Théorie Financière 2008-2009 1. Introduction Professeur André Farber

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)


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


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


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?


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


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


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


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


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


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

?


Stockholders’ problem

equity rs'Stockholde

IncomeNet ROE

InvestmentInitial

GainCapitalDivr

1

Capital marketCompany

ROEReturn on Equity

rExpected return


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


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


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


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


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


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


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


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


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


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


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


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


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


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)


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


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


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


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


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


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:


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


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


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


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


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


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.


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


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


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


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


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


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

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Théorie Financière 2008-2009 1. Introduction Professeur André Farber