théorie financière structure financière et coût du capital
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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
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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
November 14, 2009 Tfin 03 Cash flows |4
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)
November 14, 2009 Tfin 03 Cash flows |5
Leverage - example
November 14, 2009 Tfin 03 Cash flows |6
November 14, 2009 Tfin 03 Cash flows |7
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
November 14, 2009 Tfin 2005 11 Intro to capital structure |8
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
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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
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Expected ReturnExpected ReturnExpected Return
14%
P20%
M
P
8%
14%M
8%
14%
21 2 BetaSigma
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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 ?
November 14, 2009 Tfin 2005 11 Intro to capital structure |13
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)?
November 14, 2009 Tfin 2005 11 Intro to capital structure |14
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
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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
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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%
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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 +=
November 14, 2009 Tfin 2005 11 Intro to capital structure |18
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
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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
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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
November 14, 2009 Tfin 2005 11 Intro to capital structure |21
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%
November 14, 2009 Tfin 2005 11 Intro to capital structure |22
/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
November 14, 2009 Tfin 2005 11 Intro to capital structure |23
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
November 14, 2009 Tfin 2005 11 Intro to capital structure |24
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
November 14, 2009 Tfin 2005 11 Intro to capital structure |26
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
November 14, 2009 Tfin 2005 11 Intro to capital structure |27
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
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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 +=+
November 14, 2009 Tfin 2005 11 Intro to capital structure |30
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)
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WACC
CDEDTrErwacc −+= )1(
U
LCD
LE
rVr
VTr
Vrwacc
<
+ )1(
AL
A rV
r <=
November 14, 2009 Tfin 2005 11 Intro to capital structure |32
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
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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 ,
November 14, 2009 Tfin 2005 11 Intro to capital structure |34
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
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WACC = 10.53% x 0.69 + 8% x 0.60 x 0.31 = 8.78%