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Answers to Warm-Up Exercises
E13-1. Breakeven analysis
Answer: The operating breakeven point is the level of sales at which all fixed and variable operating
costs are covered and EBIT is equal to $0.
Q FC ( P – VC )
Q $12,500 ($25 $10) 833.33, or 834 units
E13-2. Changing costs and the operating breakeven point
Answer: Calculate the breakeven point for the current process and the breakeven point for the new
process, and compare the two.
Current breakeven: Q 1 $15,000 ($6.00 $2.50) 4,286 boxes
New breakeven: Q 2 $16,500 ($6.50 $2.50) 4,125 boxes
If Great Fish Taco Corporation makes the investment, it can lower its breakeven point by
161 boxes.
E13-3. Risk-adjusted discount rates
Answer: Use Equation 13.5 to find the DOL at 15,000 units.
Q
P
VC
FC
DOL at 15,000 units 1. 15,000 ($20 $12) $30,000 $90,
E13-4. DFL
Answer: Substitute EBIT $20,000, I $3,000, PD $4,000, and the tax rate ( T 0.38) into
Equation 12.7.
DFL at $20,000 EBIT $20,000 $3,000 [$4,000 (1 (1 0.38)]
E13-5. Net operating profits after taxes (NOPAT)
Answer: Calculate EBIT, then NOPAT and the weighted average cost of capital (WACC) for Cobalt
Industries.
EBIT (150,000 $10) $250,000 (150,000 $5) $500,
NOPAT EBIT (1 T ) $500,000 (1 0.38) $310,
NOPAT $310,
Value of the firm $3,647, ra 0.
Solutions to Problems
P13-1. Breakeven point—algebraic
LG1; Basic
FC
Q
P VC
Q
P13-2. Breakeven comparisons—algebraic
LG 1; Basic
a. ( )
FC
Q
P VC
Firm F:
4,000 units $18.00 $6.
Q
Firm G:
4,000 units $21.00 $13.
Q
Firm H:
5,000 units $30.00 $12.
Q
b. From least risky to most risky: F and G are of equal risk, then H. It is important to recognize
that operating leverage is only one measure of risk.
P13-3. Breakeven point—algebraic and graphical
LG 1; Intermediate
a. Q FC ( P VC )
Q $473,000 ($129 $86)
Q 11,000 units
b.
Variable costs ($6 1,500) 9,
EBIT $2,
d.
EBIT $4,000 $4,000 $8,
4,000 units $8 $6 $
FC
Q
P VC
e. One alternative is to price the units differently based on the variable cost of the unit. Those
more costly to produce will have higher prices than the less expensive production models. If
they wish to maintain the same price for all units they may need to reduce the selection from
the 15 types currently available to a smaller number that includes only those that have an
average variable cost below $5.33 ($8 $4,000/1,500 units).
P13-8. EBIT sensitivity
LG 2; Intermediate
a. and b.
8,000 Units 10,000 Units 12,000 Units
Sales $72,000 $90,000 $108,
Less: Variable costs 40,000 50,000 60,
Less: Fixed costs 20,000 20,000 20,
EBIT $12,000 $20,000 $ 28,
c.
Unit Sales 8,000 10,000 12,
Percentage (^) (8,000 10,000) 10,000 (12,000 10,000) 10,
Change in
unit sales 20% 0 20%
Percentage (12,000 20,000) 20,000 (28,000 20,000) 20,
Change in
EBIT 40% 0 40%
d. EBIT is more sensitive to changing sales levels; it increases/decreases twice as much as
sales.
P13-9. DOL
LG 2; Intermediate
a.
8,000 units ( ) $63.50 $16.
FC
Q
P VC
9,000 Units 10,000 Units 11,000 Units
b.
Sales $571,500 $635,000 $698,
Less: Variable costs 144,000 160,000 176,
Less: Fixed costs 380,000 380,000 380,
EBIT $ 47,500 $ 95,000 $142,
c.
Change in unit sales (^) 1,000 0 1,
% change in sales 1,000 10,
10%
Change in EBIT (^) $47,500 0 $47,
% Change in EBIT (^) $47,500 95,000 = 50% 0 $47,500 95,000 =
50%
d.
% change in EBIT
% change in sales
P13-11. EPS calculations
LG 2; Intermediate
(a) (b) (c)
EBIT $24,600 $30,600 $35,
Less: Interest 9,600 9,600 9,
Net profits before taxes $15,000 $21,000 $25,
Less: Taxes 6,000 8,400 10,
Net profit after taxes $ 9,000 $12,600 $15,
Less: Preferred dividends 7,500 7,500 7,
Earnings available to
common shareholders
EPS (4,000 shares) $ 0.375 $ 1.275 $ 1.
P13-12. Degree of financial leverage
LG 2; Intermediate
a.
EBIT $80,000 $120,
Less: Interest 40,000 40,
Net profits before taxes $40,000 $ 80,
Less: Taxes (40%) 16,000 32,
Net profit after taxes $24,000 $ 48,
EPS (2,000 shares) $ 12.00 $ 24.
b.
EBIT
DFL
EBIT
I PD
T
DFL 2
[$80,000 $40,000 0]
c.
EBIT $80,000 $120,
Less: Interest 16,000 16,
Net profits before taxes $64,000 $104,
Less: Taxes (40%) 25,600 41,
Net profit after taxes $38,400 $ 62,
EPS (3,000 shares) $ 12.80 $ 20.
DFL 1.
[$80,000 $16,000 0]
P13-13. Personal finance: Financial leverage
LG 2; Challenge
a.
Current DFL Initial Values Future Value
Percentage
Change
Available for making loan payment
Less: Loan payments
Available after loan payments
DFL 15% ÷ 10% 1.
Proposed DFL Initial Values Future Value
Percentage
Change
Available for making loan payment
Less: Loan payments
Available after loan payments
DFL 18.2% ÷ 10% 1.
b. Based on his calculations, the amount that Max will have available after loan payments with
his current debt changes by 1.5% for every 1% change in the amount he will have available
for making the loan payment. This is less responsive and therefore less risky than the 1.82%
change in the amount available after making loan payments with the proposed $350 in monthly
debt payments. Although it appears that Max can afford the additional loan payments, he
must decide if, given the variability of Max’s income, he would feel comfortable with the
increased financial leverage and risk.
P13-14. DFL and graphic display of financing plans
LG 2, 5; Challenge
a.
EBIT
DFL
EBIT
I PD
T
DFL 1.
[$67,500 $22,500 0]
b.
d.
* [^ (^ )]
DTL
Q P VC
PD
Q P VC FC I
T
[400,000 ($1.00 $0.84)]
DTL
DTL 2.
[$64,000 $28,000 $9,333] $26,
DTL DOL DFL
DTL 1.78 1.35 2.
The two formulas give the same result.
Degree of total leverage.
P13-16. Integrative—leverage and risk
LG 2; Intermediate
a.
[100,000 ($2.00 $1.70)] $30,
DOL 1.
[100,000 ($2.00 $1.70)] $6,000 $24,
R
DFL 1.
[$24,000 $10,000]
R
DTL R 1.25 1.71 2.
b.
[100,000 ($2.50 $1.00)] $150,
DOL 1.
[100,000 ($2.50 $1.00)] $62,500 $87,
W
DFL 1.
[$87,500 $17,500]
W
DTL R 1.71 1.25 2.
c. Firm R has less operating (business) risk but more financial risk than Firm W.
d. Two firms with differing operating and financial structures may be equally leveraged. Since
total leverage is the product of operating and financial leverage, each firm may structure
itself differently and still have the same amount of total risk.
P13-17. 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,
Less:
Fixed costs 50,
Variable costs ($3.50 30,000) 105,
EBIT 25,
Less interest expense 13,
EBT 12,
Less taxes (40%) 4,
Net profits $ 7,
c.
[ ( )]
DOL
[ ( )]
Q P VC
Q P VC FC
[30,000 ($6.00 $3.50)] $75,
DOL 3.
[30,000 ($6.00 $3.50)] $50,000 $25,
d.
EBIT
DFL
EBIT
I PD
T
DFL 75.
$25,000 $13,000 [$7,000 (1 0.6)] $333.
e. DTL DOL DFL 3 75.00 225 (or 22,500%)
f.
Change in sales 50% 30,
Percentage change in EBIT % change in sales DOL 50% 3 150%
New EBIT $25,000 ($25,000 150%) $62,
Percentage change in earnings available for common % changesales DTL
50% 225% 11,250%
New earnings available for common $200 ($200 11,250%) $$22,700,
P13-18. Capital structures
LG 3; Intermediate
a. Monthly mortgage payment ÷ Monthly gross income = $1,100 ÷ $4,500 = 24.44%
Kirsten’s ratio is less than the bank maximum of 28%.
b. Total monthly installment payment ÷ Monthly gross income
($375 + $1,100) ÷ $4,500 32.8%.
Kirsten’s ratio is less than the bank maximum of 37.0%. Since 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.
P13-19. Various capital structures
LG 3; Basic
Debt Ratio Debt Equity
Theoretically, the debt ratio cannot exceed 100%. Practically, few creditors would extend loans
to companies with exceedingly high debt ratios ( 70%).
Expected EPS ( $0.60 0.20) ($0.60 0.60) ($1.80 0.20) $0.
2 2 2 EPS [( $0.60 $0.60) 0.20] [($0.60 $0.60) 0.60] [($1.80 $0.60) 0.20]
EPS ($1.44 0.20) 0 ($1.44 0.20)
EPS $0.576 $0.
EPS
CV
d. Summary statistics
With Debt All Equity
Expected EPS $0.180 $0.
EPS $1.138^ $0.
CV EPS 6.320 1.
Including debt in Tower Interiors’ capital structure results in a lower expected EPS, a higher
standard deviation, and a much higher coefficient of variation than the all-equity structure.
Eliminating debt from the firm’s capital structure greatly reduces financial risk, which is
measured by the coefficient of variation.
P13-21. 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.
EPS EPS EPS
CV
Debt Ratio CV
P13-22. EBIT-EPS and capital structure
LG 5; Intermediate
a. Using $50,000 and $60,000 EBIT:
Structure A Structure B
EBIT $50,000 $60,000 $50,000 $60,
Less: Interest 16,000 16,000 34,000 34,
Net profits before taxes $34,000 $44,000 $16,000 $26,
Less: Taxes 13,600 17,600 6,400 10,
Net profit after taxes $20,400 $26,400 $ 9,600 $15,
EPS (4,000 shares) $ 5.10 $ 6.
EPS (2,000 shares) $ 4.80 $ 7.
Financial breakeven points:
Structure A Structure B
b.
P13-24. Integrative—optimal capital structure
LG 3, 4, 6; Intermediate
a.
Debt Ratio 0% 15% 30% 45% 60%
EBIT $2,000,000 $2,000,000 $2,000,000 $2,000,000 $2,000,
Less: Interest 0 120,000 270,000 540,000 900,
EBT $2,000,000 $1,880,000 1,730,000 $1,460,000 $1,100,
Taxes @40% 800,000 752,000 692,000 584,000 440,
Net profit $1,200,000 $1,128,000 $1,038,000 $ 876,000 $ 660,
Less: Preferred
dividends 200,000 200,000 200,000 200,000 200,
Profits available to
common stock $1,000,000 $ 928,000 $ 838,000 $ 676,000 $ 460,
shares outstanding 200,000 170,000 140,000 110,000 80,
EPS $ 5.00 $ 5.46 $ 5.99 $ 6.15 $ 5.
b. 0
EPS
s
P
r
Debt: 0% Debt: 15%
0
P 0
P
Debt: 30% Debt: 45%
0
P 0
P
Debt: 60%
0
P
c. The optimal capital structure would be 30% debt and 70% equity because this is the
debt/equity mix that maximizes the price of the common stock.
P13-25. Integrative—Optimal capital structures
LG 3, 4, 6; Challenge
a. 0% debt ratio
Probability
Sales $200,000 $300,000 $400,
Less: Variable costs (40%) 80,000 120,000 160,
Less: Fixed costs 100,000 100,000 100,
EBIT $ 20,000 $ 80,000 $140,
Less: Interest 0 0 0
Earnings before taxes $ 20,000 $ 80,000 $140,
Less: Taxes 8,000 32,000 56,
Earnings after taxes $ 12,000 $ 48,000 $ 84,
EPS (25,000 shares) $ 0.48 $ 1.92 $ 3.
20% debt ratio:
Total capital $250,000 (100% equity 25,000 shares $10 book value)
Amount of debt 20% $250,000 $50,
Amount of equity 80% 250,000 $200,
Number of shares $200,000 $10 book value 20,000 shares
Probability
EBIT $20,000 $80,000 $140,
Less: Interest 5,000 5,000 5,
Earnings before taxes $15,000 $75,000 $135,
Less: Taxes 6,000 30,000 54,
Earnings after taxes $ 9,000 $45,000 $ 81,
EPS (20,000 shares) $ 0.45 $ 2.25 $ 4.
40% debt ratio:
Amount of debt 40% $250,000 total debt capital $100,
Number of shares $150,000 equity $10 book value 15,000 shares
Probability
EBIT $20,000 $80,000 $140,
Less: Interest 12,000 12,000 12,
Earnings before taxes $ 8,000 $68,000 $128,
Less: Taxes 3,200 27,200 51,
Earnings after taxes $ 4,800 $40,800 $ 76,
EPS (15,000 shares) $ 0.32 $ 2.72 $ 5.
60% debt ratio:
Amount of debt 60% $250,000 total debt capital $150,
Number of shares $100,000 equity $10 book value 10,000 shares
Probability
EBIT $20,000 $80,000 $140,
Less: Interest 21,000 21,000 21,
Earnings before taxes $ (1,000) $59,000 $119,
Less: Taxes (400) 23,600 47,
Earnings after taxes $ (600) $35,400 $ 71,
EPS (10,000 shares) $ (0.06) $ 3.54 $ 7.
- 60 40,000,000 24,000,000 16,000,000 640,
b.
% Debt $ Total Debt Before Tax Cost of Debt, kd $ Interest Expense
c.
Debt
$ Interest
Expense EBT
Taxes
@40% Net Income
# of
Shares EPS
d.
% Debt EPS rS P 0
e. The optimal proportion of debt would be 30% with equity being 70%. This mix will maximize
the price per share of the firm’s common stock and thus maximize shareholders’ wealth.
Beyond the 30% level, the cost of capital increases to the point that it offsets the gain from
the lower-costing debt financing.
P13-27. Integrative—optimal capital structure
LG 3, 4, 5, 6; Challenge
a.
Probability
Sales $600,000 $900,000 $1,200,
Less: Variable costs (40%) 240,000 360,000 480,
Less: Fixed costs 300,000 300,000 300,
