CHAPTER 13
LEVERAGE AND CAPITAL STRUCTURE
Answers to Concepts Review and Critical Thinking Questions
1. Business risk is the equity risk arising from the nature of the firm’s operating activity, and is directly
related to the systematic risk of the firm’s assets. Financial risk is the equity risk that is due entirely
to the firm’s chosen capital structure. As financial leverage, or the use of debt financing, increases,
so does financial risk and hence the overall risk of the equity. Thus, Firm B could have a higher cost
of equity if it uses greater leverage.
2.
No, it doesn’t follow. While it is true that the equity and debt costs are rising, the key thing to
remember is that the cost of debt is still less than the cost of equity. Since we are using more and
more debt, the WACC does not necessarily rise.
3. Because many relevant factors such as bankruptcy costs, tax asymmetries, and agency costs cannot
easily be identified or quantified, it’s practically impossible to determine the precise debt/equity
ratio that maximizes the value of the firm. However, if the firm’s cost of new debt suddenly
becomes much more expensive, it’s probably true that the firm is too highly leveraged.
4.
The more capital intensive industries, such as airlines, cable television, and electric utilities, tend to
use greater financial leverage. Also, industries with less predictable future earnings, such computers
or drugs, tend to use less. Such industries also have a higher concentration of growth and startup
firms. Overall, the general tendency is for firms with identifiable, tangible assets and relatively more
predictable future earnings to use more debt financing. These are typically the firms with the
greatest need for external financing and the greatest likelihood of benefiting from the interest tax
shelter.
5.
It’s called leverage (or “gearing” in the UK) because it magnifies gains or losses.
6.
Homemade leverage refers to the use of borrowing on the personal level as opposed to the corporate
level.
7.
One answer is that the right to file for bankruptcy is a valuable asset, and the financial manager acts
in shareholders’ best interest by managing this asset in ways that maximize its value. To the extent
that a bankruptcy filing prevents “a race to the courthouse steps,” it would seem to be a reasonable
alternative to complicated and expensive litigation.
8.
As in the previous question, it could be argued that using bankruptcy laws as a sword may simply be
the best use of the asset. Creditors are aware at the time a loan is made of the possibility of
bankruptcy, and the interest charged incorporates this possibility.
9.
One side is that Continental was going to go bankrupt because its costs made it uncompetitive. The
bankruptcy filing enabled Continental to restructure and keep flying. The other side is that
Continental abused the bankruptcy code. Rather than renegotiate labor agreements, Continental
simply abrogated them to the detriment of its employees. It is important thing to keep in mind that
the bankruptcy code is a creation of law, not economics. A strong argument can always be made that
making the best use of the bankruptcy code is no different from, for example, minimizing taxes by
making best use of the tax code. Indeed, a strong case can be made that it is the financial manager’s
duty to do so. As the case of Continental illustrates, the code can be changed if socially undesirable
outcomes are a problem.
10. As with any management decision, the goal is to maximize the value of shareholder equity. To
accomplish this with respect to the capital structure decision, management attempts to choose the
capital structure with the lowest cost of capital.
Solutions to Questions and Problems
Basic
1.
2.
a.
EBIT
Interest
NI
EPS
EPS%
$4,000
0
$4,000
$1.00
– 60
b.
MV $80,000/4,000 shares = $20 per share; $35,000/$20 = 1,750 shares bought back
EBIT
$4,000
$10,000
$13,000
Interest
1,750
1,750
1,750
NI
$2,250
$8,250
$11,250
EPS
$1.00
$3.67
$5.00
– 72.8
–––
+ 36.2
EPS%
a.
EBIT
Interest
EBT
Taxes
NI
EPS
EPS%
b.
MV $80,000/4,000 shares = $20 per share; $35,000/$20 = 1,750 shares bought back
EBIT
$4,000
$10,000
$13,000
Interest
1,750
1,750
1,750
EBT
2,250
8,250
11,250
Taxes
787
2,887
3,937
NI
$1,463
$ 5,363
$ 7,313
EPS
$0.65
$2.38
$3.25
–
72.7
–––
+
36.6
EPS%
$4,000
0
4,000
1,400
$2,600
$0.65
– 60.1
$10,000
0
$10,000
$2.50
–––
$10,000
0
10,000
3,500
$ 6,500
$1.63
–––
$13,000
0
$13,000
$3.25
+ 30
$13,000
0
13,000
4,550
$ 8,450
$2.11
+ 29.4
3.
a.
b.
c.
4.
a.
b.
c.
market-to-book ratio = 1.0, so TE = MV = $80,000; ROE = NI/$80,000
ROE
.05
.125
.1625
– 60
–––
+ 30
ROE%
now, TE = $80,000 – 35,000 = $45,000; ROE = NI/$45,000
ROE
.05
.183
.25
–
72.70
–––
+
36.6
ROE%
No debt
ROE
.0325
.0813
.1056
– 60
–––
+ 30
ROE%
With debt
ROE
.0325
.1192
.1625
– 72.7
–––
+ 36.3
ROE%
Plan I:
NI = $600K ;
EPS = $600K/400K shares = $1.50
Plan II:
NI = $600K – .10($5M) = $100K;
EPS = $100K/200K shares = $0.50
Plan I has the higher EPS when EBIT is $600,000.
Plan I:
NI = $5.5M;
EPS = $5.5M/400K shares = $13.75
Plan II:
NI = $5.5M – .10($5M) = $5.0M;
EPS = $5.0M/200K shares = $25.00
Plan II has the higher EPS when EBIT is $2,500,000.
EBIT/400K = [EBIT – .10($5M)]/200K; EBIT = $1,000,000
5.
P = $10M/400K shares bought with debt = $25 per share
V1 = $25(400K shares) = $10M; V2 = $25(200K shares) + $5M debt = $10M
6.
a.
b.
c.
d.
I
II
all-equity
EBIT
$12,000
$12,000
$12,000
Interest
3,080
1,540
0
NI
$ 8,920
$10,460
$12,000
EPS
$5.58
$5.81
$6.00
The all-equity plan has the highest EPS; Plan I has the lowest EPS.
Plan I vs. all-equity: EBIT/2,000 = [EBIT – .11($28,000)]/1,600; EBIT = $15,400
Plan II vs. all-equity: EBIT/2,000 = [EBIT – .11($14,000)]/1,800; EBIT = $15,400
The break-even levels of EBIT are the same because of M&M Proposition I.
[EBIT – .11($28,000)]/1,600 = [EBIT – .11($14,000)]/1,800 ; EBIT = $15,400
This break-even level of EBIT is the same as in part (b) again because of M&M Proposition I.
I
II
all-equity
EBIT
$12,000
$12,000
$12,000
Interest
3,080
1,540
0
EBT
8,920
10,460
12,000
Taxes
3,390
3,975
4,560
NI
$ 5,530
$ 6,485
$ 7,440
EPS
$3.46
$3.60
$3.72
The all-equity plan still has the highest EPS; Plan I still has the lowest EPS.
Plan I vs. all-equity: EBIT(.62)/2,000 = [EBIT – .11($28,000)](.62)/1,600; EBIT = $15,400
Plan II vs. all-equity: EBIT(.62)/2,000 = [EBIT – .11($14,000)](.62)/1,800; EBIT = $15,400
[EBIT – .11($28,000)](.62)/1,600 = [EBIT – .11($14,000)](.62)/1,800 ; EBIT = $15,400
The break-even levels of EBIT do not change because the addition of taxes reduces the income
of all three plans by the same percentage; therefore, they do not change relative to one another.
7.
I: P = $28,000/400 shares bought with debt = $70 per share; II: P = $14,000/200 shares = $70
This shows that when there are no corporate taxes, the stockholder does not care about the capital
structure decision of the firm. This is M&M Proposition I without taxes.
8.
a.
b.
c.
d.
9.
a.
b.
c.
d.
EPS = $5,000/800 shares = $6.25; Jimbo's cash flow = $6.25(100 shares) = $625
V = $80(800) = $64,000; D = 0.40($64,000) = $25,600
$25,600/$80 = 320 shares are bought; NI = $5,000 – .07($25,600) = $3,208
EPS = $3,208/480 shares = $6.68; Jimbo's cash flow = $6.68(100 shares) = $668
Sell 40 shares of stock and lend the proceeds at 7%: interest cash flow = 40($80)(.07) = $224
cash flow from shares held = $6.68(60 shares) = $401; total cash flow = $625.
The capital structure is irrelevant because shareholders can create their own leverage or
unlever the stock to create the payoff they desire, regardless of the capital structure the firm
actually chooses.
EPS = $19,000/1,000 shares = $19.00; Rebecca’s cash flow = $19.00(100 shares) = $1,900
V = $120(1,000) = $120,000; D = 0.30($120,000) = $36,000
$36,000/$120 = 300 shares are bought; NI = $19,000 – .08($36,000) = $16,120
EPS = $16,120/700 shares = $23.03; Rebecca's cash flow = $23.03(100 shares) = $2,303
Sell 30 shares of stock and lend the proceeds at 8%: interest cash flow = 30($120)(.08) = $288
cash flow from shares held = $23.03(70 shares) = $1,612; total cash flow = $1,900.
The capital structure is irrelevant because shareholders can create their own leverage or
unlever the stock to create the payoff they desire, regardless of the capital structure the firm
actually chooses.
10. D/E = 1 implies 50% debt; VL = VU + TCD = $30M + .40($15M) = $36M
D/E = 2 implies 67% debt; VL = VU + TCD = $30M + .40($20M) = $38M
11. With no debt the value is unchanged at $30M.
D/E = 1 implies 50% debt; VL = VU + TCD = $30M + .30($15M) = $34.5M
D/E = 2 implies 67% debt; VL = VU + TCD = $30M + .30($20M) = $36M
Debt will increase the value of the firm more when the corporate tax rate is higher.
12. a.
b.
WACC = .16 = (1/2.5)RE + (1.5/2.5)(.11); RE = .2350
.16 = (1/2)RE + (1/2)(.11); RE = .2100
.16 = (1/1.5)RE + (.5/1.5)(.11); RE = .1850
.16 = (1)RE + (0)(.11); RE = WACC = .1600
13. a.
b.
c.
d.
all-equity financed: WACC = RE = .15
RE = RA + (RA – RD)(D/E) = .15 + (.15 – .09)(.25/.75) = .1700
RE = RA + (RA – RD)(D/E) = .15 + (.15 – .09)(.50/.50) = .2100
WACCB = (E/V)RE + (D/V)RD = .75(.17) + .25(.09) = .1500
WACCC = (E/V)RE + (D/V)RD = .50(.21) + .50(.09) = .1500
14. V = VU + TCD = $275,000 + .35($75,000) = $301,250
15. Interest tax shield = $42M(.38) = $15.96M. The interest tax shield represents the tax savings in
current income due to the deductibility of a firm’s qualified debt expenses.
16. No taxes: VU = VL; value of the firm is $210M
With taxes: V = VU + TCD = $210M + .40($70M) = $238M
17. E = VL – D
No taxes: E = $210M – 70M = $140M, D/E = $70M/$140M = .50
With taxes: E = $238M – 70M = $168M, D/E = $70M/$168M = .42
18. Initially, RE = WACC = RA = .13
After issuing debt: RE = .13 + (.13 – .09)(1) = .17
WACC = .17(.5) + .09(.5) = .13
Intermediate
19. no debt:
50% debt:
100% debt:
V = VU = $16,500(.62)/.18 = $56,833.33
V = $56,833.33 + .38(V/2) ; V = $70,164.60
V = $56,833.33 + .38V ;
V = $91,666.66