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CHAPTER 14
Capital Structure Decisions:
Part I
Impact of leverage on returns
Business versus financial risk
Capital structure theory
Perpetual cash flow example
Setting the optimal capital
structure in practice
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Consider Two Hypothetical Firms
Firm U
No debt
$20,000 in assets
40% tax rate
Firm L
$10,000 of 12% debt
$20,000 in assets
40% tax rate
Both firms have same operating leverage,
business risk, and EBIT of $3,000. They
differ only with respect to use of debt.
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Impact of Leverage on Returns
EBIT
Interest
EBT
Taxes (40%)
NI
ROE
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Firm U
Firm L
$3,000
0
$3,000
1 ,200
$1,800
$3,000
1,200
$1,800
720
$1,080
9.0%
10.8%
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Why does leveraging increase return?
Total dollar return to investors:
U: NI = $1,800.
L: NI + Int = $1,080 + $1,200 = $2,280.
Difference = $480.
Taxes paid:
U: $1,200; L: $720.
Difference = $480.
More EBIT goes to investors in Firm L.
Equity $ proportionally lower than NI.
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What is business risk?
Uncertainty about future operating income
(EBIT).
Probability
Low risk
High risk
0
E(EBIT)
EBIT
Note that business risk focuses on operating
income, so it ignores financing effects.
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Factors That Influence Business Risk
Uncertainty about demand (unit
sales).
Uncertainty about output prices.
Uncertainty about input costs.
Product and other types of liability.
Degree of operating leverage (DOL).
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What is operating leverage, and how
does it affect a firm’s business risk?
Operating leverage is the use of fixed
costs rather than variable costs.
The higher the proportion of fixed
costs within a firm’s overall cost
structure, the greater the operating
leverage.
(More...)
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Higher operating leverage leads to
more business risk, because a small
sales decline causes a larger profit
decline.
Rev.
$
Rev.
$
} Profit
TC
TC
FC
FC
QBE
Sales
QBE
Sales
(More...)
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Probability
Low operating leverage
High operating leverage
EBITL
EBITH
In the typical situation, higher
operating leverage leads to higher
expected EBIT, but also increases risk.
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Business Risk versus Financial Risk
Business risk:
Uncertainty in future EBIT.
Depends on business factors such as
competition, operating leverage, etc.
Financial risk:
Additional business risk concentrated
on common stockholders when financial
leverage is used.
Depends on the amount of debt and
preferred stock financing.
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From a shareholder’s perspective, how
are financial and business risk
measured in the stand-alone sense?
Stand-alone Business Financial
=
+
.
risk
risk
risk
Stand-alone risk = ROE.
Business risk = ROE(U).
Financial risk = ROE - ROE(U).
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Now consider the fact that EBIT is not
known with certainty. What is the
impact of uncertainty on stockholder
profitability and risk for Firm U and
Firm L?
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Firm U: Unleveraged
Bad
Prob.
0.25
EBIT
$2,000
Interest
0
EBT
$2,000
Taxes (40%)
800
NI
$1,200
Copyright © 2002 South-Western
Economy
Avg.
Good
0.50
$3,000
0
$3,000
1,200
$1,800
0.25
$4,000
0
$4,000
1,600
$2,400
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Firm L: Leveraged
Prob.*
EBIT*
Interest
EBT
Taxes (40%)
NI
Bad
Economy
Avg.
Good
0.25
$2,000
1,200
$ 800
320
$ 480
0.50
$3,000
1,200
$1,800
720
$1,080
0.25
$4,000
1,200
$2,800
1,120
$1,680
*Same as for Firm U.
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Bad
10.0%
6.0%
6.0%
Avg.
15.0%
9.0%
9.0%
Good
20.0%
12.0%
12.0%
8
8
Firm U
BEP
ROI*
ROE
TIE
8
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Firm L
Bad
Avg.
Good
BEP
10.0%
15.0%
20.0%
ROI*
8.4%
11.4%
14.4%
ROE
4.8%
10.8%
16.8%
TIE
1.7x
2.5x
3.3x
*ROI = (NI + Interest)/Total financing.
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Profitability Measures:
E(BEP)
E(ROI)
E(ROE)
U
15.0%
9.0%
9.0%
L
15.0%
11.4%
10.8%
Risk Measures:
CVROE
E(TIE)
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2.12%
0.24
8
ROE
4.24%
0.39
2.5x
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Conclusions
Basic earning power = BEP =
EBIT/Total assets is unaffected by
financial leverage.
L has higher expected ROI and ROE
because of tax savings.
L has much wider ROE (and EPS)
swings because of fixed interest
charges. Its higher expected return
is accompanied by higher risk.
(More...)
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In a stand-alone risk sense, Firm L’s
stockholders see much more risk
than Firm U’s.
U and L: ROE(U) = 2.12%.
U: ROE = 2.12%.
L: ROE = 4.24%.
L’s financial risk is ROE - ROE(U) =
4.24% - 2.12% = 2.12%. (U’s is zero.)
(More...)
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For leverage to be positive (increase
expected ROE), BEP must be > kd.
If kd > BEP, the cost of leveraging will
be higher than the inherent
profitability of the assets, so the use
of financial leverage will depress net
income and ROE.
In the example, E(BEP) = 15% while
interest rate = 12%, so leveraging
“works.”
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Capital Structure Theory
MM theory
Zero taxes
Corporate taxes
Corporate and personal taxes
Trade-off theory
Signaling theory
Debt financing as a managerial
constraint
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MM Theory: Zero Taxes
MM prove, under a very restrictive
set of assumptions, that a firm’s
value is unaffected by its financing
mix.
Therefore, capital structure is
irrelevant.
Any increase in ROE resulting from
financial leverage is exactly offset by
the increase in risk.
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MM Theory: Corporate Taxes
Corporate tax laws favor debt
financing over equity financing.
With corporate taxes, the benefits of
financial leverage exceed the risks:
More EBIT goes to investors and less
to taxes when leverage is used.
Firms should use almost 100% debt
financing to maximize value.
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MM Theory: Corporate and
Personal Taxes
Personal taxes lessen the advantage
of corporate debt:
Corporate taxes favor debt financing.
Personal taxes favor equity financing.
Use of debt financing remains
advantageous, but benefits are less
than under only corporate taxes.
Firms should still use 100% debt.
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Hamada’s Equation
MM theory implies that beta changes
with leverage.
bU is the beta of a firm when it has no
debt (the unlevered beta)
bL = bU(1 + (1 - T)(D/E))
In practice, D/E is measured in book
values when bL is calculated.
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Trade-off Theory
MM theory ignores bankruptcy
(financial distress) costs, which
increase as more leverage is used.
At low leverage levels, tax benefits
outweigh bankruptcy costs.
At high levels, bankruptcy costs
outweigh tax benefits.
An optimal capital structure exists that
balances these costs and benefits.
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Signaling Theory
MM assumed that investors and
managers have the same information.
But, managers often have better
information. Thus, they would:
Sell stock if stock is overvalued.
Sell bonds if stock is undervalued.
Investors understand this, so view
new stock sales as a negative signal.
Implications for managers?
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Debt Financing As
a Managerial Constraint
One agency problem is that
managers can use corporate funds
for non-value maximizing purposes.
The use of financial leverage:
Bonds “free cash flow.”
Forces discipline on managers.
However, it also increases risk of
financial distress.
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Perpetual Cash Flow Example
Expected EBIT = $500,000; will remain
constant over time.
Firm pays out all earnings as
dividends (zero growth).
Currently is all-equity financed. BV of
equity = MV of equity
100,000 shares outstanding.
P0 = $20; T = 40%; kRF = 6%; RPM = 4%
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Component Cost Estimates
Amount
Borrowed (000)
kd
$
0
250
10.0%
500
11.0
750
13.0
1,000
16.0
If company recapitalizes, debt would be
issued to repurchase stock.
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The MM and Miller models cannot
be applied directly because several
assumptions are violated.
kd is not a constant.
Bankruptcy and agency costs
exist.
In practice, Hamada’s equation is
used to find kS for the firm with
different levels of debt.
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The Optimal Capital Structure
Calculate the cost of equity at each
level of debt.
Calculate the value of equity at each
level of debt.
Calculate the total value of the firm
(value of equity + value of debt) at each
level of debt.
The optimal capital structure maximizes
the total value of the firm.
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Sequence of Events in a
Recapitalization
Firm announces the recapitalization.
Investors reassess their views and
estimate a new equity value.
New debt is issued and proceeds are
used to repurchase stock at the new
equilibrium price.
(More...)
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 Shares
Debt issued
=
.
Bought New price/share
After recapitalization firm would have
more debt but fewer common shares
outstanding.
An analysis of several debt levels is
given next.
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Cost of Equity at Zero Debt
Since the firm has 0 growth, its current
value, $2,000,000, is given by
Dividends/kS = (EBIT)(1-T)/kS
= 500,000 (1 - 0.40)/kS
kS = 15.0% = unlevered cost of equity.
bU = (kS - kRF)/RPM = (15 - 6)/4 = 2.25
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Cost of Equity at Each Debt Level
Hamada’s equation says that
bL = bU (1 + (1-T)(D/E))
Debt(000s)
D/E
bL
kS
0
2.25
15.00%
250
0.142
2.44
15.77
500
0.333
2.70
16.80
750
0.600
3.06
18.24
1,000
1.000
3.60
20.40
0
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D = $250, kd = 10%, ks = 15.77%.
(EBIT - kdD)(1 - T)
S1 =
ks
[$500 - 0.1($250)](0.6)
=
= $1,807.
0.1577
V1 = S1 + D1 = $1,807 + $250 = $2,057.
$2,057
P1 = 100 = $20.57.
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Shares
$250
=
= 12.15.
repurchased
$20.57
Shares
= n1 = 100 - 12.15 = 87.85.
remaining
Check on stock price:
S1
$1,807
P1 = n =
= $20.57.
1
87.85
Other debt levels treated similarly.
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Value of Equity at Each Debt Level
Equity Value = Dividends/kS
Debt(000s) kD
Divs
kS
E
na
300
15.00%
2,000
250
10%
285
15.77
1,807
500
11%
267
16.80
1,589
750
13%
241.5
18.24
1,324
1,000
16%
204
20.40
1,000
0
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Total Value of Firm
Debt
(000s)
E
Total
Value
Price per
Share
0
2,000
2,000
$20.00
250
1,807
2,057
20.57
500
1,589
2,089
20.89
750
1,324
2,074
20.74
1,000
1,000
2,000
20.00
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Total Value
is Maximized with
500,000 in
debt.
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Calculate EPS at debt of $0, $250K,
$500K, and $750K, assuming that the
firm begins at zero debt and recapitalizes to each level in a single step.
Net income = NI = [EBIT - kd D](1 - T).
EPS = NI/n.
D
NI
n
EPS
$ 0
$300
100.00 $3.00
250
285
87.85
3.24
500
267
76.07
3.51
750
242
63.84
3.78
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EPS continues to increase beyond
the $500,000 optimal debt level.
Does this mean that the optimal
debt level is $750,000, or even
higher?
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Find the WACC at each debt level.
D
$
S
V
kd
ks
WACC
0 $2,000 $2,000
-- 15.00%
250 1,807 2,057 10% 15.77
500 1,589 2,089 11.0 16.80
750 1,324 2,074 13.0 18.24
1,000 1,000 2,000 13.0 20.40
15.0%
14.6
14.4
14.5
15.0
e.g. D = $250:
WACC = ($250/$2,057)(10%)(0.6)
+ ($1,807/$2,057)(15.77%)
= 14.6%.
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The WACC is minimized at D =
$500,000, the same debt level that
maximizes stock price.
Since the value of a firm is the
present value of future operating
income, the lowest discount rate
(WACC) leads to the highest value.
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How would higher or lower
business risk affect
the optimal capital structure?
At any debt level, the firm’s probability
of financial distress would be higher.
Both kd and ks would rise faster than
before. The end result would be an
optimal capital structure with less debt.
Lower business risk would have the
opposite effect.
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Is it possible to do an analysis exactly
like the one above for most firms?
No. The analysis above was based
on the assumption of zero growth,
and most firms do not fit this
category.
Further, it would be very difficult, if
not impossible, to estimate ks with
any confidence.
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What type of analysis should firms
conduct to help find their optimal, or
target, capital structure?
Financial forecasting models can
help show how capital structure
changes are likely to affect stock
prices, coverage ratios, and so on.
(More...)
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Forecasting models can generate
results under various scenarios, but
the financial manager must specify
appropriate input values, interpret
the output, and eventually decide on
a target capital structure.
In the end, capital structure decision
will be based on a combination of
analysis and judgment.
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What other factors would managers
consider when setting the target
capital structure?
Debt ratios of other firms in the
industry.
Pro forma coverage ratios at
different capital structures under
different economic scenarios.
Lender and rating agency attitudes
(impact on bond ratings).
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Reserve borrowing capacity.
Effects on control.
Type of assets: Are they tangible,
and hence suitable as collateral?
Tax rates.
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