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Session 6: Capital Structure I C Corporate Finance Topics

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Outline Basic capital structure theory—irrelevance Debt and equity as options Tax effects Valuation

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Introduction to Capital Structure Problem: What is the optimal mix of debt and equity, i.e., the capital structure that maximizes the value of the firm? Approach: Begin with a simple model (a framework) that identifies the relevant issues, then add realism.

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A Road Map Perfect markets (no taxes) capital structure is irrelevant +corporate taxes more debt is better +financial distress and agency costs optimal capital structure

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Options and Corporate Finance Consider a firm that will liquidate in 1 year, with $10 million of 1-year zero coupon debt outstanding. If the firm is worth less than $10 million in 1 year, the debtholders receive everything and the stockholders receive nothing. Otherwise, the debtholders receive $10 million and the stockholders receive the residual.

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Equity and Debt Payoffs Firm value 10 Firm value 10 EquityDebt Equity: a call option on the firm Debt: firm - call = risk-free bond - put

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An example A firm undertakes a risky, zero NPV project and will be worth either $99 mill. or $44 mill. in 1 year. Value of the unlevered firm is $60 mill. Risk free rate is 10% Firm

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Introducing Debt The firm finances itself through Debt of $55 million to be paid after 1 year. Firm Equity ? 44 0 Debt ? 55 44

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Replicating Equity Replicate equity with a position in the firm financed by borrowing: 99 H B* = H B* = 0 H = 0.8, B* = 32 S = 0.8(60) - 32 = $16 million

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Replicating Debt Replicate debt with a position in the firm and a position in risk-free debt: 99 H B* = H B* = 44 H = 0.2, B* = -32 B = 0.2(60) + 32 = $44 million V = S + B = = $60 mill. Remained the same!

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Assumptions Perfect capital markets (no taxes or transaction costs) Personal and corporate borrowing at the same rate No information effects

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The Primary Result The value of the firm is independent of its capital structure, i.e., the financing mix is irrelevant (Miller & Modigliani). Proposition I: V U = V L

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Intuition Buying equity in the levered firm is firm- generated leverage Buying equity in the unlevered firm and borrowing is do-it-yourself leverage Conclusion: no one is willing to pay the firm for levering up when they are “free” to lever up individually

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Discount Rates The value result also has implications for discount rates ( r 0 is the cost of unlevered equity). Proposition II: r S = r 0 + (B/S)( r 0 - r B ) WACC = r 0 The WACC is constant and the cost of equity can be decomposed into business risk and financial risk.

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Valuation: The Dividend Discount Model The stock price today should be the discounted value of expected future dividends P = t D t /(1+r S ) t If dividends are growing at a constant rate, then the price of the stock (not including current dividend) is P 0 = D 1 / (r S - g)

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Expected Returns, Growth and P/E Ratios The valuation formula can be inverted to get expected returns: r S = (D 1 / P 0 ) + g Where does growth come from? g = b ROE b — earnings retention rate, i.e., D=(1-b)E ROE—return on equity What are the implied P/E ratios? P 0 = D 1 / (r S - g) = (1-b) E 1 / (r S – b ROE) P 0 / E 1 = (1-b) / (r S – b ROE)

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Equity Valuation The value of all the equity is just the aggregate value of all the shares outstanding, i.e., the discounted value of aggregate dividends. All the previous results apply.

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Introducing Corporate Taxes Earnings are taxed at the corporate rate Interest expense is tax deductible Dividends are not tax deductible Tax rate: T C

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Example..

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Value Implications Proposition I: V L = V U + PV(tax shield) PV(tax shield) = t [T C (interest expense) t ] / (1+ r B ) t Debt reduces the firm’s tax liability and therefore increases value The more debt, the higher the value of the firm

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An Example All equity firm with pre-tax earnings (cash flow) of $X in year 1, a retention rate of b, and growth rate g in perpetuity: V U = [(1-b)(1- T C )X] / ( r 0 -g) If this firm adds $B of perpetual debt: PV(tax shield) = [ T C ( r B B)] / r B = T C B V L = V U + T C B

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Discount Rates Prop. II: r S = r 0 + (1- T C )(B/S)( r 0 - r B ) WACC = [(S+(1- T C )B)/(S+B)] r 0 Equity risk increases with leverage (but more slowly than in the no tax case) WACC decreases as the amount of debt increases

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Recapitalization: An Example Firm characteristics: EBIT: 50% prob. of $1 million, 50% prob. of $2 million (in perpetuity) Depreciation = Cap. Ex. ΔNWC=0 100% payout (no growth, dividends = earnings) r 0 = 10% (required return on unlevered equity) T C = 40%

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Unlevered Value V U = [(1- T C )EBIT] / r 0 = [(1-0.4)1.5] / 0.1 = $9 mill. n = 1 million (shares outstanding) Share price: P = V U / n = $9.00

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Income Statement

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Recapitalization Firm issues $5 million of perpetual debt (r B = 8%) and uses the proceeds to repurchase equity. On announcement: Shareholders revalue the firm: V L = V U + T C B = (5) = $11 million Share price moves to $11/share $ 5 million repurchases shares (n = 545.5)

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Income Statement

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Assignments Reading –RWJ: Chapters , Appendix 16B –Problems: 16.2, 16.6, 16.8 Problem sets –Problem Set 2 due monday Cases –AHP due in 1 week

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