT* = $73.83 million
EPS @ EBIT* = $5.70
b. z = ($73.83 million - $100 million) / $20 million = -1.31
From Table V: p(z < -1.31) = 9.51%
33. a z = (0 – 1.5) / 1 = -1.5
p (z < -1.5) = 6.68%
c. Interest = 0.10 x $ 10 million = $1 million
Loss level = $1 million
z = (1 – 1.5) / 1 = -0.5
p (z < -0.5) = 30.85%
34. a. [(EBIT – 0)(1 – 0.4)] / 600,000 = [(EBIT – 800,000)(1 – 0.4)] / 200,000
EBIT* = $1,200,000
b. z = (1.2 – 1.0) / 0.4 = 0.5
p ( z > 0.5) = 30.85%
p (unfavorable leverage) = 100% - 30,85% = 69.15%