Professor John ZietlowMBA 621

Professor John ZietlowMBA 621

Capital Structure: Theory And TaxesCapital Structure: Theory And Taxes

Chapter 12Chapter 12

Overview Of Capital Structure Theory & PracticeOverview 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 WorldwideCapital 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

Market Value Debt Ratios, Selected U.S. Corporations, July 2002

1.190.550.69Georgia Pacific

1.620.360.54American Electric Power

1.920.250.27Walt Disney

10.130.070.12Procter & Gamble

3.650.240.27Boeing

4.120.830.84General Motors

0.820.750.77Delta Air Lines

3.720.030.04ExxonMobil

4.0300Intel

5.5400Microsoft

Market to book ratio

L-T debt to total capital

Debt to total assetsCompany

Leverage Ratios For G-7 And Selected Developing Countries, 1980-91

Leverage Ratios For G-7 And Selected Developing Countries, 1980-91

Country

Total debt to total asset

(Book value %)

L-T debt to total assets

(Book value %)

L-T debt to total capital

(Market value %)

United States

58%

37%

28%

Japan 69 53 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)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-to-Total Capital) For US Corporations, 1929-1993Market-Value Leverage Ratios (Total Debt-to-Total Capital) For US Corporations, 1929-1993

05

101520253035404550

%

19901980197019601940 19501930

Book Value Debt Measures for U.S. Non-Financial Corporations, 1951-1996

Book Value Debt Measures for U.S. Non-Financial Corporations, 1951-1996

Market Value Debt Measures for U.S. Non-Financial Corporations, 1951-1996

Market Value Debt Measures for U.S. Non-Financial Corporations, 1951-1996

Capital Structure Patterns Observed Worldwide (Continued)

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 StructureTheoretical 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 ModelThe 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

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:

r

NOI = D + E = V

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 ArbitrageProving 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)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)

Table A: Equilibrium Expected Values For Firms Unleverco (U) And Leverco (L)

Unleverco Leverco

Net Operating Income (NOI) $100,000 $100,000

Interest Paid (rd x D) 0 $30,000

Net Income (NOI - rd D) $100,000 $70,000

Required Return on Assets for Firms in Risk Class (r)

10% 10%

Total Firm Value (NOI r) $1,000,000 $1,000,000

Required Return on Equity (ru or rl) 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

Example Of An Over-Valuation Of LeverageExample 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 NIrl)

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

Table B: Disequilibrium Values For Firms U And L Allowing Arbitrage

Unleverco Leverco

Net Operating Income (NOI) $100,000 $100,000

Interest Paid (rd x D) 0 $30,000

Net Income (NOI - rdD) $100,000 $70,000

Required Return on Assets for Firms in Risk Class (r )

10% 9.43%

Total Firm Value (NOI r ) $1,000,000 $1,060,000

Reqd Return on Equity (ru or rl) 10% 12.5%

Market Value of Equity (E) $1,000,000 $560,000

Interest Rate on Debt (rd) --- 6%

Market Value of Debt (D) 0 $500,000

Indicates disequilibrium values providing an arbitrage opportunity.

Proving Proposition I Using Homemade Leverage

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)

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 IIM&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:

• 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).

Eq. 12.2 E

D r - r+ r = r dl

M&M Proposition II (Continued)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)

ReqdReturn

WACC

D/E

rd

r

rl

r + (r - r d

)D/E

Figure A: A Firm’s Cost Of Equity (rs), Debt (i), and WACC () Under M&M Proposition II

Figure A: A Firm’s Cost Of Equity (rs), Debt (i), and WACC () Under M&M Proposition II

Figure B: Pie Chart Models Of Capital Structure: Without Corporate Income Taxes

Figure B: Pie Chart Models Of Capital Structure: Without Corporate Income Taxes

Equity65%

Debt35%

Equity35%

Debt65%

Figure C: Pie Chart Models Of Capital Structure: With Corporate Income Taxes

Figure C: Pie Chart Models Of Capital Structure: With Corporate Income Taxes

Equity50%

Debt25%

Equity10%

Debt80%

Taxes25%

Taxes10%

The Valuation Of Net Operating Income (NOI) In The M&M Valuation Model

The Valuation Of Net Operating Income (NOI) In The M&M Valuation Model

0 D E(NOI) D*

Net Operating Income

Pro

bab

ilit

y

The M&M Model With Corporate And Personal Taxes

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

Table C: Income Statements For Unleverco & Leverco With Corporate Income Taxes

Unleverco Leverco

Net operating income (NOI) $100,000 $100,000

Interest paid (rdD) 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)

$65,000 $75,500

Value of tax shield each period (c x rdD) = (0.35 x Interest)

0 $10,500

Determining The Present Value Of Corporate Tax Shields

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)

$650,000 =

0.10

$65,000 =

r

NI =

r

- 1 NOI = V

cU

Eq 12.3

$175,000 = ($500,000) 0.35 = D x =

r

Dr x = shieldstax Int PV c

d

dc

Vl = Vu + PV Tax shield = Vu + cD = $650,000 + $175,000 = $825,000 Eq 12.5

Eq 12.4

• 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

The M&M Model With Corporate And Personal Taxes

• Incorporating corporate income taxes yields a straight-forward 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) 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:

D

- 1

- 1 - 1 - 1 = G

pd

pscL

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 no-tax 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 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!

D).(=D

. - 1

- 1 . - 1 - 1 =D

- 1

- 1 - 1 - 1 = G

pd

pscL 0830

40

0350

• 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

Bond Market Equilibrium In The Miller (1977) Model

Quantity of Bonds Outstanding

ro

τ - r

c1

10

Rat

e o

f In

tere

st

B*

rs(B)

rd(B)

Basic Rates of Corporate Income Tax of Central Government (%)

Upper bar, 2000; Lower bar,1986

Basic Rates of Corporate Income Tax of Central Government (%)

Upper bar, 2000; Lower bar,1986

Top Marginal Rates of Central Government Personal Income Tax (%)

Upper bar, 2000; Lower bar,1986

Top Marginal Rates of Central Government Personal Income Tax (%)

Upper bar, 2000; Lower bar,1986