专业课西南财大金融经济学lecture3costofcapital.pptx

WACC2WACCUnder the assumptions of MM,If the company undertakes a new investment project with same risk as the rest of the company,the change in value is:3WACCThe new investment is financed with debt or equity or bothThe change in value can also be seen from the liability side:4WACCIf DBo=0,and using the fact that DI=DSn+DBnThe project adds value for the shareholders if5WACCUsing(*)in(*):If we assume that there is a target capital structure and therefore that DB/DI=D/(D+E),the termis the WACC6Derivation:7WACC lessonsNotice that the standard WACC is a by product of MM,and therefore is relies on the same assumptionsNotice also there is something intrinsically contradictory in the way it is often applied:You start assuming a constant debt levelThen you assume a target debt ratioWhen the debt ratio is assumed constant,the WACC formula ought to be different8Miles-Ezzel WACC:dynamic debtIf we assume the debt ratio is constant,the WACC formula isAnd the formula for relevering betas is9Cost of equity:CAPMThe discount rate for risky investments(expected return)covers:The time value of moneyA risk premiumE(ri)=rf+bi(E(rm)-rf)This is the most used method to calculate costs of equityAlternativeAPT(see book for details if interested)10Alternative:Dividend Growth ModelGordons growth model:Thus:11Applying it:Need dividend yield and growth rate:use analysts forecastsuse the plowback ratio formula:g=b x ROE,where b is the retention ratioNote:this g is the so-called sustainable growth rate 12PitfallsThe d-growth model makes a number of assumptions:constant growth rateconstant dividend yield The validity of the model depends on the validity of these assumptions13Cost of DebtThe rate of return that debt-holders demand to hold the debtRemember:it is the expected return and not the promised oneFor high-rated bonds,promised is probably a good proxy14Discount Rate for DebtIn practice:Rate on new or recent borrowingsYield on comparable bondsBoth are measures of promised yieldExpected return depends on:Probability of defaultExposure at defaultLoss given defaultExpected loss on a loan is:PD x EAD x LGDThese are the terms used by Basel II15Discount Rate for DebtSame logic can be used to calculate expected returnsAssuming EAD=1:rD=(1 PD)x i+PD x LGDE.g.interest(i)is 14%,PD is 4%,recovery rate is 60%.Then,cost of debt is:rD=0.96 x 14%+0.04 x 40%=11.84%16Discount rate for debtAlternative ways:CAPM:if there is little debt,assume bD=0if debt is risky,use proxies based on empirical research:TypeBeta1-5 years.086-10 years.13Government BondsTypeBetaAaa.20Aa.20A.21Baa.23Lower Grade.31Corporate Bonds17ExampleCompany XYZ wants to issue a 30-year bond,coupon 5%No bonds outstanding,credit risk similar to General Tool CompanyThe latter issued last year a 31-year bond,coupon 6.0%,selling today at 97%3-month T-bills pay 5%a yearWhich discount rate should be used?18Example1.Direct comparison:19Example2.CAPM:A bond:Beta of an A-bond is 0.21Using CAPM,and a market premium of 6%:E(rD)=5.0%+.21 x 6%=6.26%Capital budgeting21Capital BudgetingThe CB problem amounts to deciding which projects a firm should undertakeNPV is the most sound rule for CBA project should be undertaken if NPV 0To implement NPV one needs:cash flow estimatescost of capital estimate22A fresh look at NPVNPV=PV investmentPV=value of a tracking portfolio that replicates the projects payoffsNPV 0 same payoffs can be obtained in a cheaper way in the(financial)marketsThus positive NPV projects are“arbitrage opportunities”Q:Why do they not disappear immediately?23Risk-free project:NPVMonth0612Project-200100120T-Bill-97100T-Bond-90100Replicating portfolio(NPV)T Bill1T Bond1.2Payoff rep.portf.10012024Risk-free project:NPV(cont)The NPV is thus the difference,the arbitrage opportunity=90 x 1.2+97CostsRepl.Port.-205Project-200Projects NPV525Risk-free project:DCF3.09%(11.11%)is the yield on the 6-month(12-month)T Bill:=120/1.1111=100/1.0309DCFDiscount rates3.09%11.11%PV cash flows-20097108NPV526Risky ProjectsThe underlying principles are the same Replicating portfolioDiscount rates(now risk-adjusted)27CAPMRewriting the CAPM formula we get:E(ri)=rf+bi(E(rm)-rf)=rf(1 bi)+bi E(rm)ie the expected return on the project equals the expected return on a portfolio consisting of:A fraction b of the investment in the market portfolio1 b in the risk-free assetwhich is the tracking portfolio for the investment.28Discount Rate for a ProjectIn theory,a projects discount rate:reflects the expected return investors require to hold financial assets(those in the replicating portfolio)whose cash flows are thus in the same risk class as the projectsApplying this principle:Estimate a beta for the projectUse CAPM to estimate the cost of capital29DR for a project(c)Normally there is no history to estimate beta(the project is yet to be undertaken)Way out:use the beta of a firm in the same line of business as the project30Betas and leverageBeta is a measure of risk,that reflects two types of it:Operational(asset)riskFinancial riskWe dont want the second one(which is firm-specific)We need an“asset beta”of the beta of the firms assetsWe need the formulas mentioned earlier to go from one to the other31ExampleMarriot identified 3 comparable firms for its restaurant division:Estimate the unlevered cost of capital for the restaurant division,assuming:rf=4%,MP=5%,Tc=34%,comparables debt is risk-free,and debt is a constant known amountFirmEq.BetaDEChurchs Chiken.75.004.096McDonalds1.002.37.70Wendys1.08.210.79032Answer33Marriots OAs beta is thenWe can average those three,to getAnd its cost of capital(unlevered):34Cash flows(Free)cash flow is:EBIT-Taxes on EBIT(=NOPLAT)+Depreciation-Changes in working capital-Capital Expenditures35Interest?We do not subtract interest because it is a financing cash flow:depends on the way the project is financednot on the projects assets themselves36Example:evaluate this projectCost of a new plant=1,000New Sales(per year)=50Save 100 in year expensesOperating costs=10/yearOld plant fully depreciated,salvage value=50 after taxNew plants salvage value=200 after 10 years;linear depreciationTaxes=34%,discount rate 10%37Cash FlowsNPV(10%)=-235.538APV approachA project can have three sources of value to the shareholders:NPV of the free cash flow from the real assetsNPV of subsidies etcNPV of financing effects39APV(b)APV decomposes the value in two parts:1.NPV assuming all equity financing2.PV of benefits and costs of debtDiscount rates:1.DR for unlevered assets2.DR for the firms debt,e.g.:rD=rf+bD MPThen:APV=NPV+B(D)-C(D)where D is the optimal debt level40ExampleInvestment=100FCF=20/year(for 10 years)beta(OA)=1rf=5%the firm can borrow 80m on the assetrD=8%No costs of financial distressTax=30%41AnswerNPV(13%)=8.52Yearly interest=.08 x 80=6.4Yearly tax shield=.30 x 6.4=1.92If the spread over the risk-free rate reflects the default risk,there is some probability the firm will default(and not enjoy the tax shield).Say that prob is 25%Then:expected yearly tax shield=.75 x 1.92=1.4442AnswerDiscount rate=cost of debt=8%PVTS=9.6APV=NPV+B(D)=8.52+9.6=18.1243Assessing APVMain problem:How to estimate the optimal capital structureMore in general,how to estimate D,C(D)and B(D)However,a capital structure must be chosen anywayUsing APV forces you to think about CS beforehand44WACC approachThe wacc approach incorporates the tax shield into the discount rateIt is the most popular method because it is simpler,not necessarily better!Downside:it is less flexible than APVCaution:use the firms beta only if the project is in the same risk class;otherwise find a projects beta45WACC or APV?Given that they are not equivalent the choice is relevantUsing WACC because it is easier is obviously a wrong argumentCriterion:known debt level or known(or target)D/E ratioother effects of debt are important(like subsidised debt)use APV46PracticeCalculate your companys cost of capitalUse Thomson One Banker to get betasRf:newspapersMarket risk premium,5%(unless you want to research yourself)Take all forms of financing into accountUse market values!Use comparable companies(see Marriot example)