INTRODUCTION TO FINANCIAL ENGINEERING Fred SongSeptember 20011IntroductoryWhat is Finance?What is Financial Engineering?Whats the role of Financial Engineering in New Economy? New economy Financial engineering and e-commerce2What is Finance?Money & Banking Monetary Economics International Finance International Economics3Corporate FinanceCapital Market(Investments)Financial EconomicsMultinational Corporate FinanceInternational Financial MarketFinancial Engineering4What is Financial Engineering?Generalizing: Financial Engineering involves the design, the development, and the implementation of innovative financial instruments and processes, and the formulation of creative solutions to problems in finance.Specializing: Financial Engineering is risk management via creative structural tools.5FINANCEI.T.ENGINEERINGF.E.6CHAPTER ONE: MM Theory and No Arbitrage1.MM Theory Two measurements of valueAccounting: book value historic costFinance: market value net present value7Assets = Liabilities + EquityAccounting Equality: duel entity systemBook value measurementFund useFund source Finance Equality: Fund use = Fund sourceMarket value measurement8 Corporate Finance Assets Liabilities and Equity Asset 1 Asset 2 Liabilities Asset 3 . . Equity . Asset nTotal Assets Total Liabilities and EquityAccounting: Yes!Finance: No!Capital MarketReal EconomyNPVFirm Value + NPV9Liabilities Value Equity ValueLiabilities Value Assets ValueCapital StructureFinancial leverage:orHas a change of financial leverage any impact on the firm value?10M&M TheoryM&M assumptions:Frictionless assumptionsNo income taxesNo transaction costsNo information asymmetryNo cost to resolve interest conflicts among stakeholdersAll liabilities are risk-free11Notes: A mini - caseTwo companies EBIT Capital structure Firm value$10 million p.abonds: $40 million, 8%shares: 600,0001.As share price: $100 per shareexpected return: 10%1 million shares $100 millionB ?A 2.Bs bond: risk-free the share number is supposed share expected return: ?12(Risk-free) NoPosition Immediate Cash Flow Cash Flow in the FutureReplication of As Stock Using Bs Stock and BondsBs Total Payments = Bs Net Earnings + Interest Payments= ( EBIT - $3.2 million) + $3.2 million= EBITSuppose price of Bs stock = $90 per shareShort sell 1% As shares at $100 per shareBuy 1% Bs shares at $90 per shareBuy 1% Bs bonds+$1,000,000 1% of EBIT $540,0001%( EBIT $3,200,000 ) $400,0001% $3,200,000 Net Cash Flow$60,0000ArbitragePrice of Bs stock= $100 per share13 M&M Proposition 1Proposition 1: Under M&M Assumption, i.e., in the frictionless environment, the total market value of a firm is independent of its capital structure.Think of the firm as a gigantic pizza, divided into quarters. If now, you cut each quarter in half into eights, the M &M proposition says that you will have more pieces, but not more pizza. Merton Miler14Probability Distribution of EBIT and EPS for the Two CompaniesState of the EconomyEBITCompany A Company B EPS Net EPS(1 million shares) Earnings (600,000 shares) Bad business $5 million $5 $1.8 million $3.00Normal business 10 10 6.8 11.33Good business 15 15 11.8 19.67Mean 10 10 6.8 11.33Standard deviation 4 6.81Beta 1.0 1.0 1.67NOTE: Each state of the economy is equally likely.15The cost of capital depends on its use and not on its source.Proposition!16Weighted Average Cost of CapitalCost of capital of the firm without liabilityRisk premium of WACCFinancial leverageM&M Proposition 2:The cost of capital of a firm equals the cost of capital of the firm without liability and the risk premium of WACC multiplied by financial leverage.17All transactions in financial markets are zero NPV transaction activities.Proposition!18Implication of M&M TheoryFrictionless environment does not exist in the real world.TaxesTransaction costsInformation asymmetryCosts resolving interest conflictLiabilities are risk-bearing19 Tax ShieldCompany A:Tax rate: T = 33%Company A Company BClaimantCreditorsShareholdersGovernment Tax Authority Total Firm Value before Taxation$100 million $100 million067 million33 millionCompany B:(1T)(EBITInterests)+Interests = (1-T)EBIT+TInterests40.0 million40.2 million19.8 million$13.2 million20 WACC with Taxes Other M&M assumptions holdHas a change of financial leverage any impact on the firm value ?Answer: Yes !Discount rate for cash flow of the firm21 Stock PriceShare Number Total Equity Share PriceCompany A:1 million67.0 million$ 67Company B:600,00040.2 million$ 67?If Company A were to announce an issue of $40 million debt to be used to repurchase and retire common stockAs capital structure = Bs capital structureMarket reaction: price of As share would go up to reflect the $13.2 million tax shield: $(67.0 + 13.2) million / 1 million = $80.2 per share.Where is the benefit of the tax shield?22State Pricesu = 1.07d = 0.98Risk-free securityRisk-free interest rateBond ABond B23 Basic SecuritiesBasic Security 1 Basic Security 2= ?= ?Portfolio Basic Security 1, Basic Security 2replicatingBond A=No Arbitrage24 Replicating risk free securityPortfolio Basic Security 1, Basic Security 2replicating=LetState Prices25 Replicating Bond A and Bond BNo ArbitrageQuestions ?1.Do there exist such kind basic securities in the real world?2.Are there enough basic securities that can be used to replicate all the payoff of securities in the market?Answers :1.Find some equivalent instruments instead of basic securities.2.It involves in market completeness.26 Replication via equivalent instrumentsPortfolio Bond A, market value risk-free securityreplicating Bond B27 Market Completeness Whenever the number of different instruments used to replicate securities equals the number of states so that we can attain any payoff of securities in future , in such a circumstance, the market is a complete one. Otherwise, themarket is incomplete.Completeness is a c o r e c o n c e p t o f finance theories !28Summary of Chapter One1.No Arbitrage Equilibrium2.Replication Methodology3.State Prices Technology29CHAPTER TWO: Time Value of Money and Term Structure of Interest Discounted Cash Flow FormulaYes ! is the expected rate of return, i.e., the mean of the discount rates for different termsLetNo ! is the discount rate that cannot be used for so long period?30 Determination of Interest1. Capital production ability the more the capitals expected return, the higher the interest rates and vice versa.2. Uncertainty of capital production ability the more the uncertainty, the higher the risk premium required and the higher the interest rates and vice versa.3. Time preference of consumption the stronger preference to current consumption, the higher the risk premium required and the higher the interest rates and vice versa. 4. Risk aversion the more the risk aversion, the higher the risk premium required and the lower the risk-free interest rates. Four basic factors31 The Benchmark of Interest Yield to Maturity (YTM) YTM varies with different financial instruments, because the exposure of financial instruments are quite different and the required risk premiums differ from each other.Risk-free interest varies with terms . Its called the term structure of interests. Risk-free interests?No!Yes!32