Advanced Finance 2007 2008 Introduction Professor Andr Farber

Advanced Finance 2007 -2008 Introduction Professor André Farber Solvay Business School Université Libre de Bruxelles Advanced Finance 2008 01 Introduction

Recently in the press • High demand for Fiat paper Financial Times February 7 2006 • Fiat, the Italian carmaker, will today sell as much as € 1 bn of high-yield bonds, providing further evidence that investors are willing to buy new deals in a choppy secondary market. Investors had placed orders worth more than € 2. 5 bn when the books closed yesterday and the issue would not exceed € 1 bn, said sources close to the deal. The 2013 bonds were offered to yield between 6. 625 and 6. 75 per cent, and the strong demand could lead the issuer to push down the borrowing cost towards the low end of the range. A yield of 6. 625 per cent would equate to about 330 basis points more than mid-swap rates for seven-year money. That would still leave a new issue premium over five-year credit default swaps, which have dropped to about 280 bp from more than 350 bp in December. Fiat has reduced debt and improved its operating performance since it lost its investment grade rating in 2002. The company's efforts were rewarded last month, when Moody's Investors Service and Fitch Ratings changed their outlook for Fiat to "stable" from "negative". Moody's rates Fiat Ba 3, three notches below investment grade, and Standard & Poor's and Fitch have assigned equivalent BB- ratings. Barclays Capital, BNP Paribas, Citigroup and UBM are lead-managing the sale. • • 6/11/2021 Advanced Finance 2008 01 Introduction 2

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? 6/11/2021 Advanced Finance 2008 01 Introduction 3

Some data – Benelux 2004 6/11/2021 Advanced Finance 2008 01 Introduction 4

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 doesn’t matter. • Hotly debated: the efficient market hypothesis 6/11/2021 Advanced Finance 2008 01 Introduction 5

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 6/11/2021 Advanced Finance 2008 01 Introduction 6

Course outline 07/02/2007 1. Introduction – Valuing uncertain cash flows 14/02/2007 2. MM 1958, 1961 21/02/2007 3. Debt and taxes 28/02/2007 4. Adjusted present value 07/03/2007 5. WACC 14/03/2007 6. Risky debt: binomial model 21/03/2007 7. Risky debt: Merton’s model 28/03/2007 8. Optimal Capital Structure Calculation: Leland 18/04/2007 9. Convertible bonds and warrants 25/04/2007 10. IPO/Seasoned Equity Issue 02/05/2007 11. Dividend policy 09/05/2007 12. Unfinished business/Review 6/11/2021 Advanced Finance 2008 01 Introduction 7

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 6/11/2021 Advanced Finance 2008 01 Introduction 8

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 6/11/2021 Advanced Finance 2008 01 Introduction 9

The message from CFOs: Capital budgeting 6/11/2021 Advanced Finance 2008 01 Introduction 10

Valuation models • In order to calculate a present value, a valuation model is required which takes into account time and uncertainty. • The time dimension is usually captured by using discounted cash flows • The uncertainty dimension is more difficult to capture. • We will use several (related) valuation models: • Capital Asset Pricing Model • State prices • Risk neutral pricing 6/11/2021 Advanced Finance 2008 01 Introduction 11

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: 6/11/2021 Advanced Finance 2008 01 Introduction 12

Risk-adjusted discount rate: CAPM Expected Return CAPM MARKOWITZ Security Market Line P P 16% r. M 10% M rf 4% 4% Sigma 6/11/2021 M Advanced Finance 2008 01 Introduction 1 2 Beta 13

The message from CFOs : cost of equity 6/11/2021 Advanced Finance 2008 01 Introduction 14

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 6/11/2021 Advanced Finance 2008 01 Introduction 15

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 or projects with unknown betas. To understand how to proceed in that case, we need to go deeper into valuation theory. 6/11/2021 Advanced Finance 2008 01 Introduction 16

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 5% Market Portfolio 1 2 0. 50 10% What is the value of the following asset? What are its expected returns? New. Asset 6/11/2021 ? 3 5 Advanced Finance 2008 01 Introduction ? 17

Valuation of project with CAPM Step 1: calculate statistics for the market portfolio: Return Up mkt Proba =. 40 Down mkt Proba =. 60 100% -50% Expected return: Market risk premium: Variance: Price of covariance: 6/11/2021 Advanced Finance 2008 01 Introduction 18

Valuation of project with CAPM (2) Step 2: Calculate statistics for the project Expected cash flow: Covariance with market portfolio: ) (Reminder: Step 3: Value the project 6/11/2021 Advanced Finance 2008 01 Introduction 19

Valuation of project with CAPM (3) Once the value of the project is known, the beta can be calculated. Cash flow Returns Value Up mkt Proba =. 40 Down mkt Proba =. 60 4. 06 3 5 -26. 17% 23. 05% Expected return: Beta: 6/11/2021 Advanced Finance 2008 01 Introduction 20

Valuation with state prices Relative pricing: Is it possible to reproduce the payoff of New. Asset by combining the bond and the stocks? To do this, we have to solve the following system of equations: The solution is: n. B = 5. 40 n. S = - 1. 33 The value of this portfolio is: V = 5. 40 × 1 + (-1. 33) × 1 = 4. 06 Conclusion: the value of New. Asset is V = 4. 06 6/11/2021 Otherwise, ARBITRAGE Advanced Finance 2008 01 Introduction 21

States prices = 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) 2 states → 2 D-options Value State = u State = d u-option vu 1 0 d-option vd 0 1 Valuation n. B = -0. 32 n. S = 0. 67 vu = 0. 35 n. B = 1. 27 n. S = -0. 67 vd = 0. 60 Prices of digital options are known as state prices 6/11/2021 Advanced Finance 2008 01 Introduction 22

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: 6/11/2021 Advanced Finance 2008 01 Introduction 23

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. 6/11/2021 Advanced Finance 2008 01 Introduction 24

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: 6/11/2021 Advanced Finance 2008 01 Introduction 25

State prices: formulas Price Value up state Proba π Value down state Proba 1 - π Risk-free bond 1 1+rf Stock S u. S d. S 6/11/2021 Advanced Finance 2008 01 Introduction 26

Risk-neutral pricing First note the following for state prices: Now define: Properties: pu and pd look like probabilities pu and pd are risk-neutral probabilities such that the expected return, using these probabilities, is equal to the risk-free rate. 6/11/2021 Advanced Finance 2008 01 Introduction 27

Risk neutral probabilities: example In previous example, state prices are: The risk neutral probabilities are: 6/11/2021 Advanced Finance 2008 01 Introduction 28

Risk-neutral pricing Risk neutral expected value Discounted at the risk free interest rate Example: Remark: 6/11/2021 Advanced Finance 2008 01 Introduction 29