• 1. Chapter Outline15.1 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
    • 2. The Capital-Structure Question and The Pie TheoryThe 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 Value of the FirmSB 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.
    • 3. The Capital-Structure QuestionThere 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.
    • 4. Financial Leverage, EPS, and ROE Current Assets $20,000 Debt $0 Equity $20,000 Debt/Equity ratio 0.00 Interest rate n/a Shares outstanding 400 Share price $50 Proposed $20,000 $8,000 $12,000 2/3 8% 240 $50Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.)
    • 5. 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
    • 6. EPS and ROE Under Proposed Capital Structure 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
    • 7. EPS and ROE Under Both Capital Structures 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 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
    • 8. Financial Leverage and EPS(2.00)0.002.004.006.008.0010.0012.001,0002,0003,000EPSDebtNo DebtBreak-even point EBI in dollars, no taxesAdvantage to debtDisadvantage to debtEBIT
    • 9. Assumptions of the Modigliani-Miller ModelHomogeneous 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
    • 10. 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:
    • 11. 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
    • 12. 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
    • 13. 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
    • 14. The MM Proposition II (No Taxes)The derivation is straightforward:
    • 15. The Cost of Equity, the Cost of Debt, and the Weighted Average Cost of Capital: MM Proposition II with No Corporate TaxesDebt-to-equity RatioCost of capital: r (%)r0rBrB
    • 16. 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
    • 17. 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
    • 18. 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 SWhich quickly reduces to
    • 19. The Effect of Financial Leverage on the Cost of Debt and Equity CapitalDebt-to-equity ratio (B/S)Cost of capital: r (%)r0rB
    • 20. 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
    • 21. Total Cash Flow to Investors Under Each Capital Structure with Corp. TaxesThe 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.SGSGB All-equity firm Levered firm
    • 22. Summary: No TaxesIn 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
    • 23. Summary: TaxesIn 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.
    • 24. Prospectus: Bankruptcy CostsSo 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. The important use of this chapter is to get comfortable with “M&M algebra”.