Capital Structure I:

Basic Concepts

The Capital-Structure Questionand The Pie Theory

The value of a firm is defined to be the sum of the value of the firm’s debt and the firm’s equity.

V = B + SIf the goal of the management of the firm is to make the firm as valuable as possible, the the firm should pick the debt-equity ratio that makes the pie as big as possible.

Value of the Firm

S BS BS BS B

The Capital-Structure Question

There are really 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.

Financial Leverage, EPS, and ROE

CurrentAssets $20,000Debt $0Equity $20,000Debt/Equity ratio 0.00Interest rate n/aShares outstanding 400Share price $50

Proposed$20,000

$8,000$12,000

2/38%240$50

Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.)

EPS and ROE Under Current Capital Structure

Recession Expected ExpansionEBIT $1,000 $2,000 $3,000Interest 0 0 0Net income $1,000 $2,000 $3,000EPS $2.50 $5.00 $7.50ROA 5% 10% 15%ROE 5% 10% 15%

Current Shares Outstanding = 400 shares

EPS and ROE Under Proposed Capital Structure

Recession Expected ExpansionEBIT $1,000 $2,000 $3,000Interest 640 640 640Net income $360 $1,360 $2,360EPS $1.50 $5.67 $9.83ROA 5% 10% 15%ROE 3% 11% 20%

Proposed Shares Outstanding = 240 shares

EPS and ROE Under Both Capital Structures

LeveredRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest 640 640 640Net income $360 $1,360 $2,360EPS $1.50 $5.67 $9.83ROA 5% 10% 15%ROE 3% 11% 20%Proposed Shares Outstanding = 240 shares

All-EquityRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest 0 0 0Net income $1,000 $2,000 $3,000EPS $2.50 $5.00 $7.50ROA 5% 10% 15%ROE 5% 10% 15%Current Shares Outstanding = 400 shares

Financial Leverage and EPS

(2.00)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1,000 2,000 3,000

EP

S

Debt

No Debt

Break-even point

EBIT in dollars, no taxes

Advantage to debt

Disadvantage to debt

Assumptions of the Modigliani-Miller Model

Homogeneous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows Perfect Capital Markets:

Perfect competition Firms and investors can borrow/lend at the same rate Equal access to all relevant information No transaction costs No taxes

Homemade Leverage: An Example

Recession Expected ExpansionEPS of Unlevered Firm $2.50 $5.00 $7.50

Earnings for 40 shares $100 $200 $300Less interest on $800 (8%) $64 $64 $64Net Profits $36 $136 $236ROE (Net Profits / $1,200) 3% 11% 20%

We are buying 40 shares of a $50 stock on margin. (40% of funds borrowed) We get the same ROE as if we bought into a levered firm.Our personal debt equity ratio is:

32

200,1$

800$ S

B

Homemade (Un)Leverage:An Example

Recession Expected ExpansionEPS of Levered Firm $1.50 $5.67 $9.83

Earnings for 24 shares $36 $136 $236Plus interest on $800 (8%) $64 $64 $64Net Profits $100 $200 $300ROE (Net Profits / $2,000) 5% 10% 15%

Buying 24 shares of an other-wise identical levered firm along with the some of the firm’s debt gets us to the ROE of the unlevered firm.This is the fundamental insight of M&M

The MM Proposition I: Capital Structure and Firm Value

Assuming a un-levered firm, and funds from equity. The after-tax profit is The operation cash flows is To maintain same asset size, the firm needs to invest, same as

Dep., on capital. So the firm’s free cash flows becomes

The value of this un-levered firm, assuming perpetuity, is defined as

ksu is the cost of capital (equity) for a un-levered firm.

EBIT t( )1

EBIT t Depr( ) .1

EBIT t Depr Investment EBIT t( ) . ( )1 1

VEBIT t

kusu

( )1

For a levered firm, funds from both equity and debt. The total cash flow for firm can be divided by that goes to

Debt holders: where D is the value of debt, and kD is risk-free rate

Stockholders:

So the total cash flows to firm becomes

EBIT(1-t) is the same as that of un-levered firm, and tkD is a risk-free cash flow. So the value of firm is

When t=0, then VL = VU

k DD

( ) (1 ) . ( ) (1 )D DEBIT k D t Depr Investment EBIT k D t

( ) (1 ) (1 )L D D DCF EBIT k D t k D EBIT t tk D

VEBIT t

k

tk D

kV tDL

su

D

Du

( )1

Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes

All-EquityRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest 0 0 0EBT $1,000 $2,000 $3,000Taxes (Tc = 35% $350 $700 $1,050

Total Cash Flow to S/H $650 $1,300 $1,950

LeveredRecession Expected Expansion

EBIT $1,000 $2,000 $3,000Interest ($800 @ 8% ) 640 640 640EBT $360 $1,360 $2,360Taxes (Tc = 35%) $126 $476 $826Total Cash Flow $234+640 $468+$640 $1,534+$640(to both S/H & B/H): $874 $1,524 $2,174

EBIT(1-Tc)+TCrBB $650+$224 $1,300+$224 $1,950+$224$874 $1,524 $2,174

The MM Proposition II, capital structure and Cost of Capital (No Taxes)

The cost of levered equity is defined as

The WACC is

V V tD S DL u

, when t=0

( )

L usu

su

EBITV V S D

k

EBIT k S D

kEBIT k D

SslD

( )

( )

su DDsl

su su D su su D

k S D k DEBIT k Dk

S SD D D

k k k k k kS S S

WACC kS

Vk

D

Vk k k

D

S

S

Vk

D

V

kS

Vk

D

Vk

D

Vk

D

Vk

S D

Vk

sl D su su D D

su su D D su su

( ) ( ) [ ( ) ]( ) ( )

( ) ( )

The Cost of Equity, the Cost of Debt, and the Weighted Average Cost of Capital: MM Proposition II with No Corporate Taxes

Debt-to-equity Ratio

Cos

t of

capi

tal:

r (%

)

r0

kD

( ) ( )sl D su

S DWACC k k k

V V

( )sl su su D

Dk k k k

S

rB

The MM Proposition II, capital structure and Cost of Capital (With Taxes)

sl

D

k

tDkEBITS

)1)((

S

tDktEBIT

S

tDkEBITk DD

sl

)1()1()1)((

tDk

tEBITtDVV

suuL

)1(

tDktEBITkV susuL )1(

susuL ktDDSktDVtEBIT )()()1(

( )(1 ) (1 )

( ) ( )(1 )

su su D DDsl

su su su D D su su D

S D k tDk k D tk DEBIT t k D tk

S SD D

k k tk k tk k k k tS S

)1(

))(1())(1()1(

))(1()]()1)(([))(1()(

V

tDk

V

Dtk

V

Dk

V

Sk

V

Dtk

V

Dtk

V

Dtk

V

Sk

V

Dtk

V

S

S

Dtkkk

V

Dtk

V

SkWACC

su

sususuDDsusu

DDsusuDsl

The MM Proposition II, capital structure and Cost of Capital (With Taxes)

The Effect of Financial Leverage on the Cost of Debt and Equity Capital with Corporate Taxes

Debt-to-equityratio (D/S)

Cost of capital (%)

ksu

kD

( )(1 )su su D

Dk k k t

S

[1 ]su

DWACC k t

S D

( )su su D

Dk k k

S

Integrate capital structure theory with the Capital Asset Pricing Model

Cost of Capital

Capital Asset Pricing Model

capital structure theory

WACC

Dk

suk

slk

DfmfD RRERk ])([

ufmfsu RRERk ])([

lfmfsl RRERk ])([

V

Dtk

V

Sk Dsl )1(

fDD Rk ,0

S

Dtkkk Dsusu )1)((

]1[V

tDk su

[ ( ) ] ( )(1 )sl f m f l su su D

Dk R E R R k k k t

S

[ ( ) ] , and 0,su f m f u D D fk R E R R k R

S

DtRRERRERRRERk ufmufmflfmfsl )1(])([])([])([

S

DtRRERRERRE ufmufmlfm )1(])([])([])([

])1(1[S

Dtul

])1[(])([])([

])1(1[])([])([

S

DtRRERRER

S

DtRRERRRERk

ufmfmuf

ufmflfmfsl

Riskfree rate fR

Operating risk premium ))(( fmu RRE

Financial risk premium ])1)[()((S

DtRRE fmu

])1(1[S

Dtul Leveled beta

Example: One firm which is currently totally equity financed. If its expected perpetual operating income is $10,000 per year, and last forever. Assuming its current cost of capital is 12%, and tax rate is 25%.

Question 1: What is the current market value for the firm?

Current value of firm is

VEBIT t

kusu

( ) $ , ( %)

.$ ,

1 10 000 1 25

0 1262 500

If the firm issues $40,000, 8%coupon bond and uses the proceeds to buy back common stock shares. What will be the new market value for the firm and equity after the leverage and buy back.

V V tDL u $ , . , $ ,62 500 0 25 40 000 72 500

V S D S V DL L , $ , $ , $ ,72 500 40 000 32 500

What is the new cost of equity after the debt financing?

( )(1 )sl su su D

Dk k k k t

S

=0.12+(0.12-0.08)(1-0.25)(40,000/32,500)=15.69%

What is the new WACC for the firm after the debt financing?

WACC= (1 )sl D

S Dk k t

V V

=15.69%(32,500/72,500)+8%(1-25%)(40,000/72,500)=10.34%

WACC= [1 ]su

tDk

V =12%[1-0.25(40,000/72,500)]= 10.34%

One firm now has 20% debt and 80% equity. The CFO believes it can increase leverage to 40% debt financing without raising its 7% cost of debt. Assuming that and marginal tax rate is 25%

What is the current cost of equity and WACC for the firm?

lfmfsl RRERk ])([ =7%+(15%-7%)*0.6=11.8%

WACC= (1 )sl D

S Dk k t

V V

=11.8%(0.8)+7%(1-.25)(0.2)=10.49%

( ) 15%, and =0.6mE R

If the firm increases its debt ratio from 20% to 40%, what will be its WACC?

When debt ratio is 20%,

WACC ktD

Vk

k

su su

su

[ ] [ . . ] . %

. %

1 1 0 25 0 20 10 49

11 04

When debt ratio increases to 40%

WACC ktD

Vsu [ ] . %[ . . ] . %1 11 04 1 0 25 0 40 9 94

Alternatively, we can apply CAPM to conduct the calculation, when debt ratio is 20%

L u u

u

tD

S

[ ( ) ], . [ ( . ).

.]

.

1 1 0 6 1 1 0 250 2

0 80 5053

When debt ratio increases to 40%

L u tD

S [ ( ) ] . [ ( . )

.

.] .1 1 0 5053 1 1 0 25

0 4

0 60 7580

lfmfsl RRERk ])([ =7%+(15%-7%)*0.7580 =13.064%

WACC= (1 )sl D

S Dk k t

V V

=13.064% (0.6)+7%(1-0.25)(0.4)=9.94%

If the firm faces a project (same risk as the firm) with a return of 9.5%, should the firm accept the project?

No it should not. The project return 9.5% is lower than that of WACC 9.94%。