Comments Straight swap of equity for debt Market prices unchanged Real asset unchanged
Financial leverage and risk Three states: bust, normal, boom. Probabilities not explicit. Look at each state separately.
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%
EPS and ROE under Proposed Capital Structure Shares Outstanding = 240 Bust Normal Boom EBIT$1,000$2,000$3,000 Interest640640640 Net income$360$1,360$2,360 EPS$1.50$5.67$9.83 ROA5%10%15% ROE3%11%20%
Financial and operating leverage Find the point of equal EPS Let x = EBIT Solve x/400 = (x - 640)/240 Solution x = 1600. EPS = 4 per share, in either structure
(2.00) 0.00 2.00 4.00 6.00 8.00 10.00 12.00 1,0002,0003,000 EBIT EPS Debt No Debt Break-even Point
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
Homemade leverage Instead of the firm leveraging or unleveraging, the investor does it herself, by borrowing or lending, leveraging or unleveraging her portfolio.
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
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.
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.
Buy the levered firm (240 shares) and lend 8000 Cost of Portfolio = 12000 + 8000 = 20000 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)
The firm is a veil A way for shareholders to hold a portfolio.
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
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 )
Quick derivation of MM II Uses MM I. Value unchanged. Uses cash flow constraint.
ValueRandom cash flow SharesSLSL sLsL BondsBb Unlevered firmSUSU s U = s L + b For instance, capital structure Conclusion: S U = S L + B
Weighted average cost of capital Go back to equation (*) in the derivation, divide by S L + B Result: r WACC = r 0
MM Proposition II no tax Debt-to- equity ratio (B/S) Cost of capital: r (%). r0r0 rSrS r WACC rBrB
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.
Conclusion Weighted average cost of capital doesn’t change because the physical asset of the firm doesn’t change.
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