资本结构和MM定理.pptx

第七章 资本结构和MM定理MM定理及扩展资本结构的经验证据 MM定理及扩展无税的MM定理（1958）有公司税的MM定理trade-off Theory（权衡理论）等加入个人税的MM定理（米勒定理1977）MM定理的其他用途The Capital-Structure Questionand The Pie TheoryThe value of a firm is defined to be the sum of the value of the firms debt and the firms equity.V=B+SIf the goal of the management of the firm is to make the firm as valuable as possible,the the firm should pick the debt-equity ratio that makes the pie as big as possible.Value of the FirmS BS BS BS BFinancial Leverage and EPS(2.00)0.002.004.006.008.0010.0012.001,0002,0003,000EPSDebtNo DebtBreak-even point EBIT in dollars,no taxesAdvantage to debtDisadvantage to debt杠杆增加了权益收益（return on equity,ROE）以及股票持有者的收益，然而也增加了股票风险MM定理认为，两方面的效应恰好抵消无税的MM定理Assumptions of the Modigliani-Miller ModelHomogeneous ExpectationsHomogeneous Business Risk ClassesPerpetual Cash FlowsPerfect Capital Markets:Perfect competitionFirms and investors can borrow/lend at the same rateEqual access to all relevant informationNo transaction costsNo taxesThe MM Propositions I&II(No Taxes)Proposition IFirm value is not affected by leverageVL=VUProposition IILeverage increases the risk and return to stockholdersrs=r0+(B/SL)(r0-rB)rB is the interest rate(cost of debt)rs is the return on(levered)equity(cost of equity)r0 is the return on unlevered equity(cost of capital)B is the value of debtSL is the value of levered equityThe MM Proposition I(No Taxes)ULVV=BrEBITB-receive firm levered ain rsShareholdeBrBreceive sBondholderThe derivation is straightforward:BrBrEBITBB+-)(is rsstakeholde all toflowcash total theThus,The present value of this stream of cash flows is VL EBITBrBrEBITBB=+-)(ClearlyThe present value of this stream of cash flows is VU The MM Proposition II(No Taxes)The derivation is straightforward:SBWACCrSBSrSBBr.+.+=0set Then rrWACC=0rrSBSrSBBSB=.+.+SSB+by sidesboth multiply 0rSSBrSBSSSBrSBBSSBSB+=.+.+.+.+0rSSBrrSBSB+=+.00rrSBrrSBSB+=+.)(00BSrrSBrr-+=杠杆率上升时，公司更多进行“低成本”的债务融资，然而其股本风险和成本也随之增大，根据MM，两项效应恰好抵消。不考虑税收，资本结构的改变不影响加权资本成本（WACC）WACC仅为资产的风险决定 The Cost of Equity,the Cost of Debt,and WACC:MM Proposition II with No Corporate TaxesDebt-to-equity RatioCost of capital:r(%)r0rBrBSB有公司税的MM定理The MM Propositions I&II(with Corporate Taxes)Proposition I(with Corporate Taxes)Firm value increases with leverageVL=VU+TC BProposition II(with Corporate Taxes)Some of the increase in equity risk and return is offset by interest tax shieldrS=r0+(B/S)(1-TC)(r0-rB)rB is the interest rate(cost of debt)rS is the return on equity(cost of equity)r0 is the return on unlevered equity(cost of capital)B is the value of debtS is the value of levered equityThe MM Proposition I(Corp.Taxes)BTVVCUL+=)1()(receive firm levered ain rsShareholdeCBTBrEBIT-.-BrBreceive sBondholderBrTBrEBITBCB+-.-)1()(is rsstakeholde all toflowcash total theThus,The present value of this stream of cash flows is VL =+-.-BrTBrEBITBCB)1()(Clearly The present value of the first term is VU The present value of the second term is TCB BrTBrTEBITBCBC+-.-.=)1()1(BrBTrBrTEBITBCBBC+-.=)1(The MM Proposition II(Corp.Taxes)Start with M&M Proposition I with taxes:)()1(00BCSrrTSBrr-.-.+=BTVVCUL+=Since BSVL+=The cash flows from each side of the balance sheet must equal:BCUBSBrTrVBrSr+=+0BrTrTBSBrSrBCCBS+-+=+0)1(Divide both sides by SBCCBSrTSBrTSBrSBr+-+=+0)1(1 BTVBSCU+=+)1(CUTBSV-+=Which quickly reduces toThe Effect of Financial Leverage on the Cost of Debt and Equity Capital with Corporate TaxesDebt-to-equityratio(B/S)Cost of capital:r(%)r0rBTotal Cash Flow to Investors Under Each Capital Structure with Corp.TaxesAll-EquityRecessionExpectedExpansionEBIT$1,000$2,000$3,000Interest000EBT$1,000$2,000$3,000Taxes(Tc=35%$350$700$1,050Total Cash Flow to S/H$650$1,300$1,950LeveredRecessionExpectedExpansionEBIT$1,000$2,000$3,000Interest($800 8%)640640640EBT$360$1,360$2,360Taxes(Tc=35%)$126$476$826Total Cash Flow$234+640$468+$640$1,534+$640(to both S/H&B/H):$874$1,524$2,174EBIT(1-Tc)+TCrBB$650+$224$1,300+$224$1,950+$224$874$1,524$2,174Total Cash Flow to Investors Under Each Capital Structure with Corp.TaxesThe levered firm pays less in taxes than does the all-equity firm.Thus,the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm.SGSGB All-equity firm Levered firmTotal Cash Flow to Investors Under Each Capital Structure with Corp.TaxesThe sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm.This is how cutting the pie differently can make the pie larger:the government takes a smaller slice of the pie!SGSGB All-equity firm Levered firm权衡理论trade-off TheoryIntegration of Tax Effects and Financial Distress CostsM&M suggest that financial leverage does not matter,or imply that taxes cause the optimal financial structure to be 100%debt.In the real world,most executives do not like a capital structure of 100%debt because that is a state known as“bankruptcy”.There is a trade-off between the tax advantage of debt and the costs of financial distress.It is difficult to express this with a precise and rigorous formula.Integration of Tax Effectsand Financial Distress CostsDebt(B)Value of firm(V)0Present value of taxshield on debtPresent value offinancial distress costsValue of firm underMM with corporatetaxes and debtVL=VU +TCBV=Actual value of firmVU=Value of firm with no debtB*Maximumfirm valueOptimal amount of debtThe Pie Model RevisitedTaxes and bankruptcy costs can be viewed as just another claim on the cash flows of the firm.Let G and L stand for payments to the government and bankruptcy lawyers,respectively.VT=S+B+G+LThe essence of the M&M intuition is that VT depends on the cash flow of the firm;capital structure just slices the pie.SGBL其他相关理论信号理论代理成本理论融资次序理论动态权衡理论SignalingThe firms capital structure is optimized where the marginal subsidy to debt equals the marginal cost.Investors view debt as a signal of firm value.Firms with low anticipated profits will take on a low level of debt.Firms with high anticipated profits will take on high levels of debt.A manager that takes on more debt than is optimal in order to fool investors will pay the cost in the long run.Shirking,Perquisites,and Bad Investments:The Agency Cost of EquityAn individual will work harder for a firm if he is one of the owners than if he is one of the“hired help”.Who bears the burden of these agency costs?While managers may have motive to partake in perquisites,they also need opportunity.Free cash flow provides this opportunity.The free cash flow hypothesis says that an increase in dividends should benefit the stockholders by reducing the ability of managers to pursue wasteful activities.The free cash flow hypothesis also argues that an increase in debt will reduce the ability of managers to pursue wasteful activities more effectively than dividend increases.The Pecking-Order TheoryTheory stating that firms prefer to issue debt rather than equity if internal finance is insufficient.Rule 1Use internal financing first.Rule 2Issue debt next,equity last.The pecking-order Theory is at odds with the trade-off theory:There is no target D/E ratio.Profitable firms use less debt.Companies like financial slackGrowth and the Debt-Equity RatioGrowth implies significant equity financing,even in a world with low bankruptcy costs.Thus,high-growth firms will have lower debt ratios than low-growth firms.Growth is an essential feature of the real world;as a result,100%debt financing is sub-optimal.加入个人税的MM定理米勒定理，The Miller Model The Miller Model shows that the value of a levered firm can be expressed in terms of an unlevered firm as:BTTTVVBSCUL.-.-+=1)1()1(1Where:TS=personal tax rate on equity incomeTB=personal tax rate on bond incomeTC=corporate tax ratePersonal Taxes:The Miller ModelThe derivation is straightforward:)1()1()(receive firm levered ain rsShareholdeSCBTTBrEBIT-.-.-)1(receive sBondholderBBTBr-.)1()1()1()(is rsstakeholde all toflowcash total theThus,BBSCBTBrTTBrEBIT-.+-.-.-.-.-.+-.-.BSCBBSCTTTTBrTTEBIT1)1()1(1)1()1()1(asrewritten becan This Personal Taxes:The Miller Model(cont.)-.-.-.+-.-.BSCBBSCTTTTBrTTEBIT1)1()1(1)1()1()1(The first term is the cash flow of an unlevered firm after all taxes.Its value=VU.A bond is worth B.It promises to pay rBB(1-TB)after taxes.Thus the value of the second term is:The total cash flow to all stakeholders in the levered firm is:The value of the sum of these two terms must be VLBTTTVVBSCUL.-.-+=1)1()1(1Personal Taxes:The Miller Model(cont.)Thus the Miller Model shows that the value of a levered firm can be expressed in terms of an unlevered firm as:In the case where TB=TS,we return to M&M with only corporate tax:BTTTVVBSCUL.-.-+=1)1()1(1BTVVCUL+=Effect of Financial Leverage on Firm Value with Both Corporate and Personal TaxesDebt(B)Value of firm(V)VUVL=VU+TCB when TS=TBVL VU+TCBwhen TS (1-TC)(1-TS)VL=VU when(1-TB)=(1-TC)(1-TS)VL VU when(1-TB)(1-TC)(1-TS)BTTTVVBSCUL.-.-+=1)1()1(1Integration of Personal and Corporate Tax Effects and Financial Distress Costs and Agency CostsDebt(B)Value of firm(V)0Present value of taxshield on debtPresent value offinancial distress costsValue of firm underMM with corporatetaxes and debtVL=VU +TCBV=Actual value of firmVU=Value of firm with no debtB*Maximumfirm valueOptimal amount of debtVL VU+TCBwhen TS (1-TC)(1-TS)Agency Cost of EquityAgency Cost of DebtMM定理的延伸远期负债相对短期负债是无关重要股息政策是无关重要风险管理是无关重要资本结构的实证问题Costs of Financial Distress1.Direct costs of bankruptcythe legal costs involved in invoking bankruptcy and liquidating the firm2.Indirect costs of bankruptcyImpaired ability to conduct business3.Agency costs of financial distressEvidence on Direct Bankruptcy CostsWarner(1977,Journal of Finance,pp.337-347)reported legal and administrative costs for 11 railroad bankruptcies.The reason railroad bankruptcies are of particular interest is that they are notoriously complicated.There are railroad cases where the time in bankruptcy court exceeded 20 years.On average,Warner found the direct costs were$2M.On average,this was 5.3%of the overall market value of the railroads debt and equity estimated just before bankruptcy.The costs decline to 1.4%of overall market value estimated 5 years prior to bankruptcy when the railroads were in better health.These magnitudes are small relative to the tax advantage of debt.最优资本结构实证权衡理论下的实证权衡理论的代表人物包括Robichek,1967)、Mayers,1984、Kraus,1973、Rubinmstein,1973、Scott,1976等 动态权衡理论的实证Jensen和Mecking关于债权代理成本与股权代理成本权衡问题：最有外部负债与股权的组合使得代理成本最小化。在这种情况下，即使不存在税收或者破产成本，也可能存在最有资本结构。行业效应、时间序列研究等，见金融理论与公司政策一书15.9节。资本结构的实践Ezra Solomon（1977）：行业之间有显著差异的资本结构，但同行业间有稳定的资本结构