# Capital Structure Basic concepts: no taxes. Chapter 15 Capital Structure: Basic Concepts  Capital-structure and pie theory  No-arbitrage pricing. 

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Capital Structure Basic concepts: no taxes

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.

Financial Leverage, EPS, and ROE CurrentProposed Assets\$20,000\$20,000 Debt\$0\$8,000 Equity\$20,000\$12,000 Debt/Equity 0.000.67 Interest raten/a8% Shares 400 240 Share price\$50\$50

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

MM I Cash flows

MM I Expected cash flows (*)

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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