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Finance and the Financial Manager Chapter 1 1.1 What is a Corporation? 1.2 The Role of the Financial Manager Two Basic Questions 1 Investment Decision 2 Financing Decision 1.3 Who is the Financial Manager (2) (1) Firm's Financial Financial (4a) Operations Manager Markets (3) (4b) 1.4 Goal of the Firm ? 1.5 Agency Problem A. Separation between Ownership and Management B. How to solve agency problem? 1 Monitoring by board of directors 2 Compensation package 3 Monitoring by outside large blockholders (Bank, insurance Co., pension, mutual fund) 4 Efficient outside managerial labor market 5 Active outside takeover market Present Value and The Opportunity Cost of Capital Chapter 2 2.1 Introduction A. Present Value PV = C / (1+r) r: NPV = PV - C0 B. Risk and Present Value C. PV and Rate of Return D. The Opportunity Cost of Capital 1 From your Investment C0 : $ 100,000 C1 : Slump : $ 80,000 Normal : $ 110,000 Boom : $ 140,000 E(C1) 2 From Stock Market Find stock X which has same risk as your project : P0 : $ 95.65 P1 : Slump : $ 80 Normal : $ 110 Boom : $ 140 E(P1) = 1/3 (80 + 110 + 140) = 110 E(R) = 110 - 95.65 = 0.15 15% k 95.65 Q : What is the Present Value of your project? PV of project = NPV = How to Calculate Present Values Chapter 3 3.1 Cash Flows in Several Periods (*) 3.2 Perpetuities and Annuities (*) 3.3 Growing Perpetuities (*) 3.4 Compounding Interest (*) 3.5 Nominal and Real Interest Nominal CF A. Real CF = (1+inflation rate) (1+ Nominal rate) B. (1+Real Rate) = (1+inflation rate) 3.6 Bond Valuation C C … ... + C+F PVbond = + 2 + 1+r (1+r) (1+r)n = C PVAF + F PVF (Ex) Coupon rate: 10%, r=5%, face value=$1,000 N=7years PVbond = 100 5.786 + 1100 0.711 = $1360.7 The Value of Common Stocks Chapter 4 4.1 How Common Stocks are Traded? A. Primary Market B. Secondary Market • NYSE • AMEX • OTC (NASDAQ) 4.2 Stock Valuation A. Today‟s Price E(R) = (P1 - P0 + DIV) / P0 = r r: market capitalization rate P1 - P0 DIV = + P0 P0 = Holding Period Return = E(R) (Ex) P0 = $100 , P1 = $110 , DIV = $5 r= P0 = (P1 + DIV) / (1+r) = (110 + 5 ) / 1.15 = 100 $ 100 ; equilibrium price if 15% is an appropriate discount rate Q: What happen if P0 is different from $100 ? B. What determines next year‟s price ? Valuation Model P0 = (P1 + D1) / (1 + r), P1 = (P2 + D2) / (1 + r) P0 = D1 / (1 + r) + (P2 + D2) / (1 + r)2 = D1 / (1 + r ) + D2 / (1+r)2 + D3 / (1 + r)3 + ……… = Dt / (1 + r)t t=1 Assume: Dividend grows at a constant rate; g P0 = [D0 • (1 + g)] / (r - g) = D1 / (r - g) 4.3 Simple Way to Estimate r r = D1 / P0 + g D1 / P0 : Dividend Yield g : Dividend Growth EX : Pinacle West Corp (p 69) P0 = $41, Div1 = $1.27, g = 5.7% r= Alternative Approach: Payout ratio = DIV1 / EPS = 0.47 Plowback Ratio = 1- Payout ratio = 0.53 ROE = EPS / Book Equity per Share = 0.1 g = Plowback ratio * ROE = r = 0.031 + 0.053 = 0.084 or 8.4% 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 DIV1=$0.05, P0=$50, Plowback Ratio=80%, ROE=25% g= r= Ex: at t=3 and thereafter ROE =16% Firm responds by plowing back 50% of earnings g = Table 4.2 YEAR1 YEAR2 YEAR3 YEAR4 Book equity 10.00 12.00 14.40 15.50 Earning per share, EPS 2.50 3.00 2.30 2.49 Return on Equity, ROE .25 .25 .16 .16 Payout ratio .20 .20 .50 .50 Dividends per share, DIV .50 .60 1.15 1.24 Growth rate of dividends - .20 .92 .08 • General DCF formula to find the capitalization rate r: DIV1 DIV2 DIV3 + P3 P0 = 1+r + (1+r)2 + (1+r)3 P3 = P0 = 50 = 4.4 The link between stock price and earning per Share Growth stock vs Income stock A. Income Stock No Growth Perpetuity Model EPS1 DIV1 P0 = = r r (EX) Expected Return = Dividend Yield = 10/100 =.10 = r Price = DIV1 / r = EPS1 / r = B. Growth Stock (r=10%) at t = 1: (once & for all) Invest $10 into project with permanent return of 10% $ 1 (each year) NPV = This investment contributes “0” to value. (EX) Return on project is higher or lower than 10%; NPV? (go to table 4-3) 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 Rate Incremental Project NPV on Share Price Share Price EPS1 of Return a in Year 0, P0 Cash Flow, C in Year 1 in Year 0 b P0 r .05 $ .50 - $ 5.00 - $ 4.55 $ 95.45 .105 .10 .10 1.00 0 0 100.00 .10 .10 .15 1.50 + 5.00 + 4.55 104.55 .096 .10 .20 2.00 + 10.00 + 9.09 109.09 .092 .10 .25 2.50 + 15.00 + 13.64 113.64 .088 .10 a Project costs $ 10.00 (EPS1). NPV = - 10 + 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 In general : EPS1 P0 = r + PVGO PVGO : Present Value of Grow Opportunity Sum of all NPVs (per share) EPS1 : Capitalized value of average earning r under a no-growth policy Determinants of P/E Ratio EPS1 P0 = + PVGO r Divide each side by EPS 1 PVGO P/E = + r E 1. Cost of Capital(r): “-” 2. Conservative accounting procedure(EPS): “-” 3. Growth opportunities(PVGO): “+” Q : Japanese firm : P/E 50 U.S. firm : P/E 17 Is Japanese firm growing fast? EX : Fledgling Electronics Case (p73) r = 15 % , D1 = $ 5 P0 = D1 / (r - g) = If EPS1 = $ 8.33, Payout ratio = D1 / EPS1 = 5 / 8.33 = 0.6 If ROE = .25, g = P0 = Analyze: $ 44.44 Plowback Ratio = .4, 8.33 * .4 = $ 3.33 Invest: $ 3.33 at 25% (ROE) .25 * 3.33 = $ .83 at t = 1; NPV1 = -3.33 + .83 / .15 = 2.22 at t = 2; Invest 3.33 * 1.1 = 3.69 (g = 10%) NPV2 = -3.33 * 1.1 + (.83 * 1.1) / .15 = 2.44 PVGO = NPV1 / (r - g) = 2.22 / (.15 - .1) = $ 44.44 This is growth stock, not because g = 10%, but because C. Some Example of Growth Opportunities Table 4-4 Estimated PVGOs (p.76) Market PVGO, Stock Capitalization PVGO Percent of Stock Price, P0 EPS* Rate, r** =P0 - EPS/r Stock Price P/ E Income Stocks: AT & T $52.00 $2.85 .094 $21.70 41.7 18.2 Conagra 26.00 1.33 .106 13.50 51.7 19.5 Duke Power 60.00 3.58 .094 21.90 36.5 16.8 Exxon 64.00 2.89 .099 34.70 54.3 22.1 Growth Stocks: Compaq 30.00 0.69 .123 24.40 81.3 43.5 Merck 120.00 4.43 .118 82.50 68.7 27.1 Microsoft 101.00 2.08 .165 85.10 84.2 48.6 Wal-Mart 60.00 0.73 .094 52.20 87.1 82.2 * 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, 1999. 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% Why NPV leads to better Why Net Present Value Leads to Investment Decisions Better Investment Decisions than Other Criteria than Other Criteria Chapter 5 5.1 Review of Basics 1 Forecast Cash Flow 2 Determine appropriate Cost of Capital 3 Discount with Cost of Capital 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 5.2 Payback Period • Number of years it takes before cumulative cash flow recovers initial investment CASH FLOWS, DOLLARS Payback NPV at Project C0 C1 C2 C3 Period, Years 10 Percent B - 2,000 + 500 + 500 + 5,000 3 2,642 C - 2,000 500 +1,800 + 5,000 2 -58 D - 2,000 + 1,800 + 500 + 0 2 +50 5.3 Book Rate of Return Book Rate of Return = Book income Book assets Cash flow vs. Book Income Problems : Example Computing the average book rate of return on an investment of $9000 in project A CASH FLOWS, DOLLARS Project A Year 1 Year 2 Year 3 Revenue 12,000 10,000 8,000 Out-of-Pocket cost 6,000 5,000 4,000 Cash flow 6,000 5,000 4,000 Depreciation 3,000 3,000 3,000 Net income 3,000 2,000 1,000 average annual income 2,000 Average book rate of return = = = .44 average annual investment 4,500 Year 0 Year 1 Year 2 Year 3 Gross book value of investment $ 9,000 $ 9,000 $ 9,000 $ 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 5-3 Internal Rate of Return: IRR Discount rate that makes NPV = 0 C0 = - 4,000 k: cost of capital C1 = 2,000 C2 = 4,000 2,000 4,000 NPV = -4,000 + + =0 (1+IRR) (1+IRR) 2 (Rule) Accept IRR>k NPV>0 Reject IRR<k NPV<0 Net Present Value, dollars 2500 2000 1500 1000 IRR=28% 500 0 -500 10 20 30 40 50 60 70 80 90 100 Discount rate (%) -1000 -1500 -2000 Pitfall 1. Lending vs. Borrowing? CASH FLOWS, DOLLARS NPV at Project C0 C1 IRR, Percent 10 Percent A - 1,000 + 1,500 + 50 B + 1,000 - 1,500 + 50 CASH FLOWS, DOLLARS NPV at Project C0 C1 C2 C3 IRR, Percent 10 Percent C + 1,000 - 3,600 + 4,320 - 1,728 + 20 - .75 Net Present Value, dollars 60 40 20 0 10 20 30 40 50 60 70 80 90 100 Discount rate (%) -20 Pitfall 2. Multiple Rates or Return 0 1 2 3 4 5 6 Pretax -1,000 300 300 300 300 300 300 Tax +500 -150 -150 -150 -150 -150 Net -1,000 800 150 150 150 150 -150 CASH FLOWS, DOLLARS NPV at Project C0 C1 C2 IRR, Percent 10 Percent D + 1,000 - 3,000 + 2,500 none + 339 NPV 1000 IRR=15.2% 500 0 Discount Rate -500 IRR=-50% -1000 Pitfall 3. Mutually Exclusive Projects 3.1 Different scale CASH FLOWS, DOLLARS NPV at Project C0 C1 IRR, Percent 10 Percent E - 10,000 + 20,000 100 F - 20,000 + 35,000 75 CASH FLOWS, DOLLARS NPV at Project C0 C1 IRR, Percent 10 Percent F-E - 10,000 + 15,000 50 + 3,636 3.2 Different pattern of cash flow over time CASH FLOWS, DOLLARS IRR, NPV at Project C0 C1 C2 C3 C4 C5 Etc. Percent 10 Percent G - 9,000 +6,000 +5,000 +4,000 0 0 … 33 3,592 H - 9,000 +1,800 +1,800 +1,800 +1,800 +1,800 … 20 9,000 I -6,000 +1,200 +1,200 +1,200 +1,200 … 20 6,000 NPV, dollars 10,000 +6,000 +5,000 33.3 Discount Rate, 0 percent 10 20 30 40 50 Project G 15.6 Project H -5000 Pitfall 4. What happens if term structure is not flat? (generally) NPV = - C0 + C1 / (1+r1) + C2 / (1+r2)2 + … IRR vs. r1 r2 ? r3 5.5 Limited Resource (Capital Rationing) <$10> t=0 CASH FLOWS, MILLIONS OF DOLLARS NPV at Project C0 C1 C2 10 Percent A - 10 + 30 +5 21 B -5 +5 + 20 16 C -5 +5 + 15 12 <$10> t=0, t=1 CASH FLOWS, MILLIONS OF DOLLARS NPV at Profitability Project C0 C1 C2 10 Percent Index A - 10 + 30 +5 21 2.1 B -5 +5 + 20 16 3.2 C -5 +5 + 15 12 2.4 D 0 - 40 + 60 13 0.4 • More Elaborate Capital Rationing Models We accept proportion A of project A. NPV of accepting A of A Previous Example NPV = Constraint: (Costs) at t = 0, 10 A + 5 B + 5 C + 0 D 10 at t = 1, 40 D 30A + 5 B + 5 C + 10 0 A , B , C , D 1 Maximize: 21 A + 16 B + 12 C + 13 D Subject to : 10 A + 5 B + 5 C + 0 D 10 -30 A - 5 B - 5 C + 40 D 10 0 A , B , C , D 1 Making Investment Decisions with the Net Present Value Rule Chapter 6 • 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? • 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” • Treat Inflation consistently. – Real CF : discount with real rate – Nominal CF: discount with nominal rate (Ex) C0 C1 C2 C3 Real CF -100 + 35 +50 +30 rN = 15%, I = 10% NPV = NPV = 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 9.5 mil annual depreciation = = $ 1.583 mil 6 Table 6 - 1 Nominal Cashflow Ex: forecast of inflation: 10% IM&C's guano project - revised projections reflecting (figures in thousands of dollars) PERIOD 0 1 2 3 4 5 6 7 1. Capital investment 10,000 -1,949* 2. Accumulated depreciation 1,583 3,167 4,750 6,333 7,917 9,500 0 3. Year-end book value 10,000 8,417 6,833 5,250 3,667 2,083 500 0 4. Working capital 550 1,289 3,261 4,890 3,583 2,002 0 5. Total book value (3 + 4) 10,000 8,967 8,122 8,511 8,557 5,666 2,502 0 6. Sales 523 12,877 32,610 48,901 35,834 19,717 7. Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 8. Other costs ** 4,000 2,200 1,210 1,331 1,464 1,611 1,772 9. Depreciation 1,583 1,583 1,583 1,583 1,583 1,583 10. Pretax profit (6 - 7 - 8 - 9) -4,000 -4,097 2,365 10,144 16,509 11,148 4,532 1,449** 11. Tax at 35% -1,400 -1,434 828 3,550 5,778 3,902 1,586 507 12. Profit after tax -2,600 -2,663 1,537 6,594 10,731 7,246 2,946 942 * Salvage value. ** The difference between the salvage value and the ending book value of $ 500 is a taxable profit IM&G‟s guano project-cash-flow analysis (thousand) Period 0 1 2 3 4 5 6 7 1. Sales 523 12,887 32,610 48,901 35,834 19,717 2. Cost of goods and sold 837 7,729 19,552 29,345 21,492 11,830 3. Other costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 4. Tax on operations -1,400 -1,434 828 3,550 5,778 3,902 1,586 5. Cash flow from -2,600 -1,080 3,120 8,177 12,314 8,829 4,529 operation 6. Change in working -550 -739 -1,972 -1,629 1,307 1,581 2,002 capital 7. Capital investment and -10,000 1,442 Disposal 8. Net cash flow -12,600 -1,630 2,381 6,205 10,685 10,136 6,110 3,444 9. Present value at 20% -12,600 -1,358 1,654 3,591 5,153 4,074 2,046 961 Net present value = +3,519(sum of 9) • Cash flow = Sales - CGS - Other costs - Taxes • Net cash flow = Cash flow from operation Networking capital [- Initial Investment + Recovery of Salvage Value] • NPV = 6.3 Project Interacting Choosing between Long & Short Equipment C0 C1 C2 C3 PV at 6% A +15 +5 +5 +5 28.37 B +10 +6 +6 21.00 Equivalent Annual Cost C0 C1 C2 C3 PV at 6% Machine A +15 +5 +5 +5 28.37 EACA x x x 28.37 Machine B +10 +6 +6 21.00 EACB y y 21.00 Risk and Return & opportunity Risk, Return & Opportunity Cost of Capital Cost of Capital Chapter 7&8 7.1 Seventy-Two year of Capital Market Dollars 5,520 Small Cap 1,828 S&P 1000 55.38 Corporate Bonds 39.07Government Bonds 10 14.25 Treasury Bills 0.1 1925 1933 1941 1949 1957 1965 1973 1981 1989 1997 Dollars 1000 613.5 Small firms 203.2 S&P 500 10 6.16 Corporate bonds 4.34 Government bonds 1.58 Treasury bills 0.1 1925 1933 1941 1949 1957 1965 1973 1981 1989 1997 Average rate of return on Treasury bills, Government bonds, Corporate bonds, and common stocks, 1926-1997 (Percent per year) AVERAGE ANNUAL AVERAGE RISK PREMIUM RATE OR RETURN (EXTRA RETURN VS. PORTFOLIO NOMINAL REAL TRESURY BILLS) Treasury bills 3.8 .7 0 Government bonds 5.6 2.6 1.8 Corporate bonds 6.1 3.0 2.3 Common stocks 13.0 9.7 9.2 (S&P 500) Small firm 17.7 14.2 13.9 common stock 7.2 Measuring Portfolio Risk • Variance (Standard Deviation) • Expected = Ri * Pi = E (R) = R • Variance = (Ri - R)2 * Pi = 2 = V • Risk Systematic Risk: market risk macro-economic variables Unsystematic Risk: firm unique or specific risk STANDARD PORTFOLIO DEVIATION() VARIANCE(2) Treasury bills 3.2 10.2 Long-term government bonds 9.2 84.6 Corporate bonds 8.7 75.7 Common stock (S&P 500) 20.3 412.1 Small-firm common stocks 33.9 1149.2 PERIOD MARKET SD() 1926-1929 23.9% 1930-1939 41.6 1940-1949 17.5 1950-1959 14.1 1960-1969 13.1 1970-1979 17.1 1980-1989 19.4 1990-1997 14.3 STANDARD STANDARD STOCK DEVIATION() STOCK DEVIATION() AT&T 22.6 General Electric 18.8 Bristol-Myers Squibb 17.1 McDonald‟s 20.8 Coca-Cola 19.7 Microsoft 29.4 Compaq 42.0 Reebok 35.4 Exxon 13.7 Xerox 24.3 Stock SD() MARKET SD() Stock SD() MARKET SD() BP 16.3 UK 12.2 LVMH 25.8 France 16.6 Deutsche 23.2 Germany 11.3 Nestle 18.9 Switzerland 14.6 Bank Fiat 35.2 Italy 24.5 Sony 27.5 Japan 17.4 Hudson Bay 26.3 Canada 11.7 Telefonia Argentina 28.6 de 52.2 KLM 30.1 Netherlands 14.2 Argentina Portfolio standard deviation Unique risk Market risk 0 5 10 15 Number of Securities 7.3 Calculating Portfolio Risk n=2 A B Between A, B Covariance; 2(,) Itself Variance; 2(,) A B A B Weights; A , B , A + B =1 A B A 2 A AB B BA 2 B Portfolio Risk = Example; Bristol-Myers : 0.55 0.171 McDonald‟s : 0.45 0.208 BM = 0.15 2 p = n=3 Variance: Covariance: n=4 Variance: Covariance: Limits to Diversification VP = 2P = N * (1/N)2 2 + (N2 - N) * (1/N2) cov 2 : average variance cov : average covariance 2P = VP = (1/N) 2 + (1 - 1/N) cov lim VP N (Ex) mutual fund Special Cases =1 2P = X12 12 + X22 22 + 2X1X2 1 2 * 1 = (X1 1 + X2 2 )2 ( a b)2 a2 + b2 2ab P = X1 1 + X2 2 , when = 1 There is: • no diversification • no risk reduction * Portfolio risk is simply weighted average of individual risk; linear combination ! =-1 2P = X12 12 + X22 22 - 2X1X2 1 2 = (X1 1 - X2 2 )2 P = X1 1 - X2 2 , when = -1 • Risk may be completely eliminated by combining X1, X2 (Ex) • Portfolio Risk is (again) a linear combination of individual risks. Example 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. • Efficient Frontier Ep • B AB = 1 A• P Ep = -1 • B = -1 A• P Generally 1 Ep • B A• P E(RP) 22 20 18 16 14 12 10 0 09 11 13 15 17 19 21 P Efficient Portfolio E(RP) P We Introduce Borrowing & Lending (p193) 2P = X12 12 + X22 22 + 2X1X2 1 2 12 (risk-free asset : 2 = 0 ) - Lending 2P = X12 12 P = X1 1 (linear combination) EP = X1R1 + X2Rf - Borrowing 2P = ( X* + 1 )2 12 + ( -X* )2 22 + 2( 1+X* )( -X* ) 12 P = (1+X*) 1 EP = (1+X*) R1 - X* Rf Portfolio Risk : Linear combination of individual risk Combination of Risky(A) and Risk Free Asset • A Rf New Efficient Portfolio C • • • D Old Efficient Portfolio A T • Rf B• EP T EM • Rf M P T is a market portfolio; M Capital Market Line CML • Risk-return relationship for efficient portfolios • Intercept: Rf price of time • slope: (EM - Rf) / M price of risk Ep = Rf + [ (EM - Rf) / M ] x P • Capital Asset Pricing Model: CAPM Apply Portfolio Theory to evaluate all risky assets Systematic Risk vs. Unsystematic Risk 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 Therefore, • Systematic Risk = Market risk = Covariance(iM) Required Risk-free Rate of Return + Risk = on Risky Asset Rate(Rf) Premium = Rf + amount of risk Price of risk = Rf + = Rf + = Rf + STOCK BETA STOCK BETA AT&T .65 General Electric 1.29 Bristol-Myers Squibb .95 McDonald‟s .95 Coca-Cola .98 Microsoft 1.26 Compaq 1.13 Reebok .87 Exxon .73 Xerox 1.25 STOCK BETA STOCK BETA BP .74 LVMH 1.00 Deutsche 1.05 Nestle 1.01 Bank Sony 1.03 Fiat 1.11 Hudson Telefonia de Bay .51 Argentina 1.31 KLM 1.13 EXPECTED RETURN STOCK BETA rf+(rm - rf) AT&T .65 10.7% Bristol-Myers Squibb .95 13.1 Coca-Cola .98 13.3 Compaq 1.13 14.5 Exxon .73 11.3 General Electric 1.29 15.8 McDonald‟s .95 13.1 Microsoft 1.26 15.6 Reebok .87 12.5 Xerox 1.25 13.9 Summary “” 1) Covariance risk (normalized) iM 2M 2) Sensitivity of stock i‟s return with respect to market Ex: Security Market Line: SML E(Ri) ? ? Rf 0 1 i 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) • C • B rm •A rf 0 0.5 1.0 1.5 Beta vs. Average Risk Premium Avg Risk Premium 1931-91 Market line 30 10 20 9 8 6 7 Investors 5 3 10 2 1 4 Market Portfolio 0 Portfolio Beta 1.0 Avg Risk Premium 1931-65 Market Line 30 10 Investors 9 20 7 8 45 6 3 2 1 Market Portfolio 10 0 Avg Risk Premium 1966-91 1.0 Portfolio Beta 30 Market Line 20 Investor 2 3 4 5 9 1 6 7 8 10 10 Market Portfolio 0 1.0 Portfolio Beta 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) R = a + b1rf1 + b2rf2 + b3rf3 + … … noise Expected Premium = r - rf = b1 (r1- rf ) + b2 (r2 - rf ) + b (r - r ) + … … 3 3 f 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 (rfactor - rf) Yield spread 5.10% Interest rate -.61 Exchange rate -.59 Real GNP .49 Inflation -.83 Market 6.63 3. Estimate the Factor Sensitivity Factor Factor risk Estimated risk Factor risk premium premium (b) (rfactor - rf) [b(rfactor - rf)] Yield spread 1.04 5.10% 5.30% Interest rate -2.25 -.61 1.37 Exchange rate .70 -.59 -.41 Real GNP .17 .49 .08 Inflation -.18 -.83 .15 Market .32 6.63 2.04 Total 8.53% Capital Budgeting and Risk Chapter 9 Are the New Projects More Risky or Less Risky than its Existing Business? Each project should be evaluated at its own Cost of Capital (implication of Value Additivity Principle) 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. r • B A• Cost of Capital rf • True Cost of Capital - depends on the use to which the capital is put - Project beta () Expected Return = r = rf + (project beta) (rm - rf) • “” 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. 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: • Measuring Betas – Using monthly stock return on IBM – Using monthly market return (Ex) 60 months R1IBM R1M R2IBM R2M …… …… R60IBM R60M ( = alpha) Average rate of price appreciation or depreciation, born by stock-holders when investors in the market as a whole earn nothing. R-squared R2 The proportion of variance of stock price change that can be explained by market movement. means systematic risk / total risk Change in prices of DEC common stock Beta = 1.30 Change in Alpha = -.65 market index = -0.65% ; -0.65 12 -7.8% 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, How Changing Capital Structure Affects Expected Return? Company = r Asset = r portfolio Cost of Capital D E (WACC) = rd + re D+E E+D (EX) B/S (market value) A 100 D 40 E 60 100 100 r d = 8% r e = 15% r Asset = • (Now) : Issue 10 equity, Retire 10 debt B/S (market value) A 100 D 30 E 70 100 100 * The change in financial structure does not affect does affect (Ex) lower leverage: rD 7.3% (Given) rAssets = How does Changing Capital Structure Affect Beta? D + E Assets = Portfolio = V D V E V=D+E D = 0.2 E = 1.2 A = After refinancing; D 0.1(Given) Expected 20 Before Refinancing return (%) requity=15 rassets=12.2 rdebt=8 Beta 0 debt= .2 assets= .8 equity=1.2 Expected return (%) 20 After Refinancing requity=14.3 rassets=12.2 rdebt=7.3 Beta 0 debt=.1 assets=.8 equity=1.1 9.3 How to Estimate the company Cost of Capital • Pinnacle West‟s Common Stock Beta Standard. Error Boston Electric .60 .19 Central Hudson .30 .18 Consolidated Edison .65 .20 DTE Energy .56 .17 Eastern Utilities Associate .66 .19 GPU Inc. .65 .18 NE Electric System .35 .19 OGE Energy .39 .15 PECO Energy .70 .23 Pinnacle West Corp. .43 .21 PP & LResources .37 .21 Portfolio Average .51 .15 requity = rf + equity [ rm - rf] = 0.045 + 0.51 0.08 = 0.0858 8.6% D E rd = 6.9%, re = 8.6%, V = 0.43, V = 0.57 WACC = Company Cost of Capital = D rd + E re V V 9.4 Discount Rates for International Projects • Foreign investments are not always riskier. Correlation Ratio Beta coefficient Argentina 3.52 .416 1.46 Brazil 3.80 .160 .62 Kazakhstan 2.36 .147 .35 Taiwan 3.80 .120 .47 • Foreign Investment in the US E(RP) 22 20 Taiwan Index 18 16 14 12 10 US Index 0 09 11 13 15 17 19 21 P 9-4 Setting Discount Rate when you can‟t calculate 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 Think about the determinant of asset beta (Ex) Q: What are industries which are risky, but have low ? • Determinants of Asset Beta: Cyclicality: Firms whose revenue depend on business cycle high Operating Leverage Commitment to fixed production charges • High fixed cost ratio High operating leverage High Asset Beta Why ? Break Even Point Analysis $ Total Cost Unit Variable Cost Fixed Cost Q TR TC Profit Loss FC BEF Low Fixed Cost (high Variable Cost) Low OL TR TC FC High Fixed Cost (Low Variable Cost) High OL 9-6 Another Look at Risk and Discounted Cash flow Risk-adjusted: n PV = [Ct / (1+r)t], t=1 r = rf + (rM - rf) (Ex) r = 6 + 0.75 8 = 12% Year CF PV 1 100 89.3 2 100 79.7 3 100 71.2 240.2 100 1.12 x = 94.658 (x = certainty equivalent cash flow) 100 = 89.3 = x (1.12)2 (1.06)2 x = 100 (1.06/1.12)2 = 89.57 • General Solution Risky 1+rf t Cash Flow Certainly equivalent Cash Flow at time t = 1+r at time t 1+rf t We call t = 1+r Certainty equivalent coefficient 1 = (1.06 / 1.12) = 0.946 2 = (1.06 / 1.12)2 = 0.896 3 = (1.06 / 1.12)3 = 0.848 Valuing CE cash flow CE(CF) CF PV = = (1 + rf) 1+r (Example) E(C) = -1,000,000 0.5 = -500,000 r = 25% NPV = -125 - 500 + 125 1.25 t=2 (1.25)t = -125 or -$125,000? Convert into Certainty Equivalent cash flow: Success NPV = -1000 + (250/0.1) = +1500 (50% chance) Failure NPV = 0 (50% chance) E(NPV) = 1500 0.5 = 750 (if = 0.5) (750 0.5) NPV = -125 + 1.07 = 225.5 or $225,000 Making Sure Managers Maximize NPV Chapter 12 12.1 Incentives A. Agency Problems in Capital Budgeting • Reduced Effort • Perquisites • Empire Building • Entrenchment • Avoiding Risk B. Monitoring C. Compensation Capital Return on Cost of EVA Invested Capital Capital Coca Cola $2,442 $10,814 36.0% 9.7% Dow Chemical 6,81 23,024 12.2 9 .0 Ford Motor 1,719 58,272 12.1 9 .1 General Electric 2,515 53,567 17.7 12 . 7 General Motors - 3,527 82,887 5.9 9 .7 Hewlett- Packard - 99 24,185 15.2 15 . 7 IBM - 2,743 67,431 7.8 11 . 8 Johnson & Johnson 1,327 18 ,138 21.8 13 . 3 Merck 1,688 22 , 219 23.0 14 . 5 Microsoft 1,727 5 , 680 47 . 1 11 . 8 Philip Morris 3,119 42 ,885 20 . 1 12 . 5 Safeway 335 4 , 963 15 . 7 8 .5 UAL 298 13 , 420 9 .8 7 .2 Walt Disney - 347 30 , 702 11 . 0 12 . 6 Corporate Financing and Market Efficiency Chapter 13 B/S ? How to spend $? How to raise $? • So far, we assume „all equity‟ financing. Stockholders supply all the firm‟s capital, bear all the business risks, and receive all the rewards. <Questions> 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 10 3,000 = +100,000 - - 100,000 = $43,200 t=1 (1.10)t (1.10)10 Difference between Investment & Financing Decisions Easy reverse Abandonment value is O.K. Lose or make money is not easy 180 Level 130 80 Month 230 Level 180 130 80 Month 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) • Test of Market Efficiency - Weak form - Semi-Strong form - Strong form • Market Anomaly - Small firm Effect - January Effect - Weekend Effect Q: Is market inefficient? The Dividend Controversy Chapter 16 Q1 : How company set dividend? Q2 : How dividend affect stock price? - So far: Investment Financing independent If dividend affects firm value, attractiveness of new project depends on where the money is coming from. Dividend Financing decision Decision Mixed with Investment Given capital budgeting & financing decision, what is the effect of change in dividend? 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 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. 16.2 Information content of Dividend Signaling Model Other Signaling Tools 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 0 D FA 9,000 10,000+NPV E 10,000 + NPV 10,000 + NPV Pay dividend by issuing new shares($1,000) We want to continue project w/t cash($1,000) • 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. (Ex) N = 1,000 shares NPV = $2,000 Vold = Vold* = Number of new shares = sold 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‟ 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” Does Debt Policy Matter? Chapter 17 B/S Asset Capital Mix of different Structure Structure 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) 17.1 The Effect of Leverage in a Tax Free Economy VU: Value of unlevered firm EL = VL - DL 1) 1% of unlevered firm $ investment $ return (NOI) .01 VU .01 profit 2) 1% of equity & debt of levered firm (I: interest) $ invest $ return Debt .01 DL .01 I NI Equity .01 EL .01 (profit -I) .01(DL + EL) .01 profit = .01 VL same profit (NOI) same cost (same investment) VU = VL 3) Buy 1% of equity of levered firm $ investment $ return .01 EL .01 (profit -I) = .01 (VL - DL) 4) Alternative way: Borrow .01 DL on your account Buy 1% of equity of unlevered firm $ investment $ return Borrowing -.01 DL -.01 I Equity .01 VU .01 profit .01(VU - DL) .01 (profit - I) Same profit same cost (same investment) VU = VL Example of Proposition I (p.477) A All Equity E(EPS) = $1.5, P = $10, E(R) = 1.5/10 = 15% N = 1,000 P = $10 VU = $10,000 NOI($) 500 1,000 1,500 2,000 EPS($) .5 1.0 1.5 2.0 ROE(%) 5 10 15 20 B Issue: debt $5000, k = 10%, repurchase: 500 shares N = 500 P = $10, k = 10% Market value of stock: $5,000 Market value of debt : $5,000 NOI($) 500 1,000 1,500 2,000 Interest 500 500 500 500 NI($) 0 500 1,000 1,500 EPS($) 0 1 2 3 ROE(%) 0 10 20 30 3.00 Equal proportions debt and equity 2.50 Expected EPS with debt and equity 2.00 Expected EPS with All equity all equity 1.50 1.00 .50 Expected operating income 500 1000 1500 2000 C Personal Leverage Borrow $10, then invest $20 in two unlevered shares (Initially, I have $10) NOI($) 500 1,000 1,500 2,000 Earnings on two shares($) 1 2 3 4 Interest($) at 10% -1 -1 -1 -1 Net Earnings($) 0 1 2 3 Return on 0% 10% 20% 30% $10 investment 17.2 How Leverage Affects Return Current structure Proposed all equity structure E(EPS) $1.5 $2.0 NOI = $1,500 V=10,000 P $10 $10 N =1,000 D=5,000 E(ROE) 15% 20% Kd = 10% E=5,000 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% Expected return NOI on asset(rA) = Market value of all security Assumption: • 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(rA). D E rA = rD + D+E rE D+E rE = rA + D (rA - rD) E Expected Expected Debt/ Expected Expected return on = return on + Equity return on - return on equity assets Ratio assets debt • Proposition II (MM) The expected return on equity (rE) of a levered firm increases in proportion to debt to equity ratio (D/E) & the rate depends on the spread between rA and rD. (Ex) rA = 15% D = 5,000 rD = 10% E = 5,000 rE = r • Figure 17-2 MM‟s proposition II. rE =Expected Return on Equity The expected return on equity rE increases linearly with the debt- equity ratio so long as debt is risk-free. But if leverage increases the risk of the debt, rA =Expected Return on Assets debtholders demand a higher return on the debt. This causes the rD rate of increase in rE to slow down. rD=Expected Return on Debt D Risk free Risky E debt debt The Risk-Return Trade-off D E A = D + E D+E D+E D E = A + (A- D) E Investors (stock-holders) require higher returns on levered equity 17.3 The Traditional Position A Moderate degree of financial leverage may increase rE although not to the degree predicted by MM proposition II Excessive debt raise rE faster rA (=WACC) decline & later rise. r rE = (MM) rE = (traditional) rA = (MM) rA = (traditional) rD rD D = debt Traditionalist believe there is an optimal E equity debt-equity ratio that minimizes rA B 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. How Much Should a Firm Borrow? Chapter 18 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 18.1 Corporate Taxes Income statement Income statement of Firm U of Firm L Earnings before interest and taxes $1,000 $1,000 Interest paid to bondholders 0 80 Pretax income 1,000 920 Tax at 35% 350 322 Net income to stockholders $650 $598 Total income to both $0 + 650 = $650 $80 + 598 = $678 bondholders and stockholders Interest tax shield (.35interest) 0 28 Interest Payment = rD D PV(Tax shield) = TC (rD• D) rD = TC D PV(Tax shield) = 0.35 0.08 1000 0.08 = $350 Normal Balance Sheet(Market Values) Asset value (present value Debt of after-tax cash flows) Equity Total assets Total value Expanded Balance Sheet(Market Values) Pretax asset value (present Debt value of pretax cash flows) Government „s claim (present value of future taxes) Equity Total pretax assets Total value Table 18.3(a) Book Values Net working capital $2,644 $1,347 Long-term debt Long-term assets 17,599 6,282 Other long-term liabilities 12,614 Equity Total assets $20,243 $20,243 Market Values Net working capital $2,644 $1,347 Long-term debt Market value of Other long-term long-term assets 131,512 6,282 liabilities 126,527 Equity Total assets $134,156 $134,156 Total value Table 18.3(b) Book Values Net working capital $2,644 Long-term debt Long-term assets 6,282 Other long-term 17,599 liabilities 11,614 Equity Total assets $20,243 $20,243 Market Values Net working capital $2,644 Long-term debt Market value of Other long-term long-term assets 131,512 6,282 liabilities Additional tax shields Equity Total assets Total value MM & Taxes: MM Prop I with corporate tax. VL = VU + PV (Tax Shield) 100% debt? 18.2 Corporate and Personal Taxes Operating income $1.00 Corporate tax Income after corporate tax Personal tax Income after all taxes Corporate Borrowing is better If (1 - TP) > (1- TPE) * (1 - Tc) (1 - TP) Relative Tax Advantage of Debt = (1 - TPE) • (1 - Tc) Special Cases: 1. TPE = TP, RTAD = 1 (1 - TC) MM‟s original 2. (1 - TP) = (1 - TPE) * (1 - Tc) RTAD = 1.0 Debt policy is irrelevant! This case happen when Tc < TP & TPE is small. (Ex) Tc = 35%, TP = 39.6% What TPE makes debt policy irrelevant? 18.3 Cost of Financial Distress Value of firm Value of all + PV(tax shield) (levered) = equity - PV (costs of financial distress) Market Value of The Firm Debt Bankruptcy Costs ACE LIMITED ACE LIMITED Payoff to (limited liability) Payoff to (unlimited liability) bondholders bondholders Payoff Payoff 1,000 1,000 500 500 Asset Asset Payoff to 500 1,000 value 500 1,000 value stockholders Payoff to Payoff stockholders Payoff 1,000 1,000 0 Asset 0 Asset 500 1,000 value 500 1,000 value -1,000 -1,000 Direct: legal fee, court fee, etc. Indirect: difficult to measure Table 18.4 SHARE PRICE NUMBER OF CHANGE FRIDAY MONDAY SHARES IN VALUE APR 10, 1987 APR 13, 1987 CHANGE (MILLIONS) (MILLIONS) Texaco $31.875 $28.50 -$3.375 242 -$ 817 Pennzoil 92.125 77.00 -15.125 41.5 -628 Total -$1,445 • 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 $ 50 Bonds outstanding Fixed assets 80 50 Common stock Total assets $100 $100 Total value Circular File company (Market Values) Net working capital $20 $25 Bonds outstanding Fixed assets 10 5 Common stock Total assets $30 $30 Total value Risk Shift: The First Game (Ex1) C0 C1 $120 (p=10%) -$10 $ 0 (p=90%) If r=50%, 1200.1+0 NPV = -10 + = -$2 1.5 Circular File company (Market Values) Net working capital $10 $20 Bonds outstanding Fixed assets 18 8 Common stock Total assets $28 $28 Total value (Ex2): Amount of Debt = $600 High Risk Project Good (p=0.5) Bad (p=0.5) V 2,000 300 D S V= D= S= Low Risk Project Good (p=0.5) Bad (p=0.5) V 1,400 1,000 D S V= D= S= Refusing to contribute equity capital: The second game Good project with NPV= + $5 by investing $10 Net working capital $20 $33 Bonds Fixed assets 25 12 Common stock Total assets $45 $45 Total value Firm value increase by $15 Bond value increase by $8 Stock value increase by $7 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. 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. 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 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 Interactions of Investment and Financing Decisions Chapter 19 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 NPV of APV = Base + financing decisions NPV caused by project acceptance (value additivity principle) 19.1 After-tax WACC WACC = rD D + rE E V V WACC = rD (1-Tc) D + rE E V V Sangria Corporation (Book Values, millions) Asset $100 $50 Debt 50 Equity Total assets $100 $100 Total value (Market Values, millions) Asset $125 $50 Debt 75 Equity Total assets $125 $125 Total value WACC =? rD =0.08 rE =0.146 TC=0.35 D = E = V V WACC = Invest: $12.5 million $ 7.5 million (Equity) $ 5 million (Debt) Pretax cashflow: $2.085 (perpetual) Tax: 35% After-tax cashflow: $1.355 million NPV = Return on Investment = Return on Equity: NOI 2.085 I -0.4 (=0.085) Earning After tax 1.685 -Tax -0.59 (=1.6850.35) 1.095 Expected return on Equity = 1.095 = 0.146 7.5 E(RE) = rE NPV=0 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) 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 $24,383 bil 29.7% Equity $57,651 bil 70.3% rd=7.2%, g=11.5%, D/P= 2.3%, TC = 35% rE = WACC = 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 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 rE=rA + D (r -r )(1-T ) E A D C 19.3 Adjusting WACC when debt ratios or business risks change Rate of Cost of Equity(rE) return Opportunity cost of capital (r) r WACC Cost of Debt(rD) Debt-Equity Ratio (Ex) D D V = 0.4 V = 0.2 Step1: unlevering the WACC Calculate opportunity cost of capital r = rD D + r E E V V * If taxes are left out, WACC equals the r and is independent of leverage Step2: Estimate rD at 20% debt ratio, & Calculate new rE rE = rA + (rA- rD) D E Step3: Recalculate the WACC at the new financing weight D Step1: current V = 0.4 r= D Step2: rd = 8%, when V= 0.2 rE= Step3: WACC= Rate of return, percent 14.6 Cost of Equity(rE) 14 13.0 Opportunity cost of capital (r) 12 11.4 10.84 WACC 10 8.0 Cost of 8 Debt(rD) Debt-Equity .25 .67 Ratio(D/E) (D/V = .2) (D/V = .4) Unlevering and Relevering - Unlevering asset = debt ( D ) + equity( E V V ) - Relevering equity = asset + (asset - debt) D E or (1+ D ) asset , if debt = “0” E *. Underlying assumption: Rebalancing Maintain the same market-value debt ratio 19.4 The Adjusted Present Value Rule Base-NPV 10 NPV = -10 + [1.8 / (1.12)t ] = $0.17 mil t=1 • 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 Table 19-1 Calculating the present value of interest tax shields on debt supported by the solar heater project (dollar figures in thousands) Debt Outstanding Interest Present Value Year at Start of Year Interest Tax Shield of Tax Shield 1 $ 5,000 $400 $140 $129.6 2 4,500 360 126 108.0 3 4,000 320 112 88.9 4 3,500 280 98 72.0 5 3,000 240 84 57.2 6 2,500 200 70 44.1 7 2,000 160 56 32.6 8 1,500 120 42 22.7 9 1,000 80 28 14.0 10 500 40 14 6.5 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. • APV = 170,000 + 576,000 = $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. APV for the Perpetual Crusher project Base case NPV = - 10 + 1.355/0.12 = $1.29 mil Financing Rule 1: Debt fixed Financing Rule 2: Debt rebalanced Under rule 1 PV (tax shield) = [0.350.08 5] ÷ 0.08 = $1.75 mil APV = 1.29 + 1.75 = $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 = 1.29 + 1.17 = $2.36 mil A. Technical Point on Financing Rule 2 • Discount at opportunity cost of capital • Multiply the resulting PV by (1+r) and divide by (1+rD) 0.14 PV(approx) = = 1.17 0.12 PV(exact) = 1.17 1.12 = 1.21 1.08 APV = 1.29 + 1.21 = $2.5 mil APV and hurdle Rates APV tells whether a project makes a net contribution to the value of the firm It tells break-even cashflow CF Tax APV = - Investment + PV Shield r CF (Ex) APV = - 10 + PV Tax 0.12 Shield CF APV = - 10 + 0.97 = 0 0.12 CF = 1.084 IRR = 10.84% General Definition of Adjusted Cost of Capital • The Opportunity 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. • The Adjusted Cost of Capital (r*) Adjusted opportunity cost or hurdle rate that reflects the financing side effects of an investment project Spotting and Valuing Options Chapter 20 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 of Price of Price Call Options Put Options October 1998 $80 $8.875 $3.25 January 1999 80 11.375 4.75 January 1999 85 8.625 6.875 Value Value of Call of Put 85 85 85 Share 85 Share (a) Price (b) Price Value of Share 85 Share Price (c) 85 Selling Calls, Puts, and Shares 85 85 0 Share 0 Share Price Price -85 -85 Value of Call Value of Put Seller‟s Position (a) Seller‟s Position (a) 85 Share 0 Price -85 Value of Stock Seller‟s Position (c) Value of Share Your Payoff Your Payoff Buy Share Sell call + = $85 Future Stock $85 Future Stock $85 Future Stock Price Price Price Value of Share Your Payoff Your Payoff Buy Share Buy Put + = $85 Future Stock $85 Future Stock $85 Future Stock Price Price Price Value Your Your of Share Payoff Payoff Buy Call Bank deposit paying $85 $85 + = $85 Future $85 Future $85 Future Stock Stock Stock Price Price Price Put - Call Parity C + PV (Ex) = P + S Expiration Date Today S* EX S* < EX V1=C+PV(EX) V2=P+S 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) Circular File Co. (MV) Asset value $30 $25 Bond: Asset - Call 5 Stock: Call $30 $30 Firm: Asset Stockholders‟ Position V<50 S= V50 S= S 0 Ex= $50 V (Promised Payment to Bondholders) Bondholders‟ Position V<50 B= V50 B= B 0 Ex= $50 V (Promised Payment to Bondholders) 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 = Value of - “p” risky debt riskless debt Circular File Co. (Market Value) Asset value $30 $25 Bond value = present value of promised payment - value of put 5 Stock value = asset value - present value of promised payment + value of put $30 $30 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 $40 0 120 160 Stock Price Pay off 0 Stock Price 120 160 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 20.3 What determines option values? Value of call Upper bound: Value of call B equals share price Lower bound: Value of call equals payoff if exercised C immediately A Exercise price Share Price Payoff to call option on firm X‟s shares Probability distribution of future price of Payoff to firm X‟s shares option on X Payoff to call Exercise price option on firm Y‟s shares Probability distribution of future price of Payoff to firm Y‟s shares option on Y Exercise price Value of calls on shares of firms X and Y Upper bound Y Lower bound X Exercise price Share Price What the price of a call options depends on 1. Increase in variables: If there is an The changes in the call increase in: option price are: Stock price (P) Positive Exercise price(EX) Negative Interest rate (rf) Positive Time to expiration(t) Positive Volatility of stock price () Positive 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 20.4 An Option-Valuation Model Constructing Option Equivalents from common stocks & borrowing Stock Price Stock Price Today 6 months later Call $68 $85 $106.25 rf =2.5% Exercise price = $85 • Hedge ratio (Option delta): Number of shares that are needed to replicate on call Option Spread of option prices delta = Spread of share 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 Option Equivalents: Buy 5 shares and borrow $36.86 today 9 6 month later Today S* = $68 S* = $106.25 Buy 5 shares 9 Borrow $36.36 Value of call today = value of shares - $36.86 bank loan = Arbitrage Opportunity EX 1: If call is priced at $12 : overpriced Strategy: Sell a call option Buy 5/9 share & borrow 36.86 today 6 month later Today S* = $68 S* = $106.25 +12 -47.22 +36.86 + $ 1.64 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 6 month later Today S* = $68 S* = $106.25 -9 +47.22 -36.86 + $ 1.36 Risk-Neutral Valuation: All investors are indifferent about risk Expected Return on any risky assets = rf = E(R) = Pu Ru + Pd Rd Ru = 106.25-85 = 85 68-85 Rd = = 85 E(R) = Pu ( ) + Pd ( )= where, Pu + Pd = 1 Pu = probability of stock price increase in the hypothetical Pu = Pd = risk-neutral world at t=1 E(C1) = at t=0 C0 = Valuing the Intel Put Option t=0 S P EX=$85 $68 $85 $106.25 Option Spread of option prices delta = Spread of share prices = = shares Intel share & Lend $46.07 How is it computed? 6 month later Today S* = $68 S* = $106.25 Sell 4 shares 9 Lend $46.07 Value of put = - 4 of share + $46.07 bank loan 9 = 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(d1) P] [N(d2) PV(EX)] Value of call=[N(d1) P] + [N(d2) PV(EX)] where Log[P/PV(EX)] t d1 = + t 2 d2 = d1 - t N(d) = cumulative normal probability density function EX = exercise price of option; PV(EX) is calculated by discounting at the risk-free interest rate, rf t = number of periods to exercise date P = price of stock now = standard deviation per period of (continuously compounded) rate of return on stock Real Options Chapter 21 Real Option 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 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 1982 1983 1984 1985 1986 1987 After-tax operating cash flow (1) * -200 +110 +159 +295 +185 0 Capital Investment (2) 250 0 0 0 0 0 Increase in working 0 50 100 100 -125 -125 capital (3) Net Cash Flow -450 +60 +59 +195 +310 +125 (1) - (2) - (3) NPV at 20% = - $46.45, or about -$46 million • Table 21-2. 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 1985. 2. 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 1982. 4. 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. • 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(d1)P - N(d2) • PV(EX) d1 = log[0.685] / 0.606 + 0.606 /2 = -0.3216 d2 = d1 - 0.606 = -0.9279 N(d1) = 0.3739 N(d2) = 0.1767 Call value = 0.3739463 - 0.1767676 = $53.59 mil 21.2 The Option to Abandon Tech A Tech B Good Demand $18.5 $18 Bad Demand 8.5 8 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) Valuing the Abandonment Put t=1 Pr Payoff Put Good Demand 0.5 $ 18 Bad Demand 0.5 $ 8 EX = $10, r = 8.3%, rf = 5% PV= E(R) = Pu ( ) + Pd ( )= = rf Pu = Pd = E(P) = 0.46 + 0.54 = E(P) P= = 1+rf Value of project = 21.3 The Timing Option: rf = 5% t=0 t=1 Project Cash Value of Value flow Call Good If invest $180, Demand $250 $25 project worth $200 Bad $160 $16 Demand 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 Value of option to invest Investment can be postponed Investment now or never 0 Project NPV RG= RB= E(R) = PG ( ) + PB ( )= = rf PG = PB = t=1, E(C) = t=0, Value of call = Q: Do you undertake project now? Warrants and Convertibles Chapter 22 22.1 What is warrant? Value of warrant Actual warrant value prior to expiration Theoretical value (lower limit on warrant value) Stock Exercise price = $15 price • Two Complications: Dividends and Dilution • Example: Valuing United Glue‟s Warrants Number of shares outstanding (N) ………….. 1 million Current stock price (P) …………………….. $12 Number of warrants issued ………….. per share outstanding (q) .10 Total number of warrants issued (Nq) ………. 100,000 Exercise price of warrants (EX) …………… $10 Time to expiration of warrants (t) …………… 4 years Annual standard deviation of stock price changes () …………… .40 Rate of interest (r):………………………….. 10% United stock pays no dividends. United Glue‟s market value balance sheet (in $ millions) Before the Issue Existing assets $16 $ 4 Existing loans 12 Common stock (1 million shares at $12 a share) Total $16 $16 Total After the Issue Existing assets $16 $ 4 Existing loans New assets financed 1.5 New loan without by debt and warrants 2 warrants 5.5 Total debt .5 Warrants 12 Common stock Total $18 $18 Total 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 = • Dilution Effect Nq = Nq EX = V: value of equity V = Total asset - debt Share price after exercise = Warrant value at maturity = Max (P - EX, 0) = Max V + Nq•EX - EX, 0 N + Nq V/N + EX = Max , 0 1+q 1 = Max V - EX , 0 1+q N $ 12.5 mil: Current equity value of alternative firm (=18 mil - 5.5 mil) Current share price of alternative firm = V = 12.5 = $12.5 N 1 mil Suppose of alternative firm: = 0.41 Black-Sholes value of call: 1 Value of call on Value of warrant = 1+q alternative firm = deal for United 22.2 What is a Convertible Bond • Difference between convertible bond vs. bond-warrant package • The price of convertible bond depends on its bond value and its conversion value Bond value: Conversion value: • Value at Maturity 3 3 Bond value, $thousand Conversion value, Bond paid $thousand 2 in full 2 Default 1 1 0 1 2 3 4 5 0 1 2 3 4 5 Value of firm ($ million) Value of firm ($ million) 3 Value of convertible, Convert $ thousand 2 Bond paid in full Default 1 0 1 2 3 4 5 Value of firm ($ million) • Value before Maturity Lower limit on Convertible, 3 3 Bond value, $thousand Conversion Value $thousand 2 2 Bond Value 1 1 0 1 2 3 4 5 0 1 2 3 4 5 Value of firm ($ million) Value of firm ($ million) 3 Value of convertible, $ thousand 2 Value of convertible Lower limit 1 on value 0 1 2 3 4 5 Value of firm ($ million) Forcing Conversion Value of Convertible Conversion Value Call price Bond Value A B C Stock price Value of Value of convertible = straight + Conversion - Redemption bond bond option option 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? Valuing Debt Chapter 23 • Present Value of Bond C C C … + (1000+C) PV = + 2 + (1+r )3 + (1+r1) (1+r2) 3 (1+rn)n r1 , r2 , r3 , …. rn : discount rates for cashflows to be received by the bond holders in periods 1, 2, …,n. Q: What determines the discount rates? (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 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) S S r1 r r r2 D D 23.2 Term Structure and Yield to Maturity PV = C 1+r C 1 C PV = 1+r + (1+r )2 1 2 r1, r2 : Spot rate The series of spot rates r1, r2 … Term structure of interest rates • Yield to Maturity Rate of return to bondholders if he/ she keeps the bond until maturity C C … + C+F n Price of Bond = + 2 + (1+y) (1+y) (1+y) PRESENT VALUE CACULATIONS 5s of „08 10s of „08 PERIOD INTEREST RATE Ct PV AT rt Ct PV AT rt t=1 r1 = .05 $ 50 $ 47.62 $ 100 $ 95.24 t=2 r2 = .06 50 44.50 100 89.00 t=3 r3 = .07 50 40.81 100 81.63 t=4 r4 = .08 50 36.75 100 73.50 t=5 r5 = .09 1,050 682.43 1,100 714.92 Totals $1,250 $852.11 $1,500 $1,054.29 YIELD TO MATURITY Bond Price Percent (IRR) 5s of „08 85.21% 8.78% 10s of „08 105.43 8.62 23.3 Duration and Volatility Duration: Average time to each payment 1 PV(C1) 2 PV(C2) D = + +… … V V PROPORTION OF TOTAL VALUE PROPORTION OF TOTA YEAR Ct PV(Ct) AT 5.5% [PVt/V] VALUE TIME 1 137.5 130.33 .092 .092 2 137.5 123.54 .087 .175 3 137.5 117.10 .083 .249 4 137.5 110.99 .079 .314 5 137.5 105.21 .075 .373 6 1137.5 824.97 .584 3.505 V = 1,412.13 1.000 Duration = 4.708 years (A) 13 ¾s of 2004 vs. (B) 7 ¼s of 2004 DA = 4.708 years DB = 5.115 years (EX) 1% changes in yield 13 ¾s of 2004 7 ¼s of 2004 NEW PRICE CHANGE NEW PRICE CHANGE Yield falls, 0.5% 144.41 +2.26% 111.42 +2.46% Yield rises, 0.5% 138.11 - 2.20 106.15 - 2.39 Difference 6.30 4.46% 5.27 +4.85% Volatility (%) Duration 1+yield VB = VA = • 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 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 + (1-x) duration of 6-year bond 1 year bond 3.9 years = x 4.6 years + (1-x) 1 years 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 = 1,000 = Forward Rate The extra return that Ms. Long gets by lending for 2 years rather than 1 Implicit & guaranteed (1+r2)2 = (1+ r1 ) (1+f2) (1.105)2 f2 = 1.1 - 1 0.11 11% Expected Payoff: L1 Certain Payoff: L2 1,000 (1+r2)2 1,000 (1+r1) [1+E(1r2)] vs. or 1,000 (1+ r1 )(1+f2) Strategy L1 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 = Certain Payoff: S1 Expected Payoff: S2 1,000 (1+r2)2 1+E(1r2) 1,000 (1+r1) vs. or 1,000 (1+ r1 )(1+f2) 1+E(1r2) Strategy S2 is better if • The Expectations Hypothesis Ms.Long and Mr. Short try to maximize their expected return f2 = E(1r2) If f2 > E(1r2) prefer 2yr. bond price bond of 2yr return of 2yr. Bond and f2 Equilibrium: f2 = E(1r2) If f2 < E(1r2) prefer 1 yr. bond The only reason for upward sloping term structure is investor expect the relationship such that f2 > r1 , E(1r2) > r1 The Liquidity Preference (Theory) • 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 holds 1 year bond only if E(1r2) f2 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 holds 2 year bond only if E(1r2) f2 Other things equal, Ms. Long will prefer to buy year bond & Mr. Short will prefer to buy year bond 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 f2 & E(1r1) Liquidity Premium In reality, there are shortage of long-term lender, liquidity premium is positive. f2 = E(1r2) + Liquidity Premium ( = LP2) f2 = E(2r3) + LP3 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 Promised yield y other risk premium Expected yield Rf Yield= Rf+ Risk Premium (EX) Rf = 9% Payoff (t=1) Probability $ 1,090 0.8 0 0.2 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, , say risk premium=2% PV = Promised yield = (expected yield = 11%) Bond Ratings “relative quality” of bond by Moody‟s Standard & Poor‟s MOODY‟S STANDARD AND POOR‟S Aaa AAA Aa AA Investment A A Baa BBB grade Ba BB B B Caa CCC Junk Ca CC bonds C C PERCENTAGE DEFAULTING WITHIN RATING AT 1 YEAR 5 YEAR 10 YEAR TIME OF ISSUE AFTER ISSUE AFTER ISSUE AFTER ISSUE AAA .00 .06 .06 AA .00 .67 .74 A .00 .22 .64 BBB .03 1.64 2.80 BB .37 8.32 16.37 B 1.47 21.95 33.01 CCC 2.28 35.42 47.46 Leasing Chapter 25 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) 25.2 Why lease ? – Convenient (short-term) – Cancellation option – Maintenance provided – Tax-shield can be used. – Etc. 25.3 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 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 0 1 2 3 4 5 6 Initial cost -75 Maintenance, insurance, selling,-12 -12 -12 -12 -12 -12 -12 and administrative costs Tax Shield on costs +4.2 +4.2 +4.2 +4.2 +4.2 +4.2 +4.2 Depreciation tax shield +5.25 +8.40 +5.04 +3.02 +3.02 +1.51 Total -82.80 -2.55 .60 -2.76 -4.78 -4.78 -6.29 NPV at 7% = -$98.15 Break-even rent (level) 26.18 26.18 26.18 26.18 26.18 26.18 26.18 Tax -9.16 -9.16 -9.16 -9.16 -9.16 -9.16 -9.16 Break-even after tax 17.02# 17.02 17.02 17.02 17.02 17.02 17.02 NPV at 7% = $98.15 * no inflation; r = 7%; Tc = 35%` * Table 6-5: depreciation * First payment: immediate # 17.02 = 65% of 26.18 7% PVA 7yrs = 5.389 5.389 * 1.07 = 5.766 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 0 1 2 3 4 5 6 7 Cost of new bus +100 Lost depreciation tax shield -7.00 -11.20 -6.72 -4.03 -4.03 -2.02 0 Lease payment -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 Tax shield of lease payment +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 Cash flow of lease +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98 D r * 5 yr: depreciation (Table 6.4), 7yrs/8 times payment, Tc = 35%, = 10% D r * After tax:* (1 - Tc) = 6.5% NPVlease = +89.02 - 17.99 - 22.19 - 17.71 - 15.02 - 15.02 - 13 - 10.98 2 3 4 5 6 7 1.065 (1.065) (1.065) (1.065) (1.065) (1.065) (1.065) = -0.7 -$700 Creating Equivalent Loan Year 0 1 2 3 4 5 6 7 Lease cash flows, +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98 thousands Table 25-3: Equivalent loan; exactly same debt service on lease. Year 0 1 2 3 4 5 6 7 Amount borrowed at year-end 89.72 77.56 60.42 46.64 34.66 21.89 10.31 0 Interest paid at 10% -8.97 -7.76 -6.04 -4.66 -3.47 -2.19 -1.03 Interest tax shield at 35% +3.14 +2.71 +2.11 +1.63 +1.21 +.77 +.36 Interest paid after tax -5.83 -5.04 -3.93 -3.03 -2.25 -1.42 -0.67 Principal repaid -12.15 -17.14 -13.78 -11.99 -12.76 -11.58 -10.31 Net cash flow of equivalent loan 89.72 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98 How much can I borrow when I pay same cash as lease payment? 25.5 When Do Financial Leases Pay? The value of the lease to the bus manufacturer would be(Tc=35%) Value of lease to lessor 17.99 22.19 17.71 15.02 15.02 13 10.98 = -89.02 + + + + + + + 1.065 (1.065)2 (1.065)3 (1.065)4 (1.065)5 (1.065)6 (1.065)7 = +.70 Zero sum game Suppose that Greymare paid no tax (Tc = 0). Then the only cash flows of the bus lease would be: Year 0 1 2 3 4 5 6 7 Cost of new bus +100 Lease payment -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 These flows would be discounted at 10 percent, because rD (1-Tc)= rD when Tc =0 10 16.9 Value of lease = 100 - (1.1)t = +100 - 99.18 = +.82 or $820 t=0 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 rD is high - if it were zero, there would be no advantage in present value terms to postponing tax Mergers Chapter 33 Selling Company Acquiring Company Payment, billions of dollars NYNEX Bell Atlantic 21.0 McDonnell Douglas Boeing 13.4 Digital Equipment Compaq Computer 9.1 Schweizerischer Union Bank of Swiz. 23.0 Energy Group PCC Texas Utilities 11.0 Amoco Corp. British Petroleum 48.2 Sun America American Intl. 18.0 BankAmerica Corp. Nationsbank Corp. 61.6 Chrysler Daimler-Benz 38.3 Bankers Trust Corp. Deutsche Bank AG 9.7 Netscape America Online 4.2 Citicorp Travelers Group Inc. 83.0 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 33.3 Estimating Merger Gains and Costs A: Buyer B: Seller Synergy Gain = PVA+B - (PVA + PVB) Cost = Cash paid - PVB NPV = Gain - Cost = PVAB - (Cash-PVB) (Ex) PVA = 200, PVB = $50, PVA+B = $275 Gain = PVAB = + $25 Cash = $65 Firm A Firm B Market price $ 200 $ 100 per share Number of share 1,000,000 500,000 Market value of firm $ 200 mil $ 50 mil Cost = Cash - PVB = Cash - MVB + (MVB - PBB) = 65 -50 + (50 - 44) = $21 mil Cash payment depends on the relative bargaining power of the two participants • Stock offer N : shares received by seller PAB: combined firm‟s worth Cost= N PAB - PVB (Ex) N = 325,000 A‟s price before merger: $200 PVB = $50 mil Apparent cost = If PVAB = $275mil (due to synergy gain) New share price = Cost = 0.325 -50 = 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 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? Leveraged Buyouts • Debt financed (junk-bond) • Going private • MBO

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