【正文】 ? Noarbitrage implies that the prices of both strategies be the same Cash Flow Strategy A Strategy B 0 0 0 600 300 300 1000 500 300+200 2020 1000 300+700 Corporate Finance Proof ? Cost of strategy A = = x 800 = 400 ? Cost of strategy B = VEL + VDL = VL ? They must be equal (why?): VL = 400 VL = 800 ? Therefore, VL = VU ? To avoid arbitrage, the two firms must have the same value. Corporate Finance Proposition II ? Under the same assumptions: 1) A firm?s cost of capital does not depend on its capital structure 2) The expected rate of return on a firm?s stock (cost of equity) increases in proportion to its debtequity ratio Corporate Finance Meaning ? Intuition: ? More debt decreases the cost of capital (debt is cheaper) ? But, it also increases the cost of capital, because it increases the risk of the equity ? The two effects must cancel each other (this is MM) Corporate Finance Proof ? Given expected cash flows {E(X1),E(X2),…,E(X T)}, the firm?s value is: (1) ? By proposition I, the value (V) is independent of the capital structure, and therefore of D ? By assumption, {E(X1),E(X2),…,E(X T)} do not change with D either TT221)W A C C1()X(E...)W A C C1()X(EW A C C1)X(EV???????Corporate Finance Proof ? From (1) follows that the cost of capital (WACC) cannot depend on D (this proves part 1) ? Part 2 of the proposition follows from rewriting the WACC: ))r(EW A CC(EDW A CC)r(E)r(EEDD)r(EEDEW A CCDEDE????????Corporate Finance Assumptions ? The following assumptions are necessary to derive the results: ? No transaction costs (this is not so important and can be relaxed) such as information asymmetries or taxes 187。 risk shifting ? MM amp。Capital Structure Corporate Finance Outline ? Modigliani amp。 Miller propositions ? No tax case ? Corporate taxes case ? Other costs and benefits of debt: ? Bankruptcy costs ? FCF Hypothesis ? Signaling amp。 CAPM ? Empirical evidence Corporate Finance The capital structure problem ? Finding the “optimal mix” of securities: ? Debt, ? Equity, ? Preferred Stock etc. that maximises the value of the firm ? We focus on two polar securities: equity and debt Corporate Finance Proposition I ? Assuming: ? Total cash flows to security holders are independent of how the firm is financed。 Which imply that cash flows are unaffected by capital structure (this is the key of the whole thing) ? Noarbitrage (this is a nonrestrictive assumption) Corporate Finance MM, the other way around ? MM show that under those assumptions, CS is irrelevant ? But this means that if those assumptions are not satisfied, CS is relevant ? The way to look at CS is to look at how it can affect the real cash flows the firm generates: ? Taxes ? Bankruptcy costs ? Agency issues Corporate Finance Corporate tax case ? Taxes ? Consider a firm with a permanent debt level D, paying r% per year ? Yearly interest expenses are rD, which are tax deductible under current tax law ? The firm saves TCrD in taxes every year, where TC is the corporate tax rate ? If we discount this in perpetuity using the interest rate, DTrrDTP V T S CC ??Corporate Finance MM with taxes: ? The difference between the aftertax cash flows of a levered and an unlevered firm is the tax shield of debt: TCrDD ? The difference between VL and VU is then the present value of the future tax shields: VL = VU + PVTS ? If debt is constant (perpetuity) this reduces to: VL = VU + TCD Corporate Finance Costs of Debt : Bankruptcy costs ? So far only benefits of debt ? Firms though don?t have alldebt financial structures ? There must be costs of debt ? The main cost of debt is the probability of financial distress ? FD: situation where a firm can not satisfy its current obligations Corporate Finance Direct Costs of FD ? A firm in financial distress: ? Renegotiate the claims ? Force liquidation (Chapter 7 in US) ? Reanise operations (Ch 11, uitstel van betaling) ? Direct costs are: ? Legal expenses, lawyers etc ? In the US, amount to 13% of firm?s ex ante value Corporate Finance Indirect Costs of FD ? Direct costs don?t seem to be significant enough (1% of market value) ? There must be thus other costs: ? Employee motivation ? Customer loss of confidence ? Credit constraints (and foing of positive NPV investments) ? Debt holderequity holder conflicts Corporate Finance The “static tradeoff theory” ? Combining the tax shield effect with the bankuptcy costs, VL = VU + TCD – BC Leverage $ D* Taxes paid Costs of FD Corporate Finance Other benefits of debt: FCF Hy