Chapter 1: The Modigliani-Miller Propositions, Taxes and Bankruptcy Costs

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1 Chapter 1: The Modigliani-Miller Propositions, Taxes and Bankruptcy Costs Corporate Finance - MSc in Finance (BGSE) Albert Banal-Estañol Universitat Pompeu Fabra and Barcelona GSE Albert Banal-Estañol (UPF and BGSE) Chapter 1 1 / 34

2 In this chapter... The Modigliani and Miller irrelevance results Taxes Bankruptcy costs Main conclusions Albert Banal-Estañol (UPF and BGSE) Chapter 1 2 / 34

3 The Modigliani and Miller irrelevance results The Modigliani and Miller (MM) irrelevance results The Modigliani-Miller results state that, if... A1 Total cash ows available for distribution to all debt and equity holders do not depend on the capital structure A2 Capital markets are perfect A3 Information is perfect A4 Arbitrage opportunities are absent...then... (P1) A rm s debt-equity ratio does not a ect its market value (P2) A rm s leverage has no e ect on its weighted average cost of capital Albert Banal-Estañol (UPF and BGSE) Chapter 1 3 / 34

4 MM Proposition 1: An example The Modigliani and Miller irrelevance results Consider a one-period economy in which two rms, U and L, provide the same payo s or cash ows at the end of the period: But... Firm U Firm L Payo in good state Payo in bad state Firm U is nanced by equity only, which gets all cash ows. Firm L is nanced by debt and equity and its cash ows are divided between these two classes of claims. Still, the sum of cash ows of L s debt and equity holders is identical to the payo s U s equity holders Claim: Their value at the beginning of the period must be the same The total value of Firm L s debt and equity must equal the value of Firm U s equity. Albert Banal-Estañol (UPF and BGSE) Chapter 1 4 / 34

5 The Modigliani and Miller irrelevance results MM Proposition 1: An example Let s assume the following regarding how rm L is nanced: Firm L s debt promises e60 and has market value of e50 Firm L s equity has market value of e50 The value of Firm L is then: V L = D L + E L = = 100. Suppose that the value of Firm U is di erent from 100, say, 105. Albert Banal-Estañol (UPF and BGSE) Chapter 1 5 / 34

6 MM Proposition 1: An example The Modigliani and Miller irrelevance results We could carry out the following arbitrage strategy: 1 Sell (short) Firm U at Buy Firm L s equity at 50 3 Buy Firm L s bond at 50 The resulting cash ows look as follows: Current cash ow is = 5 Future cash ow is Good state Bad state Long Firm L s equity Long Firm L s bond Short Firm U s equity Net 0 0 Arbitrage opportunity! This will happen as long as V L 6= V U Albert Banal-Estañol (UPF and BGSE) Chapter 1 6 / 34

7 The Modigliani and Miller irrelevance results MM Proposition 1: Intuition This means that the value of the rm (total size of the pie) is independent of its capital structure (how the total pie is shared) Hence, the nancial manager should not worry about considerations other than cash- ows from the operating activities She should worry only about identifying whether particular investment projects have positive NPVs and undertaking them. Albert Banal-Estañol (UPF and BGSE) Chapter 1 7 / 34

8 The Modigliani and Miller irrelevance results Proof of Proposition 1 Setup and notation Consider a two-dates economy (t = 0, 1), with 2 rms (i = 1, 2) Denote: which have identical cash ows x at t = 1 (uncertain at t = 0) Firm 1 is unlevered and rm 2 is levered All shareholders are protected by limited liability B: repayment promised to debtholders at t = 1 E and D market value of 2 s equity and debt at t = 0 Value at t = 0 Payo at t = 1 Debt rm 2 D minfb, xg Equity rm 2 E maxfx B, 0g Market value rm 2 V 2 = D + E x Market value rm 1 V 1 = U x P1 claims that V 1 = V 2 even if B > 0 Albert Banal-Estañol (UPF and BGSE) Chapter 1 8 / 34

9 Proof of Proposition 1 Benchmark: total payments as a function of x at t=1 The Modigliani and Miller irrelevance results x 2 Total payments (equity and debt) independent of capital structure (A1) Suppose that B = 2. Clearly, B might not be repaid; debt may be risky Albert Banal-Estañol (UPF and BGSE) Chapter 1 9 / 34

10 Proof of Proposition 1 Payments to debtholders as a function of x at t=1 (B=2) The Modigliani and Miller irrelevance results x 2 Albert Banal-Estañol (UPF and BGSE) Chapter 1 10 / 34

11 Proof of Proposition 1 Payments to equityholders as a function of x at t=1 (B=2) The Modigliani and Miller irrelevance results x 2 Albert Banal-Estañol (UPF and BGSE) Chapter 1 11 / 34

12 The Modigliani and Miller irrelevance results Proof of Proposition 1 Strategy: Suppose that V 1 6= V 2 and show that, if A1-A3 hold, there are arbitrage opportunities (contradicting A4) If V 1 < V 2, sell short equity and debt of rm 2 and buy equity of 1 If V 1 > V 2, buy equity and debt of rm 2 and sell short equity of 1 That is, buy undervalued securities and sell-short overvalued ones What if V 1 < V 2? Transaction At t = 0 At t = 1 Sell α of D αd α minfb, xg Sell α of E αe α maxfx B, 0g Buy α of U αu αx Sum αd + αe αu = α(v 2 V 1 ) > 0 0 Arbitrage opportunity!! Albert Banal-Estañol (UPF and BGSE) Chapter 1 12 / 34

13 Proof of Proposition 2 The Modigliani and Miller irrelevance results Prop 1 states that if two rms are equal except for the corporate structure: U = E + D, where U is the value of the unlevered rm and E and D are the equity and debt values of the levered one De ne: Expected return on... equity for the unlevered rm: R U E (x)/u debt for the levered rm: R D E (minfb, xg)/d equity for the levered rm: R E E (maxfx B, 0g)/E But then... UR U = E (x), DR D = E (minfb, xg) and ER E E (maxfx B, 0g) But E (x) = E (minfb, xg) + E (maxfx B, 0g), hence UR U = DR D + ER E Rearranging, and using that U = E + D, R U = D D + E R D + E D + E R E (1) Albert Banal-Estañol (UPF and BGSE) Chapter 1 13 / 34

14 The Modigliani and Miller irrelevance results Proof of Proposition 2 Denote the asset value as A and the return on assets as R A E (x)/a In an unlevered rm, all cash ows of its assets are paid out to its equity holders: Hence A = U = E + D (for any D, E) and therefore R A E (x)/a = E (x)/u = R U Substituting R U = R A and rearranging (1) R E = R A + D E (R A R D ) That is, insofar as debt is riskless, the expected return on equity of a levered rm is a positive and linearly increasing function of the debt-to-equity ratio, expressed in market values This rate of increase is given by the spread between the expected return on assets and the expected return on debt Albert Banal-Estañol (UPF and BGSE) Chapter 1 14 / 34

15 Implications of Proposition 2 The Modigliani and Miller irrelevance results As shown earlier, projects cash ows should be appropiately discounted: what is the return the rm can receive on alternative investments that bear the same risks? ( cost of capital as it measures the opportunity cost of the funds) use this return as the discount rate to compute the net present value If the rm s assets have same risk as project evaluated... and rm is unlevered use equity cost of capital as the cost of capital for the project Albert Banal-Estañol (UPF and BGSE) Chapter 1 15 / 34

16 Implications of Proposition 2 The Modigliani and Miller irrelevance results For a levered rm, equity cost of capital is... higher than cost of capital of the assets, and therefore of the project But we can compute asset returns by substituting R U = R A in (1) R A = D E R D + R E R wacc (2) D {z + E } D {z + E } Proportion in Debt Proportion in Equity The weighted average cost of capital (the expected return for an investor that holds all the equity and all the debt of a levered rm) for any leverage ratio (for any D, E ) is constant (R A is constant) Firm s WACC is independent of capital structure! Albert Banal-Estañol (UPF and BGSE) Chapter 1 16 / 34

17 The Modigliani and Miller irrelevance results Albert Banal-Estañol (UPF and BGSE) Chapter 1 17 / 34

18 Taxes Corporate taxes MM: without taxes (and without bankruptcy costs, etc,.): companies should be indi erent between debt and equity All else equal, the objective should be to minimise the tax bill: Interest rates are usually tax deductible at the corporate level!advantage to debt as a form of nancing Personal tax on equity is higher than the personal tax on debt!advantage to equity nancing and partially (but not completely o setting) the e ect of corporate taxation In practice, managers pay great attention to the tax implications Suppose rst that... companies are taxed but... investors are not (e.g. pension funds) (we will come back later to that) Albert Banal-Estañol (UPF and BGSE) Chapter 1 18 / 34

19 Taxes Example: DF Builders What was the amount available to investors in 2005? Would it have been higher or lower without leverage? Albert Banal-Estañol (UPF and BGSE) Chapter 1 19 / 34

20 Taxes Albert Banal-Estañol (UPF and BGSE) Chapter 1 20 / 34

21 Taxes What is the value of the tax shield? Consider two rms, U and L,... with identical, pre-tax, expected annual cash ows x t, t = 1... Firm U is 100% equity nanced Firm L maintains debt level D and pays perpetual interest rate r D The corporate tax is τ c and ignore personal taxes for now Albert Banal-Estañol (UPF and BGSE) Chapter 1 21 / 34

22 Taxes The expected annual after-tax cash ows of rms U and L are (1 τ c )x t and (1 τ c ) (x t r D D) + r D D = (1 τ c )x t + τ c r D D They di er by the debt tax shield created by the tax-deductibility Since it is the same in every period, it is a perpetuity, and therefore V L = V U + τ c r D D r D = V U + τ c D Risk of the rst part of the cash ow of L is identical to that of U, thus the same discount rate applies The discount rate for the cash ows to the debt holders is the same as the required rate of return on debt, r D. Albert Banal-Estañol (UPF and BGSE) Chapter 1 22 / 34

23 Taxes Personal Taxes So far, we have only considered corporate taxes which favor debt over equity Therefore the optimal capital structure should be 100% debt But most investors are also taxed when they receive cash Debt and equity also face di erential taxation at the personal level: Interest income from debt taxed as income (τ d ) Equity investors pay taxes on dividends & capital gains (τ e ) Typically... Capital gains are taxed at lower rates than dividends or interests Capital gains (and therefore taxes on them) might be deferred As a result: τ e < τ d Albert Banal-Estañol (UPF and BGSE) Chapter 1 23 / 34

24 Taxes What is the value of the tax shield? Assuming all shareholders have same tax rates, cash ows for U are and for L are: (1 τ c )(1 τ e )x t (1 τ c )(1 τ e ) (x t r D D) + (1 τ d )r D D = (1 τ c )(1 τ e )x t + [(1 τ d ) (1 τ c )(1 τ e )] r D D Discounted at the after-tax rate r D (1 τ d ), PV of second term is τ g D, where (1 τ c )(1 τ e ) τ g = 1 (1 τ d ) and therefore V L = V U + τ g D Albert Banal-Estañol (UPF and BGSE) Chapter 1 24 / 34

25 Taxes Relative advantage formula (RAF) Debt is preferred over equity if and only if τ g > 0 or i For example, RAF (1 τ d ) (1 τ c )(1 τ e ) > 1 if corporate tax is 35% (τ c = 35%) if personal income tax is 40% (τ d = 40%) if there are no dividends and capital gains are not deferred and if capital gains tax is 20% (τ e = 20%)... then... τ g = = 0.13 and RAF = 1.15 For every euro in permanent debt, value increases by 13c Albert Banal-Estañol (UPF and BGSE) Chapter 1 25 / 34

26 Bankruptcy costs Bankruptcy costs Debt might have an important disadvantage: high debt levels increase the chance of nancial distress This is only important if bankruptcy a ects revenues or costs Direct costs: legal process of restructuring (court costs, advisory fees) on average 2-3% of the assets Examples: Indirect costs: Enron $30m per month, $750 in total Worldcom (reorganisation to become MCI) $657m United Airlines, 8.6m per month for legal and professional services related to chapter 11 reorganisation Loss of customers, suppliers,... (see next slide) Albert Banal-Estañol (UPF and BGSE) Chapter 1 26 / 34

27 Bankruptcy costs Some indirect costs of nancial distress Loss of customers: Bankruptcy may enable rms to walk away from future commitments (support, future upgrades,... ) Loss of suppliers: Bankruptcy may enable rms not to pay for inventory Swissair forced to shut because suppliers refuse to fuel planes Loss of employees: Fear of job security Paci c Gas and Electric Co. paid to retain 17 key employees Loss of receivables: Debtors might have an opportunity to avoid obligations Fire sales of assets: Companies need to sell assets quickly to raise cash Albert Banal-Estañol (UPF and BGSE) Chapter 1 27 / 34

28 Bankruptcy costs Summing up: the Trade-O Theory Tax bene ts vs costs of nancial distress costs: V L = V U + PV (interest tax shield) PV ( nancial distress costs) To determine the PV(Financial distress costs), need to compute Probability, which: increases with the amount of a rm s liabilities, relative to assets increases with the volatility of a rm s cash ows and asset values increases with the strength of the competitors 2. Magnitude of costs once in distress, which depends on industry: Technology: high (loss of customers, key personnel, lack of tangible assets being liquidated) Real estate: low (assets can (in normal times) be sold relatively easily) Albert Banal-Estañol (UPF and BGSE) Chapter 1 28 / 34

29 Bankruptcy costs Practical implications Firms with high prob. of distress should minimise costs of distress: Avoid too much debt But also, if debt is need it, use easy-to-reorganize debt structure Banks rather than many bondholders Few rather than many banks Few rather than many classes of debt In general rms with mostly intangible assets have high distress costs!follow conservative debt nancing policies In contrast, rms with mostly tangible assets have low distress costs!load up on debt to get the tax shield Albert Banal-Estañol (UPF and BGSE) Chapter 1 29 / 34

30 Optimal leverage Bankruptcy costs Albert Banal-Estañol (UPF and BGSE) Chapter 1 30 / 34

31 Bankruptcy costs Empirical Evidence 1 Firms that produce steady cash ows (e.g. utilities), and have easily redeployable assets that they can use as collateral (e.g. aircraft or real estate) have high debt ratios 2 Risky rms, with little current cash ows, and rms with intangible assets (e.g. with high R&D and advertising) tend to have low leverage 3 Companies whose value consists largely of intangible growth options (high market-to-book ratios and heavy R&D spending) have lower leverage ratios 4 Most pro table companies tend not to borrow as much: they rely on internally generated funds Albert Banal-Estañol (UPF and BGSE) Chapter 1 31 / 34

32 Debt to Equity Ratios Source: Grinblatt and Titman Bankruptcy costs Albert Banal-Estañol (UPF and BGSE) Chapter 1 32 / 34

33 Bankruptcy costs Measures of net worth by industry in the US 1985 Source: White (1991) Albert Banal-Estañol (UPF and BGSE) Chapter 1 33 / 34

34 Main conclusions Main Conclusions 1 In absence of neutral taxes and bankruptcy costs (and other imperfections), a rm s value is independent of its capital structure and nancing decisions are irrelevant 2 However, the real world is di erent 1 Resources taken away as taxes depends debt/equity mix * In the presence of corporate taxes, with interest expenses being tax deductible, a rm s value increases with its debt/equity ratio * Personal taxes favour equity over debt and partially o set the e ect of corporate taxes 2 Firm value may be lost in bankruptcy, and leverage increases the likelihood * When bankruptcy is costly, there may exist an optimal capital structure with a mixture of debt and equity Albert Banal-Estañol (UPF and BGSE) Chapter 1 34 / 34

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