Modigliani and Miller
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Capital Structure and Value • Optimal capital structure is the mix of debt and equity that maximizes the value of the firm or minimizes the weighted average cost of capital • Miller & Modigliani – If markets are perfect capital structure does not affect value – Investors can accomplish any desired debt and equity mix by themselves – Weighted average cost of capital is constant Financial Leverage, EPS, and ROE Current Proposed Assets $5,000,000 $5,000,000 Debt $ 0 $2,500,000 Equity $5,000,000 $2,500,000 Debt/Equity ratio 0 1 Share price $10 $10 Shares outstanding 500,000 250,000 Interest rate n/a 10% Financial Leverage, EPS, and ROE EPS and ROE under current capital structure Recession Expected Expansion EBIT $300,000 $650,000 $800,000 Interest $ 0 $ 0 $ 0 Net income $300,000 $650,000 $800,000 EPS $0.60 $1.30 $1.60 ROE 6% 13% 16% Financial Leverage, EPS, and ROE EPS and ROE under proposed capital structure Recession Expected Expansion EBIT $300,000 $650,000 $800,000 Interest $250,000 $250,000 $250,000 Net income $ 50,000 $400,000 $550,000 EPS $0.20 $1.60 $2.20 ROE 2% 16% 22% Homemade Leverage and ROE Firm does not adopt proposed capital structure Investor put up $500 and borrows $500 at 10% to buy 100 shares Investor’s return on her investment will be, Recession Expected Expansion EPS of un-levered firm $0.60 $1.30 $1.60 Earnings for 100 shares $60.00 $130.00 160.00 less interest on $500 at 10% -$50.00 -$50.00 -$50.00 Net earnings $10.00 $80.00 $110.00 ROE $10/$500 $80/$500 $110/$500 2% 16% 22% Homemade Leverage and ROE Firm adopts proposed capital structure Investor puts up $500, $250 in stock and $250 in bonds at 10% Investor’s return on her investment will be, Recession Expected Expansion EPS of levered firm $0.20 $1.60 $2.20 Earnings for 25 shares $5.00 $40.00 $55.00 plus interest on $250 at 10% +$25.00 +$25.00 +$25.00 Net earnings $30.00 $65.00 $80.00 ROE $30/$500 $65/$500 $80/$500 6% 13% 16% Note: Remember we assume a world where there are no market imperfections such as taxes and transaction costs. The Miller & Modigliani (M&M) Propositions Financial leverage and firm value: Proposition I Since investors can costlessly replicate the financing decisions of the firm (homemade leverage), in the absence of taxes and other market imperfections, the value of the firm is unaffected by its capital structure. Implications: There is no “magic” in finance - you can’t get something for nothing. Capital restructurings don’t create value, in and of themselves. (Why is the last part of the statement so important?) The M&M Propositions The cost of equity and financial leverage: Proposition II Because of Proposition I, the WACC must be constant. With no taxes, WACC = RA = (E/V) x RE + (D/V) x RD where RA is the return on the firm’s assets Solve for RE to get MM Proposition II RE = RA + (RA - RD) x (D/E) Cost of equity has two parts: 1. RA and “business” risk 2. D/E and “financial” risk The CAPM, the SML, and Proposition II M & M Proposition II : D RE RA ( RA RD ) x E According to the CAPM : RE RF ( RM RF ) x E RA RF ( RM RF ) x A where A is the beta of the firms's assets. What is the relationship between borrowing money and systematicrisk? Assume the debt is riskless, so that R D R F , and substitute for R A in Prop. II : D RE RF ( RM RF ) x A x1 E D D E A x 1 A A x E E Ststematic risk for thefirm's stock gas two parts : 1. A and " business"risk D 2. and " financial" risk E The M&M Propositions Cost of capital (%) RE WACC = RA RD Debt-equity ration (D/E) RE = RA + (RA – RD) X (D/E) by M&M Proposition II RA = WACC = (E/V) X RE + (D/V) X RD where V = D + E Introduction of Taxes – Interest is taxed as the income of the lender, but equity income is taxed as corporate income and income of the shareholder – By borrowing corporations create interest tax shield because interest expense of corporations reduces taxable income – This leads to a firm that is almost entirely financed with debt Debt, Taxes, and Firm Value The interest tax shield and firm value For simplicity: (1) perpetual cash flows (2) no depreciation (3) no fixed asset or NWC spending A firm is considering going from zero debt to $400 at 10%: Firm U Firm L (un-levered) (levered) EBIT $200 $200 Interest 0 $40 Tax (40%) $80 $64 Net income $120 $96 Tax saving = $16 = 0.40 x 0.10 x $400 = TC x RD x D Debt, Taxes, and Firm Value What’s the link between debt and firm value? Since interest creates a tax deduction, borrowing creates a tax shield. Its value is added to the value of the firm. MM Proposition I (with taxes) PV(tax saving) = (0.40) x (10%) x ($400) / 0.10 =$160 = (TC x RD x D)/RD = TC x D VL = VU + TC x D Debt, Taxes, and Firm Value Value of the firm (VL) V L = V U + TC X D = Value of firm = TC with debt TC X D = Present value of TC= Corporate tax shield Tax Rate on debt VU VU = Value of firm with no debt VU Total debt (D) The value of the firm increases as total debt increases because of the interest tax shield. This is the basis of M&M Proposition I with taxes. If M&M proposition I with taxes is valid, how much debt a firm should use? Debt, Taxes, and Firm Value Cost of RE Capital RU RA RD(1-TC) D/E Differential Tax Rates on Debt and Equity Income – Above conclusions assume that the tax rate on equity and debt income is the same – Value of the firm with differential tax rate is the present value total cash flows (TCF) to investors – TCF = I (1 – Tp) + (NOI – I) (1 – Tc) (1 – Tg) I = interest expense Tp = personal tax rate on interest income Tc = corporate tax rate Tg = personal tax rate on equity income – TCF increases with additional debt if: (1 – Tp) > (1 – Tc) (1 – Tg) Tax Clientele Effect – Tax rates of investors vary causing preference toward debt or equity – If all companies have the same tax rate but investors experience different tax rates, companies as a group would maximize value by issuing enough debt to accommodate those investor for whom (1 – Tp) > (1 – Tc) (1 – Tg) holds • Differential Tax Rates Among Corporations – High tax rate of a corporation increases benefits of debt financing Bankruptcy Costs As the D/E ratio increases, the probability of bankruptcy increases – likelihood of operating income shortage to cover interest expense on the debt This increased probability will increase the expected bankruptcy costs At some point, the additional value of the interest tax shield will be offset by the expected bankruptcy cost At this point, the value of the firm will start to decrease and the WACC will start to increase as more debt is added Bankruptcy Costs • Bankruptcy Costs – Direct costs: legal and administrative fees • Legal costs – Indirect costs: • Lost sales of products requiring future service • Loss of best employees • Low employee morale • Inability of credit purchases • Higher financing costs and restrictions – As the amount of debt increases, the probability of bankruptcy and therefore expected costs of bankruptcy increases, reducing firm value Debt, Taxes, Bankruptcy, and Firm Value Value of the firm (VL) VL = VU + TC X D = Value of firm Present value of tax with debt shield on debt Financial distress Maximum costs firm value VL* Actual firm value VU = Value of firm with no debt Total debt D* Optimal amount of debt (D) According to the static theory, the gain from the tax shield on debt is offset by financial distress cost. An optimal capital structure exists that just balances the additional gain from leverage against the added financial distress cost. Debt, Taxes, Bankruptcy, and Firm Value Value Case II M&M (with taxes) of the Case 1 firm (VL) PV of bankruptcy With no taxes or bankruptcy costs, the value V L* costs of the firm and its weighted average cost Case III Net gain from Static theory of capital are not affected by capital leverage VU Case I M&M (no taxes) structures. Case 2 Total D* debt (D) With corporate taxes and no bankruptcy costs, the value of the firm increases and the weighted Weighted average cost of capital decreases as the amount average cost of of debt goes up. capital (%) Case I Case 3 M&M (no taxes) Case III With corporate taxes and bankruptcy costs, Static theory the value of the firm, VL, reaches a maximum at WACC* Case II D*, the optimal amount of borrowing. At the same M&M (with taxes) time, the weighted average cost of capital, WACC, D*/E* Debt-equity ratio (D/E) is minimized at D*/E*. Agency Costs – Agency costs of debt: • Managers can increase shareholders’ wealth at the expense of creditors by taking risky projects • If level of debt is low, risks are also low. High debt level requires monitoring by creditors, increasing agency costs even further – Agency costs of equity • Managers’ self fulfilling prophecies, conservatism or over-optimism in investment decisions • Higher debt level prevents managers from value reducing activities Information Signaling – Managers convey their private information to the investors by changing capital structure – High debt levels reflect managers’ information on improved future prospects of the company – Firms with bad news cannot replicate because they won’t have resources to support high debt level Additional Considerations – Unequal costs of borrowing – Higher risk of personal borrowing – Institutional restrictions on leverage Capital Structure with Informed Investors • Study the market response to determine optimal capital structure • Study the relationship between different capital structures and the weighted average cost of capital • Information from market participants Investment bankers Bond ratings and wacc Security analysts • Disequilibrium Capital Structure with Uninformed Investors • If investors are not well-informed, managers should consider future profitability, earnings variability and bankruptcy risk • Pro forma analysis of alternative capital structures • Risk analysis Ratio measures Break-even point is the sales level below which the company has a loss Crossover point is the sales or EBIT level at which the company would earn the same EPS with two different capital structures Debt capacity analysis Empirical Evidence – Bankruptcy costs are important in determining optimal capital structure – The more the physical assets the more the debt level in capital structure – Announcement of equity issues cause negative abnormal returns – Announcement of debt for equity exchange increases stock value – Announcement of equity for debt exchange decreases stock value – Abnormal price drops following leverage decreasing capital structure exchanges are positively related to unexpected earnings decreases – Stock repurchases via tender offers result in sharp price increases – If a firm becomes a takeover target, it increases debt level Harris and Raviv (1991), The Theory of Capital Structure, JOF. Modigliani and Miller Summary I. The No-Tax Case A. Proposition I: The value of the firm levered equals the value of the firm un-levered: VL = VU B. Implications of Proposition I: 1. A firm’s capital structure is irrelevant. 2. A firm’s WACC is the same no matter what mix of debt and equity is used. C. Proposition II: The cost of equity, RE, is RE = RA + (RA - RD) D/E where RA is the WACC, RD is the cost of debt, and D/E is the debt/equity ratio. D. Implications of Proposition II 1. The cost of equity rises as the firm increases its use of debt financing. 2. Equity risk depends on the risk of firm operations (business risk) and the degree of financial leverage (financial risk). Modigliani and Miller Summary II. The Tax Case A. Proposition I with Taxes: The value of the firm levered equals the value of the firm un-levered plus the present value of the interest tax shield: VL = VU + Tc D where Tc is the corporate tax rate and D is the amount of debt. B. Implications of Proposition I with taxes: 1. Debt financing is highly advantageous, and, in the extreme, a firm’s optimal capital structure is 100 percent debt. 2. A firm’s WACC decreases as the firm relies more heavily on debt.