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Théorie Financière2008-20091. Introduction
Professeur André Farber
Tfin 2008 01 Introduction |2April 18, 2023
Organisation du cours
• Ouvrages de référence:Brealey, R., Myers, S. and Allen, F. (BMA)
Principle of Corporate Finance9th ed., McGraw-Hill 2008
Farber,A. Laurent, M-P., Oosterlinck, K., Pirotte, H. (FLOP)Finance
2d ed. Pearson Education, 2008
• Site web: www.ulb.ac.be/cours/solvay/farber• Copie des transparents (PowerPoint)• Glossaire anglais - français• Notes pédagogiques, exercices, anciens examens• Liens vers d’autres sites
• Examen(s)
Tfin 2008 01 Introduction |3April 18, 2023
Exercices
• Assistants:
• Benoit Dewaele
• Ritha Sukadi
• 6 séances (Vendredi 10-12), 4 groupes
• Groupe 1: A à F
• Groupe 2: G à L
• Groupe 3: M à P
• Groupe 4: Q à Z
Semaines 2, 4, 6, 9, 11, 13
Semaines 3, 5, 8, 10, 12, 14
Tfin 2008 01 Introduction |4April 18, 2023
Plan du cours
• 1. Introduction - Fondements
• 2. Valeur actuelle
• 3. Cash flows, planning financier
• 4. Evaluation d’entreprises
• 5,6. Analyse de projets d’investissement
• 7,8. Rentabilité attendue et risque
• 9,10. Options
• 11, 12. Evaluation et financement
Tfin 2008 01 Introduction |5April 18, 2023
What is Corporate Finance?
• INVESTMENT DECISIONS: Which REAL ASSETS to buy ? • Real assets: will generate future cash flows to the firm
• Intangible assets : R&D, Marketing, ..
• Tangible assets : Real estate, Equipments,..
• Current assets: Inventories, Account receivables,..
• FINANCING DECISIONS: Which FINANCIAL ASSET to sell ?• Financial assets: claims on future cash flows
• Debt: promise to repay a fixed amount
• Equity: residual claim
• DIVIDEND DECISION: How much to return to stockholders?
Tfin 2008 01 Introduction |6April 18, 2023
Accounting View of the Firm
• Balance sheet Income statement
Sales
– Operating expenses
= Earnings before interest and taxes (EBIT)
– Interest expenses
– Taxes
= Net income (earnings after taxes)
• Retained earnings
• Dividend payments
Current assets
Fixed assets
Current liabilites
Long-term debt
Shareholders’ equity
Net Working Capital
Tfin 2008 01 Introduction |7April 18, 2023
Cash Flows of the Firm
Firm Financial markets
Firm issue securitiesFirm invest
Cash flow from operations Dividend and
debt payments
Timing of cash flows + uncertainty
Investors
Tfin 2008 01 Introduction |8April 18, 2023
Market Value of the Firm
Total capital
Fixed Assets
+
Net Working Capital
Book equity
Debt
Book values Market values
Market value of equity
Market value of
debt
Market capitalization
Tfin 2008 01 Introduction |9April 18, 2023
Value creation
• Market value added (MVA)• = Market value of the firm’s capital – Total capital employed
• VALUE CREATION : 2 strategies• Strategy 1
• Buy assets at a cost lower than the value of the future revenues– real assets– financial assets
• Strategy 2• Sell financial assets for a price higher than the value of future
payments
Market value of equity + Market value of debt
Stockholders’ equity + Financial debt
Tfin 2008 01 Introduction |10April 18, 2023
Examples (Sept 5, 2008)
Microsoft Wal-Mart
Market Cap $billionCapitalisation boursière (milliards USD)
234.19 238.95
Stockholders’ Equity $bFonds propres
36.27 63.23
Revenues ($b)Chiffre d’affaires
60.42 378.79
Net Income $bRésultat net
17.68 12.73
Price/Book 6.46 3.78
Return on Equity (ROE) 52.48% 20.75%
Price-Earnings Ratio (P/E) 13.74 18.07
Tfin 2008 01 Introduction |11April 18, 2023
The Cost of Capital
• The firm can always give cash back to the shareholders
• Capital employed by the firm has an opportunity cost
• The opportunity cost of capital is the expected rate of return offered by equivalent investments in the capital market
• The weighted average cost of capital (WACC) is the (weighted) average of the cost of equity and of the cost of debt
Project Cash
StockholderInvestment opportunities in capital markets
?
Tfin 2008 01 Introduction |12April 18, 2023
Stockholders’ problem
equity rs'Stockholde
IncomeNet ROE
InvestmentInitial
GainCapitalDivr
1
Capital marketCompany
ROEReturn on Equity
rExpected return
Tfin 2008 01 Introduction |13April 18, 2023
How to measure value creation ?
• 1. Compare market value of equity to book value
• Value creation if M/B > 1
• 2. Compare return on equity to the opportunity cost of equity
• Value creation if ROE > Opportunity Cost of Equity
shareper Book value
priceStock book(M/B)-to-Market
equity rs'Stockholde
IncomeNet )(equity on Return ROE
Tfin 2008 01 Introduction |14April 18, 2023
Value creation: Example
• Data:
• Book value of equity = € 10 b
• Net income = € 2 b / year
• Cost of equity r = 10%
• Return on equity ROE = 2 / 10 = 20% > 10%
• Market value of equity = NI / r = 2 / 10% = € 20 b
• Market value added: MVA = 20 – 10 = €10 b
• Market to Book M/B = 20 / 10 = 2
Tfin 2008 01 Introduction |15April 18, 2023
M/B vs ROE
• Simplifying assumptions:
• · Expected net income income = constant
• · Net income = dividend
• Market value determination:
• Net income = Expected return Market value of equity
• NI = r MVeq
• ROE (definition):
• Return on equity = Net income / Book value of equity
• ROE = NI / BVeq
• = r MVeq / Bveq
• Conclusion: in this simplified setting,
– M/B = MVeq/BVeq > 1 ROE> r
Tfin 2008 01 Introduction |16April 18, 2023
Drivers of ROE
• PROFITABILITY (du Pont system)
• Three determinants :
Equity
Assets
Assets
Sales
Sales
Net IncomeROE
EquityBook
IncomeNet ROE
Financial Leverage
Asset Turnover
Profit Margin
Tfin 2008 01 Introduction |17April 18, 2023
Example (Sept. 5, 2008)
Microsoft WalMartRevenues 60.42 378.79Net Income 17.68 12.73Total assets 72.79 163.514Equity 36.27 63.23
ROE 48.75% 20.13%Profit margin 29.26% 3.36%Asset turnover 0.83 2.32Leverage 2.01 2.59
Foundations of Finance
Tfin 2008 01 Introduction |19April 18, 2023
Theory of finance
• A young science
• Finance has been around for many centuries, of course…
• Main problem: calculation!!
• Imagine having to calculate the future value of 1 euro invested for 13 years when the annual interest rate is 4.35% (with annual compounding):
Future value = (1.0435)13
• A nightmare…..
• This problem disappeared after WWII with the development of computers.
• Now we have calculators and spreadsheets….
• We also have large data bases
Tfin 2008 01 Introduction |20April 18, 2023
Irving Fisher
• Finance has its roots in economics
• Irving Fisher laid the foundations of modern theory of finance.
• Takes into account the time dimension of financial decisions
• Main ideas:
• Decisions should based on present value
• Net Present Value (NPV): a measure of additional wealth
• With perfect capital markets: independent of preferences
Tfin 2008 01 Introduction |21April 18, 2023
Present value: 1 period, certainty
• Perfect capital market
• Risk-free interest rate: rf
• Future cash flow C1
• Present value:
• or:fr
CCPV
1)( 1
1
PV(C1) = v1 C1
Interpretation: v1 = 1-year discount factor
price of 1€ to be received in one year
price of unit 1-year zero coupon
with fr
v
1
11
Tfin 2008 01 Introduction |22April 18, 2023
Using present value: 1-year bond valuation
Consider a risk-free zero coupon bond:Face value = 100Maturity = 1 year
Suppose 1-year risk-free interest rate = 5%
How much would you be willing to pay for this bond?
0
100100 0.9524 95.24
1.05P
Tfin 2008 01 Introduction |23April 18, 2023
No arbitrage – 1st pass
If P0 ≠ 95.24: arbitrage opportunity
Suppose P0 = 95.50
t = 0 t = 1Sell one bond + 95.50 - 100Invest - 95.24 + 100Total = 0.26 = 0
Suppose P0 = 95
t = 0 t = 1Buy one bond - 95.00 + 100Borrow + 95.24 - 100Total = 0.24 = 0
NO FREE LUNCH
There are no arbitrage opportunities in competitive markets
Tfin 2008 01 Introduction |24April 18, 2023
Microeconomics: a review
• Consumption over time:
• 1 periods, certainty
• Perfect capital markets => budget constraint
» Slope = -(1+r)
» Intercept = W0(1+r)
• Optimum:
» Marginal Rate of Substitution (MRS) = 1+r
» Optimal consumption independent of timing of income
1 10 0 0
0 1 1 0
1 1f f
Q YQ Y W
r r
Q v Q W
Tfin 2008 01 Introduction |25April 18, 2023
Economic foundations of net present value
100
105
200Euros now
Euros next year
50
165
Slope = - (1 + rf) = - (1 + 5%)
I. Fisher 1907, J. Hirshleifer 1958
Perfect capital markets
Separate investment decisions from consumption decisions
157.5
52.5
150
Y0
Y1
Tfin 2008 01 Introduction |26April 18, 2023
Net Present Value
NPV = -I + v1 C1
= -50 + 0.9524 60 = 7.14
Suppose the risk-free rate is rf = 5%
Consider the following investment project:
Initial cost: I (50)
Future cash flow: C1 (60)
Budget constraint with project:
0 1 1 0 1 1 1 0( ) ( )Q v Q Y I v Y C W NPV
Tfin 2008 01 Introduction |27April 18, 2023
Fisher Separation Theorem
100
105
200Euros now
Euros next year
50
165
207.14
NPV
Slope = - (1 + r) = - (1 + 5%)
-50
I. Fisher 1907, J. Hirshleifer 1958
Perfect capital markets
Investment decision independent of:- initial allocation- preferences (utility functions)
Tfin 2008 01 Introduction |28April 18, 2023
Enterprise Valuation
Suppose an all equity financed company is created for this project.
Step 1: Creation
Step 2: Equity offering + investment
t = 0 t = 1-50 +60
Assets 50 Equity 50 t = 0 t = 1+60
Cash flows
Assets 0 Equity 0
Market Cap.
6050 7.14
1.05 NPV =
I+NPV =60
57.141.05
Tfin 2008 01 Introduction |29April 18, 2023
Enterprise Valuation With Debt
1817.14
1.05
4240
1.05
Suppose that the company borrows 40 to finance part of the project.
Step 1: Creation
Step 2: Borrow + investment
t = 0 t = 1-10 +60 – 42 = 18
Assets 50 Equity 10Debt 40
t = 0 t = 1+18+42
Cash flows to equity
Assets 0 Equity 0
Market Value
1810 7.14
1.05 Equity =
Equity =
Debt =
1817.14
1.05
Enterprise= 57.14
Tfin 2008 01 Introduction |30April 18, 2023
Entreprise Value Maximisation
0
Investment
Euros today
Euros next year
NPV
Investment opportunities
Market value of company
Numerical exampler = 5%
Project CF0 CF1 NPV1 -100 115 9.52 -100 110 4.83 -100 105 0.04 -100 103 -1.9
CF1 MktVal Inv NPV1 115 109.5 100 9.5
1,2 225 214.3 200 14.31,2,3 330 314.3 300 14.3
1,2,3,4 433 412.4 400 12.4
Tfin 2008 01 Introduction |31April 18, 2023
Review: Certainty – 1 period
11 1 1( )
1
CPV C C v
r
1 1 0NPV I C v
Present value:
Investment rules: 1C IIRR r
I
Meaning of NPV:
Variation of stockholder’s wealth
Independent of time preferences (if perfect capital market)
Enterprise value:
Unlevered:1 1UV C v I NPV
Levered: 1 1 1[ (1 )] (1 ) UV E D C D r v D r v V
1DIV
Tfin 2008 01 Introduction |32April 18, 2023
Uncertainty: 1952 – 1973- the Golden Years
• 1952: Harry Markowitz*
– Portfolio selection in a mean –variance framework
• 1953: Kenneth Arrow*
– Complete markets and the law of one price
• 1958: Franco Modigliani* and Merton Miller*
– Value of company independant of financial structure
• 1963: Paul Samuelson* and Eugene Fama
– Efficient market hypothesis
• 1964: Bill Sharpe* and John Lintner
– Capital Asset Price Model
• 1973: Myron Scholes*, Fisher Black and Robert Merton*
– Option pricing model
Tfin 2008 01 Introduction |33April 18, 2023
Uncertainty: 1 period - 2 states example
Value Up market (u)
Proba = 0.75
Down market (d)
Proba = 0.25
Expected return
Bond 95.24 100 100 5%
Stock Market
100 120 80 10%
NewAsset ? 200 100 ?
What is the value of the following asset? What are its expected returns?
You observe the following data:
Tfin 2008 01 Introduction |34April 18, 2023
Introducing uncertainty
Two possible approaches:
Discount the expected cash flow using a risk-adjusted discount rate
Discount the risk-adjusted expected cash flow using the risk-free interest rate
1( )
1
E CPV
r
*1( )
1 f
E CPV
r
Later in course
Today
: ( )f m fCAPM r r r r
Tfin 2008 01 Introduction |35April 18, 2023
Market statistics (details)
Price today Cash flow up state (π = 0.75)
Cash flow down state(1-π = 0.25)
Zero-coupon bond v1 = 0.9524 1 1
Stock market S = 100 S1u = uS = 120
u = 1+ru = 1.20
S1d = dS = 80
d = 1+rd = 0.80
Risk-free interest rate rf 1
1 11 5%
1 0.9524ff
v rr
Stocks: expected cash flow 1 1 1 1( ) (1 )
0.75 120 0.25 80 110u dS E S S S
Expected return on stocks 1 110 10010%
1000.75 20% 0.25 ( 20%)
C Sr
S
(1 )u dr r r
Tfin 2008 01 Introduction |36April 18, 2023
Relative Pricing
Relative pricing: Is it possible to reproduce the payoff of NewAsset by combining the bond and the stocks?
To do this, solve the following system of equations:
100 120 200
100 80 100B S
B S
n n
n n
The solution is: nB = -1.00 nS = 2.50
The value of this portfolio is: V = (-1) × 95.24 + 2.50 × 100 = 154.76
Conclusion: the value of NewAsset is V = 154.76 Otherwise, ARBITRAGE
Tfin 2008 01 Introduction |37April 18, 2023
States prices (= Digital options)
Value State = u State = d
u-option vu 1 0
d-option vd 0 1
100 120 1
100 80 0B S
B S
n n
n n
100 120 0
100 80 1B S
B S
n n
n n
nB = -0.020 nS = 0.025 nB = 0.030 nS = -0.025
vu = 0.595 vd = 0.357
A digital option is a contract that pays 1 in one state, 0 in other states
(also known as Arrow-Debreu securities, contingent claims)
2 states→ 2 D-options
Valuation
Prices of digital options are known as state prices
Tfin 2008 01 Introduction |38April 18, 2023
Valuation using state prices
Once state prices are known, valuation is straightforward.
The value of an asset with future payoffs C1u and C1d is:
1 1u u d dV v C v C
This formula can easily be generalized to S states: s ss
V v V
0.595 200 0.357 100 154.76V
Tfin 2008 01 Introduction |39April 18, 2023
State prices and absence of arbitrage
In equilibrium, the price that you pay to receive 1€ in a future state should be the same for all securities
Otherwise, there would exist an arbitrage opportunity.
An arbitrage portfolio is defined as a portfolio:
-with a non positive value (you don’t pay anything or, even better, you receive money to hold this portfolio)
-a positive future value in at least one state, and zero in other states
The absence of arbitrage is the most fundamental equilibrium condition.
Tfin 2008 01 Introduction |40April 18, 2023
Fundamental Theorem of Finance
s ss
V v VIn our example:
In complete markets (number of assets = number of states), the no arbitrage condition (NA) is satisfied if and only if there exist unique strictly positive state prices such that:
0.595 200 0.357 100 154.76V
Expected return:
200 154.76 100 154.760.75 0.25 13.08%
154.76 154.76r
Tfin 2008 01 Introduction |41April 18, 2023
State prices: formulas
Price Value up state
Proba π
Value down state
Proba 1 - π
Risk-free bond 1 1+rf 1+rf
Stock S uS dS
0.81
1.05 0.5951.2 0.8uv
11 f
u
dr
vu d
11 f
d
ur
vu d
1 1f fu d
udS udSuS dS
r rv uS v dS S
u d u d
1 fu r d
1.21
1.05 0.3571.2 0.8dv
Tfin 2008 01 Introduction |42April 18, 2023
Risk-adjusted expected cash flow
(1 )d f dp r v (1 )u f up r v Define:
1u dp p
1 , 0u dp p pu and pd look like probabilities
Properties:
pu and pd are risk-neutral probabilities such that the expected return, using these probabilities, is equal to the risk-free rate.
Pricing equation
*1 1 1
1 1
( )
1 1u u d d
u u d df f
p C p C E CV v C v C
r r
Risk-adjusted expected cash flow
Risk-free rate
Tfin 2008 01 Introduction |43April 18, 2023
Risk neutral probabilities: example
In previous example, state prices are: 0.595uv 0.357dv
The risk neutral probabilities are:
(1 ) (1.05)(0.595) 0.625u f up r v
(1 ) (1.05)(0.357) 0.375d f dp r v
Risk-adjusted expected cash flow: *1( ) 0.625 200 0.375 100 162.49E C
Present value calculation:*
1( ) 162.49154.76
1 1.05f
E CV
r
Tfin 2008 01 Introduction |44April 18, 2023
Final remarks
Had we known the risk-adjusted discount rate (that we calculated – see previous slide) r = 13.08%, then:
Expected cash flow: 1( ) 0.75 200 0.25 100 175E C
Present value calculation:
1( )
1175
154.761.1308
E CV
r
(True) Expected Cash Flow
Risk-adjusted discount rate
Tfin 2008 01 Introduction |45April 18, 2023
References
• Corporate finance textbooks (MBA level)
– Brealey, Richard, Steward Myers and Franklin Allen, Principles of Corporate Finance, 9th edition, McGraw-Hill 2006
– Ross, Stephen A., Randolph W. Westerfield and Jeffrey F. Jaffe, Corporate Finance, 6th edition, McGraw-Hill Irwin 2002
– Damoradan, Aswath, Corporate Finance: Theory and Practice, Wiley 1997
• Ouvrages de référence en français:
– Bodie, Z. et Merton, R. Finance (édition française dirigée par C. Thibierge) Pearson education 2000
• Corporate finance texts for executives
– Bertoneche, Marc and Rory Knight, Financial Performance, Butterworth Heinemann 2001
– Hawawini, Gabriel and Claude Viallet, Finance for Executives: Managing for Value Creation, South-Western College Publishing, 1999