Capital Structure Modigliani-Miller 1Finance - Pedro Barroso.

Capital StructureModigliani-Miller

1Finance - Pedro Barroso

Capital Structure and the Pie

• Market value of a firm is the sum of the value of the firm’s debt and the firm’s equity: V = D + E

• Goal of the firm’s management is to make the firm as valuable as possible, then the firm should pick the debt-to-equity ratio that makes the pie as big as possible

Value of the Firm

S DE


Stockholder Interests

There are two important questions:1.Why should the stockholders care about maximizing firm value? Perhaps they should be interested in strategies that maximize shareholder value.2.What is the ratio of debt-to-equity that maximizes the shareholder’s value?

As it turns out, changes in capital structure benefit the stockholders if and only if the value of the firm increases.


AT&TBoeingBoston EdisonJohn DeereDelta Air LinesDisneyGeneral MotorsHewlett-PackardMcDonalds3MPhilip MorrisRaytheonSafeway StoresTexacoWal-Mart

Company Name

Debt

Debt + Mkt Equity

Debt

Total Book Assets

EBITDA

Interest

20%15494053 9611315 627 9552714

29%1342373220371731123512532636

16.3614.37 3.49 2.47

1.0814.09

2.9821.67

7.1859.70

6.7237.88

3.064.707.54

Variety of Capital Structures Out There


Modigliani-Miller Assumptions • Perfect capital markets:

– no transaction costs and no taxes– no bankruptcy costs– no agency costs– no asymmetric information in capital markets– no arbitrage


• Total market value of the firm (debt + equity) is not affected by the capital structure– “The size of the pie does not change no matter

how you slice it”– A firm’s value is determined by its real assets and

growth opportunities, not by the types of securities it issues

– Cost of capital is independent of capital structure

MM Proposition I (No Taxes)


MM Proposition I (No Taxes)

• We can create a levered or unlevered position by adjusting the trading in our own account

• This homemade leverage suggests that capital structure is irrelevant in determining the market value of the firm:

VL = VU


• Consider twin firms with same assets that generate perpetual cash flow FCF

• Notice that FCF = EBIT (= 100)– No taxes– Zero growth: Depreciation = CAPEX, Working capital = 0

• Unlevered firm U: all-equity firm with value VU = E (= 1500)– VU = EBIT / rU , rU is cost of capital of unlevered firm

• Levered firm L: firm with debt and equity; firm value VL = D + E (= 500 + 1000 = 1500)

– Debt is perpetual bond with coupon of DrD (rD = 10%)

Home-Made (Un)Leverage


• Strategy A: investor buys 10% of levered firm (L) equity, which is 10%E

– Cost = 10%(VL-D)

• Strategy B: investor buys 10% of unlevered firm (U) with loan of 10%D at interest rate of rD plus own investment of 10%(VU – D)

– Cost= 10%(VU – D)



• Strategy A payoff: 10%[EBIT – DrD] – 10% [100 – 500 x 10%] = 5

• Strategy B payoff: 10%EBIT – 10%DrD = 10% [EBIT – DrD] – 10% x 100 – 10% x 500 x 10% = 5



• No arbitrage condition: investments with equal payoffs must have same initial investment10% (VL-D) = 10%(VU – D) [10% x 1000 = 10% (1500 - 500)]

VU = D + E

VU = VL

• Investors can leverage (or unleverage) a firm’s capital structure to any given level through a personal loan (or deposit)



MM Proposition II (No Taxes)

where:rU is cost of capital of unlevered firm (all-equity)

rE is cost of equity (or required return on equity)

rD is cost of debtE is market value of equityD is market value of debtWACC is weighted-average cost of capital

ED

rrrr

WACCr

DUUE

U

)(


MM Proposition II (No Taxes)• Define the weighted average cost of capital:

• Set rU = WACC (cost of capital is independent of capital structure)

ED rED

Er

EDD

WACC

ED

rrrr

EED

rED

Drr

rED

Er

EDD

r

DUUE

DUE

EDU

)(


MM Proposition II (No Taxes)

Debt-to-equity ratio

Cost

of c

apita

l

rU

rD

ED rED

Er

EDD

WACC

ED

rrrr DUUE )(

rD

ED


MM II (No Taxes)

• Increasing the debt load does not affect the riskiness of the assets, but it does increase the riskiness of the equity

• In the same firm, rD is always less than rE, because the debt has a higher priority and thus less risk

• But the weighted sum (WACC) of the costs of debt and equity is always a constant


MM (With Corporate Taxes)• Corporate taxes on profits introduce a new

claimholder on the firm’s cash flows (government)– Maximum corporate tax rate in the US is 34% and 25% in

Portugal

• Minimizing government’s share of the pie leaves more for debt and equity holders

• Financing policy can be a tool to increase firm value (i.e. market value of debt plus market value of equity)


• A firm has pre-tax cash flow FCF = EBIT and interest payments D rD

• Firm pays corporate tax at rate t• After-tax cash flow to shareholders and

debtholders: FCF = EBIT (1 – t) + t D rD

– NI + D rD = (EBIT – D rD ) (1 – t) + D rD

– t D rD is tax shield from debt (interest tax shield)• Levered firm value is present value of FCFs

MM (With Corporate Taxes)

tDVVr

tDrr

tEBITV

UL

D

D

UL

)1(


ExampleUnlevered Firm Levered Firm

EBIT 100 100

Interest expenses (rD x D) 0 10 = 10% x 100

Earnings before taxes 100 90

Taxes (t = 30%) 30 27

Net Income 70 63

FCF (NI + Interest expenses) 70 73 = 63 + 10

Finance - Pedro Barroso 18

MM Propositions I & II (With Taxes)

• Proposition I: Firm value increases with leverage

VL = VU + tD

• Proposition II: Some of the increase in equity risk and return is offset by the interest tax shield

• Optimal capital sructure: 100% debt!

ED

trrrr DUUE )1)((


MM Proposition II (With Taxes)• Expected cash flow from LHS of balance sheet can

be written as:

• Expected cash flow to debtholders and stockholders can be written as:

• Thus,

DUU tDrVr

DE DrEr

ED

trrrr

rE

Dtr

EDtE

r

rE

Dtr

EV

r

DrErtDrrV

DUUE

DUE

DUU

E

DEDUU

)1)((

)1()1(

)1(


WACC (With Taxes)• Weighted average cost of capital (WACC) with

corporate taxes:

• Thus,

EDDt

rWACC

EDD

tED

ErWACC

ED

trrrED

Ert

EDD

WACC

U

U

DUUD

1

)1(

)1)(()1(

ED rED

Ert

EDD

WACC

)1(


MM Proposition II (With Taxes)

Debt-to-equityratio (D/E)

Cost of capital

rU

rD

ED

trrrr DUUE )1)((

EDDt

rrED

Etr

EDD

WACC UED 1)1(

ED

rrrr DUUE )(


Total Cash Flow to Investors

Levered firm pays less in taxes than does the all-equity firm

Thus, the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm

This is how cutting the pie differently can make the pie “larger” - the government takes a smaller slice of the pie!

E G E G

D

All-equity firm Levered firm


Caveats• Correct tax rate to value the interest tax shield is the

expected marginal tax rate, or the expected increase in the firm’s tax liability when its taxable income increases by $1. This may not be the statutory rate!

• The firm may not always be taxable– Earnings may not be large enough to fully utilize the shield – Tax losses can be carried back 2 years or forward 20 years in

the U.S.; only carry forward 4 years in Portugal

• Non-debt tax shields may already suffice to offset earnings– Depreciation– Investment tax credit


Capital Structure Modigliani-Miller 1Finance - Pedro Barroso.

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