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Capital Structure Basic concepts: no taxes

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Chapter 15 Capital Structure: Basic Concepts Capital-structure and pie theory No-arbitrage pricing. Example: shares for debt Value Required return on the levered firm.

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Financial Leverage, EPS, and ROE CurrentProposed Assets$20,000$20,000 Debt$0$8,000 Equity$20,000$12,000 Debt/Equity Interest raten/a8% Shares Share price$50$50

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Comments Straight swap of equity for debt Market prices unchanged Real asset unchanged

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Financial leverage and risk Three states: bust, normal, boom. Probabilities not explicit. Look at each state separately.

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EPS, ROE, Current Structure Shares Outstanding = 400 Bust Normal Boom EBIT$1,000$2,000$3,000 Interest000 Net income$1,000$2,000$3,000 EPS$2.50$5.00$7.50 ROA5%10%15% ROE5%10%15%

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EPS and ROE under Proposed Capital Structure Shares Outstanding = 240 Bust Normal Boom EBIT$1,000$2,000$3,000 Interest Net income$360$1,360$2,360 EPS$1.50$5.67$9.83 ROA5%10%15% ROE3%11%20%

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Financial and operating leverage Find the point of equal EPS Let x = EBIT Solve x/400 = (x - 640)/240 Solution x = EPS = 4 per share, in either structure

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(2.00) ,0002,0003,000 EBIT EPS Debt No Debt Break-even Point

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Modigliani-Miller (MM) Model Perpetual Cash Flows (convenient) Firms and investors can borrow and lend at the same rate (convenient) No transaction costs (convenient) No taxes

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Homemade leverage Instead of the firm leveraging or unleveraging, the investor does it herself, by borrowing or lending, leveraging or unleveraging her portfolio.

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Borrow $8000, buy the unlevered firm for $20,000 Bust NormalBoom Earnings $1000$2000$3000 Interest at 8%$640$640$640 Net Profits$360$1360$2360 ROE (on $12K)3%11%20% Same as owning the levered firm

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Okay, don’t buy the whole firm Buy 10%, forty shares for $2000. Borrow $800. Total cost $1200 Same as having 10% of the levered firm, that is, 24 shares at $50 per share.

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Homemade annihilation of leverage Idea. Form a portfolio. Part lending… part the levered firm. Portfolio has the action of the unlevered firm. A levered firm is a portfolio.

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Buy the levered firm (240 shares) and lend 8000 Cost of Portfolio = = Bust NormalBoom EPS $1.50$5.67$9.83 Earnings $360$1360$2360 Interest at (8%)$640$640$640 Net cash flow$1000$2000$3000 ROE 5%10%15% (Net cash flow / $2,000)

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The firm is a veil A way for shareholders to hold a portfolio.

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Proposition I of MM (No Taxes) P1: Value is unaffected by leverage P1: V L = V U ; or S L + B = S U Pie theory

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Proposition II of M-M (no taxes) r B is the interest rate r s is the return on (levered) equity r 0 is the return on unlevered equity B is value of debt S L is value of levered equity r s = r 0 + (B / S L ) (r 0 - r B )

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Quick derivation of MM II Uses MM I. Value unchanged. Uses cash flow constraint.

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ValueRandom cash flow SharesSLSL sLsL BondsBb Unlevered firmSUSU s U = s L + b For instance, capital structure Conclusion: S U = S L + B

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MM I Cash flows

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MM I Expected cash flows (*)

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Weighted average cost of capital Go back to equation (*) in the derivation, divide by S L + B Result: r WACC = r 0

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MM Proposition II no tax Debt-to- equity ratio (B/S) Cost of capital: r (%). r0r0 rSrS r WACC rBrB

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What is the weighted average cost of capital ? Give the definitions and the formula. r WACC = S/(S+B))r S + (B/(S+B))(1-T C )r B r WACC is the market rate at which the physical asset of the firm is discounted. r WACC is the market rate for project whose risk profile is like that of the physical asset of the firm.

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Conclusion Weighted average cost of capital doesn’t change because the physical asset of the firm doesn’t change.

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