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Finance and the Financial Manager Chapter 1

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1.1 What is a Corporation? 1.2 The Role of the Financial Manager Two Basic Questions 1 Investment Decision 2 Financing Decision

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1.3 Who is the Financial Manager Financial Manager Firm's Operations Financial Markets (1)(2) (3) (4a) (4b)

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1.4 Goal of the Firm ?

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1.5 Agency Problem Monitoring by board of directors 1 Compensation package 2 Active outside takeover market 5 Efficient outside managerial labor market 4 Monitoring by outside large blockholders (Bank, insurance Co., pension, mutual fund) 3 B. How to solve agency problem? A. Separation between Ownership and Management

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Present Value and The Opportunity Cost of Capital Chapter 2

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C. PV and Rate of Return B. Risk and Present Value PV = C / (1+r) 2.1 Introduction A. Present Value NPV = PV - C 0 r:

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D. The Opportunity Cost of Capital 1 From your Investment C 0 : $ 100,000 Slump : $ 80,000 Boom : $ 140,000 Normal : $ 110,000 C 1 : E(C 1 )

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From Stock Market 2 Find stock X which has same risk as your project : P 0 : $ Slump : $ 80 Boom : $ 140 Normal : $ 110 P 1 : E(P 1 ) = 1/3 ( ) = 110 E(R) = = 0.15 15% k

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Q : What is the Present Value of your project? PV of project = NPV =

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How to Calculate Present Values Chapter 3

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3.1 Cash Flows in Several Periods ( * ) 3.2 Perpetuities and Annuities ( * ) 3.3 Growing Perpetuities ( * ) 3.4 Compounding Interest ( * )

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3.5 Nominal and Real Interest A. Real CF = Nominal CF (1+inflation rate) B. (1+Real Rate) = (1+ Nominal rate) (1+inflation rate) 3.6 Bond Valuation PV bond = C 1+r C (1+r) 2 C+F (1+r) n ++ …... + = C PVAF + F PVF (Ex) Coupon rate: 10%, r=5%, face value=$1,000 N=7years PV bond = 100 = $1360.7

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The Value of Common Stocks Chapter 4

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NYSE AMEX OTC (NASDAQ) B. Secondary Market A. Primary Market 4.1 How Common Stocks are Traded?

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(Ex) P 0 = $100, P 1 = $110, DIV = $5 r = = Holding Period Return = E(R) E(R) = (P 1 - P 0 + DIV) / P 0 = r r: market capitalization rate 4.2 Stock Valuation A. Today’s Price P 1 - P 0 P0P0 DIV P0P0 + =

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Q: What happen if P 0 is different from $100 ? $ 100 ; equilibrium price if 15% is an appropriate discount rate P 0 = (P 1 + DIV) / (1+r) = ( ) / 1.15 = 100

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B. What determines next year’s price ? P 0 = [D 0 (1 + g)] / (r - g) = D 1 / (r - g) Assume: Dividend grows at a constant rate; g P 0 = (P 1 + D 1 ) / (1 + r), P 1 = (P 2 + D 2 ) / (1 + r) P 0 = D 1 / (1 + r) + (P 2 + D 2 ) / (1 + r) 2 = D 1 / (1 + r ) + D 2 / (1+r) 2 + D 3 / (1 + r) 3 + ……… Valuation Model = = t=1 D t / (1 + r) t

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D 1 / P 0 : Dividend Yield g : Dividend Growth r = D 1 / P 0 + g 4.3 Simple Way to Estimate r EX : Pinacle West Corp (p 69) P 0 = $41, Div 1 = $1.27, g = 5.7% r =

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g = Plowback ratio * ROE = ROE = EPS / Book Equity per Share = 0.1 Plowback Ratio = 1- Payout ratio = 0.53 Payout ratio = DIV 1 / EPS = 0.47 Alternative Approach: r = = or 8.4%

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Some Warnings about Constant-Growth Formulas 1. Individual stock’s r is subject to estimation errors Portfolio approach 2. Growth rate can rarely sustained indefinitely Ex. Growth-tech DIV 1 =$0.05, P 0 =$50, Plowback Ratio=80%, ROE=25% g = r =

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YEAR1YEAR2YEAR3YEAR4 Book equity Earning per share, EPS Return on Equity, ROE Payout ratio Dividends per share, DIV Growth rate of dividends Ex: at t=3 and thereafter ROE =16% Firm responds by plowing back 50% of earnings g = Table 4.2

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General DCF formula to find the capitalization rate r: DIV 1 1+r P0P0 = DIV 2 (1+r) 2 ++ DIV 3 + P 3 (1+r) 3 P3P3 = P0P0 = 50=

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4.4 The link between stock price and earning per Share Growth stock vs Income stock A. Income Stock No GrowthPerpetuity Model P 0 = EPS 1 r = r DIV 1 (EX) Expected Return = Dividend Yield = 10/100 =.10 = r Price = DIV 1 / r = EPS 1 / r =

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B. Growth Stock (r=10%) NPV = $ 1 (each year) Invest $10 into project with permanent return of 10% at t = 1: (once & for all) This investment contributes “0” to value. (EX) Return on project is higher or lower than 10%; NPV? (go to table 4-3)

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Table 4-3 Effect on stock price investing an additional $10 in year 1 at different rates of return. Notice that the earnings-price ratio overestimates r when the project has negative NPV and underestimates it when the project has positive NPV. Project's impact Project RateIncrementalProject NPV on Share Price Share PriceEPS1 of Return Cash Flow, Cin Year 1 a in Year 0 b in Year 0, P 0 P 0 r.05 $.50- $ $ 4.55$ a Project costs $ (EPS1). NPV = C / r, where r =.10 b NPV is calculated at year 1. To find the impact on P0, discount for 1 year at r =.10

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In general : P 0 =PVGO EPS 1 r + PVGO : Present Value of Grow Opportunity Sum of all NPVs (per share) EPS 1 r Capitalized value of average earning under a no-growth policy :

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P 0 = PVGO EPS 1 r + Divide each side by EPS P/E = 1 r PVGO E + Q : Japanese firm : P/E 50 U.S. firm : P/E 17 Is Japanese firm growing fast? Determinants of P/E Ratio 1. Cost of Capital(r): “-” 2. Conservative accounting procedure(EPS): “-” 3. Growth opportunities(PVGO): “+”

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If EPS 1 = $ 8.33, Payout ratio = D 1 / EPS 1 = 5 / 8.33 = 0.6 If ROE =.25, g = P 0 = D 1 / (r - g) = r = 15 %, D 1 = $ 5 P 0 = EX : Fledgling Electronics Case (p73)

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Analyze: $ Plowback Ratio =.4, 8.33 *.4 = $ 3.33 Invest: $ 3.33 at 25% (ROE).25 * 3.33 = $.83 at t = 1; NPV 1 = /.15 = 2.22 at t = 2; Invest 3.33 * 1.1 = 3.69 (g = 10%) NPV 2 = * (.83 * 1.1) /.15 = 2.44 PVGO = NPV 1 / (r - g) = 2.22 / ( ) = $ This is growth stock, not because g = 10%, but because

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Table 4-4 Estimated PVGOs (p.76) MarketPVGO, StockCapitalizationPVGOPercent of StockPrice, P0EPS*Rate, r**=P0 - EPS/rStock PriceP / E Income Stocks: AT & T$52.00$ $ Conagra Duke Power Exxon Growth Stocks: Compaq Merck Microsoft Wal-Mart * EPS defined as the average earnings under a no-growth policy. As an estimate of EPS, we use the forecasted earnings per share for the 12 months ending March31, Source: Value Line. * The market capitalization rate was estimated using the capital asset pricing model. We describe this model and how to use it in Section 8.2 and 9.2. EX: market risk premium = 6% C. Some Example of Growth Opportunities

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Why NPV leads to better Investment Decisions than Other Criteria Why Net Present Value Leads to Better Investment Decisions than Other Criteria Chapter 5

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5.1 Review of Basics 1 Forecast Cash Flow 2 Determine appropriate Cost of Capital 3 Discount with Cost of Capital

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Q : Why NPV ? All cash flows are considered Time Value of Money NPV is not affected by manager’s taste, accounting method, profitability of existing business, and profitability of other independent business

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CASH FLOWS, DOLLARS PaybackNPV at Project C0C1C2C3 Period, Years10 Percent B- 2, ,00032,642 C - 2, ,800+ 5, D- 2,000+ 1, Payback Period Number of years it takes before cumulative cash flow recovers initial investment

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5.3 Book Rate of Return Book Rate of Return Book income Book assets = Cash flow vs. Book Income Problems :

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Computing the average book rate of return on an investment of $9000 in project A CASH FLOWS, DOLLARS Project AYear 1Year 2Year 3 Revenue12,00010,0008,000 Out-of-Pocket cost6,0005,0004,000 Cash flow6,0005,0004,000 Depreciation3,000 Net income3,0002,0001,000 Average book rate of return = average annual income = 2,000 =.44 average annual investment 4,500 Year 0Year 1Year 2Year 3 Gross book value of investment$ 9,000 Accumulated depreciation 0 3,000 6,000 9,000 Net book value of investment$ 9,000$ 6,000$ 3,000$ 0 Average net book value = $ 4,500 Example

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(Rule) Accept IRR>k NPV>0 Reject IRR

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Discount rate (%) Net Present Value, dollars IRR=28%

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Pitfall 1. Lending vs. Borrowing? CASH FLOWS, DOLLARS NPV at ProjectC0C1IRR, Percent 10 Percent A- 1,000+ 1, B+ 1,000- 1, CASH FLOWS, DOLLARS NPV at ProjectC0C1C2C3 IRR, Percent 10 Percent C+ 1,000- 3,600+ 4,320- 1,

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Discount rate (%) Net Present Value, dollars

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Pitfall 2. Multiple Rates or Return Pretax Tax Net , , CASH FLOWS, DOLLARS NPV at ProjectC0C1C2IRR, Percent10 Percent D+ 1,000- 3,000+ 2,500 none + 339

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1000 NPV Discount Rate IRR=15.2% IRR=-50%

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Pitfall 3. Mutually Exclusive Projects 3.1 Different scale CASH FLOWS, DOLLARS NPV at Project C0 C1 IRR, Percent10 Percent E- 10, , F- 20, ,00075 CASH FLOWS, DOLLARS NPV at Project C0 C1 IRR, Percent10 Percent F-E- 10, , ,636

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CASH FLOWS, DOLLARS IRR, NPV at ProjectC0C0 C1C1 C2C2 C3C3 C4C4 C5C5 Etc. Percent 10 Percent G - 9,000+6,000+5,000+4,000 00…333,592 H - 9,000+1,800 …209,000 I -6,000+1,200 …206, Different pattern of cash flow over time

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10,000 NPV, dollars Discount Rate, percent ,000 +6, Project G Project H

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(generally) IRR vs. r 1 r 2 ? r 3 NPV = - C 0 + C 1 / (1+r 1 ) + C 2 / (1+r 2 ) 2 + … Pitfall 4. What happens if term structure is not flat?

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CASH FLOWS, MILLIONS OF DOLLARS NPV at ProjectC 0 C 1 C 2 10 Percent A B C Limited Resource (Capital Rationing) t=0

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CASH FLOWS, MILLIONS OF DOLLARS NPV atProfitability ProjectC 0 C 1 C 2 10 PercentIndex A B C D t=0, t=1

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More Elaborate Capital Rationing Models We accept proportion A of project A. NPV of accepting A of A Previous Example NPV =

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Constraint: (Costs) at t = 0, 10 A + 5 B + 5 C + 0 D 10 at t = 1, 40 D 30 A + 5 B + 5 C A, B, C, D 1 Maximize: 21 A + 16 B + 12 C + 13 D Subject to : 10 A + 5 B + 5 C + 0 D A - 5 B - 5 C + 40 D 10 0 A, B, C, D 1

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Making Investment Decisions with the Net Present Value Rule Chapter 6

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How to apply the rule to practical investment problems? Question What should be discounted? CF: relevance, completeness, consistency, accuracy How NPV rule should be used when there are project interactions?

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Estimate Cash Flow on an Incremental Basis Average vs. incremental Include all incidental effects Do not forget NWC requirement Forget sunk cost Include opportunity costs Beware of allocated overhead costs Consider spillover effect “erosion”

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Treat Inflation consistently. –Real CF : discount with real rate –Nominal CF: discount with nominal rate ( Ex) C 0 C 1 C 2 C 3 Real CF r N = 15%, I = 10% NPV = NPV =

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6.2 Example - IMFC Project Initial investment: $ 10 mil Salvage value at year 7: $ 1 mil (sold) Depreciation: 6 year straight line with arbitrary salvage of : $ 500,000 annual depreciation = = $ mil 9.5 mil 6

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Table Nominal Cashflow

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Sales 2. Cost of goods and sold 3. Other costs 4. Tax on operations 5. Cash flow from operation 6. Change in working capital 7. Capital investment and Disposal 8. Net cash flow 9. Present value at 20% Net present value = +3,519(sum of 9) 4,000 -1,400 -2, , , ,200 -1,434 -1, ,630 -1,358 12,887 7,729 1, , ,381 1,654 32,610 19,552 1,331 3,550 8,177 -1,972 6,205 3,591 48,901 29,345 1,464 5,778 12,314 -1,629 10,685 5,153 35,834 21,492 1,611 3,902 8,829 1,307 10,136 4,074 19,717 11,830 1,772 1,586 4,529 1,581 6,110 2,046 2,002 1,442 3, Period IM&G’s guano project-cash-flow analysis (thousand)

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Cash flow = Sales - CGS - Other costs - Taxes Net cash flow = Cash flow from operation Networking capital [- Initial Investment + Recovery of Salvage Value] NPV =

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6.3 Project Interacting Choosing between Long & Short Equipment C1C1 C0C0 C3C3 C2C2 PV at 6% A B

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Equivalent Annual Cost C1C1 C0C0 C3C3 C2C2 PV at 6% Machine A EAC A Machine B EAC B xxx y y

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Risk, Return & opportunity Cost of Capital Risk and Return & Opportunity Cost of Capital Chapter 7&8

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7.1 Seventy-Two year of Capital Market ,828 S&P 5,520 Small Cap Corporate Bonds 39.07Government Bonds Treasury Bills Dollars

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Small firms S&P Corporate bonds 4.34 Government bonds 1.58 Treasury bills Dollars

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PORTFOLIO AVERAGE ANNUAL RATE OR RETURN NOMINALREAL AVERAGE RISK PREMIUM (EXTRA RETURN VS. TRESURY BILLS) Treasury bills Government bonds Corporate bonds Common stocks (S&P 500) Small firm common stock Average rate of return on Treasury bills, Government bonds, Corporate bonds, and common stocks, (Percent per year)

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7.2 Measuring Portfolio Risk Variance (Standard Deviation) Expected = R i * P i = E (R) = R Variance = (R i - R) 2 * P i = 2 = V Risk Systematic Risk: market risk macro-economic variables Unsystematic Risk: firm unique or specific risk

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PORTFOLIO Treasury bills Long-term government bonds Corporate bonds Common stock (S&P 500) Small-firm common stocks 3.2 STANDARD DEVIATION( ) VARIANCE( 2 ) PERIOD MARKET SD( ) %

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STOCK AT&T Bristol-Myers Squibb Coca-Cola Compaq Exxon 22.6 STANDARD DEVIATION( ) STOCK STANDARD DEVIATION( ) General Electric McDonald’s Microsoft Reebok Xerox Stock BP Deutsche Bank Fiat Hudson Bay 16.3 SD( ) KLM MARKET UK Germany Italy Canada Netherlands SD( ) Stock SD( ) MARKET SD( ) LVMH Nestle Sony Telefonia de Argentina France Switzerland Japan Argentina

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n = Calculating Portfolio Risk Itself Variance; 2( , ) Between A, B Covariance; 2( , ) A B

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A B A B

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Weights; A, B, A + B = 1 A B A B 2 A AB BA 2 B Portfolio Risk =

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Example; Bristol-Myers : McDonald’s : BMBM =0.15 2 p =

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n=3 Variance: Covariance: n=4 Variance: Covariance:

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lim V P N V P = 2 P = 2 P = V P = (Ex) mutual fund Limits to Diversification N * (1/N) 2 2 + (N 2 - N) * (1/N 2 ) cov 2 : average variance cov : average covariance (1/N) 2 + (1 - 1/N) cov

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= 1 2 P = X 1 2 X 2 2 X 1 X 2 1 2 * 1 = (X 1 1 + X 2 2 ) 2 ( a b) 2 a 2 + b 2 2ab P = X 1 1 + X 2 2, when = 1 There is: no diversification no risk reduction * Portfolio risk is simply weighted average of individual risk; linear combination ! Special Cases

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= - 1 2 P = X 1 2 X 2 2 X 1 X 2 1 2 = (X 1 1 - X 2 2 ) 2 P = X 1 1 - X 2 2, when = -1 Risk may be completely eliminated by combining X 1, X 2 (Ex) Portfolio Risk is (again) a linear combination of individual risks.

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A B E(R) 10% 12% 2 9% 16% AB = -1 Find the weights, A, B for Minimum Variance Portfolio. ( p = 0) What is the risk & return of that portfolio? * General case : -1 We need Calculus. Example

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Efficient Frontier E p B A PP AB = 1 = -1 B EpEp PP A

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Generally 1 PP EpEp B A

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PP E(R P )

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PP Efficient Portfolio E(R P )

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2 P = X 1 2 X 2 2 X 1 X 2 1 2 12 (risk-free asset : 2 = 0 ) - Lending 2 P = X 1 2 1 2 P = X 1 1 (linear combination) E P = X 1 R 1 + X 2 R f - Borrowing 2 P = ( X * + 1 ) 2 ( -X * ) 2 ( 1+X * )( -X * ) 12 P = (1+X * ) 1 E P = (1+X * ) R 1 - X * R f Portfolio Risk : Linear combination of individual risk We Introduce Borrowing & Lending (p193)

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Combination of Risky (A) and Risk Free Asset RfRf A

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New Efficient Portfolio RfRf A C Old Efficient Portfolio B T D

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RfRf T EMEM EPEP PP MM Risk-return relationship for efficient portfolios Intercept: R f price of time slope: (E M - R f ) / M price of risk Ep = R f + [ (EM - R f ) / M ] x P T is a market portfolio; M Capital Market Line CML

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Capital Asset Pricing Model: CAPM Apply Portfolio Theory to evaluate all risky assets We can eliminate unsystematic risk by combining securities. (it cancels each other) We can not eliminate systematic risk since it moves with market as a whole Systematic Risk vs. Unsystematic Risk Therefore,

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= R f + = R f + amount of risk Price of risk Systematic Risk = Market risk = Covariance( iM ) Required Rate of Return on Risky Asset Risk-free Rate(R f ) Risk Premium = + = R f +

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STOCK AT&T Bristol-Myers Squibb Coca-Cola Compaq Exxon.65 BETA STOCK General Electric McDonald’s Microsoft Reebok Xerox BETA STOCK.74 BETA STOCK BETA BP Deutsche Bank Fiat Hudson Bay KLM LVMH Nestle Sony Telefonia de Argentina 1.31

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STOCK AT&T Bristol-Myers Squibb Coca-Cola Compaq Exxon.65 BETA General Electric McDonald’s Microsoft Reebok Xerox EXPECTED RETURN r f + ( r m - r f ) 10.7%

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Summary “ ” 1) Covariance risk (normalized) iM 2 M 2) Sensitivity of stock i’s return with respect to market Ex:

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Security Market Line: SML 1) CAPM Line 2) Equilibrium Line; If asset is correctly priced (in its equilibrium), in terms of CAPM, it falls on this line. Below this line : Above this line : E(R i ) ii 0 1 ? ? RfRf

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E(R) rmrm rfrf A B C

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Market line Avg Risk Premium Portfolio Beta Investors Market Portfolio Beta vs. Average Risk Premium

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Avg Risk Premium Portfolio Beta 1.0 Market Line Investors Market Portfolio Avg Risk Premium Portfolio Beta Investor Market Portfolio Market Line

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8.4 Some Alternative Theories Arbitrary Pricing Theory Assumes that each stock’s return depends partly on macroeconomic factors or noise (event that are unique to company) Expected Premium = r - r f = b 1 (r 1 - r f ) + b 2 (r 2 - r f ) + b 3 (r 3 - r f ) + … … R = a + b 1 r f1 + b 2 r f2 + b 3 r f3 + … … noise

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APT example 1. Identify the Macroecnomic Factors Yield Spread Interest Rate Exchange Rate Real GNP Inflation 2. Estimate the Risk Premium for Each Factor Factor Estimated risk premium (r factor - r f ) Yield spread Interest rate Exchange rate Real GNP Inflation Market 5.10%

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3. Estimate the Factor Sensitivity Factor risk (b) Estimated risk premium (r factor - r f ) Yield spread Interest rate Exchange rate Real GNP Inflation Market 5.10% Total Factor Factor risk premium [b(r factor - r f )] % %

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Capital Budgeting and Risk Chapter 9

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Firm Value = PV(AB) = PV(A) + PV(B) = sum of separate assets PV(A), PV(B) are valued as if they were mini-firms in which stockholders invest directly. Each project should be evaluated at its own Cost of Capital (implication of Value Additivity Principle) Are the New Projects More Risky or Less Risky than its Existing Business?

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r rfrf A B Cost of Capital

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True Cost of Capital - depends on the use to which the capital is put - Project beta ( ) Expected Return = r = r f + (project beta) (r m - r f ) “ ” of project or division - Look at an average of similar companies (or industry beta) - Firm’s borrowing policy (leverage) affects its stock beta - Project beta shifts over time.

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Industry Beta and Divisional Cost of Capital Individual measurement error Portfolio error cancelled out If you consider across-the-board expansion, such as new division, What is the “ ” for new division? Answer:

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Measuring Betas –Using monthly stock return on IBM –Using monthly market return (Ex) 60 months R 1 IBM R 1 M R 2 IBM R 2 M R 60 IBM R 60 M …

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( = alpha) Average rate of price appreciation or depreciation, born by stock-holders when investors in the market as a whole earn nothing. R-squared R 2 The proportion of variance of stock price change that can be explained by market movement. means systematic risk / total risk

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= -0.65% ; 12 -7.8% Alpha = -.65 Change in market index Beta = 1.30 Change in prices of DEC common stock

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9.2 Capital Structure & Company Cost of Capital(COC) Cost of Capital ; hurdle rate minimum return required to make firm value unchanged. Depends on also depends on * Financial leverage does not affect the risk or the expected return on the firm’s assets. But,

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How Changing Capital Structure Affects Expected Return? Company Cost of Capital (WACC) = r d r e D D + E + E E + D = r Asset = r portfolio (EX) B/S (market value) A 100D r d = 8% r e = 15% r Asset = 60E

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(Now) : Issue 10 equity, Retire 10 debt * The change in financial structure does not affect r Assets = B/S (market value) A 100D E does affect (Ex) lower leverage: r D 7.3% (Given)

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How does Changing Capital Structure Affect Beta? Assets = Portfolio = D V E V D + EE V = D + E D = 0.2 E = 1.2 A = After refinancing; D 0.1(Given)

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Expected return (%) r debt =8 r assets =12.2 r equity = debt = Beta.8 assets = equity =1.2 Before Refinancing 20 0 Expected return (%).1 debt = r debt =7.3 r assets =12.2 r equity =14.3 Beta.8 assets = equity =1.1 After Refinancing

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9.3 How to Estimate the company Cost of Capital Pinnacle West’s Common Stock.15.51Average Portfolio ResourcesL&PP Corp.West Pinnacle EnergyPECO EnergyOGE System ElectricNE Inc. GPU Associate UtilitiesEastern EnergyDTE EdisonConsolidated HudsonCentral ElectricBoston ErrorStandard.Beta

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r equity = r f + equity [ r m - r f ] = 0.08 = % r d = 6.9%, r e = 8.6%, = 0.43, = 0.57 WACC = Company Cost of Capital = r d + r e D V E V D V E V

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9.4 Discount Rates for International Projects Foreign investments are not always riskier Taiwan Kazakhstan Brazil Argentina Beta coefficient Correlation Ratio Foreign Investment in the US

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Taiwan Index US Index 0 PP E(R P )

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9-4 Setting Discount Rate when you can’t calculate Think about the determinant of asset beta Avoid fudge factors Do not add fudge factors to the discount rate instead adjust cash flow forecasts (Ex) dry hole, FDA approval, politica1 unstability in foreign country etc

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(Ex) Q: What are industries which are risky, but have low ?

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Determinants of Asset Beta: Operating Leverage Cyclicality: Firms whose revenue depend on business cycle high Commitment to fixed production charges High fixed cost ratio High operating leverage High Asset Beta Why ?

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$ Q Unit Variable Cost Break Even Point Analysis Fixed Cost Total Cost

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Profit Loss FC TC TR Low Fixed Cost (high Variable Cost) Low OL BEF

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FC TC TR High Fixed Cost (Low Variable Cost) High OL

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9-6 Another Look at Risk and Discounted Cash flow Risk-adjusted: t=1 PV = [C t / (1+r) t ], r = r f + (r M - r f ) n (Ex) r = 8 = 12% Year CF PV x = (x = certainty equivalent cash flow) (1.12) 2 = 89.3 = x (1.06) 2 x = 100 (1.06/1.12) 2 = 89.57

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General Solution Certainly equivalent Cash Flow at time t Risky Cash Flow at time t 1+r f 1+r t We call t = = 1+r f 1+r t Certainty equivalent coefficient 1 = (1.06 / 1.12) = 2 = (1.06 / 1.12) 2 = 3 = (1.06 / 1.12) 3 = Valuing CE cash flow PV = CE(CF) (1 + r f ) CF 1 + r =

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(Example) E(C) = -1,000,000 0.5 = -500,000 r = 25% Convert into Certainty Equivalent cash flow: (1.25) t t=2 NPV = = -125 or -$125,000? NPV = (250/0.1) = (50% chance) NPV = 0 (50% chance) E(NPV) = 1500 0.5 = 750 (if = 0.5) NPV = = or $225,000 (750 0.5) 1.07 Success Failure

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Making Sure Managers Maximize NPV Chapter 12

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12.1 Incentives A. Agency Problems in Capital Budgeting Reduced Effort Perquisites Empire Building Entrenchment Avoiding Risk B. Monitoring C. Compensation

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Corporate Financing and Market Efficiency Chapter 13

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So far, we assume ‘all equity’ financing. Stockholders supply all the firm’s capital, bear all the business risks, and receive all the rewards. How to spend $?How to raise $? ? B/S

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13.1 We always come back to NPV (ex) Government offer: $100,000, 10yrs at 3% Market fair rate: 10% NPV = Amount borrowed - PV of interest payments - PV of loan payment 3,000 (1.10) t = +100,000 - t= ,000 (1.10) 10 = $43,200 Difference between Investment & Financing Decisions Easy reverse Abandonment value is O.K. Lose or make money is not easy

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Month Level

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13.2 Efficient Market Hypothesis Definition Stock price reflects information immediately and completely Level of Efficiency - Weak Form Stock price reflects previous price movement immediately and completely - Semi-Strong Form all publicly available information - Strong Form all information (public, private, and insider)

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Test of Market Efficiency - Weak form - Semi-Strong form - Strong form Market Anomaly - Small firm Effect - January Effect - Weekend Effect Q: Is market inefficient?

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The Dividend Controversy Chapter 16

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Q 1 : How company set dividend? Q 2 : How dividend affect stock price? - So far: independent InvestmentFinancing If dividend affects firm value, attractiveness of new project depends on where the money is coming from. Dividend Decision Mixed with Financing Investment decision Given capital budgeting & financing decision, what is the effect of change in dividend?

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16.1 How dividends are paid? Board of directors Record date Legal Limitation Companies are allowed to pay a dividend out of surplus but they may not distribute legal capital (par value of all outstanding shares) Share Repurchase ’80: Ford: $1.2 bil, Exxon: $15 bil, IBM, COCA etc. Just after 1987 Crash: Citi Corp $6.2 bil How to Repurchase? 1. Open market repurchase 2. Tender Offer 3. Direct negotiation

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16.2 Information content of Dividend Signaling Model Other Signaling Tools Greenmail Target of a takeover attempt buys off the hostile bidder by repurchasing any shares that it has acquired with premium at the expense of existing shareholders.

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16.3 Dividend Controversy MM(1961) - Dividend irrelevance In a world without taxes and transaction costs (efficient and perfect capital market) (Ex) B/S (Market Value) Cash 1,000 FA 9,000 0 D 10,000+NPV E 10,000 + NPV Pay dividend by issuing new shares($1,000) We want to continue project w/t cash($1,000)

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Value of original shareholders’ shares (Ex Post) = Value of company - Value of new shares = (10,000 + NPV) - 1,000 = $ 9,000 + NPV $1,000 cash dividend = $1,000 capital loss Investment and borrowing policies are unaffected by dividend [overall value 10,000 + NPV, is unchanged] * Crucial Assumption New stock holders pay fair-price Old stockholders have received $1,000 dividend and $1,000 capital loss Dividend policy doesn’t matter.

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(Ex) N = 1,000 shares NPV = $2,000 V old * = V old = Number of new shares sold =

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16.4 The Rightist Trade a safe receipt with an uncertain future gain? Sell it! –Market Imperfection Transaction costs Temporarily depressed price Information asymmetry about future Earning 16.4 The Leftist Tax Argument Weakened after 1986 ‘Tax Reform Act’

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16.6 Middle of the Roaders Without tax and transaction cost (perfect & efficient market), company’s value is not affected by dividend policy (irrelevant): MM (1961) Even if with tax and other imperfections, Q: If company increase stock price by paying more or less dividend, why have not they already done so? (perhaps) –“Supply Effect”

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Does Debt Policy Matter? Chapter 17

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B/S Asset Structure Capital Structure Mix of different securities “Maximize V” MM Proposition I Firm can not change the total value of securities just by splitting its cash flows into different streams. (RHS) Firm value is determined by its real assets. (LHS)

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17.1 The Effect of Leverage in a Tax Free Economy V U : Value of unlevered firm E L = V L - D L 1) 1% of unlevered firm $ investment $ return (NOI).01 V U.01 profit

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2) 1% of equity & debt of levered firm (I: interest) $ invest$ return Debt.01 D L.01 I Equity NI.01 E L.01(D L + E L ) =.01 V L same profit (NOI) V U = V L.01 (profit -I).01 profit same cost (same investment)

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3) Buy 1% of equity of levered firm $ investment $ return. 01 E L.01 (profit -I) =.01 (V L - D L ) 4) Alternative way: Borrow.01 D L on your account Buy 1% of equity of unlevered firm $ investment $ return same cost (same investment) -.01 D L -.01 I.01 V U.01 profit.01(V U - D L ).01 (profit - I) Same profit V U = V L Borrowing Equity

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Example of Proposition I (p.477) All Equity E(EPS) = $1.5, P = $10, E(R) = 1.5/10 = 15% N = 1,000 P = $10 V U = $10,000 NOI($) 500 1,000 1,500 2,000 EPS($) ROE(%) A

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Issue: debt $5000, k = 10%, repurchase: 500 shares B NOI($) 500 1,000 1,500 2,000 Interest NI($) ,000 1,500 EPS($) ROE(%) N = 500 P = $10, k = 10% Market value of stock: $5,000 Market value of debt : $5,000

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Equal proportions debt and equity All equity Expected EPS with debt and equity Expected EPS with all equity Expected operating income

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Personal Leverage C Borrow $10, then invest $20 in two unlevered shares (Initially, I have $10) Earnings on two shares($) Interest($) at 10% Net Earnings($) Return on $10 investment 5001,0001,5002,000 NOI($) %10%20%30%

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17.2 How Leverage Affects Return E(EPS) P E(ROE) Current structure all equity Proposed structure $1.5$2.0 $10 15%20% V=10,000 D=5,000 E=5,000 NOI = $1,500 N =1,000 K d = 10% Leverage increases EPS, but not P. The change in EPS is exactly offset by a change in the rate at which the earning are capitalized. 15% 20%

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Expected return on asset(r A ) Market value of all security NOI = In a perfect market, borrowing decision does not affect operating income or total market value of its securities. Borrowing decision does not affect expected return on firm’s assets(r A ). Assumption:

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rErE rArA = + D E ( r A - r D ) Expected return on equity Expected return on assets rArA D D+E = rDrD E + rErE Debt/ Equity Ratio = + Expected return on assets Expected return on debt -

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Proposition II (MM) The expected return on equity ( r E ) of a levered firm increases in proportion to debt to equity ratio (D/E) & the rate depends on the spread between r A and r D. (Ex) r A = 15% D = 5,000 r D = 10% E = 5,000 r E =

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Figure 17-2 MM’s proposition II. The expected return on equity r E increases linearly with the debt- equity ratio so long as debt is risk-free. But if leverage increases the risk of the debt, debtholders demand a higher return on the debt. This causes the rate of increase in r E to slow down. r DEDE rDrD Risk free debt Risky debt rArA Expected Return on Assets = rErE Expected Return on Equity = rDrD Expected Return on Debt =

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The Risk-Return Trade-off AA D D+E = DD + E EE EE AA + D E (A(A D)D) - = Investors (stock-holders) require higher returns on levered equity

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17.3 The Traditional Position Moderate degree of financial leverage may increase r E although not to the degree predicted by MM proposition II Excessive debt raise r E faster r A (=WACC) decline & later rise. A

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r DEDE rDrD Traditionalist believe there is an optimal debt-equity ratio that minimizes r A rArA (MM) = rErE = rDrD rErE (traditional) = rArA = debt equity =

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Transaction Costs Imperfections may allow firms that borrow to provide valuable service. (Ex. Economies of scale in borrowing) Levered Shares might trade at premium compared to their theoretical value in perfect market Smart financial engineer already recognize this and shift capital structure to satisfy this client. B

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How Much Should a Firm Borrow? Chapter 18

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Question: Why do we worry about debt policy? Evidence: 1. D/E ratio are different across the industry. 2. Imperfections: Tax Bankruptcy Costs (T.C.) Cost associated with financial distress Potential conflicts of interests between security holders Interactions of investment and financing decision

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18.1 Corporate Taxes Income statement of Firm U Income statement of Firm L Earnings before interest and taxes Interest paid to bondholders Pretax income Tax at 35% Net income to stockholders Total income to both bondholders and stockholders Interest tax shield (.35 interest) $1, , $650$598 $ = $650$ = $

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Interest Payment D = PV(Tax shield) = rDrD (r D TCTC D) rDrD TCTC D = PV(Tax shield) = 0.35 0.08 1000 $350 = 0.08

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Normal Balance Sheet(Market Values) Asset value (present value of after-tax cash flows) Debt Equity Total assetsTotal value Expanded Balance Sheet(Market Values) Pretax asset value (present value of pretax cash flows) Debt Government ‘s claim (present value of future taxes) Total pretax assetsTotal value Equity

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Book Values Net working capital Total assets Market Values Total assets Total value $2,644 17,599 Long-term assets $20,243 Long-term debt Other long-term liabilities Equity $1,347 6,282 12,614 $20,243 Net working capital Market value of long-term assets $134,156 $2, ,512 $134,156 Long-term debt Other long-term liabilities Equity $1,347 6, ,527 Table 18.3(a)

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Book Values Net working capital Total assets Market Values Total assets Total value $2,644 17,599 Long-term assets $20,243 Long-term debt Other long-term liabilities Equity 6,282 11,614 $20,243 Net working capital Market value of long-term assets $2, ,512 Long-term debt Other long-term liabilities Equity 6,282 Additional tax shields Table 18.3(b)

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MM & Taxes: MM Prop I with corporate tax. V L = V U + PV (Tax Shield) 100% debt?

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18.2 Corporate and Personal Taxes Operating income $1.00 Corporate tax Income after corporate tax Personal tax Income after all taxes

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Corporate Borrowing is better If (1 - T P ) > (1- T PE ) * (1 - Tc) Relative Tax Advantage of Debt = Special Cases: 1. T PE = T P, RTAD = MM’s original 2. (1 - T P ) = (1 - T PE ) * (1 - Tc) RTAD = 1.0 Debt policy is irrelevant! This case happen when Tc < T P & T PE is small. (1 - T P ) (1 - T PE ) (1 - Tc) 1 (1 - T C )

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(Ex) Tc = 35%, T P = 39.6% What T PE makes debt policy irrelevant?

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18.3 Cost of Financial Distress Value of firm (levered) Value of all equity PV(tax shield) PV (costs of financial distress) = + - Debt Market Value of The Firm

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Bankruptcy Costs Payoff Payoff to bondholders ACE LIMITED (limited liability) 1, Asset value 1, Payoff Payoff to bondholders ACE LIMITED (unlimited liability) 1, Asset value 1, Asset value Payoff Payoff to stockholders 1, ,000 Asset value Payoff Payoff to stockholders 1, ,000

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Direct: legal fee, court fee, etc. Indirect: difficult to measure SHARE PRICE FRIDAY APR 10, 1987 MONDAY APR 13, 1987 CHANGE NUMBER OF SHARES (MILLIONS) CHANGE IN VALUE (MILLIONS) Texaco Pennzoil Total $31.875$28.50-$ $ $1,445 Table 18.4

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Financial Distress without Bankruptcy When firms get into trouble, stockholders’ & bondholders’ interests conflict. reduce value of firm Circular File company (Book Values) Net working capital$ 20 Fixed assets 80 Total assets $100 $ $100 Bonds outstanding Common stock Total value Circular File company (Market Values) Net working capital $20 Fixed assets 10 Total assets $30 $25 5 $30 Bonds outstanding Common stock Total value

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Risk Shift: The First Game C0C0 C1C1 -$10 $120 $ 0 (p=10%) (p=90%) If r =50%, NPV = = -$2 Circular File company (Market Values) Net working capital $10 Fixed assets 18 Total assets $28 $20 8 $28 Bonds outstanding Common stock Total value (Ex1)

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High Risk Project Good (p=0.5)Bad (p=0.5) V D S S = 2, D = V = (Ex2): Amount of Debt = $600

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Low Risk Project Good (p=0.5)Bad (p=0.5) V D S S = 1,4001,000 D = V =

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Refusing to contribute equity capital: The second game Good project with NPV= + $5 by investing $10 Net working capital $20 Fixed assets 25 Total assets $45 $33 12 $45 Bonds Common stock Total value Firm value increase by $15 Bond value increase by $8 Stock value increase by $7

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Cost of Distress Vary with Type of Asset Firms with intangibles having value only as a part of going concern, high technology, investment opportunities, human capital, lose more in the financial distress.

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Trade off Theory of Capital Structure Trade-off between interest tax shield and the costs of financial distress Company with safe, tangible asset and plenty of taxable income High debt ratio Unprofitable company with risky, intangible assets Equity finance Trade-off theory explains what kinds of companies “go private in LBO” Trade-off theory cannot explain why some most successful companies thrive with little debt.

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18.4 The Pecking Order of Financing Choice, Information Asymmetry Asymmetric information affects the choice between internal and external financing and between new issues of debt and equity securities Pecking order: internal fund, new issue of debt, finally new issue of equity (Exception) Firm with already excessive debt High-tech, high-growth company

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Implication of Pecking Order 1. Firms prefer internal financing 2. Firms adopt target payout ratio & try to avoid sudden changes in dividend 3. Sticky dividend policy 4. If external finance is required, debt, convertible bond, then equity Financial Slack: Cash, marketable securities, readily saleable real assets, & ready access to the debt market or to bank financing More valuable to firm with plenty of positive-NPV growth opportunity

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Interactions of Investment and Financing Decisions Chapter 19

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Introduction So far, all equity financing All financing decisions are irrelevant In this chapter,we consider capital budgeting decision when investment and financing decision interact and can not be separated

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APV = Base NPV NPV of financing decisions caused by project acceptance + (value additivity principle)

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19.1 After-tax WACC WACC = rDrD D V rErE E V + r D (1-T c ) D V rErE E V +

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Sangria Corporation (Book Values, millions) Asset $100 Total assets $100 $50 50 $100 Debt Equity Total value (Market Values, millions) Asset $125 Total assets $125 $50 75 $125 Debt Equity Total value

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WACC =? rDrD =0.08 rErE =0.146 TCTC =0.35 D V = E V = WACC =

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Invest: $12.5 million Pretax cashflow: $2.085 (perpetual) Tax: 35% $ 7.5 million (Equity) $ 5 million (Debt) After-tax cashflow: $1.355 million NPV = Return on Investment =

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Return on Equity: NOI I Earning After tax -Tax (=0.08 5) Expected return on Equity ==0.146 E(R E ) = r E NPV= (=1.685 0.35)

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19.2 Using WACC - Some tricks of the trade Current Assets, Current liabilities, including cash, inventory,including accounts payable and accounts receivable and short-term debt Plant and equipment Long-term debt (D) Preferred stock (P) Growth opportunities Equity (E) Firm value (V) Total capitalization (V)

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Industry Cost of Capital Cost of capital of new subsidiary Company’s WACC vs. a weighted-average cost of capital of for a portfolio of industry An Application of the Railroad Industry Aggregate industry capital structure in 1979 Debt Equity $24,383 bil $57,651 bil 29.7% 70.3% r d =7.2%, g=11.5%, D/P= 2.3%, T C = 35% WACC = r E =

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Valuing Companies: WACC vs. Flow-to-Equity Method WACC Debt ratio is expected to be constant Calculate tax as if firm is all equity-financed Usually forecast to a median-time horizon and add a terminal value to the cashflow in the horizon year Discount at WACC evaluation of the assets and operation of the firm

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Flow-to Equity Method Evaluation of equity Discount the cashflow to equity, after interest and taxes, at the cost of equity Leverage change cost of equity change two methods give different answer r E = r A + ( r A - r D )(1-T C ) DEDE

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19.3 Adjusting WACC when debt ratios or business risks change Rate of return r Debt-Equity Ratio WACC Opportunity cost of capital (r) Cost of Equity(r E ) Cost of Debt(r D )

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(Ex) D V = 0.4 D V = 0.2 Step1: unlevering the WACC Calculate opportunity cost of capital rDrD D V rErE E V + r = Step2: Estimate r D at 20% debt ratio, & Calculate new r E rArA D E + = rErE ( r A - r D ) * If taxes are left out, WACC equals the r and is independent of leverage Step3: Recalculate the WACC at the new financing weight

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Step1: current = 0.4 D V r = Step2: r d = 8%, when = 0.2 rE=rE= Step3: WACC= D V

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Rate of return, percent Debt-Equity Ratio(D/E) WACC Opportunity cost of capital (r) Cost of Equity(r E ) Cost of Debt(r D ) (D/V =.2)(D/V =.4)

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Unlevering and Relevering - Unlevering asset = debt ( ) + equity ( ) D V E V - Relevering equity = asset + ( asset - debt ) D E or (1+ ) asset, if debt = “0” D E *. Underlying assumption: Rebalancing Maintain the same market-value debt ratio

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19.4 The Adjusted Present Value Rule Base-NPV NPV = [1.8 / (1.12) t ] = $0.17 mil Issue costs. 5% of gross proceeds of issue APV = base NPV - issue cost =.17 mil - 526,000 = -356,000 Reject it! Additions to the Firm’s debt capacity APV = base NPV + PV tax-shield t=1 10

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Table 19-1 Calculating the present value of interest tax shields on debt supported by the solar heater project (dollar figures in thousands) Debt OutstandingInterestPresent Value Year at Start of YearInterestTax Shieldof Tax Shield 1 $ 5,000 $400 $140$ , , , , , , , , Total: $576 Assumptions: 1. Marginal tax rate = Tc =.35; tax shield =.35 x interest. 2. Debt principal repaid at end of year in ten $500,000 installments. 3. Interest rate on debt is 8 percent. 4. Present value calculated at the 8 percent borrowing rate. The assumption here is that the tax shields are just as risky as the interest payments generating them.

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APV = 170, ,000 = $746,000 The value of interest Tax Shield (ITS). –We treat the interest tax shield as safe cash-inflow & discount at 8%. –We assume firm can capture interest tax shields of 35cents on every dollar of interest. You can’t use interest tax shield unless you pay taxes. Corporate tax favors debt. Personal tax favors equity. A project’s debt capacity depends on how well it does.

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APV for the Perpetual Crusher project Base case NPV = /0.12 = $1.29 mil Financing Rule 1: Debt fixed Financing Rule 2: Debt rebalanced Under rule 1 PV (tax shield) = [0.35 0.08 5] ÷ 0.08 = $1.75 mil APV = = $3.04 mil Under rule 2 Debt is rebalanced to 40% of actual project value. debt levels are not known & depend on the project’s actual performance. cost if capital is 12% PV(tax shield) = (0.35 0.08 5) 0.12 = $1.17 mil APV = = $2.36 mil

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A. Technical Point on Financing Rule 2 Discount at opportunity cost of capital Multiply the resulting PV by (1+r) and divide by (1+r D ) PV(approx) = = 1.17 PV(exact) = 1.17 = 1.21 APV = = $2.5 mil

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APV and hurdle Rates APV tells whether a project makes a net contribution to the value of the firm It tells break-even cashflow APV = - Investment + PV Tax Shield CF r (Ex) APV = PV CF 0.12 Tax Shield APV = = 0 CF 0.12 CF = 1.084IRR = 10.84%

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General Definition of Adjusted Cost of Capital The Opportunity Cost of Capital ( r ) The Adjusted Cost of Capital ( r* ) The expected rate of return offered in capital markets by equivalent-risk assets. This depends on the risk of the project’s cash flows. Adjusted opportunity cost or hurdle rate that reflects the financing side effects of an investment project

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Spotting and Valuing Options Chapter 20

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20.1 Call vs. Put Call: Right to buy underlying asset at a specified price Put: Right to sell underlying asset at a specified price American: Exercise anytime European: Exercise only at an expiration date Exercise Date Exercise Price Price of Call Options Price of Put Options October 1998 January 1999 $ $ $

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Share Price Value of Call 85 (a) Share Price Value of Put 85 (b) Value of Share 85 (c) Share Price

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Selling Calls, Puts, and Shares (c) Share Price Value of Call Seller’s Position -85 (a) 0 85 Share Price Value of Put Seller’s Position -85 (a) Value of Stock Seller’s Position Share Price

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Buy Share Value of Share $85 Future Stock Price Sell call Your Payoff $85 Future Stock Price Your Payoff $85 Future Stock Price + =

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Buy Share Value of Share $85 Future Stock Price Buy Put Your Payoff $85 Future Stock Price Your Payoff $85 Future Stock Price + =

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Bank deposit paying $85 Value of Share $85 Buy Call Your Payoff $85 Future Stock Price Your Payoff $85 Future Stock Price + = $85 Future Stock Price

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Put - Call Parity C + PV (Ex) = P + S Today V 1 =C+PV(EX) V 2 =P+S Expiration Date S* EX S* < EX

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The Difference between Safe & Risky Bonds Bond holder: Effectively acquire a firm Stock holder: Effectively purchase a call option on the assets of firm (PB=promised payment to bondholders) Asset value$30Bond: Asset - Call$25 $30 5 Stock: Call Firm: Asset Circular File Co. (MV)

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S Ex= $50 0 V (Promised Payment to Bondholders) Stockholders’ Position V<50S = V 50 S =

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B Ex= $50 0 V (Promised Payment to Bondholders) Bondholders’ Position V<50B = V 50 B =

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PB: Promised Payment to Bondholders (safe) V : Firm value (asset) S : Stock value B : Risky bond value C+ PV(EX) = P + S S+ PV(PB) = P + V S+ B = V B = V - S = PV(PB) - P Value of risky debt = Value of riskless debt “p” - ?

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Asset value $30 Bond value =$25 $30 5 Circular File Co. (Market Value) present value of promised payment - value of put Stock value = asset value - present value of promised payment + value of put

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Spotting the Option (Ex) Incentive program: Paid bonus of $50,000 for every $ that price of stock exceeds $120. Maximum bonus is set at $2 million Pay off Stock Price $40 160

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Pay off Stock Price 160 Buy call with exercise price of $120 and Sell call with exercise price of $160 * Any set of contingent payoffs can be valued as a mixture of simple options on that assets

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Share Price Exercise price Value of call A C B Upper bound: Value of call equals share price Lower bound: Value of call equals payoff if exercised immediately 20.3 What determines option values?

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Payoff to call option on firm Y’s shares Probability distribution of future price of firm Y’s shares Payoff to option on Y Exercise price Probability distribution of future price of firm X’s shares Payoff to option on X Exercise price Payoff to call option on firm X’s shares

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Share Price Exercise price Value of calls on shares of firms X and Y X Upper bound Lower bound Y

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What the price of a call options depends on 1. Increase in variables: If there is an increase in: Stock price (P) Exercise price(EX) Interest rate (r f ) Time to expiration(t) Volatility of stock price ( ) Positive Negative Positive The changes in the call option price are: 2. Other properties: a. Upper bound. The option price is less than the stock price b. Lower bound. The option price never falls below the payoff to immediate exercise (P-EX or zero, whichever is larger) c. If the stock is worthless, the option is worthless d. As the stock price becomes very large, the option price approaches the stock price less the present value of the exercise price

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20.4 An Option-Valuation Model Constructing Option Equivalents from common stocks & borrowing Stock Price Today $85 Stock Price 6 months later Call $68 $ r f =2.5% Exercise price = $85

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Hedge ratio (Option delta): Number of shares that are needed to replicate on call Option delta = Spread of share prices Spread of option prices = How much to borrow? Present value of the different between the payoff from the option and the payoff from the option delta number of shares PV(37.78) = $36.86 Amount of borrowing

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Option Equivalents: Buy shares and borrow $36.86 today 5 9 Today Buy shares Borrow $ month later S* = $68S* = $ Value of call today = value of shares - $36.86 bank loan = 5 9

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Arbitrage Opportunity EX 1: If call is priced at $12 : overpriced Strategy: Sell a call option Buy 5/9 share & borrow today Today month later S* = $68S* = $ $ 1.64

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EX 2: If call is priced at $9 : underpriced Strategy: Buy a call option Sell 5/9 share of stock short & lend(deposit) $36.86 today Today month later S* = $68S* = $ $ 1.36

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Risk-Neutral Valuation: All investors are indifferent about risk Expected Return on any risky assets = r f = E(R) = P u R u + P d R d where, P u + P d = 1 P u = probability of stock price increase in the hypothetical risk-neutral world P u = at t=1 at t=0 E(C 1 ) = C 0 = E(R) = P u ( ) + P d ( ) = R u = = R d = = P d =

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Valuing the Intel Put Option t=0 $85 SP $68 $ shares Intel share & Lend $46.07 How is it computed? Option delta = Spread of share prices Spread of option prices == EX=$85

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Today Sell shares Lend $ month later S* = $68S* = $ Value of put = - of share + $46.07 bank loan = 4 9

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20.5 The Black -Scholes Formula Construct a situation where the stock price is changing continuously and generate a continuum of possible six month prices Replicate a call option by a levered investment in the stock by adjusting the degree of leverage continuously Value of call = (delta Share price) - (bank loan) [N(d 1 ) P][N(d 2 ) PV(EX)]

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where d1d1 Log[P/PV(EX)] t + 2 t = d2d2 t = d1d1 - N(d) = cumulative normal probability density function EX = exercise price of option; PV(EX) is calculated by discounting at the risk-free interest rate, r f t = number of periods to exercise date P = price of stock now = standard deviation per period of (continuously compounded) rate of return on stock Value of call=[N(d 1 ) P] + [N(d 2 ) PV(EX)]

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Real Options Chapter 21

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Option to make follow-on investment if the immediate investment project succeeds. Option to abandon a project Option to wait before investing Option to vary the firm’s output or its production methods Real Option

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21.1 The value of follow-on investment Table 21-1 Summary of cash flows and financial analysis of the Mark I microcomputer (millions of dollars) Year After-tax operating cash flow (1) * Capital Investment (2) Increase in working capital (3) Net Cash Flow (1) - (2) - (3) NPV at 20% = - $46.45, or about -$46 million

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Table Valuing the option to invest in the Mark II microcomputer. Assumptions 1. The decision to invest in the Mark II must be made after 3 years, in The Mark II investment is double the scale of the Mark I (note the expected rapid growth of the industry). Investment required is $900 million (the exercise price), which is taken as fixed. 3. Forecasted cash inflows of the MarkII are also double those of the MarkI, which present value of about $800 million in 1985 and 800/(1.2) 3 = $463 million in The future value of the Mark II cash flows is highly uncertain. This value evolves as a stock price does with a standard deviation of 35 percent per year.(Many high-technology stocks have standard deviation higher than 35%.) 5. The annual interest rate is 10 percent.

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Interpretation The opportunity to invest in the Mark II is a 3-year call option on asset worth $463 million with a $900 million exercise price. Valuation PV(EX) = 900 (1.1) 3 = 676 Call value = N(d 1 ) P - N(d 2 ) PV(EX) d 1 = log[0.685] / /2 = d 2 = d = N(d 1 ) = N(d 2 ) = Call value = 676 = $53.59 mil

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21.2 The Option to Abandon Good Demand Bad Demand Tech ATech B $18.5$ If we bail out Tech B for $10 mil when bad demand Exercise option to sell assets Value of Tech B = DCF + Value of the abandonment Put (Value of Flexibility)

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Valuing the Abandonment Put t=1 PrPr PayoffPut Good Demand Bad Demand 0.5$ $ 8 EX = $10, r = 8.3%, r f = 5% PV= E(R) = P u ( ) + P d ( ) = = r f P u =P d = E(P) = 0.46 = P = 1+r f E(P) = Value of project =

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21.3 The Timing Option: r f = 5% t = 0 If invest $180, project worth $200 Good Demand Bad Demand Project Value Cash flow Value of Call $250$25 $160$16 t = 1 If undertake project today, capture either $25, or $16 at t=1 If delay, miss out on this cashflow at t=1, but will have more information on how the project is lively to work out

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Project NPV 0 Value of option to invest Investment now or never Investment can be postponed

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RG=RG= RB=RB= E(R) = P G ( ) + P B ( ) = = r f P G = P B = t=1, E(C) = t=0, Value of call = Q: Do you undertake project now?

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Warrants and Convertibles Chapter 22

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22.1 What is warrant? Value of warrant Exercise price = $15 Actual warrant value prior to expiration Theoretical value (lower limit on warrant value) Stock price

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Two Complications: Dividends and Dilution Example: Valuing United Glue’s Warrants Number of shares outstanding (N) Current stock price (P) Number of warrants issued per share outstanding (q) Total number of warrants issued (N q ) Exercise price of warrants (EX) Time to expiration of warrants (t) Annual standard deviation of stock price changes Rate of interest (r): United stock pays no dividends. ()() 1 million $ ,000 $10 4 years.40 10% …………………….. ………….. ………. …………… …………………………..

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United Glue’s market value balance sheet (in $ millions) Before the Issue Existing assets Total $16 $ 4 Existing loans Common stock (1 million shares at $12 a share) 12 $16 After the Issue Existing assetsExisting loans $16$ 4 New assets financed by debt and warrants 2 New loan without warrants 1.5 Total Total debt5.5.5 Warrants 12 Common stock Total $18 Total

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United Glue has just issued a $ 2million package of debt and warrant Suppose $ 1.5 mil: value of debt without warrants $ 0.5 mil: value of warrants Each warrant costs investors = Value of warrant from Black-Scholes formula =

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Dilution Effect Nq = Nq EX = V: value of equity V = Total asset - debt Share price after exercise =

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Warrant value at maturity =Max(P - EX, 0) = Max V + Nq EX N + Nq - EX, 0 Max V/N + EX 1 + q, 0 = Max V N, 0 = q - EX

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$ 12.5 mil: Current equity value of alternative firm (=18 mil mil) Current share price of alternative firm = V N = mil = $12.5 Suppose of alternative firm: = 0.41 Black-Sholes value of call: Value of warrant = q Value of call on alternative firm = deal for United

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22.2 What is a Convertible Bond Difference between convertible bond vs. bond-warrant package Bond value: Conversion value: The price of convertible bond depends on its bond value and its conversion value

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Value of firm ($ million) Bond value, $thousand Value of firm ($ million) Conversion value, $thousand Value of firm ($ million) Value of convertible, $ thousand Convert Bond paid in full Default Value at Maturity Default Bond paid in full

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Value of firm ($ million) Bond value, $thousand Value of firm ($ million) Lower limit on Convertible, $thousand Bond Value Conversion Value Value of firm ($ million) Value of convertible, $ thousand Lower limit on value Value of convertible Value before Maturity

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ABC Stock price Value of Convertible Bond Value Conversion Value Call price Forcing Conversion Value of convertible bond Value of straight bond Conversion option Redemption option = +-

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22.3 Difference between Warrants and Convertibles 1. Warrants are usually issued privately 2. Warrants can be deleted 3. Warrants may be issued on their own 4. Warrants are exercised for cash 5. A package of bond & warrants may be taxed differently 22.4 Why do companies issue Warrants and Convertibles?

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Valuing Debt Chapter 23

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Present Value of Bond Q: What determines the discount rates? PV C (1+ r 1 ) = C (1+ r 2 ) 2 C (1+ r 3 ) … (1000+C) (1+ r n ) n + r 1, r 2, r 3, …. r n : discount rates for cashflows to be received by the bond holders in periods 1, 2, …,n. (Ex) Same security offers different yields at a different time. Bonds maturing at different dates offer different rate of interest ®Borrowing rate of government is lower than your borrowing rate

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23.1 Real and Nominal Rates of Interest Real Rate: compensation for time value of money Nominal Rate = Real Rate + Perspective Rate of Inflation How Real Rate is determined? Supply of capital: time preference for today’s consumption over future consumption Demand of capital: Availability for profitable investment opportunities ( Positive NPV Projects)

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S D r r1r1 S D r r2r2

266

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23.2 Term Structure and Yield to Maturity PV =C 1+r 1 PV = C 1+r 1 C (1+r 2 ) 2 r 1, r 2 : Spot rate The series of spot rates r 1, r 2 … Term structure of interest rates +

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Yield to Maturity Rate of return to bondholders if he/ she keeps the bond until maturity Price of Bond = C (1+y) C (1+y) 2 ++ … C+F (1+y) n + PRESENT VALUE CACULATIONS 5s of ‘08 10s of ‘08 PERIOD INTEREST RATE CtCt PV AT r t CtCt t = 1 t = 2 t = 3 t = 4 t = 5 r 1 =.05 r 2 =.06 r 3 =.07 r 4 =.08 r 5 =.09 Totals $ ,050 $1,250 $ $ $ ,100 $1,500 $ $1, YIELD TO MATURITY BondPricePercent (IRR) 5s of ‘08 10s of ‘ % % 8.62

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23.3 Duration and Volatility Duration: Average time to each payment D = 1 PV(C 1 ) V + … + 2 PV(C 2 ) V … YEAR CtCt PV(C t ) AT 5.5% PROPORTION OF TOTAL VALUE [PVt/V] PROPORTION OF TOTAL VALUE TIME V = 1, Duration = years

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(A) 13 ¾s of 2004(B) 7 ¼s of 2004 V B = D B = years vs. (EX) 1% changes in yield 13 ¾s of ¼s of 2004 NEW PRICECHANGENEW PRICECHANGE Yield falls, 0.5% Yield rises, 0.5% Difference % % % % Volatility (%) Duration 1+yield V A = D A = years

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Hedging By equalizing the duration of the asset and that of the liability, we can immunize against any change in interest rate (EX) Aztec Learning has just purchased some equipment and Arranged to rent it out for $ 2mil a year over eight years at 12% Aztec finances by issuing a packaging of one year and six-year bond, each with 12% coupon to set up hedged position, find out proportion of one year and six year bond

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Solution PV of rental income = Duration of Rental income = Duration of one year bond = Duration of 6-year bond = Let : x is the proportion raised by 6-year bond 1-x is the proportion raised by 1 year bond Duration Package = x duration of 6-year bond + (1-x) duration of 1 year bond 3.9 years = x 4.6 years + (1-x) 1 years

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23.4 Explaining the Term Structure Topic Why do we observe different shape of term- structure? Ms. Long: invest $1,000 for 2 years 1,000 Forward Rate The extra return that Ms. Long gets by lending for 2 years rather than 1 Implicit & guaranteed (1+r 2 ) 2 = (1+ r 1 ) (1+f 2 ) f 2 = (1.105) % = =

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Expected Payoff: L 1 Certain Payoff: L 2 1,000 (1+r 1 ) [1+E( 1 r 2 )] vs. 1,000 (1+r 2 ) 2 1,000 (1+ r 1 )(1+f 2 ) or Strategy L 1 gives higher-return if Mr. Short: invest 1 year Buy 1 year bond: Buy 2 year bond & sell it after 1 year PV of 2 year bond at year 1 =

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Certain Payoff: S 1 Expected Payoff: S 2 1,000 (1+r 1 ) vs. or Strategy S 2 is better if 1,000 (1+r 2 ) 2 1+E( 1 r 2 ) 1,000 (1+ r 1 )(1+f 2 ) 1+E( 1 r 2 )

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The Expectations Hypothesis Ms.Long and Mr. Short try to maximize their expected return If f 2 > E( 1 r 2 ) prefer 2yr. bond price bond of 2yr return of 2yr. Bond and f 2 Equilibrium: f 2 = E( 1 r 2 ) If f 2 < E( 1 r 2 ) prefer 1 yr. bond The only reason for upward sloping term structure is investor expect the relationship such that f 2 = E( 1 r 2 ) f 2 > r 1, E( 1 r 2 ) > r 1

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Consider “risk” Long Case: horizon 2 yr. If Ms. Long buys 1 year bond: first year return is certain but, uncertain “reinvestment rate” at the end of year 1 Ms. Long h olds 1 year bond only if E ( 1 r 2 ) f 2 Short Case: horizon: 1 yr. If Mr. Short buys 2 year bond: he has to sell it next year at an “unknown price”. Mr. Short h olds 2 year bond only if E( 1 r 2 ) f 2 Other things equal, Ms. Long will prefer to buy year bond & Mr. Short will prefer to buy year bond The Liquidity Preference (Theory)

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If more companies want to issue 2 year bond than there are Ms. Long to hold them, They need to offer “Bonus” to attempt some of the Mr. Short to buy 2 year bond. Any bonus shows up as a difference between f 2 & E( 1 r 1 ) Liquidity Premium In reality, there are shortage of long-term lender, liquidity premium is positive. f 2 = E( 1 r 2 ) + Liquidity Premium ( = LP 2 ) f 2 = E( 2 r 3 ) + LP 3

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23.5 Allowing for the risk of Default Q: Why do some borrowers have to pay a higher rate of interest than others? Default risk premium Expected yield other risk premium RfRf Promised yield y Yield= R f + Risk Premium

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(EX) R f = 9% Payoff (t=1) $ 1,090 0 Probability Expected payoff ($) at t=1: If default is totally unrelated to other event of economy, = default risk is wholly diversifiable PV = Promised yield = (expected yield = 9%) Since default occurs in recession, , PV = Promised yield = (expected yield = 11%) say risk premium=2%

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Bond Ratings “relative quality” of bond by MOODY’SSTANDARD AND POOR’S Aaa Aa A Baa Ba B Caa Ca C AAA AA A BBB BB B CCC CC C Investment grade Junk bonds PERCENTAGE DEFAULTING WITHIN RATING AT TIME OF ISSUE 1 YEAR AFTER ISSUE 5 YEAR AFTER ISSUE 10 YEAR AFTER ISSUE AAA AA A BBB BB B CCC Moody’s Standard & Poor’s

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Leasing Chapter 25

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A rental agreement that extends for a year or more and involves a series of fixed payments What to lease? Lessee Lessor : Leasing industry Equipment manufacturers Banks Independent leasing company Operating Lease Capital Lease(financial/ full payment)

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25.2 Why lease ? –Convenient (short-term) –Cancellation option –Maintenance provided –Tax-shield can be used. –Etc Operating lease. In real life, idle time is considered. In operating lease, the lessor absorbs idle risk, not the lessee. The discount rate must include a premium sufficient to compensate its shareholder for the risk of idling. –For operating lease: Lease vs. Buy –For financial lease : Lease vs. Borrow

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Table 25-1 Calculating the zero-NPV rental rate (orequivalent annual cost) for Establishment Industries' pearly white stretch limo (figures in thousands of dollars) Year Initial cost -75 Maintenance, insurance, selling, and administrative costs -12 Tax Shield on costs +4.2 Depreciation tax shield Total NPV at 7% = -$98.15 Break-even rent (level) Tax Break-even after tax 17.02#17.02 NPV at 7% = $98.15 * no inflation; r = 7%; Tc = 35%` * Table 6-5: depreciation * First payment: immediate # = 65% of % PVA 7yrs = * 1.07 = 5.766

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25. 4 Financial Lease Table 25-2 Cash-flow consequences of the lease contract offered to Greymare Bus Lines (figures in thousands of dollars; some columns do not add due to rounding) NPV of 'Lease' relative to 'Buy' Year Cost of new bus+100 Lost depreciation tax shield Lease payment-16.9 Tax shield of lease payment+5.92 Cash flow of lease * 5 yr: depreciation (Table 6.4), 7yrs/8 times payment, Tc = 35%, r D = 10% * After tax: r D * (1 - Tc) = 6.5% NPV lease = (1.065) =-0.7-$700

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Year Lease cash flows, thousands Table 25-3: Equivalent loan; exactly same debt service on lease. Year Amount borrowed at year-end Interest paid at 10% Interest tax shield at 35% Interest paid after tax Principal repaid Net cash flow of equivalent loan How much can I borrow when I pay same cash as lease payment? Creating Equivalent Loan

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25.5 When Do Financial Leases Pay? The value of the lease to the bus manufacturer would be(T c =35%) Value of lease to lessor = +.70 Zero sum game Suppose that Greymare paid no tax (Tc = 0). Then the only cash flows of the bus lease would be: Year Cost of new bus +100 Lease payment These flows would be discounted at 10 percent, because r D (1-Tc)= r D when Tc = (1.065) (1.065) (1.065) (1.065) 5 13 (1.065) (1.065) 7 = t=0 10 (1.1) t Value of lease = = = +.82 or $820

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The potential gains to lessor and lessee are higher when: The lessor’s tax rate is substantially higher than the lessee’s The depreciation tax shield is received early in the lease period The lease period is long and the lease payments are concentrated toward the end of the period The interest rate r D is high - if it were zero, there would be no advantage in present value terms to postponing tax

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Mergers Chapter 33

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33.2. Sensible Motives for Mergers Economies of Scale Vertical Integration Complementary Resources Unused Tax Shields Surplus Fund Free Cash Flow ? Eliminating Inefficiencies Diversification Increasing Earning Per Share Lower Financing Cost

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33.3 Estimating Merger Gains and Costs A: BuyerB: Seller Synergy Gain = PV A+B - (PV A + PV B ) Cost = Cash paid - PV B NPV= Gain - Cost = PV AB - (Cash-PV B ) (Ex) PV A = 200, PV B = $50, PV A+B = $275 Gain = PV AB = + $25 Cash = $65

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Firm A Firm B Market price per share Number of share Market value of firm $ 200$ 100 1,000,000500,000 $ 200 mil$ 50 mil Cost = Cash - PV B = Cash - MV B + (MV B - PB B ) = ( ) = $21 mil Cash payment depends on the relative bargaining power of the two participants

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Stock offer N : shares received by seller P AB : combined firm’s worth Cost= N P AB - PV B (Ex)N = 325,000 A’s price before merger: $200 PV B = $50 mil Apparent cost = If PV AB = $275mil (due to synergy gain) New share price = Cost = -50 =

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Takeover Defense Preoffer Defenses Shark-repellent Charter Amendments –Staggered Board –Super Majority –Fair price Dual class stock Poison Pill, Poison put ESOP Postoffer Defenses Litigation Asset Restructuring Liability Restructuring

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Divestitures (sell offs) and Spin offs. - Synergy Motivated - Focus - Complementary Resources - More Efficient Contracting (Better Organization Structure) - Raising Capital Question: What is the source of gain and where it is created?

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Leveraged Buyouts Debt financed (junk-bond) Going private MBO

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