Théorie Financière Structure financière et coût du capital

Théorie Financière

Structure financière et coût du capital

P f A d é F bProfesseur André Farber

Risk and return and capital budgetingp g g

• Objectives for this session:Object ves o t s sess o :– Beta of a portfolio– Beta and leverage– Weighted average cost of capital– Modigliani Miller 1958

WACC ith ta es– WACC with taxes

November 14, 2009 Tfin 2005 11 Intro to capital structure |2

Levers of Accounting Performanceg

Return on Equity

Return on Invested Capital Leverage

fi iProfit Margin Asset Turnover

November 14, 2009 Tfin 03 Cash flows |3

Return on invested capitalp

• Return on assets (net)= Net income / Total assetsetu o assets ( et) Net co e / ota assets• Advantage: fits with DuPont system

• ROE = ROA x Equity multiplier• Limitation: Net income = EBIT - Interest expense - TaxesLimitation: Net income EBIT Interest expense Taxes

– Depends on capital structure:• 1. Interest expense: function of interest-bearing debt• 2 Interest expense : tax deductible• 2. Interest expense : tax deductible

• Preferred measure: Return on Invested Capital (ROIC)

TaxRate)-EBIT(1ROIC

NB ROIC ROA ( ) (1 T )

debt bearingInterest equity rs'StockholdeTaxRate)EBIT(1ROIC+

=

• NB: ROIC = ROA (gross) (1 - Tax rate)• = ROE of a all equity financed firm


Financial leverageg

• Financial leverage magnifies ROE only when ROA (gross) is greater than inancial leve age magnifies O only when O (g oss) is g eate thanthe interest rate on debt.

• Balance sheet: TA = SE + D• Income statement: NI = EBIT - INT- TAX• Income statement: NI EBIT - INT- TAX• Interest expense INT = r D (Interest expense = Interest rate x Interest-bearing debt)

• Taxes TAX = (EBIT - r D) Tc (Taxes = Taxable income x Tax rate)

TEBIT )1(

SED

cTrSETA

TAcTEBIT

SENIROE ×−−×

−×== )1(

)1(

DSEDTrROICROICROE c ×−−+= ))1((

• Remember : ROIC = ROAgross (1 - Tc)• ROE = ROIC + (ROAgross - r) (1-Tc) (D/SE)


Leverage - example



Beta of a portfoliop

• Consider the following portfolioCo s de t e o ow g po t o oStock Value BetaA nA × PA βA

B nB × PB βB

• The value of the portfolio is:V × P + × PV = nA × PA

+ nA × PB

• The fractions invested in each stock are: Xi = ( ni Pi) / V for i = A,Bi ( i i) ,

• The beta of the portfolio is the weighted average of the betas of the i di id l kindividual stocks

βP = XA βA + XB βB


Examplep

• Stock $ β XStock $ β X• ATT 3,000 0.76 0.60• Genetech 2,000 1.40 0.40• V 5,000

• β 0 60 * 0 76 + 0 40 * 1 40 1 02• βP = 0.60 * 0.76 + 0.40 * 1.40 = 1.02


Application 1: cost of capital for a divisionpp p

• Firm = collection of assetsco ect o o assets• Example: A company has two divisions• Value($ mio) β• Electrical 100 0.50• Chemical 500 0.90• V 600• V 600• βfirm = (100/600) * (0.50) + (500/600) * 0.90 = 0.83

• Assume: rf = 5% rM - rf = 6%• Expected return on stocks: r = 5% + 6% × 0.83 = 9.98 %• An adequate hurdle rate for capital budgeting decisions ? No• The firm should use required rate of returns based on project risks:• Electricity : 5 + 6 × 0 50 = 8% Chemical : 5 + 6 × 0 90 = 10 4%November 14, 2009 Tfin 2005 11 Intro to capital structure |10

• Electricity : 5 + 6 × 0.50 = 8% Chemical : 5 + 6 × 0.90 = 10.4%

Application 2: leverage and betapp g

• Consider an investor who borrows at the risk free rate to invest in the Co s de a vesto w o bo ows at t e s ee ate to vest t emarket portfolio

• Assets $ β X• Market portfolio 2,000 1 2• Risk-free rate -1,000 0 -1• V 1 000V 1,000

• βP = 2 × 1 + (-1) × 0 = 2


Expected ReturnExpected ReturnExpected Return

14%

P20%

M

P

8%

14%M

8%

14%

21 2 BetaSigma


Cost of capital with debtp

• Up to now, the analysis has proceeded based on the assumption that Up to ow, t e a a ys s as p oceeded based o t e assu pt o t atinvestment decisions are independent of financing decisions.

• Does • the value of a company change • the cost of capital change

• if leverage changes ?if leverage changes ?


An examplep

• CAPM holds – Risk-free rate = 5%, Market risk premium = 6%C o ds s ee ate 5%, a et s p e u 6%• Consider an all-equity firm:

• Market value V 100• Beta 1• Cost of capital 11% (=5% + 6% * 1)

• No consider borro ing 20 to b back shares• Now consider borrowing 20 to buy back shares.• Why such a move?

• Debt is cheaper than equityp q y• Replacing equity with debt should reduce the average cost of

financingWh ill b h fi l i• What will be the final impact

• On the value of the company? (Equity + Debt)?• On the weighted average cost of capital (WACC)?


On the weighted average cost of capital (WACC)?

Weighted Average Cost of Capitalg g p

• An average of:ave age o :• The cost of equity requity

• The cost of debt rdebt

• Weighted by their relative market values (E/V and D/V)

VDr

VErr debtequitywacc ×+×≡

• Note: V = E + D


Modigliani Miller (1958)g ( )

• Assume perfect capital markets: not taxes, no transaction costsssu e pe ect cap ta a ets: ot ta es, o t a sact o costs

• Proposition I: • The market value of any firm is independent of its capital structure:

V = E+D = VU

• Proposition II:• The weighted average cost of capital is independent of its capital g g p p p

structurerwacc = rA

h f l f ll f• rA is the cost of capital of an all equity firm


Using MM 58g

• Value of company: V = 100Va ue o co pa y: V 00• Initial Final• Equity 100 80• Debt 0 20• Total 100 100 MM I

• WACC = rA 11% 11% MM II

• Cost of debt - 5% (assuming risk-free debt)• D/V 0 0.20• Cost of equity 11% 12.50% (to obtain rwacc = 11%)• E/V 100% 80%


Cost of equity calculationq y

V (=VU ) = E + D

Value of equityValue of all-equity

firm

q y rE

rA

Value of debtrD

rA

Value of debt

LD

LEA V

DrVErr +=


LL VV

Why is rwacc unchanged?y wacc g

• Consider someone owning a portfolio of all firm’s securities (debt and Co s de so eo e ow g a po t o o o a s secu t es (debt a dequity) with Xequity = E/V (80% in example ) and Xdebt = D/V (20%)

• Expected return on portfolio = requity * Xequity + rdebt * Xdebt

• This is equal to the WACC (see definition):r fli = rrportoflio rwacc

• But she/he would, in fact, own a fraction of the company. The expected return would be equal to the expected return of the unlevered (all equity) fifirm

rportoflio = rA

• The weighted average cost of capital is thus equal to the cost of capital ofThe weighted average cost of capital is thus equal to the cost of capital of an all equity firm

rwacc = rA


What are MM I and MM II related?

• Assumption: perpetuities (to simplify the presentation)ssu pt o : pe petu t es (to s p y t e p ese tat o )• For a levered companies, earnings before interest and taxes will be split

between interest payments and dividends paymentsEBIT = Int + Div

• Market value of equity: present value of future dividends discounted at the cost of equityq y

E = Div / requity

• Market value of debt: present value of future interest discounted at the cost f d bof debt

D = Int / rdebt


Relationship between the value of company and p p yWACC

• From the definition of the WACC:o t e de t o o t e W CC:rwacc * V = requity * E + rdebt * D

• As requity * E = Div and rdebt * D = Intrwacc * V = EBIT

V EBIT /V = EBIT / rwacc

Market value of levered firm

EBIT is independent of

If value of company varies with leverage solevered firm independent of

leveragevaries with leverage, so does WACC in opposite direction


MM II: another presentationp

• The equality rwacc = rA can be written as:e equa ty wacc A ca be w tte as:

Drrrr d btAAit ×−+= )(

• E pected ret rn on eq it is an increasing f nction of le erage:

Errrr debtAAequity ×+ )(

• Expected return on equity is an increasing function of leverage:requity

12.5%

rA11% rwacc

Additional cost due to leverage

D/Erdebt

5%


/0.25

Why does requity increases with leverage?y equity g

• Because leverage increases the risk of equity.ecause eve age c eases t e s o equ ty.• To see this, back to the portfolio with both debt and equity.

• Beta of portfolio: βportfolio = βequity * Xequity + βdebt * Xdebt

• But also: βportfolio = βAsset

• So:• So:

DED

DEE

DebtEquityAsset +×+

+×= βββ

• orDED

DebtAssetAssetEquity ×−+= )( ββββ


Back to examplep

• Assume debt is riskless:

EV

ED

AssetAssetEquity βββ =+= )1(

25.1)201(1 =+×=Equityβ

EE AssetAssetEquity βββ )(

25.1)80

1(1 +Equityβ

%50.1225.1%6%5)( =×+=−+= E itFMFE it rrrr β %50.1225.1%6%5)( ×++ EquityFMFEquity rrrr β


Summary: the Beta-CAPM diagramy g

ED

AssetAssetEquity βββ +=β)( FMF rrrr −+= Beta

βL

βEquity

U

D/Er 0

βAsset

rE rA rD b =rf D/Er 0rEquity rAsset rDebt rf

EDrrrr DebtAssetAssetEquity )( −+=

November 14, 2009Executive Master of Finance 2007 01

Modigliani Miller |25D/E

rEquityrDebtWACC

Risky debt: Merton modely

• Limited liability: rules out negative equityted ab ty: u es out egat ve equ ty

Market value of equity

Equity similar to a call i hequity option on the company

50

Company goesbankrupt if V<F

Market value of company VFace value80


Face valueF 100

80150

Risk debt decompositionp

Risky debt = Risk‐free debt – Put

Marketvalue of

y80 = 100 ‐ 20

debt

F l f d b

Bankruptcy

Face value of debt

Market value of companyFace value 80


of debt

Figure 21.9 Beta of Debt and Equity

The blue curve is the beta of equity and the red curve is the beta of debt as a function of the firm’s debt-to-equity ratio. The black line is the approximation derived in Chapter 14—the beta of equity when the beta of debt is assumed to be zero. The firm is assumed to hold five-year zero-coupon debt and reinvest all its earnings (The firm’s beta of assets is 1 the risk free interest rate is 3% per year

November 14, 2009Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 21-28

and reinvest all its earnings. (The firm s beta of assets is 1, the risk-free interest rate is 3% per year, and the volatility of assets is 20% per year.)

Corporate Tax Shieldp

• Interest are tax deductible => tax shieldte est a e ta deduct b e ta s e d• Tax shield = Interest payment × Corporate Tax Rate

= (rD × D) × TC

• rD : cost of new debt• D : market value of debt• Val e of le ered firm• Value of levered firm

= Value if all-equity-financed + PV(Tax Shield)• PV(Tax Shield) - Assume permanent borrowing( ) p g

DTr

DrTTaxShieldPV CD

DC =×

=)(

VL=VU + TCD

rD


Cost of equity calculationq y

VU + T = E + D

Value of equityValue of all-equity

firm

q y rErA

Value of debtrD

Value of tax shield

Value of debtrD

LD

LE

L

CD

L

UA V

DrVEr

VDTr

VVr +=+


LLLL VVVV

Cost of equity calculation (2)q y ( )

VDr

VEr

VVTSr

VVTSVr DATS

LA +=+

−

G lDrErVTSrVTSVr

VVVV

DATSLA

LLLL

+=+− )(

VTSrrDrrrr )()( −−−+=

General formula

D

Err

Errrr TSADAAE )()(+=

EDTrrrr CDAAE )1)(( −−+=If rTS = rD & VTS = TCD

DT )1)((+ ββββE

TCDAAE )1)(( −−+= ββββ

Similar formulas for beta equity (replace r by β)


WACC

CDEDTrErwacc −+= )1(

U

LCD

LE

rVr

VTr

Vrwacc

<

+ )1(

AL

A rV

r <=


Examplep

A B Assume rA= 10%

Balance SheetTotal Assets 1,000 1,000

(1) Value of all-equity-firm:VU = 144 / 0.10 = 1,440

Book Equity 1,000 500Debt (8%) 0 500

I St t t

(2) PV(Tax Shield):Tax Shield = 40 x 0.40 = 16PV(T Shi ld) 16/0 08 200Income Statement

EBIT 240 240Interest 0 40Taxable Income 240 200

PV(TaxShield) = 16/0.08 = 200

(3) Value of levered company:V = 1 440 + 200 = 1 640Taxable Income 240 200

Taxes (40%) 96 80Net Income 144 120Dividend 144 120

VL = 1,440 + 200 = 1,640

(5) Market value of equity:E = V D = 1 640 - 500 = 1 140Dividend 144 120

Interest 0 40Total 144 160

EL = VL - D = 1,640 - 500 = 1,140


What about cost of equity?q y

1) Cost of equity increases with leverage:Proof:

TDrEBIT )1()( ×) q y g

EDTrrrr CDAAE ×−×−+= )1()( But VU = EBIT(1-TC)/rA

E

CD

rTDrEBITE )1()( −×−

=

2) Beta of equity increases

E and E = VU + TCD – D

Replace and solve

])1(1[ DTCAE −+= ββIn example:rE = 10% +(10%-8%)(1-0.4)(500/1,140)])1(1[

ETCAE +ββ rE 10% +(10% 8%)(1 0.4)(500/1,140)

= 10.53%orrE = DIV/E = 120/1,140 = 10.53%E ,


What about the weighted average cost of g gcapital?

• Weighted average cost of capital decreases with leverageWe g ted ave age cost o cap ta dec eases w t eve age• Weighted average cost of capital: discount rate used to calculate the market

value of firm by discounting net operating profit less adjusted taxes (NOPLAT)(NOPLAT)

• NOPLAT = Net Income + Interest + Tax Shield • = (EBIT-rDD)(1-TC) + rDD +TCrDD( D )( C) D C D

• = Net Income for all-equity-firm = EBIT(1-TC)VL = NOPLAT / WACC

• As: )1()1( CCDE TEBITDTrEr −=−+

CDE VDTr

VErWACC ×−+×= )1(

LL VVIn example: NOPLAT = 144VL = 1,640


WACC = 10.53% x 0.69 + 8% x 0.60 x 0.31 = 8.78%

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Théorie Financière Structure financière et coût du capital