51.5 Agency Problem A. Separation between Ownership and Management B. How to solve agency problem?Monitoring by board of directors1Compensation package2Monitoring by outside large blockholders(Bank, insurance Co., pension, mutual fund)3Efficient outside managerial labor market4Active outside takeover market5
6Present Value and The Opportunity Cost of Capital Chapter 2
72.1 Introduction A. Present Value B. Risk and Present Value PV = C / (1+r)r:NPV = PV - C0B. Risk and Present ValueC. PV and Rate of Return
8D. The Opportunity Cost of Capital From your Investment1C0 : $ 100,000C1 :Slump : $ 80,000Normal : $ 110,000Boom : $ 140,000E(C1)
9Find stock X which has same risk as your project : From Stock Market2Find stock X which has same risk as your project :P0 : $ 95.65P1 :Slump : $ 80Normal : $ 110Boom : $ 140E(P1) = 1/3 ( ) = 110E(R) = = 0.15 15% k95.65
10Q : What is the Present Value of your project? PV of project =NPV =
19EX : Pinacle West Corp (p 69) 4.3 Simple Way to Estimate rr = D1 / P0 + gD1 / P0 : Dividend Yieldg : Dividend GrowthEX : Pinacle West Corp (p 69)P0 = $41, Div1 = $1.27, g = 5.7%r =
20r = 0.031 + 0.053 = 0.084 or 8.4% Alternative Approach: Payout ratio = DIV1 / EPS = 0.47Plowback Ratio = 1- Payout ratio = 0.53ROE = EPS / Book Equity per Share = 0.1g = Plowback ratio * ROE =r = = or 8.4%
21Some Warnings about Constant-Growth Formulas 1. Individual stock’s r is subject to estimation errorsPortfolio approach2. Growth rate can rarely sustained indefinitelyEx. Growth-techDIV1=$0.05, P0=$50, Plowback Ratio=80%, ROE=25%g =r =
22Ex: at t=3 and thereafter ROE =16% Firm responds by plowing back 50% of earningsg =Table 4.2YEAR1YEAR2YEAR3YEAR4Book equity10.0012.0014.4015.50Earning pershare, EPS2.503.002.302.49Returnon Equity, ROE.188.8.131.52Payout ratio.184.108.40.206Dividends pershare, DIV.50.601.151.24Growth rateof dividends-.20.92.08
23General DCF formula to find the capitalization rate r: DIV11+rDIV2(1+r)2DIV3 + P3(1+r)3P0=++P3=P0=50=
24Growth stock vs Income stock 4.4 The link between stock price andearning per ShareGrowth stock vs Income stockA. Income StockNo GrowthPerpetuity ModelEPS1rDIV1P0 ==r(EX)Expected Return = Dividend Yield = 10/100 =.10 = rPrice = DIV1 / r = EPS1 / r =
25B. 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)
26Table 4-3Effect on stock price investing an additional $10 in year 1 at different rates of return.Notice that the earnings-price ratio overestimates r when the project has negative NPVand underestimates it when the project has positive NPV.Project's impactProject RateIncrementalProject NPVShare PriceEPS1on Share Priceain Year 0, P0of ReturnCash Flow, Cin Year 1in Year 0bPr.05$ .50- $ 5.00- $ 4.55$.105.10.101.00100.00.10.10.151.50104.55.096.10.202.00109.09.092.10.252.50113.64.088.10aProject costs $ (EPS1). NPV = C / r, where r = .10bNPV is calculated at year 1. To find the impact on P0, discount for 1 year at r = .10
27In general : r P0 = + PVGO r : EPS1rP0 =+PVGOPVGO : Present Value of Grow OpportunitySum of all NPVs (per share)EPS1rCapitalized value of average earningunder a no-growth policy:
28Is Japanese firm growing fast? Determinants of P/E RatioP0 =PVGOEPS1r+Divide each side by EPSP/E =1rPVGOE+1. Cost of Capital(r): “-”2. Conservative accounting procedure(EPS): “-”3. Growth opportunities(PVGO): “+”Q : Japanese firm : P/E 50U.S. firm : P/E 17Is Japanese firm growing fast?
30Analyze: $ 44.44Plowback Ratio = .4, * .4 = $ 3.33Invest: $ 3.33 at 25% (ROE).25 * 3.33 = $ .83at t = 1; NPV1 = / .15 = 2.22at t = 2;Invest 3.33 * 1.1 = 3.69 (g = 10%)NPV2 = * (.83 * 1.1) / .15 = 2.44PVGO = NPV1 / (r - g) = 2.22 / ( ) = $ 44.44This is growth stock, not because g = 10%,but because
31C. Some Example of Growth Opportunities Table 4-4 Estimated PVGOs (p.76)MarketPVGO,StockCapitalizationPVGOPercent ofPrice, P0EPS*Rate, r**=P0 - EPS/rStock PriceP / EIncome Stocks:AT & T$52.00$2.85.094$21.7041.718.2Conagra26.001.33.10613.5051.719.5Duke Power60.003.5821.9036.516.8Exxon64.002.89.09934.7054.322.1Growth Stocks:Compaq30.000.69.12324.4081.343.5Merck120.004.43.11882.5068.727.1Microsoft101.002.08.16585.1084.248.6Wal-Mart0.7352.2087.182.2* EPS defined as the average earnings under a no-growth policy. As an estimate of EPS, we use the forecastedearnings 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 EX: market risk premium = 6%
32Why NPV leads to better Investment Decisions than Other Criteria Why Net Present Value Leads to Better Investment Decisions than Other CriteriaChapter 5
335.1 Review of Basics Forecast Cash Flow 2Determine appropriate Cost of Capital3Discount with Cost of Capital
34All cash flows are considered Q : Why NPV ?All cash flows are consideredTime Value of MoneyNPV is not affected by manager’s taste,accounting method, profitability of existingbusiness, and profitability of otherindependent business
355.2 Payback Period Number of years it takes before cumulative cash flow recovers initial investmentCASH FLOWS, DOLLARSPaybackNPV atProjectC0C1C2C3Period, Years10 PercentB- 2,000+ 500+ 5,00032,642C- 2,000500+1,800+ 5,0002-58D- 2,000+ 1,8002+50
36Cash flow vs. Book Income 5.3 Book Rate of ReturnBook incomeBook Rate of Return=Book assetsCash flow vs. Book IncomeProblems :
37ExampleComputing the average book rate of return on an investment of $9000 in project ACASH FLOWS, DOLLARSProject AYear 1Year 2Year 3Revenue12,00010,0008,000Out-of-Pocket cost6,0005,0004,000Cash flow6,0005,0004,000Depreciation3,0003,0003,000Net income3,0002,0001,000average annual income2,000Average book rate of return === .44average annual investment4,500Year 0Year 1Year 2Year 3Gross book value of investment$ 9,000$ 9,000$ 9,000$ 9,000Accumulated depreciation3,0006,0009,000Net book value of investment$ 9,000$ 6,000$ 3,000$Average net book value = $ 4,500
385-3 Internal Rate of Return: IRR Discount rate that makes NPV = 0C0 = - 4, k: cost of capitalC1 = 2,000C2 = 4,000NPV = -4,000 +(1+IRR)2,000+4,000(1+IRR)2= 0(Rule) Accept IRR>k NPV>0Reject IRR<k NPV<0
453.2 Different pattern of cash flow over time CASH FLOWS, DOLLARSIRR,NPV atProjectC0C1C2C3C4C5Etc.Percent10 PercentG- 9,000+6,000+5,000+4,000…333,592H- 9,000+1,800+1,800+1,800+1,800+1,800…209,000I-6,000+1,200+1,200+1,200+1,200…206,000
4610,000NPV, dollars-5000Discount Rate,percent33.315.6+5,000+6,0001020304050Project GProject H
47Pitfall 4. What happens if term structure is not flat? (generally)NPV = - C0 + C1 / (1+r1) + C2 / (1+r2)2 + …IRR vs r1r ?r3
485.5 Limited Resource (Capital Rationing) CASH FLOWS, MILLIONS OF DOLLARSNPV atProjectC1210 PercentA- 10+ 30+ 521B- 5+ 2016+ 1512
49<$10> t=0, t=1 NPV at Profitability Project C 10 Percent Index A CASH FLOWS, MILLIONS OF DOLLARSNPV atProfitabilityProjectC1210 PercentIndexA- 10+ 30+ 5212.1B- 5+ 20163.2+ 15122.4D- 40+ 60130.4
50More Elaborate Capital Rationing Models We accept proportion A of project A. NPV of accepting A of A Previous ExampleNPV =
52Making Investment Decisions with the Net Present Value Rule Chapter 6
53How 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 areproject interactions?
54Estimate 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”
55(Ex) C0 C1 C2 C3 Treat Inflation consistently. Real CF : discount with real rateNominal CF: discount with nominal rate(Ex) C C C C3Real CFrN = 15%, I = 10% NPV = NPV =
566.2 Example - IMFC Project Initial investment: $ 10 mil Salvage value at year 7: $ 1 mil (sold)Depreciation: 6 year straight line with arbitrary salvage of : $ 500,000annual depreciation = = $ mil9.5 mil6
57Table 6 - 1 Nominal Cashflow Ex: forecast of inflation: 10%IM&C's guano project - revised projections reflecting (figures in thousands of dollars)PERIOD12345671. Capital investment10,000-1,949*2. Accumulateddepreciation1,5833,1674,7506,3337,9179,5003. Year-end book value8,4176,8335,2503,6672,0835004. Working capital5501,2893,2614,8903,5832,0025. Total book value(3 + 4)8,9678,1228,5118,5575,6662,5026. Sales52312,87732,61048,90135,83419,7177. Cost of goods sold8377,72919,55229,34521,49211,8308. Other costs **4,0002,2001,2101,3311,4641,6111,7729. Depreciation10. Pretax profit( )-4,000-4,0972,36510,14416,50911,1484,5321,449**11. Tax at 35%-1,400-1,4348283,5505,7783,9021,58650712. Profit after tax-2,600-2,6631,5376,59410,7317,2462,946942* Salvage value.** The difference between the salvage value and the ending book value of $ 500 is a taxable profit
58IM&G’s guano project-cash-flow analysis (thousand)Period123456752312,88732,61048,90135,83419,7171. Sales2. Cost of goods and sold3. Other costs4. Tax on operations5. Cash flow fromoperation6. Change in workingcapital7. Capital investment andDisposal8. Net cash flow9. Present value at 20%Net present value = +3,519(sum of 9)8377,72919,55229,34521,49211,8304,0002,2001,2101,3311,4641,6111,772-1,400-1,4348283,5505,7783,9021,586-2,600-1,0803,1208,17712,3148,8294,529-739-1,972-1,6291,3071,5812,002-550-10,0001,442-12,600-1,6302,3816,20510,68510,1366,1103,444-12,600-1,3581,6543,5915,1534,0742,046961
59Cash flow = Sales - CGS - Other costs - Taxes Net cash flow = Cash flow from operation Networking capital[- Initial Investment + Recovery of Salvage Value]NPV =
60Choosing between Long & Short Equipment 6.3 Project InteractingChoosing between Long & Short EquipmentC0C1C2C3PVat 6%A+15+5+5+528.37B+10+6+621.00
65Average rate of return on Treasury bills, Government bonds, Corporate bonds, and common stocks,(Percent per year)AVERAGE ANNUALRATE OR RETURNAVERAGE RISK PREMIUM(EXTRA RETURN VS.TRESURY BILLS)PORTFOLIONOMINALREALTreasury bills3.8.7Government bonds220.127.116.11Corporate bonds6.13.02.3Common stocks(S&P 500)13.09.79.2Small firmcommon stock17.714.213.9
667.2 Measuring Portfolio Risk Variance (Standard Deviation)Expected = Ri * Pi = E (R) = RVariance = (Ri - R)2 * Pi = 2 = VRiskSystematic Risk: market riskmacro-economic variablesUnsystematic Risk: firm unique or specific risk
67Long-term government bonds 9.2 84.6 Corporate bonds 8.7 75.7 STANDARDDEVIATION()PORTFOLIOVARIANCE(2)Treasury bills3.210.2Long-term government bonds9.284.6Corporate bonds8.775.7Common stock (S&P 500)20.3412.1Small-firm common stocks33.91149.2PERIODMARKET SD()23.9%41.617.518.104.22.168.414.3
75Limits to Diversification VP = 2P =N * (1/N)2 2 + (N2 - N) * (1/N2) cov2 : average variancecov : average covariance2P = VP =(1/N) 2 + (1 - 1/N) covlim VP N(Ex) mutual fund
76Special Cases no diversification no risk reduction = 12P = X12 X22 X1X2 1 2 * 1= (X1 1 + X2 2 )2( a b)2 a2 + b2 2abP = X1 1 + X2 2 , when = 1There is:no diversificationno risk reduction* Portfolio risk is simply weighted average ofindividual risk; linear combination !
77Risk may be completely eliminated by combining X1, X2 (Ex) = - 12P = X12 X22 X1X2 1 2= (X1 X2 2 )2P = X1 1 - X2 2 , when = -1Risk may be completely eliminated by combiningX1, X2 (Ex)Portfolio Risk is (again) a linear combination ofindividual risks.
78Example A B E(R) 10% 12% 2 9% 16% AB = -1 % %AB = -1 Find the weights, A, B for MinimumVariance Portfolio. ( p = 0) What is the risk & return of that portfolio?* General case : -1 We need Calculus.
86• M P T is a market portfolio; M Capital Market Line CML EPT•EMRfMPT is a market portfolio; MCapital Market Line CMLRisk-return relationship for efficient portfoliosIntercept: Rf price of timeslope: (EM - Rf) / M price of riskEp = Rf + [ (EM - Rf) / M ] x P
87Systematic Risk vs. Unsystematic Risk Capital Asset Pricing Model: CAPMApply Portfolio Theory to evaluate all risky assetsSystematic Risk vs. Unsystematic RiskWe can eliminate unsystematic risk by combiningsecurities. (it cancels each other)We can not eliminate systematic risk since it moveswith market as a whole Therefore,
88Systematic Risk = Market risk = Covariance(iM) RequiredRate of Returnon Risky AssetRisk-freeRate(Rf)RiskPremium=+= Rf + amount of risk Price of risk= Rf += Rf += Rf +
968.4 Some Alternative Theories Arbitrary Pricing TheoryAssumes that each stock’s returndepends partly on macroeconomicfactors or noise(event that are unique to company)R = a + b1rf1 + b2rf2 + b3rf3 + … … noiseExpectedPremium= r - rf = b1 (r1- rf ) + b2 (r2 - rf )+ b3 (r3 - rf ) + … …
97Estimated risk premium APT example1. Identify the Macroecnomic FactorsYield SpreadInterest RateExchange RateReal GNPInflation2. Estimate the Risk Premium for Each FactorEstimated risk premium(rfactor - rf)FactorYield spread5.10%Interest rate-.61Exchange rate-.59Real GNP.49Inflation-.83Market6.63
100Are the New Projects More Risky or Less Risky than its Existing Business?Each project should be evaluatedat its own Cost of Capital(implication of Value Additivity Principle)Firm Value = PV(AB) = PV(A) + PV(B)= sum of separate assetsPV(A), PV(B) are valued as if they were mini-firmsin which stockholders invest directly.
102True 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 stockbeta- Project beta shifts over time.
103Industry Beta and Divisional Cost of Capital Individual measurement errorPortfolio error cancelled outIf you consider across-the-board expansion,such as new division,What is the “” for new division?Answer:
107Average rate of price appreciation or depreciation, ( = alpha)Average rate of price appreciation or depreciation,born by stock-holders when investors in the marketas a whole earn nothing.R-squared R2The proportion of variance of stock price changethat can be explained by market movement. means systematic risk / total risk
1099.2 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 theexpected return on the firm’s assets.But,
110How Changing Capital Structure Affects Expected Return? CompanyCost of Capital= r Asset = r portfolioDE(WACC) =r d+r eD + EE + D(EX)B/S (market value)A 100D 40E60100100r d = 8%r e = 15%r Asset=
111(Now) : Issue 10 equity, Retire 10 debt B/S (market value)A 100D 30E70100100* The change in financial structure does not affect does affect(Ex) lower leverage: rD 7.3% (Given)rAssets =
112How does Changing Capital Structure Affect Beta? VEV D +EAssets = Portfolio =V = D + E D = E = 1.2A =After refinancing; D 0.1(Given)
1149.3 How to Estimate the company Cost of Capital Pinnacle West’s Common StockBetaStandard.ErrorBostonElectric.60.19CentralHudson.30.18ConsolidatedEdison.65.20DTEEnergy.56.17EasternUtilitiesAssociate.66.19GPUInc..65.18NEElectricSystem.35.19OGEEnergy.39.15PECOEnergy.70.23PinnacleWestCorp..43.21PP&LResources.37.21PortfolioAverage.51.15
1169.4 Discount Rates for International Projects Foreign investments are not always riskier..47.1203.80Taiwan.35.1472.36Kazakhstan.62.160Brazil1.46.4163.52ArgentinaBetacoefficientCorrelationRatiosForeign Investment in the US
117P E(RP) Taiwan Index US Index 22 20 18 16 14 12 10 09 11 13 15 17 19 09111315171921
1189-4 Setting Discount Rate when you can’t calculate Avoid fudge factorsDo 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
119(Ex)Q: What are industries which are risky,but have low ?
120Determinants of Asset Beta: Cyclicality:Firms whose revenue depend on business cycle high Operating LeverageCommitment to fixed production chargesHigh fixed cost ratio High operating leverage High Asset BetaWhy ?
121Break Even Point Analysis $TotalCostUnit VariableCostFixedCostQ
122TRTCProfitLossFCBEFLow Fixed Cost(high Variable Cost)Low OL
123TRTCFCHigh Fixed Cost(Low Variable Cost)High OL
1249-6 Another Look at Risk and Discounted Cash flow Risk-adjusted:t=1PV = [Ct / (1+r)t], r = rf + (rM - rf)n(Ex) r = 8 = 12%Year CF PV240.21001.12 x = (x = certainty equivalent cash flow)x100= 89.3 =(1.12)2(1.06)2 x = 100 (1.06/1.12)2 = 89.57
125= 1+rf 1+r 1+rf 1+r General Solution Risky Cash Flow at time t ÷øöçèæRiskyCash Flowat time tCertainly equivalentCash Flow at time t=1+rf1+rt÷øöçèæWe call t = Certainty equivalent coefficient1 = (1.06 / 1.12) = 0.9462 = (1.06 / 1.12)2 = 0.8963 = (1.06 / 1.12)3 = 0.848Valuing CE cash flowCE(CF)(1 + rf)CFPV ==1 + r
130Corporate Financing and Market EfficiencyChapter 13
131? 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>
13213.1 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 paymentt=1103,000(1.10)t100,000(1.10)10-= +100,000 -= $43,200Difference between Investment & Financing Decisions Easy reverse Abandonment value is O.K. Lose or make money is not easy
137Q1 : How company set dividend? Q2 : How dividend affect stock price?InvestmentFinancing- So far:independentIf dividend affects firm value, attractiveness ofnew project depends on where the money is coming from.DividendFinancingdecisionMixed withDecisionInvestmentGiven capital budgeting & financing decision,what is the effect of change in dividend?
13816.1 How dividends are paid? Board of directors Record date Legal LimitationCompanies are allowed to pay a dividend out of surplusbut 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 bilHow to Repurchase?1. Open market repurchase2. Tender Offer3. Direct negotiation
139GreenmailTarget of a takeover attempt buys off the hostile bidderby repurchasing any shares that it has acquired withpremium at the expense of existing shareholders.16.2 Information content of DividendSignaling ModelOther Signaling Tools
140- Dividend irrelevance 16.3 Dividend ControversyMM(1961)- Dividend irrelevanceIn a world without taxes and transaction costs(efficient and perfect capital market)(Ex)B/S (Market Value)Cash 1,000DFA ,00010,000+NPV E10,000 + NPV10,000 + NPVPay dividend by issuing new shares($1,000)We want to continue project w/t cash($1,000)
141Value 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 lossInvestment and borrowing policies are unaffected by dividend[overall value 10,000 + NPV, is unchanged]* Crucial AssumptionNew stock holders pay fair-priceOld stockholders have received $1,000 dividendand $1,000 capital lossDividend policy doesn’t matter.
143The RightistTrade a safe receipt with an uncertain future gain? Sell it!Market ImperfectionTransaction costsTemporarily depressed priceInformation asymmetry about future EarningThe LeftistTax Argument Weakened after 1986 ‘Tax Reform Act’
14416.6 Middle of the RoadersWithout tax and transaction cost (perfect & efficient market), company’s value is not affected by dividend policy (irrelevant): MM (1961)Even if with tax and other imperfections,Q: If company increase stock price by paying more or less dividend, why have not they already done so? (perhaps)“Supply Effect”
146MM Proposition I B/S Asset Structure Capital Structure Mix of differentsecurities“Maximize V”MM Proposition IFirm can not change the total value of securities just bysplitting its cash flows into different streams. (RHS)Firm value is determined by its real assets. (LHS)
14717.1 The Effect of Leverage in a Tax Free Economy VU: Value of unlevered firmEL = VL - DL1) 1% of unlevered firm$ investment $ return (NOI).01 VU profit
149same cost (same investment) 3) Buy 1% of equity of levered firm$ investment $ return.01 EL (profit -I)= .01 (VL - DL)4) Alternative way: Borrow .01 DL on your accountBuy 1% of equity of unlevered firm$ investment $ returnBorrowingEquity-.01 DL-.01 I.01 VU.01 profit.01(VU - DL).01 (profit - I)Same profitVU = VLsame cost (same investment)
150All Equity Example of Proposition I (p.477) P = $10 VU = $10,000 E(EPS) = $1.5, P = $10, E(R) = 1.5/10 = 15%N = 1,000P = $10VU = $10,000NOI($) , , ,000EPS($)ROE(%)A
151debt $5000, k = 10%, repurchase: 500 shares Issue:debt $5000, k = 10%, repurchase: 500 sharesN = 500P = $10, k = 10%Market value of stock: $5,000Market value of debt : $5,000NOI($) , , ,000InterestNI($) , ,500EPS($)123ROE(%)
1523.00Equal proportionsdebt and equity2.50Expected EPS withdebt and equity2.00All equityExpected EPS withall equity1.501.00.50Expectedoperatingincome500100015002000
153Personal Leverage NOI($) CBorrow $10, then invest $20 in two unlevered shares(Initially, I have $10)NOI($)5001,0001,5002,000Earnings on two shares($)1234Interest($) at 10%-1-1-1-1Net Earnings($)123Return on0%10%20%30%$10 investment
15417.2 How Leverage Affects Return Current structureall equityProposedstructureE(EPS)$1.5$2.0NOI = $1,500V=10,000P$10$10N =1,000D=5,000E(ROE)15%20%Kd = 10%E=5,000Leverage increases EPS, but not P. The change in EPS is exactly offset by a change in therate at which the earning are capitalized.15% 20%
155Expected returnon asset(rA)NOI=Market value of all securityAssumption:In a perfect market, borrowing decision does not affectoperating income or total market value of its securities.Borrowing decision does not affect expected returnon firm’s assets(rA).
156rA rE rD rE rA D D+E E = + D+E = + D E (rA - rD) - Expected return ondebtExpectedreturn onequityExpectedreturn onassetsDebt/EquityRatioExpectedreturn onassets+-=
157Proposition 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 = 5,000rD = 10% E = 5,000rE =
158rE rA rD rD r = = = Figure 17-2 Expected Return on Equity MM’s proposition II. 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, debtholders demand a higher return on the debt. This causes the rate of increase in rE to slow down.rEExpected Return on Equity=rAExpected Return on Assets=rDrDExpected Return on Debt=DERisk free debtRisky debt
16017.3 The Traditional Position Moderate degree of financial leveragemay increase rE although not to the degreepredicted by MM proposition IIExcessive debt raise rE faster rA (=WACC) decline & later rise.
161r rE rE rA rA rD rD = = = = (MM) (traditional) (MM) (traditional) D E debtequity=Traditionalist believe there is an optimal debt-equity ratio that minimizes rA
162BTransaction CostsImperfections may allow firms that borrowto provide valuable service.(Ex. Economies of scale in borrowing)Levered Shares might trade at premiumcompared to their theoretical valuein perfect marketSmart financial engineer already recognize thisand shift capital structure to satisfy this client.
164Question: Why do we worry about debt policy? Evidence:1. D/E ratio are different across the industry.2. Imperfections:TaxBankruptcy Costs (T.C.)Cost associated with financial distressPotential conflicts of interests between security holdersInteractions of investment and financing decision
16518.1 Corporate TaxesIncome statementof Firm Uof Firm LEarnings beforeinterest and taxesInterest paid to bondholdersPretax incomeTax at 35%Net income to stockholdersTotal income to bothbondholders and stockholdersInterest tax shield (.35interest)$1,000801,000920350322$650$598$ = $650$ = $67828
167Normal Balance Sheet(Market Values) Asset value (present valueof after-tax cash flows)DebtEquityTotal assetsTotal valueExpanded Balance Sheet(Market Values)Pretax asset value (presentvalue of pretax cash flows)DebtGovernment ‘s claim(present value of futuretaxes)EquityTotal pretax assetsTotal value
168Book Values Market Values Net working capital Long-term debt Table 18.3(a)Book ValuesNet working capitalLong-term debt$2,644$1,347Other long-termliabilitiesLong-term assets17,5996,28212,614EquityTotal assets$20,243$20,243Market ValuesNet working capital$2,644$1,347Long-term debtMarket value oflong-term assetsOther long-termliabilities131,5126,282126,527EquityTotal assets$134,156$134,156Total value
169Book Values Market Values Net working capital Long-term debt Table 18.3(b)Book ValuesNet working capitalLong-term debt$2,644Other long-termliabilities6,282Long-term assets17,59911,614EquityTotal assets$20,243$20,243Market ValuesNet working capital$2,644Long-term debtMarket value oflong-term assetsOther long-termliabilities131,5126,282Additional tax shieldsEquityTotal assetsTotal value
170MM & Taxes: MM Prop I with corporate tax. VL = VU + PV (Tax Shield)100% debt?
17118.2 Corporate and Personal Taxes Operating income$1.00Corporate taxIncome aftercorporate taxPersonal taxIncome afterall taxes
172Corporate Borrowing is better If (1 - TP) > (1- TPE) * (1 - Tc)Relative Tax Advantage of Debt =Special Cases:1. TPE = TP, RTAD = MM’s original2. (1 - TP) = (1 - TPE) * (1 - Tc)RTAD = 1.0Debt policy is irrelevant!This case happen when Tc < TP & TPE is small.(1 - TP)(1 - TPE) • (1 - Tc)1(1 - TC)
176Direct: legal fee, court fee, etc. Indirect: difficult to measure Table 18.4SHARE PRICEFRIDAYAPR 10, 1987MONDAYAPR 13, 1987CHANGENUMBER OFSHARES(MILLIONS)IN VALUETexacoPennzoilTotal$31.875$28.50-$3.375242-$ 817-62892.12577.0041.5-$1,445
177Financial Distress without Bankruptcy When firms get into trouble,stockholders’ & bondholders’ interests conflict. reduce value of firmCircular File company (Book Values)Net working capital$ 20Fixed assets80Total assets$100$ 5050Bonds outstandingCommon stockTotal valueCircular File company (Market Values)Net working capital$20Fixed assets10Total assets$30$255Bonds outstandingCommon stockTotal value
178Risk Shift: The First Game (Ex1)C0C1$120(p=10%)-$10$ 0(p=90%)If r=50%,NPV = -10 +1200.1+01.5= -$2Circular File company (Market Values)Net working capital$10Fixed assets18Total assets$28$208Bonds outstandingCommon stockTotal value
181Refusing to contribute equity capital: The second game Good project with NPV= + $5 by investing $10Net working capital$20$33BondsFixed assets2512Common stockTotal assets$45$45Total valueFirm value increase by $15Bond value increase by $8Stock value increase by $7
182Cost 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.
183Trade off Theory of Capital Structure Trade-off between interest tax shield and the costsof financial distressCompany with safe, tangible asset and plenty oftaxable incomeHigh debt ratioUnprofitable company with risky, intangible assetsEquity financeTrade-off theory explains what kinds of companies“go private in LBO”Trade-off theory cannot explain why some mostsuccessful companies thrive with little debt.
18418.4 The Pecking Order of Financing Choice, Information Asymmetry Asymmetric information affects the choicebetween internal and external financing andbetween new issues of debt and equity securitiesPecking order: internal fund, new issue of debt,finally new issue of equity(Exception) Firm with already excessive debt High-tech, high-growth company
185Implication of Pecking Order 1. Firms prefer internal financing2. Firms adopt target payout ratio &try to avoid sudden changes in dividend3. Sticky dividend policy4. If external finance is required,debt, convertible bond, then equityFinancial Slack: Cash, marketable securities, readilysaleable real assets, & ready access to the debt marketor to bank financingMore valuable to firm with plenty of positive-NPVgrowth opportunity
186Interactions of Investment and Financing Decisions Chapter 19
187Introduction So far, all equity financing All financing decisions are irrelevantIn this chapter,we consider capital budgeting decisionwhen investment and financing decision interactand can not be separated
192Invest: $12.5 million$ 7.5 million (Equity)$ million (Debt)Pretax cashflow: $2.085 (perpetual)Tax: 35%After-tax cashflow: $1.355 millionNPV =Return on Investment=
193Return on Equity:NOI2.085-0.4(=0.085)IEarningAfter tax1.685-Tax-0.59(=1.6850.35)1.0951.095Expected return on Equity==0.1467.5E(RE) = rENPV=0
19419.2 Using WACC - Some tricks of the trade Current Assets, Current liabilities,including cash, inventory, including accounts payableand accounts receivable and short-term debtPlant and equipment Long-term debt (D)Preferred stock (P)Growth opportunities Equity (E)Firm value (V)Total capitalization (V)
195Industry Cost of Capital Cost of capital of new subsidiaryCompany’s WACC vs. a weighted-average costof capital of for a portfolio of industryAn Application of the Railroad IndustryAggregate industry capital structure in 1979DebtEquity$24,383 bil$57,651 bil29.7%70.3%rd=7.2%,g=11.5%,D/P= 2.3%,TC = 35%rE =WACC =
196Valuing Companies: WACC vs. Flow-to-Equity Method WACC Debt ratio is expected to be constantCalculate tax as if firm is all equity-financedUsually forecast to a median-time horizon and adda terminal value to the cashflow in the horizon yearDiscount at WACC evaluation of the assets andoperation of the firm
197rE=rA + (rA-rD)(1-TC) Flow-to Equity Method Evaluation of equity Discount the cashflow to equity, after interestand taxes, at the cost of equityLeverage change cost of equity changetwo methods give different answerDErE=rA (rA-rD)(1-TC)
198r 19.3 Adjusting WACC when debt ratios or business risks change Cost of Equity(rE)Rate ofreturnOpportunity cost of capital (r)rWACCCost of Debt(rD)Debt-Equity Ratio
199rD rE r rE rA (Ex) D V D V = 0.4 = 0.2 (rA- rD) Step1: unlevering the WACCCalculate opportunity cost of capitalrDDVrEE+r=* If taxes are left out, WACC equals the r andis independent of leverageStep2: Estimate rD at 20% debt ratio, &Calculate new rErErA(rA- rD)DE+=Step3: Recalculate the WACC at the new financingweight
200r = rE= Step1: current = 0.4 Step2: rd = 8%, when = 0.2 Step3: WACC= D VStep1: current = 0.4r =DVStep2: rd = 8%, when = 0.2rE=Step3:WACC=
201Opportunity cost of capital (r) Rate ofreturn, percent14.6Cost of Equity(rE)1413.0Opportunity cost of capital (r)1211.410.84WACC10Cost of Debt(rD)8.08Debt-Equity Ratio(D/E).25.67(D/V = .2)(D/V = .4)
202Unlevering and Relevering asset = debt ( ) + equity( )- Relevering DEequity = asset + (asset - debt)DEor ( )asset, if debt = “0”*. Underlying assumption: RebalancingMaintain the same market-value debt ratio
20319.4 The Adjusted Present Value Rule Base-NPVNPV = [1.8 / (1.12)t ] = $0.17 milIssue costs.5% of gross proceeds of issueAPV = base NPV - issue cost= .17 mil - 526,000 = -356,000 Reject it!Additions to the Firm’s debt capacityAPV = base NPV + PV tax-shieldt=110
204Table 19-1Calculating the present value of interest tax shields on debt supported bythe solar heater project (dollar figures in thousands)Debt OutstandingInterestPresent ValueYearat Start of YearInterestTax Shieldof Tax Shield1$ 5,000$400$140$129.624,500360126108.034,00032011288.943,5002809872.053,0002408457.262,5002007044.172,0001605632.681,5001204222.791,000802814.01050040146.5Total: $576Assumptions: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 isthat the tax shields are just as risky as the interest payments generating them.
205APV = 170, ,000 = $746,000The 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.
206APV for the Perpetual Crusher project Base case NPV = /0.12 = $1.29 milFinancing Rule 1: Debt fixedFinancing Rule 2: Debt rebalancedUnder rule 1PV (tax shield) = [0.350.08 5] ÷ 0.08 = $1.75 milAPV = = $3.04 milUnder rule 2Debt is rebalanced to 40% of actual project value. debt levels are not known & depend on theproject’s actual performance. cost if capital is 12%PV(tax shield) = (0.35 0.08 5) 0.12 = $1.17 milAPV = = $2.36 mil
207A. Technical Point on Financing Rule 2 Discount at opportunity cost of capitalMultiply the resulting PV by (1+r) anddivide by (1+rD)0.140.12PV(approx) == 1.171.121.08PV(exact) =1.17= 1.21APV = = $2.5 mil
208APV and hurdle RatesAPV tells whether a project makes a net contributionto the value of the firmIt tells break-even cashflowCFrTaxShieldAPV =- Investment+ PVCF0.12TaxShield(Ex)APV =- 10+ PVCF0.12APV =- 10= 0CF = 1.084IRR = 10.84%
209Adjusted Cost of Capital General Definition ofAdjusted Cost of CapitalThe Opportunity Cost of Capital (r)The expected rate of return offered in capital marketsby 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 reflectsthe financing side effects of an investment project
21120.1 Call vs. PutCall: Right to buy underlying asset at a specified pricePut: Right to sell underlying asset at a specified priceAmerican: Exercise anytimeEuropean: Exercise only at an expiration dateExercise DateExercisePricePrice ofCall OptionsPut OptionsOctober 1998January 1999$808085$8.87511.3758.625$3.254.756.875
212(b) (a) (c) Value of Call Value of Put 85 85 85 Share Price Share of Share85SharePrice85(c)
213Selling Calls, Puts, and Shares 8585SharePriceSharePrice-85-85Value of Call Seller’s PositionValue of Put Seller’s Position(a)(a)85SharePrice-85Value of Stock Seller’s Position(c)
214+ = $85 $85 $85 Value of Share Your Payoff Your Payoff Buy Share Sell call+=Future Stock Price$85Future Stock Price$85$85Future Stock Price
215+ = $85 $85 $85 Value of Share Your Payoff Your Payoff Buy Share Buy Put+=$85Future Stock Price$85Future Stock Price$85Future Stock Price
216+ = $85 $85 $85 $85 Value of Share Your Payoff Your Payoff Buy Call Bank deposit paying $85$85+=$85FutureStockPrice$85FutureStockPrice$85FutureStockPrice
217Put - Call Parity C + PV (Ex) = P + S Expiration Date S* EX TodayS* EXS* < EXV1=C+PV(EX)V2=P+S
218The Difference between Safe & Risky Bonds Bond holder: Effectively acquire a firmStock holder: Effectively purchase a call optionon the assets of firm(PB=promised payment to bondholders)Circular File Co. (MV)Asset value$30$25Bond: Asset - Call5Stock: Call$30$30Firm: Asset
219Stockholders’ Position V<50 S = V50 S = VEx= $50(Promised Payment to Bondholders)
220Bondholders’ Position V<50 B = V50 B = VEx= $50(Promised Payment to Bondholders)
221PB: Promised Payment to Bondholders (safe) V : Firm value (asset)S : Stock valueB : Risky bond valueC+ PV(EX) = P + S?S+ PV(PB) = P + VS+ B = VB = V - S = PV(PB) - PValue ofrisklessdebtValue ofrisky debt=-“p”
222Circular File Co. (Market Value) Asset value$30$25Bond value =present value of promisedpayment - value of put5Stock value = asset value - present valueof promised payment +value of put$30$30
223(Ex) Incentive program: Spotting the Option(Ex) Incentive program:Paid bonus of $50,000 for every $ thatprice of stock exceeds $120. Maximumbonus is set at $2 millionPay off120Stock Price$40160
224Buy call with exercise price of $120 and Pay off120160Stock PriceBuy call with exercise price of $120 andSell call with exercise price of $160* Any set of contingent payoffs can be valuedas a mixture of simple options on that assets
22520.3 What determines option values? of callUpper bound:Value of callequals sharepriceBLower bound:Value of callequals payoffif exercisedimmediatelyCAShare PriceExercise price
226Payoff to calloption on firmX’s sharesProbabilitydistribution offuture price offirm X’s sharesPayoff tooption on XPayoff to calloption on firmY’s sharesExercise priceProbabilitydistribution offuture price offirm Y’s sharesPayoff tooption on YExercise price
227Y X Upper bound Lower bound Share Price Exercise price Value of calls on shares offirms X and YUpper boundYLower boundXShare PriceExercise price
228What the price of a call options depends on 1. Increase in variables:If there is anincrease in:The changes in the calloption price are:Stock price (P)Exercise price(EX)Interest rate (rf)Time to expiration(t)Volatility of stock price ()PositiveNegative2. Other properties:a. Upper bound. The option price is less than the stock priceb. Lower bound. The option price never falls below the payoffto immediate exercise (P-EX or zero, whichever is larger)c. If the stock is worthless, the option is worthlessd. As the stock price becomes very large, the option price approachesthe stock price less the present value of the exercise price
230Hedge ratio (Option delta): Number of shares that are needed to replicate on callOptiondeltaSpread of option prices=Spread of share prices=How much to borrow?Present value of the different between the payoff fromthe option and the payoff from the option delta numberof sharesPV(37.78) = $36.86Amount of borrowing
231Buy shares and borrow $36.86 today Option Equivalents:59Buy shares and borrow $36.86 today6 month laterTodayS* = $68S* = $106.2559Buy sharesBorrow $36.36Value of call today= value of shares - $36.86 bank loan=
232Arbitrage Opportunity EX 1: If call is priced at $12 : overpricedStrategy: Sell a call optionBuy 5/9 share & borrow today6 month laterTodayS* = $68S* = $106.25+12-47.22+36.86+ $ 1.64
233EX 2: If call is priced at $9 : underpriced Strategy: Buy a call optionSell 5/9 share of stock short& lend(deposit) $36.86 today6 month laterTodayS* = $68S* = $106.25- 9+47.22-36.86+ $ 1.36
234Pu = probability of stock price increase in the hypothetical Risk-Neutral Valuation: All investors are indifferent about riskExpected Return on any risky assets = rf =E(R) = Pu Ru + Pd Rd85Ru ==68-8585Rd ==E(R) = Pu ( ) + Pd ( ) =where, Pu + Pd = 1Pu = probability of stock priceincrease in the hypotheticalrisk-neutral worldPu =Pd =at t=1E(C1) =at t=0C0 =
235Valuing the Intel Put Option SPEX=$85$68$85$106.25OptiondeltaSpread of option prices=Spread of share prices==shares Intel share &Lend $ How is it computed?
236Value of put = - of share + $46.07 bank loan 6 month laterTodayS* = $68S* = $106.2549Sell sharesLend $46.0749Value of put = of share + $ bank loan=
23720.5 The Black -Scholes Formula Construct a situation where the stock price ischanging continuously and generate a continuumof possible six month pricesReplicate a call option by a leveredinvestment in the stock by adjustingthe degree of leverage continuouslyValue of call = (delta Share price) - (bank loan)[N(d1) P][N(d2) PV(EX)]
238Value of call=[N(d1) P] + [N(d2) PV(EX)] whereLog[P/PV(EX)]td1+=t2d2=d1-tN(d) = cumulative normal probability density functionEX = exercise price of option; PV(EX) is calculatedby discounting at the risk-free interest rate, rft = number of periods to exercise dateP = price of stock now = standard deviation per period of(continuously compounded) rate of return on stock
240Real 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 itsproduction methods
24121.1 The value of follow-on investment Table 21-1Summary of cash flows and financial analysis ofthe Mark I microcomputer(millions of dollars)Year198219831984198519861987After-tax operating-200+110+159+295+185cash flow (1) *Capital Investment (2)250Increase in working50100100-125-125capital (3)Net Cash Flow-450+60+59+195+310+125(1) - (2) - (3)NPV at 20% = - $46.45, or about -$46 million
242Table 21-2. Valuing the option to invest in the Mark II microcomputer. Assumptions1. The decision to invest in the Mark II must be made after3 years, in 1985.2. The Mark II investment is double the scale of the Mark I(note the expected rapid growth of the industry). Investmentrequired is $900 million (the exercise price), which is takenas fixed.3. Forecasted cash inflows of the MarkII are also double thoseof the MarkI, which present value of about $800 million in 1985and 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 deviationof 35 percent per year.(Many high-technology stocks havestandard deviation higher than 35%.)5. The annual interest rate is 10 percent.
243InterpretationThe opportunity to invest in the Mark II is a 3-year call option on asset worth $463 million with a $900 million exercise price.Valuation900PV(EX) == 676(1.1)3Call value = N(d1)P - N(d2) • PV(EX)d1 = log[0.685] / /2 =d2 = d =N(d1) =N(d2) =Call value = 676 = $53.59 mil
24421.2 The Option to AbandonTech ATech BGood Demand$18.5$18Bad Demand8.58If we bail out Tech B for $10 mil when bad demandExercise option to sell assetsValue of Tech B= DCF + Value of the abandonment Put(Value of Flexibility)
245Valuing the Abandonment Put PrPayoffPutGood Demand0.5$ 18Bad Demand0.5$ 8EX = $10, r = 8.3%, rf = 5%PV=E(R) = Pu ( ) + Pd ( ) = = rfPu =Pd =E(P) = 0.46 =1+rfE(P)P ==Value of project =
24621.3 The Timing Option: rf = 5% ProjectValueCashflowValue ofCallGoodDemandIf invest $180,project worth $200$250$25BadDemand$160$16 If undertake project today,capture either $25, or $16 at t=1 If delay, miss out on this cashflow at t=1, butwill have more information on how the projectis lively to work out
25022.1 What is warrant? Value of warrant Actual warrant value prior to expirationTheoretical value (lower limit on warrant value)Stock priceExercise price = $15
251Two Complications: Dividends and Dilution Example: Valuing United Glue’s Warrants………….. Number of shares outstanding (N)1 million$12.10100,000$104 years.4010%…………………….. Current stock price (P) Number of warrants issuedper share outstanding…………..(q)………. Total number of warrants issued (Nq)…………… Exercise price of warrants (EX)…………… Time to expiration of warrants (t) Annual standard deviation ofstock price changes……………() Rate of interest (r):………………………….. United stock pays no dividends.
252United Glue’s market value balance sheet (in $ millions) Before the IssueExisting assets$16$ 4Existing loans12Common stock(1 million sharesat $12 a share)Total$16$16TotalAfter the IssueExisting assets$16$ 4Existing loansNew assets financedby debt and warrants1.5New loan withoutwarrants25.5Total debt.5Warrants12Common stockTotal$18$18Total
253United Glue has just issued a $ 2million package of debt and warrantSuppose$ 1.5 mil: value of debt without warrants$ 0.5 mil: value of warrantsEach warrant costs investors =Value of warrant from Black-Scholes formula=
254Dilution EffectNq =Nq EX =V: value of equityV = Total asset - debtShare price afterexercise=
256$ 12.5 mil: Current equity value of alternative firm (=18 mil mil)Current share priceof alternative firmVN12.5=== $12.51 milSuppose of alternative firm: = 0.41Black-Sholes value of call:11 + qValue of call onalternative firmValue of warrant ==deal for United
25722.2 What is a Convertible Bond Difference between convertible bond vs.bond-warrant packageThe price of convertible bond depends on its bondvalue and its conversion valueBond value:Conversion value:
258Value at Maturity Value of firm ($ million) Bond value, $thousand 12345Value of firm ($ million)Bond value, $thousand12345Value of firm ($ million)Conversion value,$thousandBond paidin fullDefault3ConvertBond paidin full2Value of convertible,$ thousandDefault112345Value of firm ($ million)
259Lower limit on Convertible, Value before Maturity12345Value of firm ($ million)Lower limit on Convertible,$thousandBond ValueConversion Value12345Value of firm ($ million)Bond value, $thousand3Value of convertible2Value of convertible,$ thousandLower limiton value112345Value of firm ($ million)
260Forcing Conversion Value of convertible bond Value of straight bond Call priceBond ValueABCStock priceValue ofconvertiblebondValue ofstraightbondConversionoptionRedemptionoption=+-
26122.3 Difference between Warrants and Convertibles 1. Warrants are usually issued privately2. Warrants can be deleted3. Warrants may be issued on their own4. Warrants are exercised for cash5. A package of bond & warrants may betaxed differentlyWhy do companies issueWarrants and Convertibles?
263Present Value of Bond C (1+r1) C (1+r2)2 C (1+r3)3 (1000+C) PV … = + + (1+rn)nr1 , r2 , r3 , …. rn : discount rates for cashflows to be receivedby 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 differentrate of interestBorrowing rate of government is lower than yourborrowing rate
26423.1 Real and Nominal Rates of Interest Real Rate: compensation for time value of moneyNominal Rate = Real Rate + Perspective Rate of InflationHow Real Rate is determined?Supply of capital: time preference for today’s consumptionover future consumptionDemand of capital: Availability for profitable investmentopportunities ( Positive NPV Projects)
26723.2 Term Structure and Yield to Maturity PV =C1+r1C1+r1C(1+r2)2+PV =r1, r2 : Spot rateThe series of spot rates r1, r2 …Term structure of interest rates
268Yield to MaturityRate of return to bondholders if he/ she keeps the bonduntil maturityC(1+y)C(1+y)2C+FPrice of Bond =++…+(1+y)nPRESENT VALUE CACULATIONS5s of ‘0810s of ‘08PERIODINTEREST RATECtPV AT rtt = 1t = 2t = 3t = 4t = 5r1 = .05r2 = .06r3 = .07r4 = .08r5 = .09Totals$501,050$1,250$44.5040.8136.75682.43$852.11$ 1001001,100$1,500$89.0081.6373.50714.92$1,054.29YIELD TO MATURITYBondPricePercent (IRR)5s of ‘0885.21%8.78%10s of ‘08105.438.62
26923.3 Duration and Volatility Duration: Average time to each payment1 PV(C1)V2 PV(C2)……D =++VPROPORTION OF TOTAL VALUE[PVt/V]PROPORTION OF TOTAL VALUE TIMEYEARCtPV(Ct) AT 5.5%123456137.51137.5130.33123.54117.10110.99105.21824.97.092.087.083.079.075.584.092.175.249.314.3733.505V = 1,412.131.000Duration = years
270vs. (A) 13 ¾s of 2004 (B) 7 ¼s of 2004 DA = 4.708 years DB = years(EX) 1% changes in yield13 ¾s of 20047 ¼s of 2004NEW PRICECHANGENEW PRICECHANGEYield falls, 0.5%144.41+2.26%111.42+2.46%Yield rises, 0.5%138.11- 2.20106.15- 2.39Difference6.304.46%5.27+4.85%Duration1+yieldVolatility (%) VB =VA =
271HedgingBy 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 andArranged to rent it out for $ 2mil a year over eight years at 12%Aztec finances by issuing a packaging of one year and six-yearbond, each with 12% coupon to set up hedged position, find outproportion of one year and six year bond
272Solution = = = = + rental income PV of Duration of Rental income Duration of one year bond=Duration of 6-year bond=Let : x is the proportion raised by 6-year bond1-x is the proportion raised by 1 year bondduration of6-year bondduration of1 year bondDuration Package =x +(1-x) 3.9 years = x years (1-x) 1 years
27323.4 Explaining the Term Structure TopicWhy do we observe different shape of term- structure?Ms. Long: invest $1,000 for 2 years1,000=1,000=Forward RateThe extra return that Ms. Long gets by lending for 2 yearsrather than 1Implicit & guaranteed(1+r2)2 = (1+ r1 ) (1+f2)(1.105)21.1- 1 0.1111% f2 =
274vs. Expected Payoff: L1 Certain Payoff: L2 1,000 (1+r2)2 1,000 (1+r1) [1+E(1r2)]or1,000 (1+ r1 )(1+f2)Strategy L1 gives higher-return ifMr. Short: invest 1 yearBuy 1 year bond:Buy 2 year bond & sell it after 1 yearPV of 2 year bond at year 1 =
275vs. Certain Payoff: S1 Expected Payoff: S2 1,000 (1+r1) or1,000 (1+ r1 )(1+f2)1+E(1r2)Strategy S2 is better if
276Ms.Long and Mr. Short try to maximize their expected The Expectations HypothesisMs.Long and Mr. Short try to maximize their expectedreturnIf f2 > E(1r2) prefer 2yr. bondprice bond of 2yrreturn of 2yr. Bond and f2Equilibrium: f2 = E(1r2)If f2 < E(1r2) prefer 1 yr. bondThe only reason for upward sloping term structure is investor expect the relationship such thatf2 = E(1r2)f2 > r1 , E(1r2) > r1
277The Liquidity Preference (Theory) Consider “risk”Long Case: horizon 2 yr.If Ms. Long buys 1 year bond: first year return is certainbut, uncertain “reinvestment rate” at the end of year 1Ms. Long holds 1 year bond only if E(1r2) f2Short 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) f2Other things equal, Ms. Long will prefer to buy year bond& Mr. Short will prefer to buy year bond
278If 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 theMr. Short to buy 2 year bond.Any bonus shows up as a difference betweenf2 & E(1r1) Liquidity PremiumIn reality, there are shortage of long-term lender,liquidity premium is positive.f2 = E(1r2) + Liquidity Premium ( = LP2)f2 = E(2r3) + LP3
27923.5 Allowing for the risk of Default Q: Why do some borrowers have to pay a higher rateof interest than others?Default risk premiumPromisedyield yother risk premiumExpected yieldRfYield= Rf+ Risk Premium
280(EX) Rf = 9%Payoff (t=1)Probability$ 1,0900.80.2Expected payoff ($) at t=1:If default is totally unrelated to other event of economy,= default risk is wholly diversifiablePV =Promised yield =(expected yield = 9%)Since default occurs in recession, ,say risk premium=2%PV =Promised yield =(expected yield = 11%)
281Bond Ratings “relative quality” of bond by Moody’s Standard & Poor’s STANDARD AND POOR’SAaaAaABaaBaBCaaCaCAAAAAABBBBBBCCCCCCInvestmentgradeJunkbondsPERCENTAGE DEFAULTING WITHINRATING ATTIME OF ISSUE1 YEARAFTER ISSUE5 YEARAFTER ISSUE10 YEARAFTER ISSUEAAAAAABBBBBBCCC.00.03.371.472.28.06.67.221.648.3221.9535.42.06.74.642.8016.3733.0147.46
283A rental agreement that extends for a year or more and involves a series of fixed paymentsWhat to lease?LesseeLessor : Leasing industryEquipment manufacturersBanksIndependent leasing companyOperating LeaseCapital Lease(financial/ full payment)
28425.2 Why lease ? 25.3 Operating lease. Convenient (short-term) Cancellation optionMaintenance providedTax-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. BuyFor financial lease : Lease vs. Borrow
285Calculating the zero-NPV rental rate (or equivalent annual cost Table 25-1Calculating the zero-NPV rental rate (orequivalent annual cost) for EstablishmentIndustries' pearly white stretch limo (figures in thousands of dollars)Year123456Initial cost-75Maintenance, insurance, selling,-12-12-12-12-12-12-12and administrative costsTax Shield on costs+4.2+4.2+4.2+4.2+4.2+4.2+4.2Depreciation tax shield+5.25+8.40+5.04+3.02+3.02+1.51Total-82.80-2.55.60-2.76-4.78-4.78-6.29NPV at 7% = -$98.15Break-even rent (level)26.1826.1826.1826.1826.1826.1826.18Tax-9.16-9.16-9.16-9.16-9.16-9.16-9.16Break-even after tax17.02#17.0217.0217.0217.0217.0217.02NPV at 7% = $98.15* no inflation; r = 7%; Tc = 35%`* Table 6-5: depreciation* First payment: immediate# = 65% of 26.187% PVA 7yrs = 5.3895.389 * 1.07 = 5.766
28625. 4 Financial Lease NPV of 'Lease' relative to 'Buy' 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'Year1234567Cost of new bus+100Lost depreciation taxshield-7.00-11.20-6.72-4.03-4.03-2.02Lease payment-16.9-16.9-16.9-16.9-16.9-16.9-16.9-16.9Tax shield of leasepayment+5.92+5.92+5.92+5.92+5.92+5.92+5.92+5.92Cash flow of lease+89.02-17.99-22.19-17.71-15.02-15.02-13.00-10.98* 5 yr: depreciation (Table 6.4), 7yrs/8 times payment, Tc = 35%, r= 10%D* After tax: r* (1 - Tc) = 6.5%DNPV=+89.02-17.99-22.19-17.71-15.02-15.02-13-10.98lease1.065(1.065)2(1.065)3(1.065)4(1.065)5(1.065)6(1.065)7=-0.7-$700
287Creating Equivalent Loan Year1234567Lease cash flows,+89.02-17.99-22.19-17.71-15.02-15.02-13.00-10.98thousandsTable 25-3: Equivalent loan; exactly same debt service on lease.Year1234567Amount borrowed at89.7277.5660.4246.6434.6621.8910.31year-endInterest paid at 10%-8.97-7.76-6.04-4.66-3.47-2.19-1.03Interest tax shield at 35%+3.14+2.71+2.11+1.63+1.21+.77+.36Interest paid after tax-5.83-5.04-3.93-3.03-2.25-1.42-0.67Principal repaid-12.15-17.14-13.78-11.99-12.76-11.58-10.31Net cash flow ofequivalent loan89.72-17.99-22.19-17.71-15.02-15.02-13.00-10.98How much can I borrow when I pay same cash as lease payment?
288Value of lease to lessor 25.5 When Do Financial Leases Pay?The value of the lease to the bus manufacturer would be(Tc=35%)Value of lease to lessor17.9922.19(1.065)217.71(1.065)315.02(1.065)415.02(1.065)513(1.065)610.98(1.065)7=-89.02+++++++1.065Zero sum game= +.70Suppose that Greymare paid no tax (Tc = 0).Then the only cash flows of the bus lease would be:Year1234567Cost of new bus+100Lease payment-16.9-16.9-16.9-16.9-16.9-16.9-16.9-16.9These flows would be discounted at 10 percent,because rD (1-Tc)= rD when Tc =0t=01016.9Value of lease =100 -== +.82 or $820(1.1)t
289The potential gains to lessor and lessee are higher when: The lessor’s tax rate is substantially higher than the lessee’sThe depreciation tax shield is received early in the leaseperiodThe lease period is long and the lease payments are concentrated toward the end of the periodThe interest rate rD is high - if it were zero, there would be no advantage in present value terms to postponing tax
294Firm BFirm AMarket priceper share$ 200$ 100Number of share1,000,000500,000Market value of firm$ 200 mil$ 50 milCost = Cash - PVB = Cash - MVB + (MVB - PBB)= ( ) = $21 milCash payment depends on the relative bargainingpower of the two participants
295Stock offerN : shares received by sellerPAB: combined firm’s worthCost= N PAB - PVB(Ex)N = 325,000A’s price before merger: $200PVB = $50 milApparent cost =If PVAB = $275mil (due to synergy gain)New share price =Cost = 0.325 =
296Takeover Defense Preoffer Defenses Shark-repellent Charter Amendments Staggered BoardSuper MajorityFair priceDual class stockPoison Pill, Poison putESOPPostoffer DefensesLitigationAsset RestructuringLiability Restructuring
297Divestitures (sell offs) and Spin offs. - Synergy Motivated- Focus- Complementary Resources- More Efficient Contracting(Better Organization Structure)- Raising CapitalQuestion:What is the source of gain and where it is created?