1、1Corporate Finance(Econ 906)Lecture Capital StructureRead:Hillier,Grinblatt&Titman Chapters 14-17Copeland/Weston Chapter 15Brealey and Myers Chapter 16-19Modigliani and Miller,“The Cost of Capital,Corporation Finance,and the Theory of Investment,American Economic Review,1958,pp 261-97.Myers,Stewart
2、C.,The Capital Structure Puzzle,Journal of Finance,1984,pp 575-92 2Capital Structure The Capital-Structure Question and The Pie Theory Maximizing Firm Value versus Maximizing Stockholder Wealth Financial Leverage and Firm Value Modigliani and Miller:Proposition I and II-with no taxes and taxes 3MM I
3、rrelevance Arguments-Intuition The total market value of a firm(debt plus equity)equals the PV of its cash flow stream.Capital structure determines only the division of the pie(firm value)among different claim holders but not the size of the pie.4Assumptions of the Modigliani-Miller(MM)Model Homogen
4、eous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows Perfect Capital Markets:Perfect competition Firms and investors can borrow/lend at the same rate Equal access to all relevant information No transaction costs,no cost of bankruptcy No taxes5Arbitrage S u p p o s e t w o i d e n
5、 t i c a l s e c u r i t i e s (w i t h t h e s a m e e x p e c t e d r e t u r n a n d r i s k c h a r a c t e r i s t i c s)t r a d e a t different market prices.T h e n t h e r e w o u l d b e a n a r b i t r a g e o p p o r t u n i t y:intelligent arbitrageurs would seek to buy the cheaper secur
6、ity a n d s e l l (s h o r t)t h e m o r e expensive one.Trading by arbitrageurs bids up the price of the cheaper security and depresses the price of the more expensive one.6ArbitrageAll arbitrage opportunities are e x p l o i t e d,w h e n t h e t w o securities trade at the same price.Arbitrage pr
7、icing arguments a s s u m e t h a t a l l a r b i t r a g e opportunities are exploited(almost)instantaneously and that the market prices of financial securities are such that there are no arbitrage opportunities.7MMs Arbitrage Pricing Argument:Consider two firms in the same risk class,one all-equit
8、y financed(u n l e v e r e d ),t h e o t h e r levered with both debt(D)and equity(E).Investment 1:buy 10%of unlevered firm.Initial Cost of Investment (0.1)VuExpected Return(0.1)NOI 8MMs Arbitrage Pricing Argument:Investment 2:buy 10%of equity plus 10%of debt of levered firm.Initial Cost of Investme
9、nt Expected ReturnDebt:(0.1)D (0.1)rdDEquity:(0.1)E(0.1)(NOI-rdD)Total:(0.1)(D+E)=(0.1)VL(Initial cost)(0.1)rdD+(0.1)(NOI-rdD)=(0.1)NOI(Expected Return)9MMs Arbitrage Pricing Argument:Since both investments have the same expected return:(0.1)NOI,they must have the same initial cost,i.e.same value V,
10、so that no arbitrage opportunities remain to be exploited MM Proposition 1:Vu=VL=D+E.10The MM Propositions I&II(No Taxes)Proposition I Firm value is not affected by leverage VL=VU Proposition II Leverage increases the risk and return to stockholders rL=rU+(D/EL)(rU-rD)rD is the interest rate(cost of
11、 debt)rL is the return on(levered)equity(cost of equity)rU is the return on unlevered equity(cost of capital)D is the value of debt EL is the value of levered equity11The MM Propositions I&II(with Corporate Taxes)Proposition I(with Corporate Taxes)Firm value increases with leverage VL=VU+TC D Propos
12、ition II(with Corporate Taxes)Some of the increase in equity risk and return is offset by interest tax shield rE=rU+(D/EL)(1-TC)(rU-rD)rD is the interest rate(cost of debt)rE is the return on equity(cost of equity)rU is the return on unlevered equity(cost of capital)D is the value of debt EL is the
13、value of levered equity12Firm Value with Taxes(Recap.)Assume no growthVU=PV of unlevered firm E(FCF)=perpetual free cash flow after taxes=discount rate)(FCFEVU13Firm Value with TaxesNOI=Rev VC FC-DepAfter tax cash flow:NOI Tc(NOI)=(Rev VC FC-Dep)(1-Tc)Note:Depreciation is a noncash-fixed cost.Hence,
14、Cash Flow=(Rev VC FC-Dep)(1-Tc)+DepFree cash flow=(Rev VC FC-Dep)(1-Tc)+Dep I=(Rev VC FC Dep)(1-Tc).Dep=I 14Firm Value with TaxesHence,when cash flows are assumed to be perpetuities:FCF=NOI(1-Tc)FCF and discount rate(WACC)used to determine firm value.Perpetual FCF case:)(FCFEVU)1)(CUTNOIEV15Firm Val
15、ue with TaxesAssume firm issues debt:Share holders receive net cash flows after interest,taxes,and replacement investment(NOI+dep-I)Bondholders receive interest on debt(kdD)Total payment=NOI+Dep I+kdD=(Rev VC FC Dep-kdD)(1-Tc)+Dep I+kdDDep=INI+kdD=(Rev VC FC Dep)(1-Tc)-kdD+kdD Tc+kdD =NOI(1-Tc)+kdD
16、Tc 16Firm Value with TaxesWhereKb=before-tax cost of risk-free debt=Discount rate(for same risk)bCdCLkDTkTNOIEV)1)(17Firm Value with TaxesB=market value of bond=KdD/kbTherefore,Tax shield(gain from leverage)BTVVCUL18Leverage and Returns19WACC WACC is the traditional view of capital structure,risk an
17、d return.20WACC Example-A firm has 2m of debt and 100,000 of outstanding shares at 30 each.If they can borrow at 8%and the stockholders require 15%return what is the firms WACC?D=2mE=100,000 shares X 30 per share=3mV=D+E=2+3=5m21rEWACCrDDVWACC(traditional view)r22WACC(M&M view)DVrDWACCrEr23WACC-Impl
18、ications:1.If corporate tax rate is zero,the cost of capital is independent of the ratio of debt to total assets(capital structure)2.If corporate taxes are paid,the c o s t o f c a p i t a l d e c l i n e s steadily as the proportion of new investment financed by debt increases(100%debt financing is
19、 good if debt is risk free)3.资本成本会随着资本成本会随着 因为债务增加而上升的新投资融资百分比逐渐下降因为债务增加而上升的新投资融资百分比逐渐下降24Cost of Equity The opportunity cost of capital to shareholders increases linearly with changes in the market value ratio of debt to equity 随着随着权益市场价值的比例变化，给股东的资本的机会成本呈线性增加If the firm has no debt in its capital
20、structure,the cost of capital is equal to the cost of equity for an all-equity firm,.如果公司的资本结构中没有债券，那么资本成本等于一个全部投资股权的公司的权益成本如果公司的资本结构中没有债券，那么资本成本等于一个全部投资股权的公司的权益成本SBkTkbCs)(1(25Common Definition of WACCSBSkSBBkTWACCsbC)1(26RISK,M-M and the CAPMCAPM:=the expected rate of return on asset jRf=the(const
21、ant)risk-free rate=the expected rate of return on the market portfolioj=COV(Rj,Rm)/VAR(Rm)jfmfjRRERRE)()()(jRE)(jRE27Estimating Systematic Risk for an Unlevered Equity(U)无杠杆股票的系统性风险无杠杆股票的系统性风险 Cost of unlevered equity depends on the systematic risk of the firms after-tax operating cash flows无杠杆股票的成本
22、取决于无杠杆股票的成本取决于 公司的税后营业性现金流的系统性风险公司的税后营业性现金流的系统性风险Unlevered beta is not directly observable 无杠杆无杠杆是不能直接观察的是不能直接观察的 Assume relationship between the two betas by equating the M-M and CAPM definitions of the cost of levered equity:SBTkRRERCbLfmf)1)()(28Estimating Systematic Risk for an Unlevered Equity(
23、U)Cntd.Assume kb=RfReplace by the CAPM defn.for unlevered equity:SBTRRRERCfLfmf)1)()(UfmfRRER)(UCLSBT)1(129Estimating Systematic Risk for an Unlevered Equity(U)Cntd.The levered beta can be obtained from the returns series observed on stock market Using the functional relationship presented on pp 28,
24、the systematic risk of unlevered equity is calculated30Effect of Risky Debt On Firm Value(Without Bankruptcy Costs)M M Given complete and perfect capital markets,change in capital structure does not make difference to the total value of a firm在完美资金在完美资金市场市场 资本结构的变化并不影响公司总价值资本结构的变化并不影响公司总价值 Hence,so
25、long as bankruptcy costs破产成本破产成本(such as payments to trustees and law firms)are not incurred,risky debt危险债务危险债务 also does not affect the value of the firm Value of firm equals to the sum of discounted cash flows from investment VL=VU+TCB31Personal Taxes and Capital Structure Preferences Tax-exempt i
26、nvestor 免税投资者免税投资者is indifferent regarding 不关心不关心the mode of cash inflows such as:interest on debt,dividends on equity股息股息,and capital gains on equity as long as the amounts received are the same.Tax-exempt investors will prefer firms to have high gearing传动装置？传动装置？since gearing increases the value o
27、f the firm and thereby their share too.On the other hand,investors who pay personal taxes prefer capital gains 资本收益资本收益(less leverage):Deferral option for capital gains延迟期权的资本收益延迟期权的资本收益 TE(tax on equity income)rDD.interest payment(X-rDD)Tc is the corporate tax企业税企业税(X-rDD)(1-Tc)amount due to equity
28、 holders before personal tax税前应付股东个人所得税前应付股东个人所得(X-rDD)(1-Tc)TE personal taxes on equity income个个人股票所得税人股票所得税(X-rDD)(1-Tc)(1-TE)after taxes cash flow to equity holders股权持有人税后利润股权持有人税后利润 rDD(1-TD)after tax cash flow to debt holders债权债权人税后利润人税后利润34Personal Taxes and Debt and Equity Rates of Returns Le
29、t C=total after-tax cash flow stream flowing to debt and equity holders Let X=EBIT C=(X-rDD)(1-Tc)(1-TE)+rDD(1-TD)=X(1-Tc)(1-TE)+rDD(1-TD)-(1-Tc)(1-TE)The RHS term represents the tax gain税后收益税后收益 from leverage Assuming the level of debt债务水平债务水平 is permanently fixed永久固定永久固定,the gain from leverage can
30、 be valued by discounting the perpetuity payments at the after-(personal)tax rate of debt,rD(1-TD)or equivalently at the after-(personal)tax rate of equity,rE(1-TE).35Personal Taxes and Debt and Equity Rates of ReturnsrDD(1-TD)-(1-Tc)(1-TE)/rD(1-TD)=TgDWhere:Hence:If Tg 0 Firms issue enough debt to
31、eliminate their tax liability消除应纳税额消除应纳税额If Tg 0 Firms include no debt in their capital structureIf Tg=0 Firms will be indifferent about their debt level,i.e.(1-TD)=(1-Tc)(1-TE)DECgTTTT1)1)(1(136Financial Leverage and Financial Distress财务困境财务困境 Financial distress occurs when a firm has difficulty in
32、 meeting its contractual obligations合同义务合同义务Bankruptcy is an extended state of financial distress Firms with greater level of gearing are more likely to encounter financial distress财务杠杆程度财务杠杆程度越高越高 越容易陷入财务困境越容易陷入财务困境 The expected costs of financial distress -probability of distress times actual cost
33、s -will increase with gearing杠杆程度越高杠杆程度越高 预期财务困境预期财务困境成本也会越高成本也会越高37Costs of Financial Distress财务困境成本财务困境成本 The present value of the expected costs of financial distress increases with leverage.随着杠杆增加随着杠杆增加 VL=VU+PV(tax shelter)-PV(Costs of financial distress)The inclusion of financial distress in t
34、he analysis leads to the conclusion that initially,borrowing is beneficial to the company,but that an optimal capital structure exists and places limits on the amount managers should try to borrow通过对财务困境的分析得出这样的结通过对财务困境的分析得出这样的结论：借款有利于公司，但是只有当借款额度适当是才能达到最后论：借款有利于公司，但是只有当借款额度适当是才能达到最后资金结构资金结构38Agency
35、 Costs and Capital Structure代理成本和资本结构代理成本和资本结构 Stakeholders of modern corporations include:shareholders,creditors债权人债权人,employees,managers,suppliers,distributors and consumers Conflicts among stakeholders(e.g.in the case of financial distress)can affect the firms financial strategy股东之间的冲突会影响企业财政战略股东
36、之间的冲突会影响企业财政战略 The agency conflict between managers and outside shareholders can arise as a result of:(a)managements tendency to consume管理层的消费管理层的消费倾向倾向 various perquisites such as fancy offices花花式办事处式办事处,corporate jets公司喷气式飞机公司喷气式飞机,excessive pay rises过度加薪过度加薪,etc.39Agency Costs and Capital Structu
37、re As the level of borrowing increases,the danger of the misuse of the borrowed funds increases,resulting in increasing agency costs as the degree of gearing increases随着举债增加随着举债增加 滥用借入资滥用借入资金的危险也在增加金的危险也在增加 结果导致由资产负债过度引发的代理费用增结果导致由资产负债过度引发的代理费用增加加 With the use of leverage the agency costs of debt in
38、crease and the agency costs of equity decrease.According to this view,total agency costs reach a minimum at some optimal degree of leverage.由于杠杆的使用由于杠杆的使用 债券的代理费用增加债券的代理费用增加 股票的代理股票的代理费用减少费用减少 据此据此 总额代理费用会在最佳杠杆位置达到最小总额代理费用会在最佳杠杆位置达到最小40Making Leverage Decisions in Practice Estimate the effective tax
39、 advantage税收优势税收优势 of the company.The higher the tax advantage,the more debt should be employed,other things being equal.Assess the expected costs of financial distress and avoid additional debt if estimated costs are high enough to balance the tax advantage.评评估财务困境的预计成本估财务困境的预计成本 如果预计成本高到足以抵消税收优势则如
40、果预计成本高到足以抵消税收优势则要避免更多的债务要避免更多的债务 Interpret and react解读和反应解读和反应 to external signals外部信号外部信号 such as changes in interest rates,stock price,and bond rating.A lowered rating would make the cost of new borrowing higher and reduce the advantage of debt financing.低评级会使新的借债费用增加低评级会使新的借债费用增加 从而减少债务融资从而减少债务融资的优势的优势
