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Topic 6 – Capital Structure [Perfect Markets, Taxes, Bankruptcy costs] (CWS – Chapter 15, primarily pages 557-573) A firm’s value is the present value of the expected cash flows from its assets Assuming perfect markets, the discount rate used to value these cash flows is the firm’s weighted average of the cost of each source of funds (e.g., interest and capital gains payments to bondholders and dividend and capital gain payments to stockholders) In other words, the discount rate is the firm’s WACC What if a firm can lower its cost of capital? What affect will this have on firm value? The purpose of this topic is to explore whether there is some way to adjust the firm’s capital structure (how much debt versus how much equity we use to finance the firm’s assets) such that the cost of capital is decreased – thereby increasing firm value. Modigliani and Miller, 1958, The cost of capital, corporation finance and the theory of investment, American Economic Review 48, 261-297, provided the seminal paper addressing this topic. We will concentrate on pages 261-271. Even though many papers have been published since that address capital structure (many with different conclusions), it is very important to have a solid understanding of the M&M paper. 1 Modigliani and Miller (1958) - Assumptions (1) Perfect capital markets No transaction costs - to allow for costless purchases and short sales No income taxes No bankruptcy costs (2) There exists a group of homogeneous firms which have assets that yield a perpetual stream of uncertain positive cash flows: yearly cash flows are random drawings from the same distribution, i.e., no growth. Since all firms have the same cash flows (or cash flows times a constant) in every state of nature, then these firms also have the same risk and therefore the same expected return, ρk. Example Firm A (e.g., $10, $20, or $30, each with a 1/3 chance) Firm B (e.g., $10, $20, or $30, each with a 1/3 chance) Cash flows are aligned _ What is X (i.e., the expected value of each firm’s cash flows)? If ρk = 0.1, then what are the values of these two firms? (3) These firms can either be all equity or part debt and part equity (4) Equity of firms is risky. Debt is risk free, paying a constant interest rate, r. Investors can borrow and lend at interest rate r. 2 Modigliani and Miller (1958) – Other Implicit Assumptions (5) Managers always work to maximize shareholder wealth (i.e., no conflicts of interest between managers and stockholders) and a firm’s investment decision is unaffected by its financing decision How might a firm’s leverage ratio affect manager’s incentives (and therefore management’s decisions on which projects to select or reject)? Note - stockholder / bondholder conflicts are another important conflict of interest, but are assumed away because debt is risk-free (6) Corporate insiders and outsiders have the same information What if corporate insiders have more information than outsiders? How might this affect their capital structure decisions? (7) 100% dividend payout ratio When one of the firms in the set of “identical firms” issues debt, the stock of that firm becomes more risky. Thus, even though the assets of the firm remain unchanged, risk-averse investors will not view the stock in the levered firm as a perfect substitute for the stock in the unlevered firm. 3 Modigliani and Miller (1958) – Proposition 1 Proposition 1: The market value of the firm, V j , which is the sum of the market value of the bonds, D j , and the stock, S j , is independent of the particular capital structure chosen by management. _ Xj This value, V j , is equal to for any firm in risk class k k _ _ Xj Xj Equivalent to this is that the WACC, k , is the same for all firms in class k, regardless of the DJ S J Vj particular capital structure chosen To prove, M&M show that arbitrage profits will result if proposition 1 does not hold. Since there should be no arbitrage profits in equilibrium, then capital structure cannot affect firm value. _ Consider two companies from the same risk class, with the same expected cash flow, X , and same cash flows in each state of nature, X. Let company 1 be all equity and company 2 have some debt. According to proposition 1, these two firms must have the same value to prevent arbitrage What is an arbitrage profit in M&M (1958)? Zero investment at time 0 Guaranteed positive cash flows in future years Why shouldn’t arbitrage profits exist in equilibrium? 4 Modigliani and Miller (1958) – Arbitrage Proof (V2 > V1) A short sale of α of the stock of company 2 will require the investor to pay every year in perpetuity (or until the short position is closed out): Y2 ( X rD2 ) (1) To see arbitrage profits, sell αS2 short and personally borrow αD2. Use the proceeds to buy a portion of company ( D2 S 2 ) 1’s stock (remember company 1 is all equity). The portion purchased is . S1 Note that the cost of the purchase of company 1 stock is completely offset by the proceeds of the short sale and the borrowed funds (net cost at t = 0 is $0) Future cash flows from the three positions are: ( D2 S 2 ) ( X rD2 ) rD2 X (2) S1 The first term = The second term = The third term = 5 Modigliani and Miller (1958) – Arbitrage Proof (V2 > V1) – continued Simplifying: V2 X X 0 (3) V1 Since V2 > V1, by assumption, you receive a perpetual stream of positive future cash flows at no t = 0 cost (i.e., an arbitrage profit) Arbitrage profits indicate disequilibrium (i.e., excess demand or supply) In this case, there is excess demand for stock 1 and excess supply for stock 2 What should happen to the price of company 1’s stock? What about company 2’s stock? Prices will continue to move until V1 = V2 Note that there is no requirement that investors are rational. It is the actions of arbitragers that ensure that V2 is never greater than V1. 6 Modigliani and Miller (1958) – Arbitrage Proof (V2 < V1) Now sell αS1 short. This obligates the investor to pay αX per year. Take the proceeds of the short sale and buy S2 D stock and bonds of company 2 in the proportions and 2 (i.e., the proportions of equity and debt in company 2’s V2 V2 capital structure). Net cost at t = 0 equals zero. The proportion held in the stock of company 2 is: S2 S1 V2 S1 (4) S2 V2 In the debt of company 2: D2 S1 V2 S1 (5) D2 V2 Thus, S2 D2 S1 S1 V2 V2 S1 (6) S2 D2 V2 7 Modigliani and Miller (1958) – Arbitrage Proof (V2 < V1) - continued The cash flows from these three positions are: S1 S X ( X rD2 ) 1 rD2 (7) V2 V2 The first term = The second term = The third term = Simplifying: S1 V1 X 1 X 1 V 0 (8) V2 2 Since V1 > V2, again, the cash flow stream is positive. To prevent arbitrage, the market value of S2 has to increase and/or S1 decrease. In summary, for two firms with identical assets, the no arbitrage condition requires that: S1 V1 V2 D2 S 2 (9) In other words, the value of the firm is created by the cash flow generating power of the assets, not by the particular capital structure chosen. 8 Modigliani and Miller (1958) – Proposition 2 Proposition 2: The expected rate of return for the common stock of levered firm j in risk class k, ij, is equal to: Dj i j k (k r) (10) Sj To see, note that by definition _ X j rD j ij (11) Sj As stated, the WACC is _ Xj k (12) Dj S j Rearranging the WACC formula _ X j k (D j S j ) (13) Plugging into equation (11) k ( D j S j ) rD j ij (14) Sj Dj Sj Dj i j k k r (15) Sj Sj Sj Dj i j k (k r) (16) Sj So, while the WACC remains the same as leverage increases (since the value of the firm remains unchanged), the expected (or required) return for the stock (which is equal to ρk when unlevered), increases as the firm's debt to equity ratio increases. 9 Modigliani and Miller (1963) – Capital Structure with Corporate Taxes Modigliani and Miller, 1963, Corporate income taxes and the cost of capital: A correction, American Economic Review 53, 433-443 examine capital structure decisions with corporate income taxes They conclude that capital structure does matter. In particular, firms with more debt should have higher values. The key change in assumption is that corporations pay a tax on their income and the tax law provides for a deduction for interest expense Therefore, firms with debt have lower taxable income and pay less income tax than all-equity firms The reduction in income taxes means more cash flow to the firm’s owners, resulting in a higher firm value M&M (1963) serves as the foundation for the “tradeoff model.” In the tradeoff model, firms maximize value by considering the tradeoff between the: Increased value from additional debt (associated with lower income taxes) Decreased value from additional debt (associated with increase chances of bankruptcy and/or debt agency costs 10 Modigliani and Miller (1963) – Assumptions and Cash Flows Assumptions Corporate taxable income is taxed at rate τc Taxable income equals cash flow from assets (X) less interest on debt (rD) The other assumptions in M&M (1958) still apply (including that there is no individual income tax) _ Two identical firms (with perpetual expected cash flows equal to X ), one all equity and one levered (with a perpetual risk-free bond with a face of D and an interest rate of r). Cash flows Expected cash flows to all security holders, net of taxes, for the all equity firm and the levered firm are: _ CFU X (1 c ) (17) _ CFL rD ( X rD)(1 c ) (18) _ CFL X (1 c ) c rD (19) 11 Modigliani and Miller (1963) – Valuation of Levered and Unlevered Firms The values of unlevered and levered firms can be determined by discounting the respective cash flow streams. Following the discussion of the M&M (1958) paper, assume that ρk is the appropriate discount rate for the unlevered firm in class k. Therefore, its current market value is _ X (1 c ) VU (20) k What is assumed about the nature of the tax code in order to use ρk as the discount rate? The cash flow stream for the levered firm is the same as the unlevered firm plus τcrD. To calculate the levered firm’s value, discount the two cash flow streams at the appropriate discount rates. The first cash flow stream can be discounted at ρk (same as above) The discount rate for the second cash flow stream is r. For example, if the debt is risk free, then discount τcrD at the risk-free rate. What are the implied assumptions with using r? Therefore the current market value of the levered firm is: _ X (1 c ) c rD VL VU c D (21) k r This equation implies near 100% debt. Why “near” 100% debt? This equation assumes that the tax rate τc is applied to positive and negative amounts of taxable income 12 The Tradeoff Model A natural counter weight to the tax advantage of debt is bankruptcy costs. The inclusion of bankruptcy costs leads to the development of the tradeoff model. With the tradeoff model, firms maximize the following equation: VL VU c D PV [ E ( BC )] (22) Note – Some versions of the tradeoff model also subtract the PV of the expected agency costs. What are bankruptcy costs? Examples of direct bankruptcy costs = fees charged by lawyers, accountants, and trustees Examples of indirect bankruptcy costs = lost sales, inefficient decisions by management and/or the bankruptcy trustee One of the early papers is this area is Warner, Jerold. “Bankruptcy costs: Some evidence.” Journal of Finance 32 (1977), 337-348. He finds in his sample of 11 railroad bankruptcies that direct bankruptcy costs were 1% of firm market value 84 months before bankruptcy and 5.3% of market value as of the filing date. Altman (1984), reviewed in the textbook on page 593) estimates indirect bankruptcy costs at 17.5% of market value. What adjustment is needed to calculate “expected” bankruptcy costs? What is the “PV” of expected bankruptcy costs? What if courts don’t follow absolute priority in bankruptcy proceedings? Taking into account the “PV” and the “expected” in the calculation of PV[E(BC)], and the fact that the courts don’t always follow absolute priority, bankruptcy costs would have to be extremely high to offset the tax benefits of debt. 13 Capital Structure with Corporate and Personal Taxes Miller, Merton. “Debt and taxes.” Journal of Finance 32 (1977), 261-276, in commenting on the tradeoff model, notes: Corporate income tax rates have increased over the years in the U.S. (10% to 11% in the 20’s to 52% in the 50’s), yet debt-equity ratios have stayed pretty much constant With bankruptcy costs, why have any debt prior to the income tax? Why do some firms like IBM and Kodak have little debt, while other firms (public utilities) have a lot of debt? Are managers of public utility firms smarter? The Miller (1977) model: ~ ~ 1) An all equity firm (firm U) receives a cash flow perpetuity of X from its assets (and, X = taxable income) 2) Corporate income tax rate = c Personal tax rate on income from equity ownership (dividends and capital gains) = PS Personal tax rate on debt ownership (interest income) = PB Note: PB is also the rate that individuals receive tax benefits from an interest expense deduction 14 The Miller (1977) Model – continued 3) Assuming a 100% payout ratio, equity owners receive after-tax cash flow per year of: ~ Unlevered firm: X (1 c )(1 PS ) (23) ~ Levered firm: ( X rBL )(1 c )(1 PS ) (24) 4) Consider a long position in αSU and a short position in the amount of (1 c )(1 PS ) BL (25) (1 PB ) 5) Cash flow from the long and short positions are: ~ (1 c )(1 PS ) X (1 c )(1 PS ) rBL (1 PB ) (26) (1 PB ) 6) After simplification ~ ( X rBL )(1 c )(1 PS ) (27) Compare to the cash flow from owning a long position in the levered firm (with the same assets) in the amount of αSL (see equation 24) 15 The Value Gain from Leverage 7) Two identical cash flow streams must have the same value: (1 c )(1 PS ) S L SU B L (28) (1 PB ) 8) Add BL to both sides, and recognize that VL S L BL , and VU SU (1 c )(1 PS ) V L BL VU BL (29) (1 PB ) (1 c )(1 PS ) V L VU BL 1 (30) (1 PB ) 9) So, the gain from leverage is: (1 c )(1 PS ) G L BL 1 (31) (1 PB ) 10) Notice that if PS PB (a special case is when both are equal to zero), then: G L C BL … Compare to M&M (1963) (32) 16 The Value Gain from Leverage – continued 11) The gain from leverage formula again: (1 c )(1 PS ) G L BL 1 (33) (1 PB ) 12) When PS PB , then G L C BL . What about when PS PB ? 13) Compare and note in each case if additional leverage increases or decreases firm value (1 C )(1 PS ) (1 PB ) (1 C )(1 PS ) (1 PB ) (1 C )(1 PS ) (1 PB ) 14) Assume that PS = 0. (Note: PS = 0 is not a necessary assumption, but simplifies the presentation.) In this case: (1 c ) G L BL 1 (34) (1 PB ) Is there any logic behind assuming PS = 0? How is “equity income” taxed? 17 The Miller (1977) Equilibrium 15) Assume: A. PS = 0 B. Progressive individual income tax rates on interest income, PB , lowest rate = 0 and highest rate greater than C C. The exists an unlimited supply of tax-free securities that individuals can purchase that pay r0 D. Individuals decide whether to invest in taxable debt issued by corporations or tax-free debt based on their tax rate PB a. Assume all debt is risk-free – so investment decisions are based on after-tax returns b. In the U.S., debt issued by state and local governmental agencies are tax free c. Although not allowed in the U.S. tax code, we could also assume that corporations have a choice of issuing tax-deductible debt and receiving a tax deduction at rate C or tax-exempt debt (with interest rate r0 ) and receiving no tax deduction E. All firms (without regard to their taxable income) are faced with a corporate tax rate equal to C and therefore receive a tax benefit from interest at rate C for unlimited amounts of their (“taxable”) debt 18 The Miller (1977) Equilibrium - continued 16) Initially, consider the case where the economy has no debt and the first firm issues debt to individuals with an interest rate equal to r0 A. Who would buy this debt security (i.e., what is PB )? B. What is GL? 17) Since GL > 0, other firms have the incentive to issue debt until the supply of funds available from tax-exempt investors is fully used and any additional debt must be sold to individuals with PB > 0. r0 A. The next firm to sell bonds will need to pay . Why? 1 PB B. However, if C PB , then GL > 0 C. Firms will continue to issue debt (at ever higher interest rates) as long as C PB 18) The debt market is in equilibrium if GL = 0. In equilibrium: A. PB C r0 B. The interest rate on corporate debt = 1 C 19 The Miller (1977) Equilibrium - continued 19) Description of the Miller equilibrium: A. There is an optimal capital structure, but only on the macro (economy-wide) level B. Assuming the debt market is in equilibrium, individual firms have no incentive to change their capital structure since there is no gain from either a higher or lower debt level Therefore, in this equilibrium, there is no incentive for IBM (with little debt) to increase its debt/equity ratio. Why? Verify that GL < 0 if any addition debt is issued by IBM Likewise, there is no incentive for a public utility with a lot of debt to decrease leverage by issuing new equity to repurchase bonds. Why? (Again verify that GL < 0 if any debt is retired.) r0 C. Investor surplus is created in that investors with PB C receive interest rate but require interest rate 1 C r0 . 1 PB D. The difference between tax rates on tax-exempt bonds and corporate bonds approximately reflect the corporate tax rate E. What is the after-tax cost of debt for corporations? Compare to the tax exempt rate (i.e. assume corporations have the choice of issuing tax deductible debt or tax-exempt debt). 20 The Miller (1977) Equilibrium – some questions 20) A. What about observed regularities in capital structure across firms in different industries? B. What if the maximum PB is less than c ? C. How would changes in tax laws (i.e., changes in corporate or personal tax rates) affect the equilibrium? D. Miller (1977) assumes that corporations receive full tax benefit (equal to C ) for unlimited amounts of debt. What if firms receive no tax benefit (or reduced tax benefit) from debt if taxable income is less than zero and if there is uncertainty in the amount of their income? See DeAngelo, Harry and Ron Masulis. “Optimal capital structure under corporate taxes.” Journal of Financial Economics 8 (1980), 5-29 DeAngelo and Masulis (1980) extend the Miller argument by allowing for more realistic assumptions. 1) They find a unique interior optimal capital structure for each firm (so capital structure decisions are important) 2) They find the existence of an optimal capital structure even without the use of bankruptcy costs (although the analysis could have been done including these costs) 3) In their model, they allow for firms to have access to varying amounts of non-debt tax shields, such as depreciation expense and investment tax credits 21 DeAngelo and Masulis (1980) assumptions The following is a simplified discussion, which describes the essence of the DeAngelo and Masulis (1980) model, without all the complicating detail (many thanks to Professor Avner Kalay). The (simplified) model: 1) Two dates, t = 0 and t = 1. Firms make leverage decisions and individuals make portfolio decisions at t = 0. At t = 1, liquidating payments are made to the firm's debt and equity holders where the payments are state- contingent. All participants are risk neutral. 2) Interest is tax deductible, but the firm also has non-debt tax shields. (We will ignore the investment tax credits.) 3) is the amount of non-debt tax shields for the corporation (e.g., depreciation expense). 4) R0 is the interest rate on tax-free municipal bonds 5) pb is the personal tax rate on interest income, ps is the personal tax rate on equity income, and c is the corporate tax rate 6) Zero tax on taxable income at or below $0. No carrybacks or carryforwards of losses allowed. 22 DeAngelo and Masulis (1980) example 1) State contingent t = 1 firm cash flows (i.e., EBIT) = $1000, $1500, $2000, or $2500 (equally probable) 2) = $500 (depreciation) 3) R0 = 6% 4) pb = 25%, ps = 0%, and c = 40% 5) The demand for bonds from these marginal individual investors is: R d ( B) R0 /(1 PB ) 6% / 0.75 8% (35) 6) Taxable income and corporate tax across all four states (no interest) State 1 2 3 4 Expected Probability 0.25 0.25 0.25 0.25 Cash Flow $1000 $1500 $2000 $2500 $1750 Depreciation -$500 -$500 -$500 -$500 -$500 Interest $0 $0 $0 $0 $0 Taxable Income $500 $1000 $1500 $2000 $1250 Inc. Tax at 40% $200 $400 $600 $800 $500 23 DeAngelo and Masulis (1980) example (continued) 7) Taxable income and corporate tax across all four states ($500 of interest) State 1 2 3 4 Expected Probability 0.25 0.25 0.25 0.25 Cash Flow $1000 $1500 $2000 $2500 $1750 Depreciation -$500 -$500 -$500 -$500 -$500 Interest -$500 -$500 -$500 -$500 -$500 Taxable Income $0 $500 $1000 $1500 $750 Inc. Tax at 40% $0 $200 $400 $600 $300 What is the marginal reduction in expected income tax? $200 What is the percentage expected tax benefit from the interest deduction? $200 / $500 = 40% 8) Taxable income and corporate tax across all four states (another $500 of interest) State 1 2 3 4 Expected Probability 0.25 0.25 0.25 0.25 Cash Flow $1000 $1500 $2000 $2500 $1750 Depreciation -$500 -$500 -$500 -$500 -$500 Interest -$1000 -$1000 -$1000 -$1000 -$1000 Taxable Income -$500 $0 $500 $1000 $250 Inc. Tax at 40% $0 $0 $200 $400 $150 What is the marginal reduction in expected income tax? $150 What is the percentage expected tax benefit from the interest deduction? $150 / $500 = 30% 24 DeAngelo and Masulis (1980) example (continued) 9) Taxable income and corporate tax across all four states (another $500 of interest) State 1 2 3 4 Expected Probability 0.25 0.25 0.25 0.25 Cash Flow $1000 $1500 $2000 $2500 $1750 Depreciation -$500 -$500 -$500 -$500 -$500 Interest -$1500 -$1500 -$1500 -$1500 -$1500 Taxable Income -$1000 -$500 $0 $500 -$250 Inc. Tax at 40% $0 $0 $0 $200 $50 What is the marginal reduction in income tax? $100 What is the percentage tax benefit from the interest deduction? $100 / $500 = 20% 10) Taxable income and corporate tax across all four states (another $500 of interest) State 1 2 3 4 Expected Probability 0.25 0.25 0.25 0.25 Cash Flow $1000 $1500 $2000 $2500 $1750 Depreciation -$500 -$500 -$500 -$500 -$500 Interest -$2000 -$2000 -$2000 -$2000 -$2000 Taxable Income -$1500 -$1000 -$500 $0 -$750 Inc. Tax at 40% $0 $0 $0 $0 $0 What is the marginal reduction in income tax? $50 What is the percentage tax benefit from the interest deduction? $50 / $500 = 10% Note - Any additional borrowing will have a zero corporate tax benefit! 25 DeAngelo and Masulis (1980) example (continued) 11) Remember, from Miller (1977), firms were willing to supply debt securities to the market at: R s ( B) R0 /(1 c ) (36) In this environment, the effective corporate rate depends on the amount of interest: Interest [$0,$500] ($500,$1000] ($1000,$1500] ($1500,$2000] ($2000,) Effect. Tax Rate 40% 30% 20% 10% 0% Max int. rate offered 10% 8.57% 7.5% 6.67% 6% Demand int. rate 8% 8% 8% 8% 8% What is the optimal capital structure for this firm? 12) What about a firm with = $1000? 13) What does aggregate supply and demand look like in the DeAngelo and Masulis (1980) world? 14) Some questions / issues: What are the implications of this “imperfect” tax shield? Multi-period tax code – how would the allowance of carrybacks and carryforwards affect the supply curve? Mergers and leases – the market for tax shields What are the implications of a “perfect” market for tax shields? 26 DeAngelo and Masulis (1980) hypotheses 15) Testable hypothesis: H1) Capital structure changes (holding investment constant) have an impact on firm value H2) In equilibrium 1 - PD > (1 - PE)(1 - c) . Assuming no personal tax on equity income, then PD < c H3) Other things equal, firms with lower non-debt tax shields will use more debt H4) Other things equal, firms with higher bankruptcy costs will use less debt H5) Other things equal, as c increases, firms will use more debt financing Masulis (1980) finds an increase in firm value around exchange offers supporting H1. Also supporting H3, firms with more non-debt tax shields have less debt. For example, drug, mining, oil industries have lowest debt ratios. They also have the highest non-debt tax shields [Scott-Martin (1975)]. High inflation reduces the value of depreciation, so according to H3, there should be an increase in debt during inflationary periods. H5 says that there should be increases in debt ratios as corporate tax rates increase. Holland-Myers (1977) find support for this. Sharpe (1978) backs P D out of the difference between municipal and corporate interest rates and finds .30 = PD < c = .48 . This is inconsistent with the Miller model which would find these two rates should be the same (assuming the personal tax rate on equity income is zero), but supportive of H2. 27 DeAngelo and Masulis (1980) and Bankruptcy Costs 16) Bankruptcy costs can be added to this model. While it is argued that the corporate tax advantage overwhelms the PV of the expected bankruptcy costs, in this model, the addition of bankruptcy costs will decrease the unique optimal capital structure for the firm. Any additional costs associated with additional leverage needs to be subtracted from the declining corporate tax advantage to additional debt - yielding a lower B* 28

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