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**Corporate Finance Ross Westerfield Jaffe**

Sixth Edition 15 Chapter Fifteen Capital Structure: Basic Concepts Prepared by Gady Jacoby University of Manitoba and Sebouh Aintablian American University of Beirut

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**Chapter Outline 15.1 The Capital-Structure Question and The Pie Theory**

15.2 Maximizing Firm Value versus Maximizing Stockholder Interests 15.3 Financial Leverage and Firm Value: An Example 15.4 Modigliani and Miller: Proposition II (No Taxes) 15.5 Taxes 15.6 Summary and Conclusions

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**15.1 The Capital-Structure Question and The Pie Theory**

The value of a firm is defined to be the sum of the value of the firm’s debt and the firm’s equity. V = B + S If the goal of the management of the firm is to make the firm as valuable as possible, then the firm should pick the debt-equity ratio that makes the pie as big as possible. S B Value of the Firm

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**The Capital-Structure Question**

There are really two important questions: Why should the stockholders care about maximizing firm value? Perhaps they should be interested in strategies that maximize shareholder value. What is the ratio of debt-to-equity that maximizes the shareholder’s value? As it turns out, changes in capital structure benefit the stockholders if and only if the value of the firm increases.

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**15.3 Financial Leverage, EPS, and ROE**

Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.) Proposed $20,000 $8,000 $12,000 2/3 8% 240 $50 Current Assets $20,000 Debt $0 Equity $20,000 Debt/Equity ratio 0.00 Interest rate n/a Shares outstanding 400 Share price $50 The firm borrows $8,000 and buys back 160 shares at $50 per share.

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**EPS and ROE Under Current Capital Structure**

Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 0 0 0 Net income $1,000 $2,000 $3,000 EPS $2.50 $5.00 $7.50 ROA 5% 10% 15% ROE 5% 10% 15% Current Shares Outstanding = 400 shares

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**EPS and ROE Under Proposed Capital Structure**

Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest Net income $360 $1,360 $2,360 EPS $1.50 $5.67 $9.83 ROA 5% 10% 15% ROE 3% 11% 20% Proposed Shares Outstanding = 240 shares

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**EPS and ROE Under Both Capital Structures**

All-Equity Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 0 0 0 Net income $1,000 $2,000 $3,000 EPS $2.50 $5.00 $7.50 ROA 5% 10% 15% ROE 5% 10% 15% Current Shares Outstanding = 400 shares Levered Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest Net income $360 $1,360 $2,360 EPS $1.50 $5.67 $9.83 ROA 5% 10% 15% ROE 3% 11% 20% Proposed Shares Outstanding = 240 shares

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**Financial Leverage and EPS**

12.00 Debt 10.00 8.00 No Debt 6.00 Advantage to debt Break-even point EPS 4.00 2.00 0.00 1,000 2,000 3,000 Disadvantage to debt (2.00) EBIT EBI in dollars, no taxes

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**Assumptions of the Modigliani-Miller Model**

Homogeneous Expectations Homogeneous Business Risk Classes Perpetual Cash Flows Perfect Capital Markets: Perfect competition Firms and investors can borrow/lend at the same rate Equal access to all relevant information No transaction costs No taxes

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**Homemade Leverage: An Example**

Recession Expected Expansion EPS of Unlevered Firm $2.50 $5.00 $7.50 Earnings for 40 shares $100 $200 $300 Less interest on $800 (8%) $64 $64 $64 Net Profits $36 $136 $236 ROE (Net Profits / $1,200) 3% 11% 20% We are buying 40 shares of a $50 stock on margin. We get the same ROE as if we bought into a levered firm. Our personal debt equity ratio is:

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**Homemade (Un)Leverage: An Example**

Recession Expected Expansion EPS of Levered Firm $1.50 $5.67 $9.83 Earnings for 24 shares $36 $136 $236 Plus interest on $800 (8%) $64 $64 $64 Net profits $100 $200 $300 ROE (Net profits / $2,000) 5% 10% 15% Buying 24 shares of an otherwise identical levered firm along with some of the firm’s debt gets us to the ROE of the unlevered firm. This is the fundamental insight of M&M

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**The MM Propositions I & II (No Taxes)**

Proposition I Firm value is not affected by leverage VL = VU Proposition II Leverage increases the risk and return to stockholders rs = r0 + (B / SL) (r0 - rB) rB is the interest rate (cost of debt) rs is the return on (levered) equity (cost of equity) r0 is the return on unlevered equity (cost of capital) B is the value of debt SL is the value of levered equity

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**The MM Proposition I (No Taxes)**

The derivation is straightforward: The present value of this stream of cash flows is VL The present value of this stream of cash flows is VU

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**15.4 The MM Proposition II (No Taxes)**

The derivation is straightforward:

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The Cost of Equity, the Cost of Debt, and the Weighted Average Cost of Capital: MM Proposition II with No Corporate Taxes Cost of capital: r (%) r0 rB rB Debt-to-equity Ratio

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**15.5 Taxes The MM Propositions I & II (with Corporate Taxes)**

Proposition I (with Corporate Taxes) Firm value increases with leverage VL = VU + TC B Proposition II (with Corporate Taxes) Some of the increase in equity risk and return is offset by interest tax shield rS = r0 + (B/S)×(1-TC)×(r0 - rB) rB is the interest rate (cost of debt) rS is the return on equity (cost of equity) r0 is the return on unlevered equity (cost of capital) B is the value of debt S is the value of levered equity

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**The MM Proposition I (Corp. Taxes)**

The present value of this stream of cash flows is VL The present value of the first term is VU The present value of the second term is TCB

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**The MM Proposition II (Corp. Taxes)**

Start with M&M Proposition I with taxes: Since The cash flows from each side of the balance sheet must equal: Divide both sides by S Which quickly reduces to

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**The Effect of Financial Leverage on the Cost of Debt and Equity Capital**

Cost of capital: r (%) r0 rB Debt-to-equity ratio (B/S)

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**Total Cash Flow to Investors Under Each Capital Structure with Corp**

Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes All-Equity Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 0 0 0 EBT $1,000 $2,000 $3,000 Taxes (Tc = 35% $350 $700 $1,050 Total Cash Flow to S/H $650 $1,300 $1,950 Levered Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 8% ) EBT $360 $1,360 $2,360 Taxes (Tc = 35%) $126 $476 $826 Total Cash Flow $ $468+$640 $1,534+$640 (to both S/H & B/H): $874 $1,524 $2,174 EBIT(1-Tc)+TCrBB $650+$224 $1,300+$224 $1,950+$224 $874 $1,524 $2,174

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**Total Cash Flow to Investors Under Each Capital Structure with Corp**

Total Cash Flow to Investors Under Each Capital Structure with Corp. Taxes All-equity firm Levered firm S G S G B The levered firm pays less in taxes than does the all-equity firm. Thus, the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm.

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Summary: No Taxes In a world of no taxes, the value of the firm is unaffected by capital structure. This is M&M Proposition I: VL = VU Prop I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage. In a world of no taxes, M&M Proposition II states that leverage increases the risk and return to stockholders

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Summary: Taxes In a world of taxes, but no bankruptcy costs, the value of the firm increases with leverage. This is M&M Proposition I: VL = VU + TC B Prop I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage. In a world of taxes, M&M Proposition II states that leverage increases the risk and return to stockholders.

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**Prospectus: Bankruptcy Costs**

So far, we have seen M&M suggest that financial leverage does not matter, or imply that taxes cause the optimal financial structure to be 100% debt. In the real world, most executives do not like a capital structure of 100% debt because that is a state known as “bankruptcy.” In the next chapter we will introduce the notion of a limit on the use of debt: financial distress. Use this chapter to get comfortable with “M&M algebra.”

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