Let s Build a Capital Structure

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Kelley Carroll
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1 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 of instruments tart with a benchmark: irrelevance of mix when does capital structure not impact firm value? M&M propositions: beginning of modern finance! Examine factors determining debt-equity mix taxes risk: financial and operating financial slack asset charateristics cost of financial distress 3/22/2011 Capital-tructure Design Robert.H. Hauswald 2

2 Of Capital tructures and Pies 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 = + = D + E 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. Value of the Firm 3/22/2011 Capital-tructure Design Robert.H. Hauswald 3 Financial Risk: Riskless Leverage Current Proposed Assets $20,000 $20,000 Debt $0 $8,000 Equity $20,000 $12,000 Debt/Equity ratio Interest rate n/a 8% hares outstanding hare price $50 $50 3/22/2011 Capital-tructure Design Robert.H. Hauswald 4

3 EP and ROE under Current Capital tructure Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest Net income $1,000 $2,000 $3,000 EP $2.50 $5.00 $7.50 ROA 5% 10% 15% ROE 5% 10% 15% Current hares Outstanding = 400 shares 3/22/2011 Capital-tructure Design Robert.H. Hauswald 5 EP and ROE under Proposed Capital tructure Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest Net income $360 $1,360 $2,360 EP $1.50 $5.67 $9.83 ROA 5% 10% 15% ROE 3% 11% 20% Proposed hares Outstanding = 240 shares 3/22/2011 Capital-tructure Design Robert.H. Hauswald 6

4 Financial Leverage and EP Debt 8.00 No Debt EP reak-even point Advantage to debt (2.00 1,000 2,000 3,000 Disadvantage to debt EIT in dollars, no taxes 3/22/2011 Capital-tructure Design Robert.H. Hauswald 7 Fundamental Question Does the debt and equity mix affect firm value? if so, when? The classics: Modigliani-Miller Propositions foundation of modern finance: two Nobel Laureates Irrelevance of capital structure: firm value first arbitrage argument (proof in Finance concept of Homemade (with love Leverage Modigliani-Miller Proposition I: the firm s value is independent of its capital structure under certain assumptions 3/22/2011 Capital-tructure Design Robert.H. Hauswald 8

5 Assumptions of the Modigliani- Miller Propositions 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 3/22/2011 Capital-tructure Design Robert.H. Hauswald 9 Modigliani-Miller Propositions I and II: No Taxes Proposition I: irrelevance of capital structure Firm value is not affected by leverage V L = V U Proposition II: cost of equity capital for a levered firm = constant overall cost of capital + a risk premium Leverage increases the risk and return to stockholders r s = r 0 + ( / L (r 0 - r 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 is the value of debt L is the value of levered equity 3/22/2011 Capital-tructure Design Robert.H. Hauswald 10

6 Modigliani-Miller Propositions I and II: with Taxes Proposition I (with corporate taxes: firm value increases with leverage V L = V U + T C Proposition II (with corporate taxes: interest tax shield partially offsets rise in equity risk and return r = r 0 + (/ (1-T C (r 0 - r r is the interest rate (cost of debt r is the return on equity (cost of equity r 0 is the return on unlevered equity (cost of capital is the value of debt is the value of levered equity 3/22/2011 Capital-tructure Design Robert.H. Hauswald 11 Effects of Financial Leverage with Corporate Taxes Cost of capital: r (% r = r 0 + ( r 0 r r = r0 + ( 1 TC ( r0 r L L r 0 L r WACC = r (1 TC + r + L + L r 3/22/2011 Capital-tructure Design Robert.H. Hauswald 12 Debt-to-equity ratio (/

7 Total Investor Cash Flow: Taxes All-Equity Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest ET $1,000 $2,000 $3,000 Taxes (Tc = 35% $350 $700 $1,050 Total Cash Flow to /H $650 $1,300 $1,950 Levered Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest 8% ET $360 $1,360 $2,360 Taxes (Tc = 35% $126 $476 $826 Total Cash Flow $ $468+$640 $1,534+$640 (to both /H & /H: $874 $1,524 $2,174 EIT(1-Tc+T C r $650+$224 $1,300+$224 $1,950+$224 $874 $1,524 $2,174 3/22/2011 Capital-tructure Design Robert.H. Hauswald 13 The Tax Advantage of Debt: Total Cash Flows to Investors All-equity firm Levered firm G G The levered firm pays less in taxes than does the allequity firm. Thus, the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm. 3/22/2011 Capital-tructure Design Robert.H. Hauswald 14

8 Personal Taxes Personal taxes negate some of the tax benefits of issuing corporate debt firms pay higher interest because of individuals taxdisadvantage relative to capital gains Miller (1977 shows that the value of a levered firm in terms of an unlevered firm is: (1 TC (1 T VL = VU T T = personal tax rate on equity income T = personal tax rate on bond income T C = corporate tax rate 3/22/2011 Capital-tructure Design Robert.H. Hauswald 15 MM Assumptions: ankruptcy Violations of MM assumptions: start with bankruptcy Including bankruptcy costs gives an optimum with both debt AND equity V L = V + td - U where = PV of financial distress costs (what are they? Hone your intuition: what would the previous graphs look like if you include bankruptcy costs? Including the cost of enforcing debt contracts shifts the debt optimum to the left shift s size affected by how the enforcement costs vary with the amount of the debt. 3/22/2011 Capital-tructure Design Robert.H. Hauswald 16

9 Agency Costs eparation of ownership and control managers are agents of shareholders costly conflicts of interests arise: examples? Investment opportunities not fixed managers may have incentives to decrease risk stockholders may have incentives to increase risk Differential information: managers control investors have less information than management or insiders about the firm s prospects and investments capital structure as signal for firm s prospects 3/22/2011 Capital-tructure Design Robert.H. Hauswald 17 How much Debt is Right for Your Company? 1. Taxes debt is deductible: more debt reduces the income tax paid IF the company is in a tax-paying position, i.e., firm profitable other potential tax shields: accelerated write-offs but gain to leverage (Miller 1977: tax advantage is smaller the more firms have to gross up interest on bonds to compensate personal investors for tax dis-advantage 2. Risk: financial and operating financial: directly controlled by managers. This can be noted in the formula for unleveraging and levering etas. The following example shows how the risk increases for the firm as it increases debt operating or asset risk: Can be controlled by managers through their choice of scale or size of fixed assets. 3/22/2011 Capital-tructure Design Robert.H. Hauswald 18

10 Corporate orrowing and Homemade Leverage Continue with deviations from ideal world of M&M taxes, financial and operating risks, etc. Homemade leverage - investors can create or adjust leverage how they see fit suppose the firm does not change its capital structure but investors want high debt: continue our example management might prefer low debt: why? An investor can replicate the returns of the proposed borrowing on personal account by making his or her own D/E ratio to be 0.67 for the investment 3/22/2011 Capital-tructure Design Robert.H. Hauswald 19 Example of EP and ROE All-Equity Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest Net income $1,000 $2,000 $3,000 EP $2.50 $5.00 $7.50 ROA 5% 10% 15% ROE 5% 10% 15% Current hares Outstanding = 400 shares Levered Recession Expected Expansion EIT $1,000 $2,000 $3,000 Interest Net income $360 $1,360 $2,360 EP $1.50 $5.67 $9.83 ROA 5% 10% 15% ROE 3% 11% 20% Proposed hares Outstanding = 240 shares 3/22/2011 Capital-tructure Design Robert.H. Hauswald 20

11 Retail Investing 2000 (or 1929? uppose an investor invests a total of $2,000 but has only $1,200 takes out a loan for $800 to buy additional shares Total investment: home-made leverage 24 shares bought with own money and 16 shares by borrowing $800 at 8% interest What is the investor s leverage? individual investors can also "unleverage" the firm's borrowing by lending to the firm investors can do or undo any pattern of financing for themselves! Pre-requisites for this strategy? 3/22/2011 Capital-tructure Design Robert.H. Hauswald 21 Homemade with Love: Leverage Recession Expected Expansion EP 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 $1, /22/2011 Capital-tructure Design Robert.H. Hauswald 22 = =

12 Homemade with Love: (UnLeverage Recession Expected Expansion EP 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 other-wise identical levered firm long with the some of the firm s debt = ROE of the unlevered firm. Fundamental insight of M&M: less leverage desired than company offers: undo it! 3/22/2011 Capital-tructure Design Robert.H. Hauswald 23 ummary Conclusions from example: 1. effect of financial leverage depends on EIT 2. with high EIT: leverage raises EP and ROE 3. variability of EP and ROE increases with financial leverage 4. does this matter? what about vitamin C? Next steps: capital structure design factors the debt-equity cocktail but: home made leverage (same example introduction to agency conflicts and costs 3/22/2011 Capital-tructure Design Robert.H. Hauswald 24

13 Valuation Exercise: MM II 1. Assume that cash flows in previous example continue for ever with 1/3 probability for each state the company s discount rate is 10% with no debt what is the value of the company? 2. Assume the firm issues debt with a YTM of 10% worth 50% of the firm s value found above what is the new discount rate for equity? use MMII what is the new value of equity? find expected cash flow what is the new TOTAL value of the company? 3. How would the above answers to Part 2 change if the corporate tax rate was 34%? use MMII with taxes and find new discount rate combine to find new WACC if using total firm cash flows alternatively: find new cash flows to equity and use equity discount rate 3/22/2011 Capital-tructure Design Robert.H. Hauswald 25 MM I Derivation: No Taxes The derivation is straightforward: hareholders in a levered firm receive ( EIT r + r EIT r Thus, the total cash flow to all stakeholders is ondholders receive The present value of this stream of cash flows is V L Clearly ( EIT r + r = EIT r The present value of this stream of cash flows is V U V = L V U 3/22/2011 Capital-tructure Design Robert.H. Hauswald 26

14 MM II Derivation: No Taxes The derivation is straightforward: r + + Then set r WACC = r WACC = r + r 0 + r + r = r 0 multiply both sides by r + + r + r = + + r + r 0 + = r 0 r + r = r 0 + r 0 r = r 0 + ( r 0 r 3/22/2011 Capital-tructure Design Robert.H. Hauswald 27 MM Proposition II without Corporate Taxes Cost of capital: r (% r 0 r = r 0 + ( r 0 r L r WACC = r + r + + r r Debt-to-equity Ratio 3/22/2011 Capital-tructure Design Robert.H. Hauswald 28

15 MM Value of the Firm: Taxes Value of the Firm (Leveraged/With Debt = value of the unlevered firm + present value of the tax shield V L = V U + td where yearly tax shield t = t c *Interest rate*debt/expected return => Optimal capital structure: 100 debt % financed ince above equation does not hold for risky debt MM II is a benchmark case for a firm with risky debt, MM II is more useful than the equation to releverage a firm s eta All you need is observed YTM on risky debt. 3/22/2011 Capital-tructure Design Robert.H. Hauswald 29 MM I Derivation: with Taxes hareholders in a levered firm receive ( EIT r (1 T C Thus, the total cash flow to all stakeholders is ( EIT r (1 TC + r ondholders receive r The present value of this stream of cash flows is V L Clearly ( EIT r (1 TC + r = The present value of the first term is V U The present value of the second term is T C VL = VU + T 3/22/2011 Capital-tructure Design Robert.H. Hauswald 30 = EIT (1 TC r (1 TC + r = EIT (1 T r + r T r C C + C

16 MM II Derivation: with Taxes tart with M&M Proposition I with taxes: ince V L = + + = V V = + 1 T U ( C VL = VU + T The cash flows from each side of the balance sheet must equal: r + T + r = VU r0 U + r + r = [1 + (1 TC ] r0 + TC r Which quickly reduces to r = r + ( 1 TC ( r0 r 0 3/22/2011 Capital-tructure Design Robert.H. Hauswald 31 C r r + r = [ + (1 TC ] r0 + T Divide both sides by T C C r C CAPM and MM Proposition II oth address equity risk: in fact, equivalent MM II has the advantage of showing directly how equity risk depends on capital structure 1. recall the following expressions (1 r e = r f + β e (r m r f CAPM for equity (2 r a = r f + β a (r m r f CAPM for firm with NO debt (3 β e = β a * (1+ D/E*(1-t (equation to releverage etas 2. substitute (3 into (1 and then 3. substitute (2 into this new expression, and rearrange 4. MM Proposition II for a firm with RIKLE debt (3 does not hold for risky debt: is debt riskless? 3/22/2011 Capital-tructure Design Robert.H. Hauswald 32

17 Introducing Taxes: MM II and WACC Cost of capital: r (% r = r0 + ( 1 TC ( r0 r L r 0 L r WACC = r (1 TC + r + L + L r 3/22/2011 Capital-tructure Design Robert.H. Hauswald 33 Debt-to-equity ratio (/

EMBA in Management & Finance. Corporate Finance. Eric Jondeau

EMBA in Management & Finance. Corporate Finance. Eric Jondeau EMA in Management & Finance Corporate Finance EMA in Management & Finance Lecture 3: Capital Structure Modigliani and Miller Outline 1 The Capital-Structure Question 2 Financial Leverage and Firm Value