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Capital Structure and Value
• Optimal capital structure is the mix of debt and equity that
maximizes the value of the firm or minimizes the weighted
average cost of capital
• Miller & Modigliani
– If markets are perfect capital structure does not affect
value
– Investors can accomplish any desired debt and equity mix
by themselves
– Weighted average cost of capital is constant
Financial Leverage, EPS, and ROE
Current Proposed
Assets $5,000,000 $5,000,000
Debt $ 0 $2,500,000
Equity $5,000,000 $2,500,000
Debt/Equity ratio 0 1
Share price $10 $10
Shares outstanding 500,000 250,000
Interest rate n/a 10%
Financial Leverage, EPS, and ROE
EPS and ROE under current capital structure
Recession Expected Expansion
EBIT $300,000 $650,000 $800,000
Interest $ 0 $ 0 $ 0
Net income $300,000 $650,000 $800,000
EPS $0.60 $1.30 $1.60
ROE 6% 13% 16%
Financial Leverage, EPS, and ROE
EPS and ROE under proposed capital structure
Recession Expected Expansion
EBIT $300,000 $650,000 $800,000
Interest $250,000 $250,000 $250,000
Net income $ 50,000 $400,000 $550,000
EPS $0.20 $1.60 $2.20
ROE 2% 16% 22%
Homemade Leverage and ROE
Firm does not adopt proposed capital structure
Investor put up $500 and borrows $500 at 10% to buy 100 shares
Investor’s return on her investment will be,
Recession Expected Expansion
EPS of un-levered firm $0.60 $1.30 $1.60
Earnings for 100 shares $60.00 $130.00 160.00
less interest on $500 at 10% -$50.00 -$50.00 -$50.00
Net earnings $10.00 $80.00 $110.00
ROE $10/$500 $80/$500 $110/$500
2% 16% 22%
Homemade Leverage and ROE
Firm adopts proposed capital structure
Investor puts up $500, $250 in stock and $250 in bonds at 10%
Investor’s return on her investment will be,
Recession Expected Expansion
EPS of levered firm $0.20 $1.60 $2.20
Earnings for 25 shares $5.00 $40.00 $55.00
plus interest on $250 at 10% +$25.00 +$25.00 +$25.00
Net earnings $30.00 $65.00 $80.00
ROE $30/$500 $65/$500 $80/$500
6% 13% 16%
Note: Remember we assume a world where there are no market
imperfections such as taxes and transaction costs.
The Miller & Modigliani (M&M) Propositions
Financial leverage and firm value: Proposition I
Since investors can costlessly replicate the financing
decisions of the firm (homemade leverage), in the absence of
taxes and other market imperfections, the value of the firm is
unaffected by its capital structure.
Implications:
There is no “magic” in finance - you can’t get something for
nothing.
Capital restructurings don’t create value, in and of themselves.
(Why is the last part of the statement so important?)
The M&M Propositions
The cost of equity and financial leverage: Proposition II
Because of Proposition I, the WACC must be constant.
With no taxes,
WACC = RA = (E/V) x RE + (D/V) x RD
where RA is the return on the firm’s assets
Solve for RE to get MM Proposition II
RE = RA + (RA - RD) x (D/E)
Cost of equity has two parts:
1. RA and “business” risk
2. D/E and “financial” risk
The CAPM, the SML, and Proposition II
M & M Proposition II :
D
RE RA ( RA RD ) x
E
According to the CAPM :
RE RF ( RM RF ) x E
RA RF ( RM RF ) x A
where A is the beta of the firms's assets.
What is the relationship between borrowing money and systematicrisk?
Assume the debt is riskless, so that R D R F , and substitute for R A in Prop. II :
D
RE RF ( RM RF ) x A x1
E
D D
E A x 1 A A x
E E
Ststematic risk for thefirm's stock gas two parts :
1. A and " business"risk
D
2. and " financial" risk
E
The M&M Propositions
Cost of capital
(%) RE
WACC = RA
RD
Debt-equity ration
(D/E)
RE = RA + (RA – RD) X (D/E) by M&M Proposition II
RA = WACC = (E/V) X RE + (D/V) X RD
where V = D + E
Introduction of Taxes
– Interest is taxed as the income of the lender, but
equity income is taxed as corporate income and
income of the shareholder
– By borrowing corporations create interest tax shield
because interest expense of corporations reduces
taxable income
– This leads to a firm that is almost entirely financed
with debt
Debt, Taxes, and Firm Value
The interest tax shield and firm value
For simplicity: (1) perpetual cash flows
(2) no depreciation
(3) no fixed asset or NWC spending
A firm is considering going from zero debt to $400 at 10%:
Firm U Firm L
(un-levered) (levered)
EBIT $200 $200
Interest 0 $40
Tax (40%) $80 $64
Net income $120 $96
Tax saving = $16 = 0.40 x 0.10 x $400 = TC x RD x D
Debt, Taxes, and Firm Value
What’s the link between debt and firm value?
Since interest creates a tax deduction, borrowing creates a tax
shield. Its value is added to the value of the firm.
MM Proposition I (with taxes)
PV(tax saving) = (0.40) x (10%) x ($400) / 0.10 =$160
= (TC x RD x D)/RD = TC x D
VL = VU + TC x D
Debt, Taxes, and Firm Value
Value of
the firm
(VL)
V L = V U + TC X D
= Value of firm
= TC with debt
TC X D = Present
value of TC= Corporate
tax shield Tax Rate
on debt
VU VU = Value of firm
with no debt
VU
Total debt
(D)
The value of the firm increases as total debt increases because of
the interest tax shield. This is the basis of M&M Proposition I with taxes.
If M&M proposition I with taxes is valid, how much debt a firm should use?
Debt, Taxes, and Firm Value
Cost of RE
Capital
RU
RA
RD(1-TC)
D/E
Differential Tax Rates on Debt and Equity Income
– Above conclusions assume that the tax rate on
equity and debt income is the same
– Value of the firm with differential tax rate is the
present value total cash flows (TCF) to investors
– TCF = I (1 – Tp) + (NOI – I) (1 – Tc) (1 – Tg)
I = interest expense
Tp = personal tax rate on interest income
Tc = corporate tax rate
Tg = personal tax rate on equity income
– TCF increases with additional debt if:
(1 – Tp) > (1 – Tc) (1 – Tg)
Tax Clientele Effect
– Tax rates of investors vary causing preference toward
debt or equity
– If all companies have the same tax rate but investors
experience different tax rates, companies as a group
would maximize value by issuing enough debt to
accommodate those investor for whom
(1 – Tp) > (1 – Tc) (1 – Tg) holds
• Differential Tax Rates Among Corporations
– High tax rate of a corporation increases benefits of
debt financing
Bankruptcy Costs
As the D/E ratio increases, the probability of bankruptcy
increases – likelihood of operating income shortage to
cover interest expense on the debt
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 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
Bankruptcy Costs
• Bankruptcy Costs
– Direct costs: legal and administrative fees
• Legal costs
– Indirect costs:
• Lost sales of products requiring future service
• Loss of best employees
• Low employee morale
• Inability of credit purchases
• Higher financing costs and restrictions
– As the amount of debt increases, the probability of
bankruptcy and therefore expected costs of
bankruptcy increases, reducing firm value
Debt, Taxes, Bankruptcy, and Firm Value
Value of
the firm
(VL)
VL = VU + TC X D
= Value of firm
Present value of tax with debt
shield on debt Financial distress
Maximum costs
firm value VL*
Actual firm value
VU = Value of firm
with no debt
Total debt
D* Optimal amount of debt (D)
According to the static theory, the gain from the tax shield on debt is offset by financial distress cost.
An optimal capital structure exists that just balances the additional gain from leverage against the
added financial distress cost.
Debt, Taxes, Bankruptcy, and Firm Value
Value Case II
M&M (with taxes)
of the Case 1
firm
(VL) PV of bankruptcy With no taxes or bankruptcy costs, the value
V L*
costs of the firm and its weighted average cost
Case III
Net gain from Static theory of capital are not affected by capital
leverage
VU Case I
M&M (no taxes)
structures.
Case 2
Total
D* debt (D)
With corporate taxes and no bankruptcy costs,
the value of the firm increases and the weighted
Weighted average cost of capital decreases as the amount
average
cost of
of debt goes up.
capital
(%)
Case I Case 3
M&M (no taxes)
Case III
With corporate taxes and bankruptcy costs,
Static theory the value of the firm, VL, reaches a maximum at
WACC*
Case II D*, the optimal amount of borrowing. At the same
M&M (with taxes)
time, the weighted average cost of capital, WACC,
D*/E*
Debt-equity ratio
(D/E)
is minimized at D*/E*.
Agency Costs
– Agency costs of debt:
• Managers can increase shareholders’ wealth at the
expense of creditors by taking risky projects
• If level of debt is low, risks are also low. High debt
level requires monitoring by creditors, increasing
agency costs even further
– Agency costs of equity
• Managers’ self fulfilling prophecies, conservatism
or over-optimism in investment decisions
• Higher debt level prevents managers from value
reducing activities
Information Signaling
– Managers convey their private information to the
investors by changing capital structure
– High debt levels reflect managers’ information
on improved future prospects of the company
– Firms with bad news cannot replicate because
they won’t have resources to support high debt
level
Additional Considerations
– Unequal costs of borrowing
– Higher risk of personal borrowing
– Institutional restrictions on leverage
Capital Structure with Informed Investors
• Study the market response to determine optimal
capital structure
• Study the relationship between different capital
structures and the weighted average cost of capital
• Information from market participants
Investment bankers
Bond ratings and wacc
Security analysts
• Disequilibrium
Capital Structure with Uninformed Investors
• If investors are not well-informed, managers should
consider future profitability, earnings variability and
bankruptcy risk
• Pro forma analysis of alternative capital structures
• Risk analysis
Ratio measures
Break-even point is the sales level below which the
company has a loss
Crossover point is the sales or EBIT level at which the
company would earn the same EPS with two different
capital structures
Debt capacity analysis
Empirical Evidence
– Bankruptcy costs are important in determining optimal capital
structure
– The more the physical assets the more the debt level in capital
structure
– Announcement of equity issues cause negative abnormal
returns
– Announcement of debt for equity exchange increases stock
value
– Announcement of equity for debt exchange decreases stock
value
– Abnormal price drops following leverage decreasing capital
structure exchanges are positively related to unexpected
earnings decreases
– Stock repurchases via tender offers result in sharp price
increases
– If a firm becomes a takeover target, it increases debt level
Harris and Raviv (1991), The Theory of Capital Structure, JOF.
Modigliani and Miller Summary
I. The No-Tax Case
A. Proposition I: The value of the firm levered equals the value of the firm
un-levered: VL = VU
B. Implications of Proposition I:
1. A firm’s capital structure is irrelevant.
2. A firm’s WACC is the same no matter what mix of debt and equity is used.
C. Proposition II: The cost of equity, RE, is
RE = RA + (RA - RD) D/E
where RA is the WACC, RD is the cost of debt, and D/E is the debt/equity
ratio.
D. Implications of Proposition II
1. The cost of equity rises as the firm increases its use of debt financing.
2. Equity risk depends on the risk of firm operations (business risk) and the
degree of financial leverage (financial risk).
Modigliani and Miller Summary
II. The Tax Case
A. Proposition I with Taxes: The value of the firm levered equals the
value of the firm un-levered plus the present value of the interest tax
shield:
VL = VU + Tc D
where Tc is the corporate tax rate and D is the amount of debt.
B. Implications of Proposition I with taxes:
1. Debt financing is highly advantageous, and, in the extreme, a
firm’s optimal capital structure is 100 percent debt.
2. A firm’s WACC decreases as the firm relies more heavily on
debt.
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