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### Advanced Finance2007-2008Introduction

Professor André Farber

Solvay Business School

Université Libre de Bruxelles

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.

Advanced Finance 2008 01 Introduction

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?

Advanced Finance 2008 01 Introduction

Some data – Benelux 2004

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

The message from CFOs: Capital budgeting

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

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:

Advanced Finance 2008 01 Introduction

Risk-adjusted discount rate: CAPM

Expected Return

Expected Return

CAPM

MARKOWITZ

Security Market Line

P

P

16%

10%

M

M

rM 10%

rf4%

4%

2

Beta

Sigma

1

Advanced Finance 2008 01 Introduction

The message from CFOs : cost of equity

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

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.

Advanced Finance 2008 01 Introduction

Example

You observe the following data:

What is the value of the following asset? What are its expected returns?

Advanced Finance 2008 01 Introduction

Valuation of project with CAPM

Step 1: calculate statistics for the market portfolio:

Expected return:

Market risk premium:

Variance:

Price of covariance:

Advanced Finance 2008 01 Introduction

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

Advanced Finance 2008 01 Introduction

Valuation of project with CAPM (3)

Once the value of the project is known, the beta can be calculated.

Expected return:

Beta:

Advanced Finance 2008 01 Introduction

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: 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

Advanced Finance 2008 01 Introduction

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

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

Advanced Finance 2008 01 Introduction

Valuation using state prices

Once state prices are known, valuation is straightforward.

The value of an asset with future payoffs Vu and Vdis:

This formula can easily be generalized to S states:

Advanced Finance 2008 01 Introduction

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.

Advanced Finance 2008 01 Introduction

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:

Advanced Finance 2008 01 Introduction

State prices: formulas

Advanced Finance 2008 01 Introduction

Risk-neutral pricing

First note the following for state prices:

Now define:

Properties:

puand pd look like probabilities

puand pd are risk-neutral probabilities such that the expected return, using these probabilities, is equal to the risk-free rate.

Advanced Finance 2008 01 Introduction

Risk neutral probabilities: example

In previous example, state prices are:

The risk neutral probabilities are:

Advanced Finance 2008 01 Introduction

Risk-neutral pricing

Risk neutral expected value

Discounted at the risk free interest rate

Example:

Remark:

Advanced Finance 2008 01 Introduction

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