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

2. 6/4/2015 Advanced Finance 2008 01 Introduction |2 Recently in the press High demand for Fiat paper Financial Times February 7 2006 Fiat, the Italian carmaker, will today sell as much as €1bn 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 €2.5bn when the books closed yesterday and the issue would not exceed €1bn, 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 280bp from more than 350bp 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 Ba3, 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.

3. 6/4/2015 Advanced Finance 2008 01 Introduction |3 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?

4. 6/4/2015 Advanced Finance 2008 01 Introduction |4 Some data – Benelux 2004

5. 6/4/2015 Advanced Finance 2008 01 Introduction |5 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. 6/4/2015 Advanced Finance 2008 01 Introduction |6 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

7. 6/4/2015 Advanced Finance 2008 01 Introduction |7 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

8. 6/4/2015 Advanced Finance 2008 01 Introduction |8 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

9. 6/4/2015 Advanced Finance 2008 01 Introduction |9 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 CF op = Net Income + Depreciation -  Working Capital Requirement

10. 6/4/2015 Advanced Finance 2008 01 Introduction |10 The message from CFOs: Capital budgeting

11. 6/4/2015 Advanced Finance 2008 01 Introduction |11 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

12. 6/4/2015 Advanced Finance 2008 01 Introduction |12 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 = r f + Risk premium 2. Discount the risk-adjusted expected cash flow at a risk-free discount rate:

13. 6/4/2015 Advanced Finance 2008 01 Introduction |13 Risk-adjusted discount rate: CAPM r f 4% r M 10% 1 2 Beta M P 4% 10% 16% Sigma Expected Return M P Security Market Line MARKOWITZ CAPM

14. 6/4/2015 Advanced Finance 2008 01 Introduction |14 The message from CFOs : cost of equity

15. 6/4/2015 Advanced Finance 2008 01 Introduction |15 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

16. 6/4/2015 Advanced Finance 2008 01 Introduction |16 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.

17. 6/4/2015 Advanced Finance 2008 01 Introduction |17 Example ValueUp market (u) Proba = 0.40 Down market (d) Proba = 0.60 Expected return Bond11.05 5% Market Portfolio 120.5010% NewAsset?35? What is the value of the following asset? What are its expected returns? You observe the following data:

18. 6/4/2015 Advanced Finance 2008 01 Introduction |18 Valuation of project with CAPM Step 1: calculate statistics for the market portfolio: Up mkt Proba =.40 Down mkt Proba =.60 Return100%-50% Expected return: Variance: Market risk premium: Price of covariance:

19. 6/4/2015 Advanced Finance 2008 01 Introduction |19 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

20. 6/4/2015 Advanced Finance 2008 01 Introduction |20 Valuation of project with CAPM (3) Once the value of the project is known, the beta can be calculated. ValueUp mkt Proba =.40 Down mkt Proba =.60 Cash flow4.0635 Returns-26.17%23.05% Expected return: Beta:

21. 6/4/2015 Advanced Finance 2008 01 Introduction |21 Valuation with state prices Relative pricing: Is it possible to reproduce the payoff of NewAsset 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 NewAsset is V = 4.06 Otherwise, ARBITRAGE

22. 6/4/2015 Advanced Finance 2008 01 Introduction |22 States prices = Digital options ValueState = uState = d u-optionvuvu 10 d-optionvdvd 01 n B = -0.32 n S = 0.67 n B = 1.27 n S = -0.67 v u = 0.35 v d = 0.60 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

23. 6/4/2015 Advanced Finance 2008 01 Introduction |23 Valuation using state prices Once state prices are known, valuation is straightforward. The value of an asset with future payoffs V u and V d is: This formula can easily be generalized to S states:

24. 6/4/2015 Advanced Finance 2008 01 Introduction |24 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.

25. 6/4/2015 Advanced Finance 2008 01 Introduction |25 Fundamental Theorem of Finance In 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: Valuing Asset 3: Expected return:

26. 6/4/2015 Advanced Finance 2008 01 Introduction |26 State prices: formulas PriceValue up state Proba π Value down state Proba 1 - π Risk-free bond11+r f StockSuSdS

27. 6/4/2015 Advanced Finance 2008 01 Introduction |27 Risk-neutral pricing Now define: p u and p d look like probabilities Properties: First note the following for state prices: p u and p d are risk-neutral probabilities such that the expected return, using these probabilities, is equal to the risk-free rate.

28. 6/4/2015 Advanced Finance 2008 01 Introduction |28 Risk neutral probabilities: example In previous example, state prices are: The risk neutral probabilities are:

29. 6/4/2015 Advanced Finance 2008 01 Introduction |29 Risk-neutral pricing Risk neutral expected value Discounted at the risk free interest rate Example: Remark: