Managerial Finance Problem Set Solutions Capital Structure and Leverage




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Managerial Finance – Problem Set Solutions – Capital Structure and Leverage

1)

Use of debt in financing Answer: a



2)

Financial leverage Answer: b

3)

Operating and financial leverage Answer: a



If one firm's sales and earnings were more volatile than those of the other, it could have greater EPS variability in spite of identical financial and operating leverage.
4)

Target debt ratio Answer: a


5)

Target capital structure Answer: e


6)

Operating leverage Answer: e

More operating leverage generally means a greater use of automation, which means more fixed assets. If fixed assets increase, but sales do not, then the fixed asset turnover (S/FA) will decline.
7)

Leverage and capital structure Answer: c


8)

Debt's effect on ROE Answer: a

Assets $200,000

D/A 65%


EBIT $25,000

Interest rate 8%

Tax rate 40%
EBIT $25,000

−Interest 10,400

EBT $14,600

−Tax 5,840

NI $ 8,760
ROE = NI avail to common/Common equity

ROE = 12.51%


9)

Calculating the unlevered beta Answer: e



bL 1.10

D/A 0.40


Tax rate 40%

D/E = (D/A) / (1-D/A) 0.67

bU = bL/(1 + (D/E) × (1 − T)) 0.79

10)


Differences in ROE Answer: c

Applicable to Both Firms Firm HD's Data Firm LD's Data

Assets $200 Debt ratio 50% Debt ratio 30%

EBIT $40 Interest rate 12% Interest rate 10%

Tax rate 35%


Debt = $100.0 $60.0

Interest = I = $12.0 $6.0

Taxable income = EBIT − I = $28.0 $34.0

NI = (Taxable Income)(1 − T) = $18.2 $22.1

Equity = A − Debt = $100.0 $140.0

ROE = NI/Equity = 18.20% 15.79%

Difference in ROEs = 2.41%

11)


Recapitalization Answer: b

Shares outstanding 200,000 Interest rate 10%

EBIT $2,000,000 Risk-free rate 6.5%

Dividend payout ratio 100% Market risk premium 5.0%

Tax rate 40% Beta - before recap 0.90

Bonds issued = stock repurchased $5,000,000 Beta - after recap 1.10


Before the recapitalization

rs = rRF + bold(RPM) 11.00%

DPS = EPS = (EBIT)(1 – T)/Shares $6.00

P0 = DPS/rs $54.55

Shares repurchased = Bonds issued/P0 91,667
After the recapitalization

rs = rRF + bnew(RPM) 12.00%

DPS = EPS = (EBIT − rd × Bonds)(1 – T)/Shares $8.31

P0 = DPS/rs $69.23


12)

MM models Answer: b


13)

Miller model Answer: b

14)

MM and Miller Answer: d


15)

MM with tax Answer: c

EBIT: $100,000 rd: 12% Tc: 30%

Debt: $500,000 rsU: 16%


VU = EBIT(1 – T)/rsU = $100,000(0.7)/0.16 = $437,500

VL = VU + TD = $437,500 + 0.3($500,000) = $587,500


16)

MM with tax Answer: e

First, note that the leveraged value of the firm is $587,500 as found in Problem 23. Note also that the firm has $500,000 of debt. Therefore, the value of its equity must be $87,500. Using these data, we find the leveraged cost of equity as follows:
rsL = rsU + (rsU – rd)(1 – T)(D/S) = 16% + (16% – 12%)(0.7)($500,000/$87,500) = 32.0%
17)

Miller model Answer: e

Tc: 30% Gain from leverage: $126,667

Ts: 20% Debt: $500,000


[1 – (1 – Tc)(1 – Ts)/(1 – Td)]D = $126,667 (1 − Tc) = 0.70

[1 – (0.7)(0.8)/X]$500,000 = $126,667 (1 − Ts) = 0.80

1 – 0.56/X = 0.25333 (1 − Tc) × (1 − Ts) = 0.56

0.56/X = 0.74667 Gain/Debt = 0.25333

X = 0.75000 Gain/Debt − 1 = -0.74667

1 − Td = 0.75000 X = -0.56/-0.74666 = 0.75000



Td = 25.00% X = 1 − Td


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