资本结构的计算方法.pptx

CAPITAL STRUCTUREAIMSThe aim of this section of the module is to provide students with an introduction to the theory and practice of firms capital structure decisions.INTENDED LEARNING OUTCOMESOn the successful completion of this section of the module students will be able to:1.Explain the scope and significance of capital structure theory.2.Explain and critically evaluate competing theories of capital structure.3.Evaluate the evidence on,and implications of capital structure theory.TOPIC OUTLINEi.Introductionii.Modigliani-Miller Hypothesisi.Scope&Significanceii.Measuring Gearingiii.Impact of Debt Financingiv.Assumptionsv.Measures of Cost of Capitali.Assumptionsii.Propositionsiii.Rationaleiv.Arbitrage Proofv.Market Imperfectionsvi.Extension-Capital Structure in a CAPM contextiii.Static Trade Off Theoryiv.Other Theoriesv.Evidence&Implicationsi.Impact of Taxationii.Impact of Bankruptcy Costsiii.Option Pricing&Capital Structureiv.Agency Costsi.Tax Exhaustionii.Debt Capacityiii.Controliv.Managerial Preferencesv.Industryvi.Pecking Order Theoryi.Empirical Evidenceii.Implications for Investment AppraisalCAPITAL STRUCTURESCOPECapital structure concerned with the levels of debt and equity financing employed by firms to finance their activities.Two questions:i.What effect does capital structure have on the value of the firm to its owners?ii.What effect does capital structure have on the cost of capital to the firm?SIGNIFICANCEOPTIMUM CAPITAL STRUCTUREIf capital structure affects firm value there may be some optimal capital structure for the firm.INVESTMENT APPRAISAL If capital structure affects the cost of capital then we may have to consider how a project is financed when evaluating it.GEARINGOPERATING GEARINGRefers to the extent to which the firms operating costs are fixed.FINANCIAL GEARINGMeasures the relationship between debt and equity in the firms capital structure.May be measured as:i.Income Gearingii.Capital GearingIMPACT OF DEBT FINANCINGDebt appears cheaper than equity as a source of finance for firms:i.Lower risk for investorsii.Tax advantages iii.Lower transactions costsBut debt is is a riskier source of finance for firms:i.Increases risk of financial distressii.Increases volatility of returns to shareholdersFulthor plc is to be set up with a total capital of 10 million.Expected results for the company depend on trading conditions shown below:Trading ConditionsPoorNormalGoodEBIT(000)6001,5002,400ROCE6%15%24%Three possible financing structures are being considered:i.Gearing 0%(Equity 10 million 1 shares)ii.Gearing 20%(Equity 8 million 1 shares,10%Debt 2 million)iii.Gearing 60%(Equity 4 million 1 shares,10%Debt 6 million)i.Gearing 0%EBIT6001,5002,400 Shareholder Earnings6001,5002,400EPS(pence)61524Return on Equity6%15%24%ii.Gearing 20%EBIT6001,5002,400 Debt Interest200200200Shareholder Earnings4001,3002,200EPS(pence)516.2527.5Return on Equity5%16.25%27.5%iii.Gearing 60%EBIT6001,5002,400Debt Interest600600600Shareholder Earnings09001,800EPS(pence)022.545Return on Equity0%22.5%45%Return on Equity%4560%gearing42393633302720%gearing240%gearing211815129630024681012141618202224 ROCE%ASSUMPTIONS1.The capital structure of the firm is altered by substituting debt for equity and vice versa.2.The firm pays out its entire net income(earnings after interest and taxes)asdividends.3.The net operating income of the firm is not expected to grow.4.The capital structure of the firm comprises equity and perpetual debt only.MEASURES OF COST OF CAPITALCost of equity(ke):E/VeCost of debt(kd):I/VdOverall Cost of Capital(ko):ke(Ve/Vo)+kd(Vd/Vo)=X/VoWhere:E=Net Income=X-II=Debt InterestX=Net Operating Income=E+IVe=Value of EquityVd=Value of DebtVo=Total Value of Firm=Ve+VdTHE CAPITAL STRUCTURE DEBATETwo basic views on capital structure:1.Capital structure has no impact on the overall cost of capital to the firm or its total value.(Modigiani-Miller Hypothesis)2.There is an optimum capital structure for the firm at which its total value is maximised.(Traditional Theory,Static Trade-off Theory)MODIGLIANI-MILLER HYPOTHESISASSUMPTIONS1.Perfect Capital Markets2.Firms can be categorised into equivalent risk classes3.Investors have homogeneous expectations4.No TaxesPROPOSITIONS1.The total value of the firm is independent of its capital structure.2.The cost of equity increases to exactly offset any benefits from increased use of cheaper debt.3.The cut-off rate for investment appraisal is independent of the firms capital structure and therefore of the way in which the project is financed.keCost ofCapital ko kd Leverage(Vd/Ve)Cost of Capital under Modigliani-Miller Hypothesis The cost of equity increases to exactly offset any benefits from increased use of cheaper debt.The cost of equity for a geared firm is given by:Keg=Kou+(kou-kd)(Vd/Ve)Where Kou=Cost of equity of ungeared firm of same risk Kd=Cost of debt in geared firmVd=Value of debt in geared firmVe=Value of equity in geared firm For example assume Ur plc and Gor plc are firms in the same industry with the same risk.Ur is all equity whereas Gor is financed 60%by equity and 40%by debt.The cost of equity to Ur is 12%,the cost of debt to Gor plc is 5%.The cost of equity to Gor plc will be:Ke=.12+(.12-.05)(40/60)=16.67%The overall cost of capital to Gor plc is:Ko=.60(.1667)+.40(.05)=12%VoMarketValue Vd Ve Leverage(Vd/Ve)Value of Firm under Modigliani-Miller HypothesisRATIONALEi.The value of the firm is determined solely by the amount of its net operating income(NOI)and the business risk attached to that NOI.ii.Capital structure affects neither of those factors-all it affects is the distribution of the risk of the NOI between different classes of investor in the firm.iii.Therefore capital structure cannot affect the value of the firm or its overall cost of capital.ARBITRAGE PROOFMM argue that two companies identical in terms of the amount and business risk of their net operating income must have identical total values.If the values differ investors could gain by moving out of the relatively overvalued firm into the relatively undervalued one.This process would drive the values of the two firms together.The following information relates to Ur plc&Gor plc,companies which operate in the same industry.Ur plc Gor plcShare Capital(1 shares)20,000,00020,000,0005%Irredeemable Debt 040,000,000Net Operating Income12,000,00012,000,000Debt Interest02,000,000Net Income12,000,00010,000,000The net operating income of both companies is expected to remain at current levels.Both companies pay out all net income as dividends and are expected to continue doing so.1.Value of Gor Value of Ur Ur GorShare Price 5 4Value of Equity100,000,00080,000,000Value of Debt040,000,000Value of Firm100,000,000120,000,000Bod owns 20,000 shares(i.e 0.1%)in Gor plcIncome:0.001 x 10,000,000=10,000Cost:20,000 x 4=80,000 Bod should sell shares in Gor plc,buy 0.1%(20,000)of the shares in Ur plc and borrow an amount equal to 0.1%of Gor plcs debt i.e 40,000.New IncomeIncome from Ur plc:0.001 x 12,000,000=12,000Less debt interest:0.05 x 40,000=-2,000Net Income:=10,000Cost of InvestmentCost of Shares 20,000 x 5=100,000Less amount borrowed=40,000Net Investment=60,000Bod receives the same income for a lower net outlay.2.Value of Gor Value of Ur Ur GorShare Price 6 3Value of Equity120,000,00060,000,000Value of Debt040,000,000Value of Firm120,000,000100,000,000Bod owns 20,000 shares(i.e 0.1%)in Ur plcIncome:0.001 x 12,000,000=12,000Cost:20,000 x 6=120,000 Bod should sell shares in Ur plc,buy 0.1%(20,000)of the shares in Gor plc and buy 0.1%(40,000)of Gor plcs debt.New IncomeIncome from shares in Gor plc:0.001 x 10,000,000=10,000Plus debt interest:0.05 x 40,000=2,000Total Income:=12,000Cost of InvestmentCost of Shares 20,000 x 3=60,000Cost of Debt=40,000Net Investment=100,000Bod receives the same income for a lower net outlay.In perfect capital markets arbitrage would ensure that the values of two companies identical in all respects except capital structure were equal.But real world markets are not perfect:i.Transaction costs hinder the arbitrage process.ii.Personal&corporate leverage are not perfect substitutes.CAPM&CAPITAL STRUCTURECAPM supports Modigliani-Miller view that capital structure has no impact on the firms cost of capital or total value.The overall cost of capital of the firm depends on the systematic risk of its operations i.e.its asset beta.The systematic risk of a share can be split into:Business Systematic RiskFinancial Systematic RiskThe equity beta of a geared company can be estimated from:e=a+(a d)(Vd/Ve)Where:e=Equity betaa=Asset Betad=Debt BetaVd=Value of DebtVe=Value of EquityFor example Ur&Gor operate in the same industry with the same asset beta(1.4).UrGorAsset Beta1.41.4Value of Equity(million)10060Value of 5%Debt(million)040Assuming a debt beta of zero for Gor plcs debt,the equity betas for the two companies will be Ur e=a=1.4Gor e=1.4+(1.4 0)(40/60)=2.333Assuming the return on the market portfolio is 10%and the risk free rate is 5%the cost of equity and overall cost of capital to the companies is:UrKe=Ko=.05+1.4(.10-.05)=12%GorKo=.05+1.4(.10-.05)=12%Ke=.05+2.333(.10-.05)=16.67%IMPACT OF TAXATIONDebt capital is more favourably treated for tax purposes than equity.A geared company will have a higher after tax net operating income than an ungeared company with an identical pre-tax net operating income.In a world with tax,therefore,MM state:i.The geared firm will have a higher value and lower post tax cost of capital than the ungeared firm.ii.Optimum gearing level is effectively 100%.For example,Ur is all equity financed and Gor is financed by a mixture of equity and debt.The value of Urs equity is 100 million.Gor plcs debt comprises 40 million 5%loan stock quoted at par.The pre tax net operating income for each company is 12 million.The tax rate is 30%Ur plcGor plcPre tax operating income(EBIT)12,00012,000Less Debt interest02,000Pre tax net income12,00010,000Tax at 30%3,6003,000Post tax net income8,4007,000Add debt interest02,000Post tax operating income8,4009,000The market value of the geared company is given by:Vg=Vu+tcVdwhere:Vg=value of geared firmVu=value of identical ungeared firmVd=value of geared firm debttc=corporate tax rateThe value of Gor plc is therefore:Vg=100,000,000+0.3(40,000,000)=112,000,000IMPLICATIONSi.The higher the gearing the greater the value of the firm.ii.The higher the tax rate the greater the value of the firm.iii.The tax savings are valued at the cost of debt.The post-tax cost of equity to the geared firm is given by:Keg=Keu +(Keu Kd)(1 tc)Vd/Vegwhere Keg=cost of equity for geared firmKeu=cost of equity for ungeared firmKd=cost of debt for geared firmVeg=value of equity of geared firmThe post tax cost of equity to Gor is therefore:Keu=8,400/100,000=8.4%Keg=.084+(.084-.05)(1-.3)(40/72)=9.72%The post-tax overall cost of capital to the geared firm is given by:Kog=Keu 1 (tcVd/Vg)whereKog=cost of capital for geared firmKeu=cost of equity for ungeared firmThe overall cost of capital to Gor is therefore:Kog=.0841 (.3)(40/112)=7.5%Cost ofCapitalkeg kogkd Leverage(Vd/Ve)Cost of Capital:Modigliani-Miller with tax Vg(tax)Value ofFirmtax shield Vu Vg(no tax)Leverage(Vd/Ve)Value of Firm:Modigliani-Miller with taxPERSONAL TAXESPersonal taxes may affect the value of the tax shield.Taking account of this the value of the tax shield becomes:1-(1-tc)(1-te)/(1-td)x Vdwhere tc=corporate tax ratete=personal tax rate on equity incometd=personal tax rate on debt incomeFor example using the previous data and assuming personal tax rates of 0%on equity and 20%on debt,the value of Gors tax shield is:1-(1-.3)(1-0)/(1-.2)x 40 million=5 millionThis compares to 12 million ignoring personal taxes.The value of Gor would be 105 million instead of 112 million.IMPACT OF BANKRUPTCY COSTSHigh gearing increases the risk of financial distress and bankruptcy.There are high costs to bankruptcy/financial distress:Direct costs:Administration costsSale of assets at distress pricesIndirect costs:Loss of reputationCost of ko(bankruptcy costs)Capital ko(nobankruptcy costs)Leverage(Vd/Ve)Cost of Capital with bankruptcy costs Cost ofCapital Vo(no bankruptcy costs)bankruptcy costs ko(bankruptcy costs)Leverage(Vd/Ve)Value of firm with bankruptcy costs STATIC TRADE OFF THEORYCombining tax&bankruptcy costs leads to a trade-off theory of capital structure.Value of geared firm becomes:Vg=Vu+tcVd -Bcosts Where:Bcosts=cost of bankruptcy/financial distress.Company should gear up until the marginal tax benefits equal the marginal bankruptcy costs.STATIC TRADE-OFF THEORYCost ofCapital Bankruptcy Costs Tax+Bankruptcy Tax Leverage(Vd/Ve)Cost of Capital:Tax and Bankruptcy Costs STATIC TRADE-OFF THEORY Vo(tax)Vo(tax&bankruptcy costs)Cost of Tax ShieldCapital Vo(notax/bankruptcy costs)Bankruptcy Costs Vo(bankruptcy costs)Leverage(Vd/Ve)Value of firm with Tax&Bankruptcy Costs OPTION PRICING&CAPITAL STRUCTUREEquity shares in a geared company can be viewed as a call option on the underlying assets of the firm.Option Value:Value of equityCurrent Share Price:Value of firms assetsExercise Price:Redemption price of debtVolatility of Share:Volatility of firms assets Expiry date:Redemption date of debtThe value of the shares when the debt matures is given by:Ve=Max(Vf-D),0where Vf=Value of firms assets D=Redemption price of debtThe equity and debt can be valued before the maturity date using the Black-Scholes model.For example,assume Goska plc is financed by a mixture of equity and zero coupon debt repayable at par in 4 years.Current Value of Assets(million)120Face Value of Debt(million)40Time to Maturity(years)4Risk free rate5%Volatility of Assets 30%d1=ln(120/40)+.05+.5(.3)24/.3(4)0.5 =2.4644d2=2.4644-.3(4)0.5 =1.8644Therefore:N(d1)=0.9931;N(d2)=0.9689.The value of the equity is therefore:Ve=120(0.9931)-(40/e0.2)(0.9689)=87.441 millionThe value of the debt is thereforeVd=120-87.441=32.559 millionIf Goska plc increases the volatility of its assets from 30%to 70%:d1=ln(120/40)+.05+.5(.7)24/.7(4)0.5 =1.6276d2=1.6276-.7(4)0.5 =0.2276Therefore:N(d1)=0.9482;N(d2)=0.5901The value of the equity is therefore:Ve=120(0.9482)-(40/e0.2)(0.5901)=94.459 millionThe value of the debt is thereforeVd=120-94.459=25.541 millionThus by increasing the firms volatility shareholders can increase their wealth at the expense of the debtholders.Assume Goska plc increases gearing by issuing a further 40 million zero coupon debt repayable in 4 years and repurchases some equity:d1=ln(120/80)+.05+.5(.3)24/.3(4)0.5=1.3091d2=1.3091-.3(4)0.5 =0.7091Therefore:N(d1)=0.9047;N(d2)=0.7608The value of the equity is therefore:Ve=120(0.9047)-(80/e0.2)(0.7608)=58.733 millionThe value of the debt is thereforeVd=120-58.733=61.267 millionThe new debt has identical rights to the old debt thereforeValue of new debt:61.267(40/80)=30.6335 million Value of old debt:61.267(40/80)=30.6335 million The value of the old debt has fallen by 1.9255 million.The shareholders wealth will be:Value of shares58.733Proceeds of debt