Capital Structure (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, the the firm should pick the debt-equity ratio that makes the pie as big as possible. S B Value of the Firm

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.) 40% ownership 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.

EPS and ROE Under Current Capital Structure No Debt 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

EPS and ROE Under Proposed Capital Structure 40% ownership Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 640 640 640 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

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 40% ownership Levered Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 640 640 640 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

Financial Leverage and EPS 12.00 Does leverage increase Shareholders’ Value? 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) EBI in dollars, no taxes

Cost of Capital and Leverage Ratio This is impossible! Cost of Capital rE WACC rD Debt ratio

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

No Magic in Financial Leverage MM'S PROPOSITION I If capital markets are doing their job, firms cannot increase value by tinkering with capital structure. V is independent of the debt ratio. AN EVERYDAY ANALOGY It should cost no more to assemble a chicken than to buy one whole.

Homemade Leverage: An Example Recession Expected Expansion EPS of Unlevered Firm $2.50 $5.00 $7.50 ROE 3% 11% 20% 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:

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 other-wise identical levered firm along with the some of the firm’s debt gets us to the ROE of the unlevered firm. This is the fundamental insight of M&M

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

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

The MM Proposition II (No Taxes) The derivation is straightforward:

MM Proposition II with No Corporate Taxes Cost of capital: r (%) r0 rB rB Debt-to-equity Ratio

The Effect of Tax on WACC Firm value: shareholders plus bondholders a. Unlevered After-tax earnings = Pre-tax Earnings * (1-Tc) b. Levered After-tax Earnings = (Pre-Tax Earnings – Interest Paid to bondholders) * (1-Tc) + Interest Paid to bondholders) = Pre-tax Earnings * (1-Tc) + Tc * Interest Paid to Bondholders

Tax Shield Tax Shield: Tc * Interest Paid to Bondholders If this is a permanent steady flow: PV( Tax Shield) = Tc * Interest / Cost of debt = Tc * (D*rD) / rD = Tc * D Firm value increases with leverage VL = VU + TC B

rS = r0 + (B/S) × (r0 - rB) × (1-TC) M&M Proposition II Proposition II (with Corporate Taxes) Some of the increase in equity risk and return is offset by interest tax shield rS = r0 + (B/S) × (r0 - rB) × (1-TC) Compared with no-tax case rs = r0 + (B / SL) (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

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 ($800 @ 8% ) 640 640 640 EBT $360 $1,360 $2,360 Taxes (Tc = 35%) $126 $476 $826 Total Cash Flow $234+640 $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

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.

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

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.

Tax Shield The more we borrow, the higher the PV of tax shield we obtain! Is it good for firm to borrow more? Bottom line: Higher personal tax reduce the effect of tax shield Tax shield requires a positive taxable profits. Borrowing is not the only way for tax shield: depreciation, R&D expense and contribution to pension funds.

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.