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Chapter 16 Capital Structure Decisions: Part II

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16-2 Topics in Chapter MM models: Without corporate taxes (1958) With corporate taxes (1963) Miller model: (1977) With corporate and personal taxes Extension to MM with growth and the tax shield is risky Equity as an option

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16-3 Modigliani and Miller (MM) Published theoretical papers that changed the way people thought about financial leverage Nobel prizes in economics MM 1958 MM 1963 Miller 1977 The papers differed in their assumptions about taxes.

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16-4 Model Assumptions 1.No taxes 2. Business risk measured by σ EBIT Firms with same risk = “homogeneous risk class” 3.Homogeneous expectations All investors have same estimates of firm’s future EBIT

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16-5 4.Perfect capital markets No transactions costs All can borrow and lend at riskfree rate 5.Debt is riskless Interest rate on all debt = r f 6.All cash flows are perpetuities All firms are expect zero growth All bonds are perpetuities Model Assumptions

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16-6 Proposition I: MM with Zero Taxes (1958) No agency or financial distress costs. V F = EBIT capitalized at WACC L = Leveredr rL = levered return U = Unleveredr rU =unlevered return (16-1)

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16-7 MM (1958) Proposition I Implications: When there are no taxes, the value of the firm is independent of its leverage The WACC is completely independent of a firm’s capital structure Regardless of the amount of debt a firm uses, its WACC = cost of equity that it would have if it used no debt

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16-8 Proposition II: r sL = r sU + (r sU - r d )(D/S) MM with Zero Taxes (1958) r rL = levered return r rU =unlevered return D = market value of firm’s debt S = market value of firm’s equity r d = constant cost of debt (16-2)

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16-9 MM (1958) Proposition II When there are no taxes: (1) The cost of equity to an unlevered firm in the same risk class, r sU, plus (2) A risk premium depending on the difference between an unlevered firm’s costs of debt and equity and the amount of debt used As debt increases, the cost of equity also increases, and in a mathematically precise manner.

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16-10 MM (1958) Implications Using more debt will noe increase the value of the firm The benefits of additional debt will be exactly offset by the increase in the cost of equity In a world without taxes, both the value of the firm and its WACC would be unaffected by its capital structure.

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16-11 MM (1958) Arbitrage Proof Assume all firms = 0 growth EBIT remains constant All earnings paid out as dividends (16-3)

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16-12 Firms U and L are in same risk class EBIT (U,L) = $900,000 Firm U has no debt; r sU = 10% Firm L has $4,000,000 debt at r d = 7.5% All net income is paid out as dividends No corporate or personal taxes Both firms are “no growth” (g=0) MM (1958) Arbitrage Proof

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16-13 Before Any Arbitrage

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16-14 V U = $9,000,000Dis-equilibrium V L = $10,000,000 Situation Suppose you own 10% of L’s stock Market value = $600,000 If V L >V U, then you can increase your income without increasing your risk Before Any Arbitrage

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16-15 Arbitrage Proof 1. Sell your 10% of L’s stock for $600,000 2. Borrow an amount = 10% of L’s debt ($400,000) 3. Buy 10% of U’s stock for $900,000 4. Invest the remaining $100,000 at 7.5%

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16-16 Before & After Arbitrage

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16-17 Arbitrage Proof Propositions I and II Substitute $400,000 of “homemade leverage” for L’s leverage Neither effective debt nor risk has changed Profit motive would force price of L’s stock down and U’s up until market values are equal.

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16-18 Propositions I & II r sL = r sU + (r sU - r d )(D/S) Proposition I: Proposition II:

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16-19 Without taxes Cost of Capital (%) 26 20 14 8 020406080100 Debt/Value Ratio (%) rsrs WACC rdrd MM Relationships Between Capital Costs and Leverage (D/V)

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16-20 The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost. Although r d remains constant, r s increases with leverage. The increase in r s is exactly sufficient to keep the WACC constant. MM Relationships Between Capital Costs and Leverage (D/V)

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16-21 With corporate taxes added, the MM propositions become: Proposition I: V L = V U + TD Proposition II: r sL = r sU + (r sU - r d )(1 - T)(D/S) MM (1963) with Corporate Taxes (16-4) (16-6)

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16-22 Tax Shield and Value of U (16-5)

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16-23 Hamada’s Equation (16-7) Beta increases with leverage

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16-24 Notes About the New Propositions 1. When corporate taxes are added, V L ≠ V U. V L increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. 2. r sL increases with leverage at a slower rate when corporate taxes are considered.

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16-25 Frederickson Water Company No debt E(EBIT) = $2,400,000 No growth All income paid out as dividends If uses debt, r D =8% Any debt would be used to repurchase stock Beta = 0.80 (b U ) Risk-free rate = 8%r sU = 12% Market risk premium = 5%

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16-26 V U = = = $20.0m EBIT r sU $2.4 m 0.12 Value of FWC (No Taxes) With No Debt & No Taxes With $10.0m Debt & No Taxes S=V-D = $20 m - $10 m = $10 m r sL = r sU + (r sU - r d )(D/S) = 12% + (12%-8%)($10/$10) = 16%

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16-27 FWC’s WACC Value of the firm and the firm’s WACC are independent of the amount of debt

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16-28 FWCC with Corporate Taxes Tax rate = 40% Debt = $10 m EBIT = $4,000,000* Taxes will reduce net income and EBIT EBIT increased to make comparison easier

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16-29 FWCC With Corporate Taxes

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16-30 FWCC with Corporate Taxes

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16-31 Cost of Capital (%) 26 20 14 8 020406080100 Debt/Value Ratio (%) rsrs WACC r d (1 - T) MM: Capital Costs vs. Leverage with Corporate Taxes

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16-32 Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used. Value of Firm, V (%) 43214321 00.51.01.52.02.5 Debt (Millions of $) VLVL VUVU TD MM: Value vs. Debt with Corporate Taxes

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16-33 Miller’s Proposition I: V L = V U + [ 1 - ] D T c = corporate tax rate T d = personal tax rate on debt income T s = personal tax rate on stock income (1 - T c )(1 - T s ) (1 - T d ) Miller Model with Personal Taxes (16-12)

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16-34 V L = V U + [ 1 - ] D = V U + (1 - 0.75)D = V U + 0.25D (1 - 0.40)(1 - 0.12) (1 - 0.30) T c = 40%, T d = 30%, T s = 12% Value rises with debt; each $100 increase in debt raises L’s value by $25.

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16-35 Miller vs. MM Model with Corporate Taxes If only corporate taxes, then V L = V U + T c D = V U + 0.40D Here $100 of debt raises value by $40. Personal taxes lowers the gain from leverage, but the net effect depends on tax rates.

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16-36 Miller Model Implications 1. The right-hand term = gain from leverage 2. If taxes ignored, then Miller=Original MM 3. If personal taxes ignored, then Miller = MM with corporate taxes (16-12)

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16-37 Miller Model Implications 4. If T s =T d, right-hand term = T c 5. If (1-T)(1-T) =(1-T), right-hand term= 0 No gain to leverage (16-12)

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16-38 Criticisms of MM and Miller No one believes the models holds precisely Models assume personal and corporate leverage are perfect substitutes Homemade leverage puts stockholders in grater risk of bankruptcy Brokerage costs are assumed to be 0

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16-39 Criticisms of MM and Miller No one believes the models holds precisely 4. Individuals cannot borrow at the risk- free rate 5. For the Miller equilibrium to be reached, the tax benefit from debt mustbe the same for all firms 6. MM and Miller assumed no cost to financial distress

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16-40 Under MM (with taxes; no growth) V L = V U + T D This assumes the tax shield is discounted at the cost of debt. The debt tax shield will be larger if the firms grow MM with Nonzero Growth & A Risky Tax Shield

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16-41 MM with Nonzero Growth & a Risky Tax Shield Value of (growing) tax shield = Value of levered firm with growth: (16-14) (16-15)

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16-42 MM with Nonzero Growth & a Risky Tax Shield If r TS = r sU : (16-16) (16-17) (16-18)

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16-43 Risky Debt MM and Hamada assume riskless debt Β d = 0 If B d ≠ 0:

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16-44 MM Extension with Growth Peterson Power Illustration E(FCF) = $1 m G = 7% r sU = 12% T = 40% V U = $20 m $10 m debt r d = 8%

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16-45 Peterson Power

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16-46 FWC vs. PPI

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16-47 Cost of Capital for MM and Extension

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16-48 Equity as an Option: Kunkel, Inc. Firm value (Debt + Equity) = $20 m Firm has $10 million face value of 5-year zero coupon debt coming due soon If the current value of the firm (D+S) = $9 m: Firm will default on debt; equity holders get 0 If firm value > $10 m: Firm pays off the debt; equity holders keep the firm Payoff to stockholders = Max(P-$10m,0)

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16-49 Notation V = Value of the option P = Value of the firm (S+D) X = strike = value of debt r RF = risk-free rate σ = volatility of the underlying asset T = time to maturity in years

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16-50 Kunkel Variables P = $20 million (firm value) X = $10 million (face value of debt) T = 5 years (maturity of debt) r RF = 6% σ = 40%

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16-51 The Black-Scholes Formulas (16-19) (16-21) (16-20)

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16-52 Formula Functions ln = natural log N(x) = the probability that a normally distributed variable with a mean of zero and a standard deviation of 1 is less than x N(d1) and N(d2) denote the standard normal probability for the values of d1 and d2.

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16-53 BSOPM Kunkel Example P = $20r RF = 6% σ = 40% X = $10T = 5

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16-54 BSOPM Call Price Example d 1 = 1.5576N(1.5576) = 0.9403 d 2 = 0.6632N(0.6632) = 0.7464

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16-55 Zero-Coupon Debt Yield Debt yield for 5-year zero coupon debt = (Face value / Price) 1/5 – 1 = ($10 million/ $6.72 million) – 1 = 8.27% Yield on debt depends on: Probability of default Value of the option

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16-56 Managerial Incentives Managers can change a firm's by changing the assets the firm invests in. Changing can: Change the value of the equity, even if it doesn't change the expected cash flows Transfer wealth from bondholders to stockholders by making the option value of the stock worth more, which makes what is left, the debt value, worth less.

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16-57 Effect on Option Values Volatility = σ Increased volatility increased upside potential and downside risk Increased volatility is NOT good for the holder of a share of stock Increased volatility is good for an option holder Option holder has no downside risk Greater potential for higher upside payoff

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16-58 Bait and Switch Managers who know the effect of volatility, might tell debtholders they are going to invest in one kind of asset, and, instead, invest in riskier assets. “Bait and Switch” Bondholders will require: Higher coupon rates Strict bond covenants as protection

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16-59 Risky Coupon Debt More complex analysis With each coupon payment management has an option on an option: If it makes the interest payment then it purchases the right to later make the principal payment and keep the firm This is called a compound option.

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16-60 Capital Structure Theory The Authors’ View 1. Debt financing has the benefit of tax deductibility so firms should have some debt in their capital structure 2. Financial distress and agency costs place limits on debt usage

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16-61 Capital Structure Theory The Authors’ View 3. “Pecking Order” Due to problems from asymmetric information and flotation costs, low- growth firms should follow a pecking order in raising funds (R/E, debt, new equity) High-growth firms whose growth involves tangible assets should follow the same pecking order (r/e, debt. Equity)

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16-62 Capital Structure Theory The Authors’ View 3. “Pecking Order” High-growth firms whose growth is primarily in intangible assets should emphasize stock rather than debt 4. Firms should maintain reserve borrowing power

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