EMBA in Management & Finance. Corporate Finance. Eric Jondeau

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1 EMA in Management & Finance Corporate Finance

2 EMA in Management & Finance Lecture 3: Capital Structure Modigliani and Miller

3 Outline 1 The Capital-Structure Question 2 Financial Leverage and Firm Value 3 Modigliani - Miller Propositions (No Taxes) 4 Modigliani - Miller Propositions (With Taxes) 5 Summary and Conclusions EMA 3/27

4 1. The Capital Structure Question 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 = + 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 EMA 4/27

5 The Capital Structure Question There are really two important questions: 1. Why should the stockholders care about maximizing firm value? Perhaps they should be interested in strategies that maximize shareholder value. 2. 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. EMA 5/27

6 2. Financial Leverage and Firm Value Consider an all-equity firm that is considering going into debt. (Maybe some of the original shareholders want to cash out.) 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 $50 EMA 6/27

7 EPS and ROE under current capital structure Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest 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 EMA 7/27

8 EPS and ROE under proposed capital structure Recession Expected Expansion EIT $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 EMA 8/27

9 EPS and ROE under both capital structures All-Equity Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest 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 EIT $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 EMA 9/27

10 Financial leverage and EPS EPS (dollars) reak-even point Debt No Debt Advantage to debt (2.00) Disadvantage to debt 1,000 2,000 3,000 EIT in dollars, no taxes EMA 10/27

11 3. Modigliani-Miller Propositions (No Taxes) Assumptions of the Modigliani-Miller model Homogeneous Expectations Homogeneous usiness 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 EMA 11/27

12 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: $800 2 S = $1, 200 = 3 EMA 12/27

13 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% uying 24 shares of an otherwise 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 MM. EMA 13/27

14 The MM Propositions I & II (No Taxes) Proposition I Firm value is not affected by leverage: V L = V U Proposition II Leverage increases the risk and return to stockholders r is the interest rate (cost of debt) r S is the return on (levered) equity (cost of equity) r 0 is the return on unlevered equity (cost of capital) S L is the value of levered equity is the value of debt r = r + ( / S )( r r ) S 0 L 0 r = 0 Expected earnings to unlevered firm Unlevered equity EMA 14/27

15 The MM Proposition I Derivation Shareholders in a levered firm receive ondholders receive EIT r r Total cash flow to all stakeholders: ( EIT r ) + r The present value of this stream of cash flows is V L Clearly ( EIT r ) + r = EIT The present value of this stream of cash flows is V U V L = V U EMA 15/27

16 The MM Proposition II Derivation S r = r + r + S + S WACC S S r + rs = r + S + S r WACC is constant for a firm regardless of its capital structure. It is therefore equal to the cost of capital for an allequity firm r = r Multiply both sides by + S + S S + S r + rs = r S + S S + S S 0 0 WACC + S r + rs = r0 S S r rs r0 r0 S + = S + rs = r 0 + ( r 0 r ) S 0. + S S EMA 16/27

17 The MM Proposition II Derivation Cost of Capital r (%) r = r + ( r r ) S 0 0 SL r 0 S r = r + r WACC S + SL + SL r r Debt-to-equity Ratio (/S) EMA 17/27

18 4. Modigliani-Miller Propositions (With Taxes) Proposition I (with Corporate Taxes) Firm value increases with leverage: VL = VU +τ C Proposition II (with Corporate Taxes) Some of the increase in equity risk and return is offset by interest tax shield r = r + ( / S )(1 τ )( r r ) S 0 L C 0 r is the interest rate (cost of debt) r S is the return on equity (cost of equity) r 0 is the return on unlevered equity (cost of capital) is the value of debt S is the value of levered equity EMA 18/27

19 The MM Proposition I Derivation Shareholders in a levered firm receive ondholders receive Total cash flow to all stakeholders: The present value of this stream of cash flows is V L Clearly ( EIT r ) (1 τ ) r ( EIT r ) (1 τ ) + r The present value of the first term is V U The present value of the second term is τ C C C ( EIT r ) (1 τ ) + r C = EIT (1 τ ) r (1 τ ) + r C C = EIT (1 τ ) + τ r C C VL = VU +τc EMA 19/27

20 The MM Proposition II Derivation Start with MM Proposition I with taxes: Since The cash flows from each side of the balance sheet must equal: Divide both sides by S which reduces to V = S + S + = V + τ L U C V = S + (1 τ ) U Sr + r = V r + τ r S U 0 C C Sr + r = [ S + (1 τ )] r + τ r S C 0 C r + r = [1 + (1 τ )] r + τ r S S S C 0 S C VL = VU +τ C rs = r0 + (1 τc )( r0 r ) S EMA 20/27

21 The Effect of Financial Leverage with Corp Taxes Cost of Capital r (%) rs = r0 + ( r0 r ) SL r = r + (1 τ )( r r ) S 0 C 0 SL r 0 SL r = (1 ) r r S τ + + L + S WACC C S L r Debt-to-equity Ratio (/S) EMA 21/27

22 Total Cash Flow to Investors Under Each Capital Structure with Corporate Taxes All-Equity Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest ET $1,000 $2,000 $3,000 Taxes (35%) $350 $700 $1,050 Total Cash Flow to S/H $650 $1,300 $1,950 Levered Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest ($8000 at 8% ) $640 $640 $640 ET $360 $1,360 $2,360 Taxes (35%) $126 $476 $826 Total Cash Flow $ $468+$640 $1,534+$640 (to both S/H & /H): $874 $1,524 $2,174 EIT(1-τ C )+τ C r $650+$224 $1,300+$224 $1,950+$224 $874 $1,524 $2,174 EMA 22/27

23 Total Cash Flow to Investors Under Each Capital Structure with Corporate Taxes All-equity firm Levered firm S G S G 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. EMA 23/27

24 Total Cash Flow to Investors Under Each Capital Structure with Corporate Taxes All-equity firm Levered firm S G S G The sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm. This is how cutting the pie differently can make the pie larger: the government takes a smaller slice of the pie! EMA 24/27

25 Summary: No Taxes In a world of no taxes, the value of the firm is unaffected by capital structure. This is MM Proposition I: V L = V U Proposition I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage. In a world of no taxes, MM Proposition II states that leverage increases the risk and return to stockholders r = r + ( r r ) S 0 0 SL EMA 25/27

26 Summary: Taxes In a world of taxes, but no bankruptcy costs, the value of the firm increases with leverage. This is MM Proposition I: VL = VU +τ C Proposition I holds because shareholders can achieve any pattern of payouts they desire with homemade leverage. In a world of taxes, MM Proposition II states that leverage increases the risk and return to stockholders. r = r + (1 τ )( r r ) S 0 C 0 SL EMA 26/27

27 Prospectus: ankruptcy Costs So far, we have seen MM 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 session is to get comfortable with MM algebra. EMA 27/27

Let s Build a Capital Structure

Let s Build a Capital Structure FIN 614 Capital tructure Design Principles Professor Robert.H. Hauswald Kogod chool of usiness, AU Let s uild a Capital tructure Determinants of firms debt-equity mix operations funded with a combination