金融学概论讲义(北大光华管理学院)lecture08
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Principles of FinanceLecture 08Capital Structure and Dividend PolicyDifferent sources of finance∙Internal financing: retained earnings∙External financingSources of funds from outside lenders and investors.∙Common stocksThe residua l claim to the corporation’s assets (and cash flows)∙Debt financingA contractual obligation of the corporation to make regular interestpayments and to repay the principal at maturity in return for funds provided to itMM Proposition I∙The firm’s mix of different securities is known as its capital structure∙MM Proposition I: In a frictionless world, the value of the corporation is unaffected by its choice of capital structure∙The total market value of all securities issued by the firm is determined by the earning power and risk of its underlying real assets∙MM Proposition I allows complete separation of investment and financing decisionsAssumptions∙No taxes∙No transaction costs of issuing debt/equity∙Stakeholders are able to resolve conflicts of interest costlessly ∙Investors can borrow on the same terms as the firmExample∙Firm U-Unlevered (100% equity financed)-EBIT (dividends): $10 million-Market capitalisation rate: 10%-Market value: $100 million∙Firm L (otherwise identical to firm U)-Levered (50% equity and 50% debt)-Market value of debt: $50 million-Riskfree rate: 8%-Interest payment: $4 million; dividends: $6 million ∙Market value of firm L?Example (Cont’d)∙Portfolio A: 10% of equity in firm L-Dividends: $0.6 million∙Portfolio B: borrowing $5 million and 10% of equity in firm U -Dividends: $1 million-Interest payments: $0.4 million-Net payoff: $0.6 million∙As portfolio A and portfolio B offer the same payoff, they must have the same value. Which is:-⨯10%=5million5$100Example (Cont’d)∙ 10% of equity in L worths $5 million: Market value of equity of firm L: $50 million∙ Market value of firm L: value of equity + value of debt = $50 million + $50 million = $100 million∙ L firm of Value Market U firm of Value Market =∙ If the ratio between the number of shares is the same as the ratio between market values of equity of the two firms, their stock prices should be the same. Otherwise, there will be arbitrage opportunities (see Bodie and Merton, pp424-425)MM Proposition I: GeneralizationMM Proposition I: GeneralizationSince the two strategies produce the same amount of cashflow, no arbitrage requires that they have the same costs:()U V D E αα-=Therefore, U L V D E V =+=, leverage does not affect firm value.Suppose an investor holds all of L ’s equity and debt. The return on his portfolio, or the weighted average cost of capital (WACC) of L is the weighted average return on debt and equity:()E D A r ED Er E D D WACC r +++=According to MM Proposition I, leverage does not affect the value of his portfolio, so A r is the same as the return on an all-equity portfolio. A r is therefore the cost of equity without leverage.MM Proposition II∙ The expected rate of return on common stock of a levered firm increases in proportion to its debt-equity (D/E) ratio∙ ()E D A r E D E r E D D WACC r +++= ⇔ ()D A A E r r EDr r -+=Where- :A r the cost of equity without leverage - E r : the cost of equity for levered firm - :D r the riskfree interest rate (cost of debt) - E : market value of equity - D : market value of debtrD Er Dr E r ARisk free debtRisky debtExample (Cont’d)∙ The WACC of a livered firm is equivalent to the expected return of the equity of an unlivered firm (which produces same amount of cash flow), so ()%10==U A r r∙ The required retun on L ’s equity is:()()%12%8%1055%10=-+=-+=D A A E r r E D r rExample (Cont’d)Dividends per shareNo of Shares EBIT$5 million $15 million Firm U 1 million $5 $15Firm L 0.5 million $2 $22 Firm L has to deduct $4 million interest payment before making dividends! The dividend stream becomes more volatile.Example (Cont’d)The levered portfolio produce the same cash flow stream as the unlevered portfolio. Therefore, they have the same risk, or β. Therefore A U ββ=Remember the βof a portfolio is the weighted average of the βof individual constituents:∙ E D A E D E E D D βββ+++= ⇔ ()D A A E EDββββ-+=So, the risk of the equity increases with the leverage. And investors require higher returns on levered equity.Corporate Tax ShieldsAssume corporate tax rate c τTax shield: c D r D τ⨯⨯()assuming perpetuity PV of Tax Shield D cc DD r D r ττ⨯⨯==⨯ Value of levered firm = Value of all equity firm + Value of corporatetax shields()()(1)())1E U c U D A c D E Dr r r r E D Er WACC r r D E D Eττ=+--==-+++Corporate Tax ShieldsPortfolio A: total cost m dolloars.Buy L ’s shares: (1)c Em E D τ⨯+-Hold cash: (1)(1)c c Dm E D ττ-⨯+-Portfolio B: total cost m dollars. Buy U ’s shares: mSince they have the same costs, no arbitrage requires that they produce the same cash flow.Corporate Tax ShieldsCash flow of portfolio A:()(1)(1) (1)(1)(1)(1)D c c D c c c c EBIT r D r D m mE D E D EBIT mE Dττττττ---++-+--=+-Cash flow of portfolio B:(1)c UmEBIT V τ⨯- No arbitrage requires they produce the same cash flow:(1)(1)(1)(1)c c c U c U L U c EBIT m EBIT m E D V E D V E D V V Dτττττ-⋅-⋅=+-+-=+==+Corporate Tax ShieldsThe return on the equity of L is the cash flow to equity holders divided by the value of equity:(1)(1)(1)(1)()()(1)(1)(1) ()(1)(1)(1) ()(1)c c c U U L c c c U c D c c c D E U c c D U c c D U U U D c EBIT EBIT EBIT r V V D D E D EBIT r D E D EBIT r D EBIT r Dr E Er D E D r D r D r Dr E EDr r r Eτττττττττττττττ---===-+-⇒-=+------==+------==+=+-- ()()1A c D E D E r WACC r r D E D Eτ==-+++Market Value of the FirmDebtExample (Cont’d)∙Assume the corporate tax rate is 35%∙After-tax cash flow for firm U: 10*(1-35%)=$6.5 million After-tax cash flow for firm L: cash flow to shareholders + cash flow to debtholders: 6 - (10-4)*35% + 4=$7.9 million∙Tax shields: $1.4 million, PV of tax shields (assuming perpetuity):1.4/0.08=$17.5 million∙Value of firm U: 6.5/0.1=$65 million,Value of firm L= Value of U + PV of tax shields:65 + 17.5 =$82.5 million.Value of its equity = Value of L – value of debt = 82.5 – 50 =$32.5 millionValuation of Levered InvestmentEBIT: 15million; Tax rate: 30%; Capital Structure: 80% equity, 20% debt; Interest rate: 8%. The required rate of return on an otherwise identical all-equity financed project is 10%. What is the value of this levered project?Method 1:Value of L = Value of U + PV of tax shields15(10.3)0.20.310%L L V V ⨯-=+⨯⨯ 111.70L V =Valutation of Levered InvestmentMethod 2:()()()(1)0.20.10(0.10.08)(10.3)0.10350.8)1 0.2(10.3)0.080.80.10350.09415(10.3)111.70.094E U U D C A c D E L Dr r r r E D Er WACC r r D E D EV ττ=+--=+--===-+++=⨯-⨯+⨯=⨯-==Valutation of Levered InvestmentMethod 3:0.1035After-tax cash flow to shareholders:(1)15(10.3)0.080.30.0810.50.05610.50.0560.2510.50.0560.2589.360.10350.2522.34111.7E C D C D L r EBIT r D r D D D D EE E D E V E D ττ=⨯--⨯+⨯⨯=⨯--⨯+⨯⨯=-⨯=-⨯-⨯=====+=Costs of Financial Distress∙ Issuing debt involves risk of bankrupticy. Costs arising from bankruptcy or distorted business decisions before bankruptcyDistressFinancial of Costs PV ShieldsTax of PV rm Equity Fi All of Value Firm Levered of Value -+=DebtHow Dividends are Paid?∙Cash dividends: Payment of cash by the firm to its shareholders -Regular cash dividends-Special (one-off) cash dividends∙Share dividends: Distribution of additional shares to a firm’s shareholders∙Stock repurchase: Firm buys back shares from its shareholdersHow Dividends are Determined?Stylised Facts:∙Firms have long-run target dividend payout ratios∙Managers forces more on dividend changes than on absolute levels ∙Dividend changes follow shifts in long-run changes in earnings∙Managers are reluctant to make dividend changes that might have to be reversedMM Proposition IIIWhat are shareholders’ preferences for dividends versus capital gains? ∙Dividend Irrelevance (MM Proposition III, 1961)In a perfect capital market, investors are indifferent betweendividends and capital gains∙Bird-in-the Hand (Gordon and Lintner)-Investors prefer a dollar of actual dividends to a dollar of retained earnings (and capital gains)- A dollar of dividends in the hand is less risky than a dollar of potential future capital gains in the bushMM Proposition III∙Investors do not need dividends to convert shares into cash∙Investors will not pay higher prices for firms with higher dividend payouts∙In the perfect world (no taxes, no transaction costs, etc.), dividend policy have no impact on the value of the firm (and shareholders’ wealth)Dividend Irre levance (MM, 1961) (Cont’d)Assuming a company which has $1,000 cash and requires $1,000 for a new project. The project’s NPV is $2,000. There are 1000 shares outstanding.Paying no dividends versus paying $1 dividend per share and issuing $1000 new equityNo dividend Dividend payment Cash $1,000 $1,000Asset Value $8,000 $8,000New Proj NPV $2,000 $2,000Total Value $11,000 $11,000 Number of Shares 1,000 1,100Share Price $11 $10MM Proposition IIIExisting shareholders’ value before dividend p ayment = value of company = 11000Share price before dividend payment = 11000/1000 = $11Existing shareholders’ value after dividend payment = value of company – value of new shares = 11000 – 1000 = $10000Share price after dividend payment = $10Dividend per share = 1000/1000 = $1Therefore, shareholders are indifferent between dividends and capital gains.Dividend Policy Theories (Cont’d)∙Tax Preference Theory-Since capital gains are taxed at a lower (effective) rate than dividend income, companies should pay the lowest dividendpossible-Investors are willing to accept a lower pre-tax return on high capital gains stocksDividends as Signals∙Dividend increases send good news about future cash flows;dividend cuts send bad news∙Because a high dividend payout ratio will be costly to firms that do not have cash flows to support it, dividend increases signal acompany’s good fortune and its manager’s confidence in futurecash flows∙Announcement of dividend increases (cuts) often result in an increase (or decrease) in the stock price∙The announcement of the dividend (initiations) resulted in 4% increase in the stock priceClientele Effect∙There are natural clients for high-payout or low-payout stocks ∙Retirees, pension funds prefer high-payout stocksAgency Costs∙Management may not spend the retained earnings wisely; the money may be plowed back into building a large empire rather than a more profitable one∙Problem of monitoring management’s actions is s ubstantially reduced if management has to raise external capital on a regular basis。
