Key Concepts and Skills
Understand the effect of financial leverage on cash flows and the cost of equity
Understand the impact of taxes and bankruptcy on capital structure choice
Understand the basic components of the bankruptcy process
Definition of Capital Structure
A firm’s capital structure is the relative proportions of debt, equity, and other securities that a
firm has outstanding.
Or
How a firm pays for its assets.
The Capital Structure Question
What is the optimal Capital Structure?
Firm Value and Stock Value
The value of the firm equals the market value of the debt plus the market value
of the equity (firm value identity). This is just V = D + E. When the market
value of debt is given and constant, any change in the value of the firm results in
an identical change in the value of the equity. The key to this reasoning lies in
the fixed nature of debt and the derivative nature of stock.
Capital Structure and the Cost of Capital
The “optimal” or “target” capital structure is that debt/equity mix that
simultaneously (a) maximizes the value of the firm, (b) minimizes the weighted
average cost of capital, and (c) maximizes the market value of the common
stock.
Maximizing the value of the firm is the goal of managing capital structure.
The Effect of Financial Leverage
The Basics of Financial Leverage
How does leverage affect the EPS and ROE of a firm? When we increase the
amount of debt financing, we increase the fixed interest expense. If we have a
really good year, then we pay our fixed cost and we have more left over for our
stockholders. If we have a really bad year, we still have to pay our fixed costs
and we have less left over for our stockholders.
Raven Roost Corporation currently has no debt in its capital structure. The firm is considering
issuing debt to buy back some of its equity. Both its current and proposed capital structures are
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presented in the following table. The interest rate is 10 percent. We will ignore the effect of
taxes at this stage.
Current
Assets
Proposed
$5,000,000 $5,000,000
Debt
$0 $2,500,000
Equity
$5,000,000 $2,500,000
Debt/Equity Ratio
0
1
$10
$10
500,000
250,000
N/A
10%
Share Price
Shares Outstanding
Interest rate
Current Capital Structure: No Debt
Recession
EBIT
$300,000
Interest
Net Income
0
$300,000
Expected
Expansion
$650,000 $1,000,000
0
0
$650,000 $1,000,000
ROE
6.00%
13.00%
20.00%
EPS
$0.60
$1.30
$2.00
Proposed Capital Structure: Debt = $2.5 million
Recession
EBIT
$300,000
Expected
Expansion
$650,000 $1,000,000
Interest
250,000
250,000
250,000
Net Income
$50,000
$400,000
$750,000
ROE
2.00%
16.00%
30.00%
EPS
$0.20
$1.60
$3.00
What happens to EPS and ROE when we issue debt and buy back shares of
stock?
What happens to the variability of EPS and ROE when we issue debt and buy
back shares of stock?
Variability in ROE
Current: ROE ranges from 6% to 20%
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Proposed: ROE ranges from 2% to 30%
Variability in EPS
Current: EPS ranges from $0.60 to $2.00
Proposed: EPS ranges from $0.20 to $3.00
The variability in both ROE and EPS increases when financial leverage is
increased
What is the difference between ROE and ROA for an all equity firm given
various sales levels? It’s easy to show that ROE = ROA in this case because total
equity = total assets. The substitution of debt for equity results in ROE equaling
ROA at only one level of sales. The fixed interest expense and lower number of
common shares outstanding cause ROE to change by a larger percentage than
the change in ROA, for any given change in sales.
Break-Even EBIT
Find EBIT where EPS is the same under both the current and proposed capital
structures. If we expect EBIT to be greater than the break-even point, then
leverage may be beneficial to our stockholders and if we expect it to be less than
the break-even point, then leverage is detrimental to our stockholders
Break-Even EBIT Example
EBIT
500 ,000
EBIT
EBIT
EBIT
EPS
EBIT 250 ,000
250 ,000
500 ,000
EBIT
250 ,000
250 ,000
2 EBIT 500 ,000
$500 ,000
500 ,000
$1.00
500 ,000
We can conclude that:
The effect of financial leverage depends on EBIT. Financial leverage increases
ROE and EPS when EBIT is greater than the cross-over point and decreases ROE
and EPS when it is less than the cross-over point.
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$3.50
$3.00
$2.50
EPS
$2.00
$1.50
$1.00
$0.50
$0.00
$300,000
$650,000
$1,000,000
EBIT
Current
Proposed
If a company expects to achieve the break-even EBIT, should it automatically
issue debt?
This is a break-even point relative to EBIT and EPS. Beyond this point, EPS will
be larger under the debt alternative, but with additional debt, the firm will have
additional financial risk that would increase the required return on its common
stock. A higher required return might offset the increase in EPS, resulting in a
lower firm value despite the higher EPS. The M&M models, described in
upcoming sections, will offer key points to make about this relationship.
Corporate Borrowing and Homemade Leverage
Homemade leverage – if all market participants have equal access to the capital
markets, there’s nothing special about corporate borrowing.
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Homemade Leverage and ROE Example
Suppose Raven Roost does not change its capital structure. An investor can
replicate the returns of the proposed borrowing by making her own D/E ratio
equal to 1 for the investment. Suppose an investor buys 50 shares with her own
money and 50 shares by borrowing $500 at 10% interest. The payoffs are:
Recession Expected Expansion
EPS – unlevered firm
Earnings for 100 shares
Less interest on $500 at 10%
Net earnings
Return on investment = net earnings / $500
$0.60
$1.30
$2.00
$60.00
$130.00
$200.00
50.00
50.00
50.00
$10.00
$80.00
$150.00
2%
16%
30%
The investor has been able to convert her return to what she would have gotten
if the company had undertaken the proposed capital structure and she had just
purchased $500 worth of stock.
Suppose instead the firm does switch to the proposed capital structure. An
investor can “unlever” the firm by purchasing both the firm’s stock and bonds.
Consider an investor who invests $250 in the stock and $250 in the bonds
paying 10%. (Note that in both situations, the investor’s total cash outlay is
$500.)
Recession Expected Expansion
EPS – levered firm
Earnings for 25 shares
Plus interest on $250 at 10%
Net earnings
Return on investment = net earnings / $500
$0.20
$1.60
$3.00
5.00
40.00
75.00
25.00
25.00
25.00
$30.00
$65.00
$100.00
6%
13%
20%
In this case, the investor is able to earn the same return as she would have
earned if the firm did not change capital structure and she just invested in stock.
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Capital Structure and the Cost of Equity Capital
Modigliani and Miller (MM) developed a theory of Capital Structure. They
received the Nobel Prize in Economics in 1990
The value of the firm is determined by the cash flows to the firm and the risk of
the assets
To change the firm value, you must change the cash flows or the risk.
MM Proposition I: Examines firm value
MM Proposition II: Examines the WACC
MM Assumptions:
Capital markets are frictionless.
Firms and individuals can borrow and lend at the risk-free rate.
There are no costs to bankruptcy
Firms issue two types of claims: risk-free debt and risky equity.
All firms are assumed to be in the same risk class.
Corporate and personal taxes are zero.
All cash flow streams are perpetuities (i.e., no growth).
Corporate insiders and outsiders have the same information (i.e., no signaling opportunities).
Managers always maximize shareholders’ wealth (i.e., no agency costs).
Why are we even considering a situation in which taxes do not exist? We are
trying to determine what risk-return trade-off is best for the firm’s stockholders.
One way to get a good understanding of what is relevant to the capital structure
decision is to start in a “perfect” world and then relax assumptions as we go. By
relaxing one assumption at a time, we can get a better idea of the impact on the
capital structure decision. This is the classic process of “model building” in
economics – start simple and add complexity one step at a time.
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MM Proposition 1:
VU = VL
“The market value of any firm is independent of its capital structure”
or:
“Financial leverage has no effect on shareholders’ wealth.”
Value
of
Firm
VU
Prop 1 (No Taxes)
VL
Debt
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MM Proposition 2:
“The rate of return they can expect to receive on their shares increases as the firm’s debtequity ratio increases.”
Cost of
Capital
Prop 2 (No Taxes)
rE
rA
WACC
rD
rD
D/E
WACC = rA = (E/V)RE + (D/V)RD
rE: cost of equity
rD: cost of debt
rA: return on assets or cost of equity in an all equity firm (the “cost” of the firm’s business
risk, i.e., the risk of the firm’s assets)
(rA – rD)(D/E) is the “cost” of the firm’s financial risk, i.e., the additional return required by
stockholders to compensate for the risk of leverage
An alternative explanation is as follows: In the absence of debt, the required
return on equity equals the return on the firm’s assets, RA. As we add debt, we
increase the variability of cash flows available to stockholders, thereby increasing
stockholder risk.
Business and Financial Risk
The key point is that Proposition II shows that return on equity depends on both
business risk and financial risk.
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Business risk:
The risk inherent in a firm’s operations; it depends on the
systematic risk of the firm’s assets and it determines the first component of the
required return on equity, RA.
Financial risk:
The extra risk to stockholders that results from debt financing; it
determines the second component of the required return on equity,
(RA – RD)(D/E).
Therefore, the systematic risk of the stock depends on:
Systematic risk of the assets, A, (Business risk)
Level of leverage, D/E, (Financial risk)
Proposition II suggests that even if a firm could issue risk-free debt, its financial
risk would exceed zero. The focus here is on the risk (and required return) to
the shareholder. Regardless of the certainty associated with the promised
returns to bondholders (default risk), higher levels of debt imply greater volatility
of earnings to stockholders.
Fans Example
Fans, Inc. is an all-equity firm with 1,000 shares of common stock outstanding. Investors
require a 20 percent return on Frodo’s unlevered equity. The company distributes all of its
earnings to equity holders as dividends at the end of each year. Fans estimates that its annual
earnings before interest and taxes (EBIT) will be $1,000, $2,000, or $4,200 with probabilities of
0.1, 0.4, and 0.5 respectively. The firm’s expectations about earnings will be unchanged in
perpetuity. There are no corporate or personal taxes.
What is the value of the firm?
Suppose Fans issues $7,500 of debt at an interest rate of 10 percent and uses the proceeds to
repurchase 500 shares of common stock.
What is the new value of the firm?
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What is the new value of the firm’s equity?
What is the required return on the firm’s levered equity?
What is the firm’s weighted average cost of capital?
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The CAPM, the SML and Proposition II
How does financial leverage affect systematic risk?
CAPM: RA = Rf +
Where
assets
A
A
(RM – Rf)
is the firm’s asset beta and measures the systematic risk of the firm’s
Proposition II
Replace RA in the CAPM equation with the WACC equation and assume that the
debt is riskless (RD = Rf)
RE = Rf +
E
=
A
A
(1+D/E)(RM – Rf)
(1 + D/E)
Therefore, the systematic risk of the stock depends on:
Systematic risk of the assets,
A
, (Business risk)
Level of leverage, D/E, (Financial risk)
Intuitively, an increase in financial leverage should increase systematic risk since
changes in interest rates are a systematic risk factor and will have more impact
the higher the financial leverage.
The assumption that debt is riskless is for simplicity and to illustrate that even if
debt is default risk-free, it still increases the variability of cash flows to the
stockholders, and thus increases the systematic risk.
M&M Propositions I and II with Corporate Taxes
The Interest Tax Shield
Interest is tax deductible
Therefore, when a firm adds debt, it reduces taxes, all else equal
The reduction in taxes increases the cash flow of the firm
Tax savings arise from the deductibility of interest. It is the key benefit from
borrowing over issuing equity.
How should an increase in cash flows affect the value of the firm?
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Taxes and M&M Proposition I
Unlevered Firm
Levered Firm
5,000
5,000
0
500
Taxable Income
5,000
4,500
Taxes (34%)
1,700
1,530
Net Income
3,300
2,970
CFFA
3,300
3,470
EBIT
Interest
Annual interest tax savings = D(RD)(TC)
If we assume perpetual debt, then the present value of the interest tax savings
= D(RD)(TC) / RD = DTC
We also assume perpetual cash flows to the firm. This is done for simplicity, but
the ultimate result is the same even if you use cash flows that change through
time.
Value of an unlevered firm, VU = EBIT(1 – TC)/RU, where RU is the cost of capital
for an all equity firm.
Value of a levered firm = value of an unlevered firm + PV of interest tax shield
Value of a levered firm, VL = VU + DTC
The levered firm has 6,250 in 8% debt,
interest expense = .08(6,250) = 500
Annual tax shield = .34(500) = 170
Present value of annual interest tax shield
Assume perpetual debt for simplicity
PV = 170 / .08 = 2,125
PV = D(RD)(TC) / RD = DTC = 6,250(.34) = 2,125
The value of the firm increases by the present value of the annual interest tax
shield
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Value of equity = Value of the firm – Value of debt
Value
of
Firm
Prop 1 with TC
VL
VL = VU + TCD
VU
Debt
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Taxes, The WACC, and Proposition II
The WACC decreases as D/E increases because of the government subsidy on
interest payments
RA = (E/V)RE + (D/V)(RD)(1-TC)
RE = RU + (RU – RD)(D/E)(1-TC)
Example
RU = 12
RD = 9
D = 75
E = 86.67
T = 35%
RE = 12 + (12-9)(75/86.67)(1-.35) = 13.69%
RA = (86.67/161.67)(13.69) + (75/161.67)(9)(1-.35)
RA = 10.05%
Suppose that the firm changes its capital structure so that the debt-to-equity
ratio becomes 1.
What will happen to the cost of equity under the new capital structure?
RE = 12 + (12 - 9)(1)(1-.35) = 13.95%
What will happen to the weighted average cost of capital?
RA = .5(13.95) + .5(9)(1-.35) = 9.9%
Can financing decisions generate positive NPVs? Put simply, a positive NPV
decision is one for which the firm obtains something for less than market value.
Just as the relative inefficiency of the physical asset markets makes the search for
positive NPV projects worthwhile, the efficiency of the financial markets makes
positive NPV financing projects unlikely. This can change in the presence of
financial market imperfections; and differential tax treatment between MM
Proposition 1 with Corporate Taxes: interest and dividends is a big market
imperfection. Further discussion of the successes and failures of financial
engineering in the last two decades may serve to illustrate the core concepts:
(1) firm value comes largely from the asset side of the balance sheet
(2) positive NPV financing projects can also be created, but in general, financing
is a zero-NPV proposition.
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MM Proposition I1 with Corporate Taxes:
Cost of
Capital
Prop 2 with TC
rE
rA
WACC
rD
rD
D/E
Fans Example (Continued)
Suppose that Fans’s earnings are subject to a corporate tax rate of 40 percent.
Will the presence of corporate taxes increase or decrease the value of the firm? Why?
What is the value of the firm? What is the price of a share of stock?
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What is the required return on the firm’s levered equity?
Bankruptcy Costs
Now we add bankruptcy costs
As the D/E ratio increases, the probability of bankruptcy increases
This increased probability will increase the expected bankruptcy costs
At some point, the additional value of the interest tax shield will be offset by the
increase in expected bankruptcy cost
At this point, the value of the firm will start to decrease, and the WACC will
start to increase as more debt is added
The key disadvantage of the use of debt is bankruptcy costs.
Direct bankruptcy costs are the legal and administrative expenses directly
associated with bankruptcy. Generally, these costs are quantifiable and
measurable.
Direct Bankruptcy Costs
Legal and administrative costs
Ultimately cause bondholders to incur additional losses
Disincentive to debt financing
Financial distress
Financial distress – the direct and indirect costs of avoiding bankruptcy.
Significant problems in meeting debt obligations
Firms that experience financial distress do not necessarily file for bankruptcy
In 1997, the remaining assets of Fruehauf Corporation, described by Barrons as
“the once-dominant” manufacturer of truck trailers, were sold off for a mere
$50 million, bringing an end to the story of a great firm laid low by over-reliance
on debt financing.
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Founded in the 1940’s, the firm controlled one-third of the trailer market in the
early 1980’s, but then went private in a leveraged buyout in 1986 to avoid a
hostile takeover bid. Saddled with debt it found difficult to service, the firm
went through a number of restructurings until the firm filed for chapter 11 in
1996. At that time its shares were delisted from the NYSE. And, as Barrons
notes, “… the shareholders had been wiped out, leaving the carcass to be picked
over by those with secure claims to Fruehauf’s assets … [b]lood was in the
water.” By 1997, the last division was sold and the remaining assets were sold
to Wabash National.
Indirect Bankruptcy Costs
Indirect bankruptcy costs (e.g., difficulties in hiring and retaining good people
because the firm is in financial difficulty) are hard to measure and generally take
the form of forgone revenues, opportunity costs, etc.
Larger than direct costs, but more difficult to measure and estimate
Stockholders want to avoid a formal bankruptcy filing
Bondholders want to keep existing assets intact so they can at least receive that money
Assets lose value as management spends time worrying about avoiding bankruptcy instead of
running the business
The firm may also lose sales, experience interrupted operations and lose valuable employees
MM Proposition 1 with Corporate Taxes and Bankruptcy Costs:
Value
of
Firm
Prop 1 with TC and
Financial Distress Costs
VL = VU + TCD
Present Value of
financial distress
Max
Value
of
Firm
Present Value of
the Tax Shield
VU
B*
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Debt
Page 17
MM Proposition 1I with Corporate Taxes and Bankruptcy Costs:
Cost of
Capital
Prop 2 with TC and
Financial Distress Costs
rA
Min
WACC
WACC
B*
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D/E
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Optimal Capital Structure
What is the primary goal of financial managers?
Maximize stockholder wealth
We want to choose the capital structure that will maximize stockholder wealth.
We do this by maximizing the value of the firm or minimizing the WACC
Why does minimizing WACC maximize firm value? Remember the WACC is
the appropriate discount rate for the risk of the firm’s standard assets. We can
find the value of the firm by discounting the firm’s expected future cash flows at
the discount rate – the process is the same as finding the value of anything else.
Since value and discount rate move in opposite directions, firm value will be
maximized when WACC is minimized.
Remember, a firm is just a portfolio of projects, some with positive NPVs and
some with negative NPVs when evaluated at the WACC. The value of the firm
is the sum of the NPVs of its component projects. We already know that lower
discount rates increase NPVs; consequently, decreasing the WACC will increase
firm value.
The Static Theory of Capital Structure
Firms borrow because tax shields are valuable
The tax benefit is only important if the firm has a large tax liability
Risk of financial distress
The greater the risk of financial distress, the less debt will be optimal for the firm
The cost of financial distress varies across firms and industries, and as a manager you need to
understand the cost for your industry
Borrowing is constrained by the costs of financial distress
The optimal capital structure balances the incremental benefits and costs of borrowing
Optimal Capital Structure and the Cost of Capital
The optimal capital structure is the debt-equity mix that minimizes the WACC.
Conclusions
No taxes or bankruptcy costs
No optimal capital structure; firm value is unaffected by the choice of capital
structure
Corporate taxes but no bankruptcy costs
Optimal capital structure is almost 100% debt or firm value is maximized
when the firm uses as much debt as possible due to the interest tax shield
Each additional dollar of debt increases the cash flow of the firm
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Corporate taxes and bankruptcy costs
Optimal capital structure is part debt and part equity
Firm value is maximized where the additional benefit from the interest tax
shield is just offset by the increase in expected bankruptcy costs – there is an
optimal capital structure
Capital Structure: Some Managerial Recommendations
Taxes – tax shields are more important for firms with high marginal tax rates
Financial distress – the lower the risk (or cost) of distress, the more likely a firm
is to borrow funds
In theory, the static model of capital structure described in this section applies to
multinational firms as well as to domestic firms. The multinational firm should
seek to minimize its global cost of capital by balancing the debt-related tax
shields across all of the countries in which the firm does business against global
agency and bankruptcy costs. However, this assumes that worldwide capital
markets are well-integrated and that foreign exchange markets are highly
efficient. In such an environment, financial managers would seek the optimal
global capital structure. In practice, of course, the existence of capital market
segmentation, differential taxes, and regulatory frictions make the determination
of the global optimum much more difficult than the theory would suggest.
The Value of the Firm
Value of the Firm = Marketed Claims + Nonmarketed Claims
Marketed claims are claims against cash flow that can be bought and sold (bonds,
stock).
Nonmarketed claims are claims against cash flow that cannot be bought and sold
(taxes)
VM = value of marketed claims
VN = value of nonmarketed claims
VT = value of all claims = VM + VN = E + D + G + B + …
Given the firm’s cash flows, the optimal capital structure is the one that
maximizes VM or minimizes VN.
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The Pecking-Order Theory
Asymmetric information between buyers and sellers means that existing firm
owners know more than potential investors. The view is that existing owners
will sell equity when it is overvalued, which is a negative signal to investors. Thus,
this is avoided at all costs, particularly since equity issuance is also costly.
Internal Financing and the Pecking Order
Rules of the pecking order:
#1: Use internal financing first
#2: Issue debt next and new equity last
Implications of the Pecking Order
The pecking-order theory is in contrast to the tradeoff theory in that:
there is no target D/E ratio
profitable firms will use less debt
companies like financial slack
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