Chapter 12 CFIN6
Chapter 12 Solutions
12-1 Sales $200,000
Variable operating costs (60%) (120,000)
Fixed operating costs ( 48,000)
12-2 Total assets = $6,000,000 Shares of stock = 80,000
EBIT = $700,000 Marginal tax rate = T = 40%
70% debt 40% debt
ROE 6.5% 8.1%
Net income
EPS 80,000 shares
=
Net income
ROE Common equity
=
Amount of debt = Total assets x Debt/Assets ratio:
70% Debt: Total debt = $6,000,000(0.7) = $4,200,000; Equity = $6,000,000(0.3) = $1,800,000
Chapter 12 CFIN6
12-3 Both firms have the following characteristics:
Total assets = $200,000 Shares of stock = 5,000
EBIT = $40,000 Marginal tax rate = 40%
ROE 17.0% 21.0%
Net income
EPS 5,000 shares
=
Net income
ROE Common equity
=
Amount of debt = Total assets x Debt/Assets ratio:
Firm AB: Total debt = $200,000(0.4) = $80,000; Equity = $200,000(0.6) = $120,000
Firm AB’s capital structure is better based on EPS, because EPSAB > EPSYZ. But, ROEAB < ROEYZ.
12-4 The following information is given:
Firm LM Firm QR
Total assets $800,000 $400,000
Shares of stock 15,000 25,000
Chapter 12 CFIN6
Firm LM Firm QR
Net income
EPS # shares
=
Net income
ROE Common equity
=
Amount of debt = Total assets x Debt/Assets ratio:
Firm LM’s capital structure is better based on EPS, because EPSLM > EPSQR. But, ROELM < ROEQR.
Firm LM’s EPS is higher primarily because it has fewer shares of stock outstanding than Firm QR. If
both firms had the same number of shares of stock outstanding, then based on both EPS and ROE, the
capital structure of Firm QR would clearly be better than the capital structure of Firm LM.
12-5 E(EPS) = 0.2($4.50) + 0.6($1.50) + 0.2(-$1.80) = $1.44
Variance = 2 = 0.2($4.50 – $1.44)2 + 0.6($1.50 – $1.44)2 + 0.2(-$1.80 – $1.44)2 = 3.9744
12-6 Firm 1:
E(EPS1) = 0.3($2.00) + 0.6($1.30) + 0.1(-$1.20) = $1.26
Variance =
2
1
= 0.3($2.00 – $1.26)2 + 0.6($1.30 – $1.26)2 + 0.1(-$1.20 – $1.26)2 = 0.7704
Chapter 12 CFIN6
1 =
0.7704
= $0.88
CV1 = $0.88/$1.26 = 0.70
12-7 Given:
Assets = $5,000,000
Marginal tax rate = 40%
Debt/Assets = 20%:
0.2 0.5 0.3
EBIT $1,200,000 $800,000 $500,000
Interest ( 60,000) ( 60,000) ( 60,000)
EBT $1,140,000 $740,000 $440,000
Taxes (40%) (456,000) (296,000) (176,0000)
Net income $684,000 $444,000 $264,000
Chapter 12 CFIN6
CV = $0.49/$1.46 = 0.34
Debt/Assets = 50%:
0.2 0.5 0.3
EBIT $1,200,000 $800,000 $500,000
EPS $2.85 $1.65 $0.75
E(EPS) $1.62
Standard deviation, $0.73
Coefficient of variation, CV 0.45
=
0.5301
= $0.73
CV = $0.73/$1.62 = 0.45
12-8 The capital structure that contains 40 percent debt ($20 million) provides the highest market price per
share. As a result, this is the optimal capital structure.
12-9 The capital structure with 30 percent debt is optimal because it provides the highest stock price.
Because 30 percent debt is the optimal capital structure, it is the capital structure that results in the
lowest WACC.
Chapter 12 CFIN6
= = =
Gross profit $45,000
DTL 4.5
Earnings before taxes $10,000
12–11 If they turn out to be $940,500, sales will be 4.5 percent higher than forecast:
Actual Forecasted
Forecasted
Sales Sales $313,500 $300,000
% Difference 0.045 4.5%
Sales $300,000
−−
= = = =
12–12
% in NOI % in EBIT
DOL % in sales % in sales
==
0.12 1.5
0.08
−
==
−
Check:
12–13 DOL = 2.5
DFL = 3.0
If EBIT is 5 percent greater than expected, the effect on EPS will be 15 percent (= 3.0 x 5%) higher than
expected:
12–14 DOL = 3.0
DFL = 2.0
DTL = 3.0 x 2.0 = 6.0
Chapter 12 CFIN6
12–15 DFL = 4.0
= = =
% in EPS 36%
DTL 6.0
% in sales 6%
12–16 EBIT = $750,000
Interest = $250,000
Common dividends = $320,000
Marginal tax rate = 40%
12–17 DOL = 5.0
DFL = 2.0
DTL = DOL x DFL = 5.0 x 2.0 = 10.0
12–18 a.
−
= = = =
−−
Gross profit $560,000 $560,000(0.75) $140,000
DOL 2.8
NOI $560,000 $560,000(0.75) $90,000 $50,000
b. If sales turn out to be $588,000 rather than $560,000, the percent increase from the forecasted
amount is:
Chapter 12 CFIN6
12–19 At sales = $900,000:
DOL = 3.0
Forecasted EPS = $2.00
−
= =
$2.60 $2.00
% in EPS= 0.3 30.0%
$2.00
% in EPS 30%
6.0 = 3.0 x DFL
DFL= 6.0/3.0 = 2.0
12–20 The following table summarizes the degrees of leverage for EAR:
Company DOL DFL DTL
Acme 1.5 6.0 9.0