2. 1 CHAPTER ONE: MM Theory and No Arbitrage 1.MM Theory Two measurements of value Accounting: book value — historic cost Finance: market value — net present value

3. 2 Assets = Liabilities + Equity Accounting Equality: duel entity system Book value measurement Fund use Fund source Finance Equality: Fund use = Fund source Market value measurement

4. 3 Corporate Finance Assets Liabilities and Equity Asset 1 Asset 2 Liabilities Asset 3.. Equity. Asset n Total Assets Total Liabilities and Equity Accounting: Yes! Finance: No! Capital Market Real Economy NPV Firm Value + NPV

5. 4 Liabilities Value Equity Value Liabilities Value Assets Value Capital Structure Financial leverage: or Has a change of financial leverage any impact on the firm value?

6. 5 M&M Theory M&M assumptions: Frictionless assumptions –No income taxes –No transaction costs –No information asymmetry –No cost to resolve interest conflicts among stakeholders All liabilities are risk-free

7. 6 Notes: A mini – case: does capital structure matter? Two companies EBIT Capital structure Firm value $10 million p.a bonds: $40 million, 8% shares: 600,000 1.A’s share price: $100 per share expected return: 10% 1 million shares $100 million B? A 2.B’s bond: risk-free the share number is supposed share expected return: ?

8. 7 (Risk-free) No Position Immediate Cash Flow Cash Flow in the Future Replication of A’s Stock Using B’s Stock and Bonds B’s Total Payments = B’s Net Earnings + Interest Payments = ( EBIT - $3.2 million) + $3.2 million = EBIT Suppose price of B’s stock = $90 per share Short sell 1% A’s shares at $100 per share Buy 1% B’s shares at $90 per share Buy 1% B’s bonds +$1,000,000  1% of EBIT  $540,0001%  ( EBIT  $3,200,000 )  $400,0001%  $3,200,000 Net Cash Flow$60,0000 Arbitrage Price of B’s stock = $100 per share

9. 8 M&M Proposition 1 Proposition 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 Miller

10. 9 The cost of capital depends on its use and not on its source. Proposition!

11. 10 Comparison of Stocks between A and B State of the Economy EBIT Company A Company B EPS Net EPS (1 million shares) Earnings (600,000 shares) Bad business $5 million $5 $1.8 million $3.00 Normal business 10 10 6.8 11.33 Good business 15 15 11.8 19.67 Mean 10 10 6.8 11.33 Standard deviation 4 6.81 Beta 1.0 1.0 1.67 NOTE: Each state of the economy is equally likely.

12. 11 Weighted Average Cost of Capital Cost of capital of the firm without liability Risk premium of WACC Financial leverage M&M Proposition 2: The cost of equity of a firm equals the cost of capital of the firm without liability and the risk premium of WACC multiplied by financial leverage.

13. 12 All transactions in financial markets are zero – NPV transaction activities. Proposition!

14. 13 Implication of M&M Theory Frictionless environment does not exist in the real world. –Taxes –Transaction costs –Information asymmetry –Costs resolving conflict of interest Liabilities are risk-bearing

15. 14 — Tax Shield Company A: Tax rate: T = 33% Company A Company BClaimant Creditors Shareholders Government Tax Authority Total Firm Value before Taxation $100 million 0 67 million 33 million Company B: (1–T)(EBIT–Interests)+Interests = (1-T)EBIT+T  Interests 40.0 million 40.2 million 19.8 million $13.2 million

16. 15 — WACC with Taxes Other M&M assumptions hold Has a change of financial leverage any impact on the firm value ? Answer: Yes ! Discount rate for cash flow of the firm

17. 16 — Stock Price Share Number Total Equity Share Price Company A:1 million 67.0 million $ 67 Company 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 stock A’s capital structure = B’s capital structure Market reaction: price of A’s 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?

18. 17 State Prices u = 1.07 d = 0.98 Risk-free security Risk-free interest rate Bond ABond B

19. 18 — Basic Securities Basic Security 1 Basic Security 2 = ?= ? = ?= ? Portfolio { Basic Security 1, Basic Security 2} replicating Bond A = No Arbitrage

20. 19 Replicating risk – free security Portfolio { Basic Security 1, Basic Security 2} replicating = Let State Prices P=E[mX]

21. 20 Replicating Bond A and Bond B No Arbitrage Questions ? 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.

22. 21 Replication via equivalent instruments Portfolio { Bond A, market value risk-free security} replicating Bond B

23. 22 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, the market is incomplete. Completeness is a core concept of finance theories !

24. 23 P=E(mx) In complete market, there is a unique m that is consistent with market observable security prices In incomplete market, there are many m’s that are consistent with the market observable security prices.

25. 24 Summary of Chapter One 1.No Arbitrage Equilibrium 2.Replication Methodology 3.State Prices Technology: P=E[mX]

26. 25 CHAPTER TWO: Time Value of Money and Term Structure of Interest — Discounted Cash Flow Formula Yes ! is the expected rate of return, i.e., the mean of the discount rates for different terms Let No ! is the discount rate that cannot be used for so long period ?

27. 26 — Determination of Interest 1. Capital production ability —— the more the capital’s 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 factors

28. 27 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. It’s called the term structure of interests. — Risk-free interests ? ? No! Yes!