Capital StructureOutlineModigliani There are no transaction costs, No arbitrage opportunities exist, Then the total market value of the firm (the sum of the values all sources of capital) is independent of how the firm is financedProof Suppose firms U and L are identical, except for their capital structuresU (unlevered) is 100% equity financed, and is worth 800 L (levered) is (partially) financed with debt. It has a zero coupon bond with a face value of 600 Consider two time periods only: t = 0 (now) and t = 1 CF at t = 1 is random: x 0, 600, 1000, 2000, all equally likelyProof For the levered firm, payoffs to equity and debt are:xD =xD = 600xD = 600xD = 600xD = 0xD =xE = 0xE = 1400xE = 400xE = 0Proof Claim: VU = VL , where VL = VEL + VDL Suppose not. Then: Strategy A: Buy 50% of firm U Strategy B: buy 50% of the debt of L and 50% of its equityProof The two strategies provide exactly the same payoffs No-arbitrage implies that the prices of both strategies be the sameCash FlowStrategy AStrategy B 000 600300300 1000500300+200 20001000300+700Proof Cost of strategy A = 0.5VU = 0.5 x 800 = 400 Cost of strategy B = 0.5 VEL + 0.5 VDL = 0.5 VL They must be equal (why?):0.5 VL = 400VL = 800 Therefore, VL = VU To avoid arbitrage, the two firms must have the same value. Proposition II Under the same assumptions:A firms cost of capital does not depend on its capital structure The expected rate of return on a firms stock (cost of equity) increases in proportion to its debt-equity ratioMeaning 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 equityThe two effects must cancel each other (this is MM)Proof Given expected cash flows E(X1),E(X2),E(XT), the firms 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(XT) do not change with D either 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: 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 Which imply that cash flows are unaffected by capital structure (this is the key of the whole thing)No-arbitrage (this is a non-restrictive assumption)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 issuesCorporate tax case TaxesConsider 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 rateIf we discount this in perpetuity using the interest rate, MM with taxes:The difference between the after-tax 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 + PVTSIf debt is constant (perpetuity) this reduces to:VL = VU + TCDCosts of Debt : Bankruptcy costs So far only benefits of debtFirms though dont have all-debt 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 obligationsDirect Costs of FD A firm in financial distress:Renegotiate the claims Force liquidation (Chapter 7 in US) Reorganise operations (Ch 11, uitstel van betaling) Direct costs are:Legal expenses, lawyers etcIn the US, amount to 1-3% of firms ex ante valueIndirect Costs of FD Direct costs dont seem to be significant enough (1% of market value) There must be thus other costs:Employee motivation Customer loss of confidence Credit constraints (and forgoing of positive NPV investments) Debt holder-equity holder conflictsThe “static trade-off theory” Combining the tax shield effect with the bankuptcy costs, VL = VU + TCD BCLeverage$D*Taxes paidCosts of FDOther benefits of debt: FCF HypothesisJensen (1986) (page 766)Example: Armand Hammer (Occidental Petroleum) spend $120 m in an art museum Why shareholders allow this? FCF definition (here): funds available for managemenet after financing all projects with NPV0These funds should be paid out (otherwise are likely to be invested in negative NPV projects)How can management commit to indeed pay out?Debt is a solution: it forces management to pay interest and repay principal Signaling theories Suppose firms are divided into two groups, good and bad firms If a bad firm increases debt above a certain level, X*,