Chapter 12
Capital Structure: Theory And Taxes
Professor John Zietlow
MBA 621
Overview Of Capital Structure Theory & Practice
• The capital structure question: can the mix of debt and equity
a firm issues affect its total market valuation?
– Has been a key issue in finance theory & practice since 1958
• Capital Structure patterns observed worldwide
– Similarities & differences between US, other OECD countries
• The Agency Cost/Tax Trade-Off Theory of capital structure
– Not perfect, but works better than principal competitors
– Time won’t allow examination of other two theories
• The Modigliani-Miller capital structure irrelevance propositions
– Perfect capital markets assumption underlying Proposition I
– Proposition II’s implications for corporate financial policy
• The impact of income taxes on the irrelevance propositions
– Corporate income tax: 100% debt is optimal
– Irrelevance perhaps rescued by personal taxes
Capital Structure Patterns Observed Worldwide
• Capital structures have strong industry patterns, and these
are the same around the world.
– High debt-to-equity industries: utilities, transport cos, and
mature, capital-intensive manufacturing firms
– Low D/E industries: service firms, mining companies, most
rapidly growing or technology-based manufacturing firms
– Implies an industry's optimal asset mix influences CSs
chosen by firms in that industry anywhere
• Observed capital structures show distinct national patterns.
– US, UK, German, Australian & Canadian firms have lower
book debt ratios than firms in Japan, France, and Italy
– UK & German firms have lowest market value debt ratios
– Historical, institutional, & cultural factors play a part, but so
does a nation's reliance on capital markets versus banks for
corporate financing
Market Value Debt Ratios, Selected U.S.
Corporations, July 2002
Company
Debt to total
assets
L-T debt to
total capital
Market to
book ratio
Microsoft
0
0
5.54
Intel
0
0
4.03
ExxonMobil
0.04
0.03
3.72
Procter & Gamble
0.12
0.07
10.13
Boeing
0.27
0.24
3.65
Walt Disney
0.27
0.25
1.92
American Electric Power
0.54
0.36
1.62
Georgia Pacific
0.69
0.55
1.19
Delta Air Lines
0.77
0.75
0.82
General Motors
0.84
0.83
4.12
Leverage Ratios For G-7 And Selected
Developing Countries, 1980-91
Country
United States
Japan
Total debt to
total asset
(Book value %)
L-T debt to total L-T debt to total
assets
capital
(Book value %) (Market value %)
58%
69
37%
53
28%
29
Germany
73
38
23
France
71
48
41
Italy
70
47
46
United Kingdom
54
28
35
Canada
56
39
35
India
67
34
35
South Korea
73
49
64
Turkey
59
24
11
Source: Rajan and Zingales, “What do We Know About Capital Structure: Some Evidence from
International Data,” Journal of Finance 50 (1995).
CS Patterns Observed Worldwide (Continued)
• Leverage ratios are inversely related to the perceived costs
of financial distress.
– Both across industries & across countries, the more costly is
financial distress, the less debt will be used.
– Companies rich in collateralizeable assets have higher
leverage than firms rich in growth options.
• Within industries, leverage is inversely related to profitability
– In all industries, the most profitable companies typically
borrow the least, suggesting that CS at least partly residual
• Corporate & personal taxes influence capital structures, but
they neither cause nor prevent corporate leverage.
– US corps used as much debt before 1913 as after
– Increased corporate tax rates yield increased debt usage
– Decreases in the personal tax rates on equity income yield
decreased corporate debt usage.
Market-Value Leverage Ratios (Total Debt-toTotal Capital) For US Corporations, 1929-1993
%
50
45
40
35
30
25
20
15
10
5
0
1930
1940
1950
1960
1970
1980
1990
Book Value Debt Measures for U.S. NonFinancial Corporations, 1951-1996
Market Value Debt Measures for U.S. NonFinancial Corporations, 1951-1996
Capital Structure Patterns Observed
Worldwide (Continued)
• Existing S/Hs consider leverage-increasing events "good
news" and leverage-decreasing events "bad news"
– Stock prices rise when leverage-increasing events
announced, but fall for leverage-decreasing events.
• Corporations that are forced away from a preferred capital
structure tend to return to that structure over time
– Has occurred frequently, particularly for US firms that have
taken on large amounts of new debt to finance takeovers.
– More generally, corporations like to operate within target
leverage zones, and will issue new equity when debt ratios
get too high and will issue debt if they fall too low.
Theoretical Models Of Capital Structure
• First important theoretical model in corporate finance was
Modigliani & Miller’s (M&M) capital structure model in 1958
– In frictionless capital markets, with no taxes or transactions
costs, CS is irrelevant--doesn’t affect valuation
• Today’s best theoretical explanation for observed CS
patterns is the Agency Cost/Tax Shield Trade-Off Model
– Assumes that observed CSs result from firms trading off the
tax benefits of debt usage against the increasingly severe
agency costs as debt ratios approach critical levels
• The Pecking Order Theory based on two key assumptions
– (1) managers are better informed about the investment
opportunities faced by their firms than are outsiders; (2)
managers act in the best interests of existing shareholders.
• Signaling Model of CS also assumes asymmetric information
– but managers use debt as a costly signal to differentiate their
firms from weaker competitors
The M&M Capital Structure Model
• Assumptions of the M&M Capital Structure Model
– All physical assets are owned by corporations;
– Frictionless Capital markets: no corporate or personal income
taxes, securities are traded costlessly, no bankruptcy costs;
– Corporations can issue only risky equity and risk-free debt;
– Both individuals and corporations can borrow or lend at the
risk-free interest rate;
– Investors have identical expectations about the future stream
of corporate profits;
– There is no growth; all cash flow streams are perpetuities and
– All corps can be classified into one of several "equivalent
return classes" with returns on shares of all firms proportional
to, and perfectly correlated with, all other firms in that class.
• Seems absurdly unrealistic, but model very robust
– Only costless bankruptcy and no taxes are critical
assumptions.
M&M’s Proposition I: Capital Structure
Irrelevance
• Assume a company is operating in a world of frictionless capital
markets--but also where there is uncertainty about corporate
revenues and earnings.
• Assume also that a company belonging to a given risk class is
expected to earn operating profits averaging NOI each period
for the foreseeable future.
• Denote the market value of this firm's debt as D , its equity as E,
and the total value of its outstanding securities as V, where
• V = E + D . M&M’s Proposition I then asserts:
V = E + D  =
NOI
r
Eq. 12.1
• Meaning, "the market value of any firm is independent of its
capital structure & is given by capitalizing its expected return at
the rate r appropriate to its class."
Proving Proposition I Using Arbitrage
•
M&M proved their proposition using an arbitrage argument
– M&M demonstrate that an arbitrage opportunity exists if the
market value of the combined debt and equity of a levered
firm differs from that of an otherwise identical all-equity firm.
• Consider two firms, U and L, that belong to same risk class
and have same expected operating profit, $100,000 per year
– If reqd return r for firms of this risk class is 10%, both U&L
should have market values of $100,000  0.10 = $1,000,000
• Firm U has no debt ; instead has 20,000 shares outstanding
– Each share should be worth $50 since this price would offer
investors an expected return of 10%
• Levered firm L has both debt and equity outstanding.
– Assume it recently issued $500,000 worth of debt (at 6%) &
used proceeds of the issue to repurchase half of its
outstanding equity--10,000 shares at $50 each.
– Firm thus has 10,000 shares remaining O/S that should also
be worth $50 each, for a total of $500,000
Proving Proposition I Using Arbitrage (Cont)
• What return can firm L's shareholders expect to receive on
their levered shares?
– To compute an expected return, first note that firm is
obligated to pay 0.06 x $500,000 = $30,000 in interest (rdD)
from its expected NOI of $100,000
• The remaining $100,000 - $30,000 = $70,000 in net income
(NI) can either be distributed to shareholders or reinvested
– Expected return to firm L's S/Hs is this NI divided by market
value of its shares $70,000  $500,000 = 0.14, or 14%.
• We will refer to this as rl , the required return on levered
equity for firms in this risk class
– Table A summarizes what the financial values should be for
our two firms in a world where M&M's assumptions hold.
Table A: Equilibrium Expected Values For
Firms Unleverco (U) And Leverco (L)
Unleverco
Leverco
$100,000
$100,000
0
$30,000
$100,000
$70,000
10%
10%
$1,000,000
$1,000,000
10%
14%
Market Value of Equity (E)
$1,000,000
$500,000
Interest Rate on Debt (rd )
---
6%
Market Value of Debt (D)
0
$500,000
Net Operating Income (NOI)
Interest Paid (rd x D)
Net Income (NOI - rd D)
Required Return on Assets for
Firms in Risk Class (r)
Total Firm Value (NOI  r)
Required Return on Equity (ru or rl)
Example Of An Over-Valuation Of Leverage
• How could an "arbitrageur" profit from any valuation other
than that in Table A?
– For illustration, assume that investors are willing to pay a
premium price for the shares of levered firms
• Assume firm L's shares sell to yield a 12.5% expected return
– Implies a market value for firm L's equity (computed as NIrl)
of $70,000  0.125 = $560,000, or $56 per share.
• Added to MV of the firm's debt ($500,000), this implies a total
market value for firm L of $560,000 + $500,000 = $1,060,000
– But firm U's market value remains $1,000,000
– These "disequilibrium" relative values presented in Table B
• Market is clearly over-valuing levered equity, but how would
an arbitrageur exploit this and correct the mis-valuation?
– M&M demonstrated process now called “homemade leverage”
Table B: Disequilibrium Values For Firms U
And L Allowing Arbitrage
Net Operating Income (NOI)
Interest Paid (rd x D)
Net Income (NOI - rdD)
Unleverco
Leverco
$100,000
$100,000
0
$30,000
$100,000
$70,000
Required Return on Assets for
Firms in Risk Class (r )
Total Firm Value (NOI  r )
10%
9.43%
$1,000,000
$1,060,000
Reqd Return on Equity (ru or rl)
10%
12.5%
$1,000,000
$560,000
Interest Rate on Debt (rd)
---
6%
Market Value of Debt (D)
0
$500,000
Market Value of Equity (E)
Indicates disequilibrium values providing an arbitrage opportunity.
Proving Proposition I Using Homemade
Leverage
• To understand arbitrage process, keep in mind the firms U
& L are industrially equivalent
– Must therefore have the same business and operating risk.
• Remember also that investors can borrow on their own
account at the risk-free rate of interest.
– This allows them to make or unmake any corporate leverage
ratio they want within their own portfolios.
• Thus an investor who currently owns say 1% of firm L's
stock expects to earn a 12.5% return on that investment
– In dollar terms, 0.125 x $5,600 = $700.
• He or she could earn an arbitrage profit from the following:
– Sell firm L shares, borrow an amount equal to 1% of Firm L’s
debt, use proceeds to purchase Firm U shares
– This creates a levered equity position in Firm U
Proving Proposition I Using Homemade
Leverage (Continued)
• Arbitrageur initially held 1% of Firm L (50% debt: 50% equity)
– Above steps transformed this into an equally risky levered
equity stake (also 1%) in all-equity Firm U.
• Using homemade leverage, our investor has built a p/f of
$10,000 worth of firm U's stock with $5,000 in (personal) debt
– The net return to this new p/f is thus $1,000 return on stock $300 interest paid = $700 per year, the same return expected
on the original 1% stake in firm L's shares.
• But arbitrageur still has $600 remaining after investing only
$10,000 of the $10,600 raised.
– Assume invested into firm L stock to earn 0.125 x $600 = $75.
• Thus the total return from arbitrage is $700 + $75 = $775
– This exceeds the return on the original 1% stake in firm L's
stock, for no additional risk.
M&M Proposition II
• M&M's Proposition II specifies what the expected return on
levered equity must be for market equilibrium to hold.
• It asserts that the expected return, rl , on a levered firm's
equity is a linear function of that firm's debt-to-equity ratio:
rl = r
+ r
D

- rd
Eq. 12.2
E
• In M&M's words, "the expected yield of a share of stock is
equal to the appropriate capitalization rate r for a pure equity
stream in the class, plus a premium related to financial risk
equal to the debt-to-equity ratio times the spread between r and
rd (risk-free interest rate).
M&M Proposition II (Continued)
• Cost of equity rises steadily as debt is substituted for equity
in the firm’s CS but cost of debt & WACC remains constant
– Therefore, economic value derives solely from the stream of
operating profits a firm's assets will generate (Figure A).
• Valuation cannot be increased or decreased by repackaging
claims on the CF stream into "debt" & "equity" income
– Value is derived from a company's investments and
operations, not from financial marketing decisions.
• Expected NOI of a firm over time expressed as a mean value
& a probability distribution of possible outcomes
– Firm's assets will generate this stream of profits, and an
investor will discount each CF to the present using a discount
rate appropriate to a firm with this degree of business risk
• M&M developed for a world without income taxes
– With corporate income taxes, optimal CS becomes (almost)
100% debt, since interest tax deductibility minimizes
government’s tax claim on firm’s income stream (Figure C)
Figure A: A Firm’s Cost Of Equity (rs), Debt (i),
and WACC () Under M&M Proposition II
Reqd
Return
rl
WACC
r
rd
D/E
Figure B: Pie Chart Models Of Capital
Structure: Without Corporate Income Taxes
Equity
65%
Debt
35%
Equity
35%
Debt
65%
Figure C: Pie Chart Models Of Capital
Structure: With Corporate Income Taxes
Debt
25%
Taxes
25%
Equity
50%
Equity
10%
Taxes
10%
Debt
80%
Probability
The Valuation Of Net Operating Income (NOI)
In The M&M Valuation Model
0
D
E(NOI)
Net Operating Income
D*
The M&M Model With Corporate And
Personal Taxes
• Incorporating corporate taxes into M&M model changes
basic result fundamentally.
– Irrelevance no longer holds; leverage becomes preferred
• Demonstrate with two companies: Unleverco (U) and
Leverco (L), identical except for use of leverage
– Both operate in same industry, have NOI of $100,000
– Unleverco has no debt; Leverco has $500,000 at 6% interest
• Assume initially that corporate profits are taxed at company
level, at a 35% rate (c =0.35)
– No tax at personal level on interest or dividends
• Income statements for Unleverco and Leverco shown in
Table C.
Table C: Income Statements For Unleverco &
Leverco With Corporate Income Taxes
Unleverco
Leverco
$100,000
$100,000
0
(30,000)
Taxable income (NOI – rdD)
$100,000
$70,000
Corporate income tax (c = 0.35)
(35,000)
(24,500)
Net Income (NI)
$65,000
$45,500
Total income to private investors
(Interest + net income=dividends)
Value of tax shield each period
(c x rdD) = (0.35 x Interest)
$65,000
$75,500
0
$10,500
Net operating income (NOI)
Interest paid (rdD)
Determining The Present Value Of Corporate
Tax Shields
• Since Leverco pays interest, a tax-deductible expense, this
reduces taxable income.
• Can now use Eq. 12.3-5 to compute value of Unleverco (Vu),
the PV of the interest tax shields, and value of Leverco (Vl)
VU =
 NOI 1 -  c  = NI = $65,000 = $650,000
r
PV Int tax shields =
r
0.10
 c x r d D  =
rd
Eq 12.3
 c x D = 0.35 ($500,000) = $175,000
Vl = Vu + PV Tax shield = Vu + cD = $650,000 + $175,000 = $825,000
Eq 12.4
Eq 12.5
• The PV of tax shields on (perpetual) debt equals tax rate
times the face value of debt outstanding, and:
• The value of Leverco equals value of Unlverco, plus the PV
of debt tax shields!
The M&M Model With Corporate And
Personal Taxes
• Incorporating corporate income taxes yields a straightforward result: firms should use maximum (100%) leverage.
– This was an embarrassing, but obvious prediction of model
– Since not observed, something must be missing
• Two obvious candidates: personal taxes and deadweight
costs of corporate bankruptcy.
– Perhaps personal taxes offset corporate taxes.
– Direct b/r costs are small, indirect larger but not large
enough.
• Interest and dividends both taxed at personal level in US,
but capital gains are taxed less--and only upon realization.
– If profits are re-invested instead of paid as dividends, equity
income might enjoy tax preference at personal level.
Miller (1977) And The Gain From Leverage
• Miller (1977) proposed a model where corporate tax benefits
of leverage partially or fully offset by personal taxes.
• Presented “gains from leverage” formula, Eq 12.6:

1 -  c  1 -  ps 
G L = 1  D


1

pd


Eq 12.6
• Where: c = Tax rate on corporate profits
ps= Personal tax rate on income from stock (capital gain &dividends)
pd= Personal tax rate on income from debt (interest income)
D = Market value of a firm's outstanding debt
• This is a very general formulation; it includes original notax model (c = ps= pd= 0) as special case, where GL=0.
• Also includes case where only corporate taxes. If c = 0.35,
then gain from leverage, GL = [1- (1- 0.35)]xD= 0.35xD.
Miller (1977) And The Gain From Leverage
• For some combination of tax rates, the gain from leverage
disappears--or even becomes negative (benefit to equity).
• If (c =0.35), (ps= 0) and (pd= 0.40), as could happen if equity
income escapes personal taxation, GL becomes negative!

1 -  c  1 -  ps 

1 - 0.35 1 - 0 = ( 0.083 )
=
1
G L = 1 D
D


D




1
1
0
.
4
 pd




• Most people believe that actual combination of effective
corporate and personal tax rates partially (but not fully)
offsets tax benefits of corporate leverage.
– Figure 12.6 shows corporate & personal tax rates in OECD
• Miller went on to show how interest rate could be “grossed
up” to reflect tax benefit of corporate debt (Fig 12.5).
Bond Market Equilibrium In The Miller (1977)
Model
Rate of Interest
rd(B)
r0
1
1 - τ c 
rs(B)
ro
B*
Quantity of Bonds Outstanding
Basic Rates of Corporate Income Tax of Central
Government (%)
Upper bar, 2000; Lower bar,1986
Germany
Italy
United States
Netherlands
20
19
France
Britain
Sweden
Canada
Japan
Switzerland
0
10
20
30
40
50
60
Top Marginal Rates of Central Government
Personal Income Tax (%)
Upper bar, 2000; Lower bar,1986
Germany
Italy
United States
Netherlands
20
19
France
Britain
Sweden
Canada
Japan
Switzerland
0
10
20
30
40
50
60
70
80