Advanced Finance 2005-2006 Introduction

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Advanced Finance2005-2006Introduction

• Professor André Farber
• Solvay Business School
• Université Libre de Bruxelles

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How to finance a company?

• Should a firm pay its earnings as a dividends?
• When should it repurchase some of its shares?
• If money is needed, should a firm issue stock or
  borrow?
• Should it borrow short-term or long-term?
• When should it issue convertible bonds?

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Some data Benelux 2004
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Divide and conquer the separation principle

• Assumes that capital budgeting and financing
  decision are independent.
• Calculate present values assuming all-equity
  financing
• Rational in perfect capital markets,
  NPV(Financing) 0
• 2 key irrelevance results
• Modigliani-Miller 1958 (MM 58) on capital
  structure
• The value of a firm is independent of its
  financing
• The cost of capital of a firm is independent of
  its financing
• Miller-Modigliani 1961 (MM 61) on dividend policy
• The value of a firm is determined by its free
  cash flows
• Dividend policy doesnt matter.

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Market imperfections

• Issuing securities is costly
• Taxes might have an impact on the financial
  policy of a company
• Tax rates on dividends are higher than on capital
  gains
• Interest expenses are tax deductible
• Agency problems
• Conflicts of interest between
• Managers and stockholders
• Stockholders and bondholders
• Information asymmetries

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Course outline

• 08/02/2006 1. Introduction Valuing uncertain
  cash flows
• 15/02/2006 2. MM 1958, 1961
• 22/02/2006 3. Debt and taxes
• 01/03/2006 4. Adjusted present value
• 08/03/2006 5. WACC
• 15/03/2006 6. Option valuation Black-Scholes
• 22/03/2006 7. Capital structure and options
  Mertons model
• 29/04/2005 8. Optimal Capital Structure
  Calculation Leland
• 20/04/2005 9. Convertible bonds and warrants
• 27/04/2005 10. IPO/Seasoned Equity Issue
• 04/05/2005 11. Dividend policy
• 11/05/2005 12. Unfinished business/Review

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Practice of corporate finance evidence from the
field

• Graham Harvey (2001) survey of 392 CFOs
  about cost of capital, capital budgeting, capital
  structure.
• ..executives use the mainline techniques that
  business schools have taught for years, NPV and
  CAPM to value projects and to estimate the cost
  of equity. Interestingly, financial executives
  are much less likely to follows the academically
  proscribed factor and theories when determining
  capital structure
• Are theories valid? Are CFOs ignorant?
• Are business schools better at teaching capital
  budgeting and the cost of capital than at
  teaching capital structure?
• Graham and Harvey Journal of Financial Economics
  60 (2001) 187-243

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Finance 101 A review

• Objective Value creation increase market value
  of company
• Net Present Value (NPV) a measure of the change
  in the market value of the company
• NPV ?V
• Market Value of Company present value of
  future free cash flows
• Free Cash Flow CF from operation CF from
  investment
• CFop Net Income Depreciation - ?Working
  Capital Requirement

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The message from CFOs Capital budgeting
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Valuing uncertain cash flows
Consider an uncertain cash flow in 1 year
2 possibilities to compute the present value
1. Discount the expected cash flow at a
risk-adjusted discount rate
where r rf Risk premium
2. Discount the risk-adjusted expected cash flow
at a risk-free discount rate
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Risk-adjusted discount rate
Expected Return
Expected Return
CAPM
MARKOWITZ
Security Market Line
P
P
16
10
M
M
rM 10
rf 4
4
2
Beta
1
Sigma
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The message from CFOs cost of equity
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CAPM two formulations
Consider a future uncertain cash flow C to be
received in 1 year. PV calculation based on CAPM
See Brealey and Myers Chap 9
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Risk-adjusted expected cash flow
Using risk-adjusted discount rates is OK if you
know beta.
The adjusted risk-adjusted discount rate does not
work for OPTIONS. To understand how to proceed in
that case, we need to go deeper into valuation
theory.
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Example
You observe the following data
Value Up market (u) Proba 0.40 Down market (d) Proba 0.60 Expected return
Bond 1 1.05 1.05 5
Stock 1 2 0.50 10
What is the value of the following asset? What
are its expected returns?
NewAsset ? 3 5 ?
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Creating a synthetic NewAsset
Relative pricing Is it possible to reproduce the
payoff of NewAsset by combining the bond and the
stock?
To do this, we have to solve the following system
of equations
The solution is nB 5.40 nS
- 1.33
The value of this portfolio is V 5.40 1
(-1.33) 1 4.06
Conclusion the value of NewAsset is V 4.06
Otherwise, ARBITRAGE
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Digital options
A digital option is a contract that pays 1 in one
state, 0 in other states (also known as
Arrow-Debreu securities, contingent claims)
Value State u State d
u-option vu 1 0
d-option vd 0 1
2 states? 2 D-options
Valuation
nB -0.32 nS 0.67
nB 1.27 nS -0.67
vu 0.35
vd 0.60
Prices of digital options are known as state
prices
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Valuation using state prices
Once state prices are known, valuation is
straightforward. The value of an asset with
future payoffs Vu and Vd is
This formula can easily be generalized to S
states
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State prices
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 dont 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.
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Fundamental Theorem of Finance
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
In our example
Valuing Asset 3
Expected return
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A more general formulation
Price Value up state Proba p Value down state Proba 1 - p
Risk-free bond 1 1rf 1rf
Stock S uS dS
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Risk-neutral pricing
Define
As
pu and pd look like probabilities
Expected value
Discounted at the risk free interest rate
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Risk-neutral probabilities
pu and pd are risk-neutral probabilities such
that the expected return, using these
probabilities, is equal to the risk-free rate.
Check
For the stock
For any security
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Binomial option pricing model

• Used to value derivative securities PVf(S)
• Evolution of underlying asset binomial model
• u and d capture the volatility of the underlying
  asset
• Replicating portfolio Delta S M
• Law of one price f Delta S M

uS
fu
S
dS
fd
?t
M is the cash positionMgt0 for investmentMlt0 for
borrowing
r is the risk-free interest rate per period
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Risk neutral pricing

• The value of a derivative security is equal to
  risk-neutral expected value discounted at the
  risk-free interest rate
• p is the risk-neutral probability of an up
  movement

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State prices Digital options

• Consider digital options with the following
  payoffs
• Using the binomial option pricing equation

uS dS
Up vu 1 0
Down vd 0 1
Calculation of present values using state prices
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Using state prices

• Calculation of present values using state prices

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Cost of capital with debt

• CAPM holds Risk-free rate 5, Market risk
  premium 6
• Consider an all-equity firm
• Market value V 100
• Beta 1
• Cost of capital 11 (5 6 1)
• Now consider borrowing 20 to buy back shares.
• Why such a move?
• Debt is cheaper than equity
• Replacing equity with debt should reduce the
  average cost of financing
• What will be the final impact
• On the value of the company? (Equity Debt)?
• On the weighted average cost of capital (WACC)?

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Modigliani Miller (1958)

• Assume perfect capital markets not taxes, no
  transaction costs
• Proposition I
• The market value of any firm is independent of
  its capital structure
• V ED VU
• Proposition II
• The weighted average cost of capital is
  independent of its capital structure
• WACC rAsset
• rAsset is the cost of capital of an all equity
  firm

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MM 58 Proof by arbitrage

• Consider two firms (U and L) with identical
  operating cash flows X
• VU EU VL EL DL
• Current cost Future payoff
• Buy a shares of U aEU aVU aX
• 
  ______________________________
• Buy a bonds of L aDL arDL
• Buy a shares of L aEL a(X rDL)
• ______________________________
• Total aDL aEL aVL aX
• As the future payoffs are identical, the initial
  cost should be the same. Otherwise, there would
  exist an arbitrage opportunity

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MM 58 Proof using CAPM

• 1-period company
• C future cash flow, a random variable
• Unlevered company
• Levered (assume riskless debt)
• So E D VU

VU
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MM 58 Proof using state prices

• 1-period company, risky debt VugtF but VdltF
• If Vd lt F, the company goes bankrupt

Current value Up Down
Cash flows VUnlevered Vu Vd
Equity E Vu F 0
Debt D F Vd
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Weighted average cost of capital
V (VU ) E D
Value of equity
rEquity
Value of all-equity firm
rAsset
rDebt
Value of debt
WACC
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Using MM 58

• Value of company V 100
• 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 WACC
  11)
• E/V 100 80

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Why are MM I and MM II related?

• Assumption perpetuities (to simplify the
  presentation)
• For a levered companies, earnings before interest
  and taxes will be split between interest payments
  and dividends payments
• EBIT Int Div
• Market value of equity present value of future
  dividends discounted at the cost of equity
• E Div / rEquity
• Market value of debt present value of future
  interest discounted at the cost of debt
• D Int / rDebt

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Relationship between the value of company and the
WACC

• From the definition of the WACC
• WACC V rEquity E rDebt D
• As rEquity E Div and rDebt D
  Int
• WACC V EBIT
• V EBIT / WACC

Market value of levered firm
If value of company varies with leverage, so does
WACC in opposite direction
EBIT is independent of leverage
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MM II another presentation

• The equality WACC rAsset can be written as
• Expected return on equity is an increasing
  function of leverage

rEquity
12.5
Additional cost due to leverage
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WACC
rA
5
rDebt
D/E
0.25
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Why does rEquity increases with leverage?

• Because leverage increases the risk of equity.
• To see this, back to the portfolio with both debt
  and equity.
• Beta of portfolio ?Portfolio ?Equity
  XEquity ?Debt XDebt
• But also ?Portfolio ?Asset
• So
• or

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Back to example

• Assume debt is riskless
• Beta asset 1
• Beta equity 1(120/80) 1.25
• Cost of equity 5 6 ? 1.25 12.50

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Summary the Beta-CAPM diagram
?
?
Beta
L
ßEquity
U
ßAsset
r
rAsset
rDebtrf
0
rEquity
D/E
?
?
rEquity
D/E
rDebt
WACC