VIEWS: 44 PAGES: 76 CATEGORY: Accounting POSTED ON: 8/28/2010
On Capital Structure The impact of debt financing on firm and project value To borrow or not to borrow…? Objective To analyze the relationship between capital structure decision and firm value Outline • The effect of financial leverage • Measures of financial leverage • Capital structure and firm value • Empirical evidence on capital structure The effect of financial leverage What do borrowing does to firm’s earnings? Case A: The firm is all equity The firm has 400,000 shares outstanding, selling at $20/share Case A: The firm is all equity The firm has 400,000 shares outstanding, selling at $20/share Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Case A: The firm is all equity The firm has 400,000 shares outstanding, selling at $20/share Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest 0 0 0 Case A: The firm is all equity The firm has 400,000 shares outstanding, selling at $20/share Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest 0 0 0 Net Income $500,000 $1,000,000 $1,500,000 Case A: The firm is all equity The firm has 400,000 shares outstanding, selling at $20/share Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest 0 0 0 Net Income $500,000 $1,000,000 $1,500,000 ROE 6.25% 12.5% 18.75% Case A: The firm is all equity The firm has 400,000 shares outstanding, selling at $20/share Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest 0 0 0 Net Income $500,000 $1,000,000 $1,500,000 ROE 6.25% 12.5% 18.75% EPS $1.25 $2.5 $3.75 Case B: The firm has $4 million in long-term debt @10%/year and 200,000 shares selling at $20/share. Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Case B: The firm has $4 million in long-term debt @10%/year and 200,000 shares selling at $20/share. Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest $400,000 $400,000 $400,000 Case B: The firm has $4 million in long-term debt @10%/year and 200,000 shares selling at $20/share. Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest $400,000 $400,000 $400,000 Net Income $100,000 $600,000 $1,100,000 Case B: The firm has $4 million in long-term debt @10%/year and 200,000 shares selling at $20/share. Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest $400,000 $400,000 $400,000 Net Income $100,000 $600,000 $1,100,000 ROE 2.5% 15% 27.5% Case B: The firm has $4 million in long-term debt @10%/year and 200,000 shares selling at $20/share. Recession Normal Boom EBIT $500,000 $1,000,000 $1,500,000 Interest $400,000 $400,000 $400,000 Net Income $100,000 $600,000 $1,100,000 ROE 2.5% 15% 27.5% EPS $0.5 $3 $5.5 Discussion The standard deviation of ROE and EPS has increased when compared to the no-debt case. Conclusion: With more debt, EPS and ROE become more volatile Several measures of financial leverage • The debt-to-equity ratio • The total debt ratio • The dynamic degree of financial leverage • The static degree of financial leverage • Times interest earned • The cash coverage ratio The debt-to-equity ratio D/E is the ratio of debt to equity. In case A, D/E = 0 In case B, D/E =1 The total debt ratio Total debt ratio = D/(D+E) D/(D+E) compares the value of debt to the total firm value In case A, D/(D+E) =0 In case B, D/(D+E) = 0.5 The dynamic degree of financial leverage (DDFL) measures the elasticity of EPS with respect to EBIT. DDFL= (%Chg. in EPS)/(%Chg. in EBIT) Consider the change in EBIT and EPS from the normal state to the booming state of the economy. In A, DDFL = 1 In B, DDFL = 1.67. Note: If you consider the change in EBIT and EPS from the booming state to the normal state of the economy the calculation yields a different ratio. The static degree of financial leverage SDFL = EBIT/(EBIT - Interest) In A, SDFL =1 for all three states of the nature. In B, one has to use expected values SDFL = 1,000,000/600,000 = 1.67 Attention: SDFL is not always equal to DDFL. Each ratio captures a different aspect of the degree of financial leverage Times interest earned TIE= EBIT/Interest TIE compares EBIT to the annual interest payment In B, TIE =2.5 The cash coverage ratio Cash coverage = (EBIT + Depreciation)/Interest Cash coverage compares EBIT plus depreciation to the annual interest payment. In B, cash coverage is no less than 2.5 (we don't know the annual amount of depreciation) Measuring and evaluating leverage: A summary Debt makes cash flows more volatile. There are several ways to measure leverage. Each method offers a unique vantage point. Leverage and optimal capital structure The static view Miller & Modigliani’s view Leverage and optimal capital structure:The static view There is an optimal capital structure: That debt-to-equity ratio that maximizes total firm value. The two opposite effects of leverage Risk increase (as discussed above) Discount rate becomes higher -> Total firm value goes down Tax savings Cash flows to stakeholders increase -> Total firm value goes up Remember: Assets are financed by shareholders and creditors The cash flow from assets go back to shareholders and creditors The present value of cash flows from assets is the total market value of the firm, V: PV CF from assets = V At the same time, V = market value of equity + market value of debt Hence, PV CF from assets = market value of equity + market value of debt Tax savings: Exemplification Project A: Levered Project A: Unlevered EBIT $100 $100 Interest $50 - EBT $50 $100 Tax (40%) $20 $40 NI $30 $60 Tax savings: Exemplification Project A: Levered Project A: Unlevered EBIT $100 $100 Interest $50 - EBT $50 $100 Tax (40%) $20 $40 NI $30 $60 Tax savings: Exemplification Project A: Levered Project A: Unlevered EBIT $100 $100 Interest $50 - EBT $50 $100 Tax (40%) $20 $40 NI $30 $60 Tax savings: Exemplification Project A: Levered Project A: Unlevered EBIT $100 $100 Interest $50 - EBT $50 $100 Tax (40%) $20 $40 NI $30 $60 Tax savings: Exemplification Project A: Levered Project A: Unlevered EBIT $100 $100 Interest $50 - EBT $50 $100 Tax (40%) $20 $40 NI $30 $60 Tax savings: Exemplification Project A: Levered Project A: Unlevered EBIT $100 $100 Interest $50 - EBT $50 $100 Tax (40%) $20 $40 NI $30 $60 Cash flow from assets: Levered case = $50 + $30 =$80 Unlevered case = $60 By leveraging the project, we increase its total cash flows Optimal capital structure:The static view A little debt will generates tax savings without adding too much risk A lot of debt will dramatically increase risk more than offsetting tax savings V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E V Static view: Leverage and firm value VU D/E D/E* The static view: A summary The optimal capital structure is simply a matter of balancing corporate debt tax shields against the risk of financial distress (bankruptcy costs) The cost of bankruptcy The overall cost of bankruptcy is also called the cost of financial distress: direct (legal and administrative expenses) indirect (opportunity costs caused by the increasing difficulties of running a business on the brink of bankruptcy) The theory of optimal capital structure (Merton Miller and Franco Modigliani) This theory is known as the irrelevance theory because M&M argue that capital structure doesn’t really matter M&M 1958 I. The overall market value of the firm and the WACC are completely independent of firm's capital structure. II. The cost of equity is a linear function of firm's leverage Proposition I (assume perpetual CF) Proof: VL = (CF to s/h + CF to b/h)/(wacc) VL = [(EBIT - rD) +rD]/(wacc) = VU Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B buy aSU = a VU invest today buy aSL = a(VL - D) borrow aD receive the payoff a(EBIT - rD) a(EBIT - rD) Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B buy aSU = a VU invest today buy aSL = a(VL - D) borrow aD receive the payoff a(EBIT - rD) a(EBIT - rD) Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B buy aSU = a VU invest today buy aSL = a(VL - D) borrow aD receive the payoff a(EBIT - rD) a(EBIT - rD) Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B buy aSU = a VU invest today buy aSL = a(VL - D) borrow aD receive the payoff a(EBIT - rD) a(EBIT - rD) Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B buy aSU = a VU invest today buy aSL = a(VL - D) borrow aD receive the payoff a(EBIT - rD) a(EBIT - rD) Since the payoffs are equal: a(VL - D) = aVU - aD VL = VU. Proposition II II. The cost of equity is a linear function of firm's leverage, that is a function of its debt/equity ratio ke = wacc + (wacc - r)(D/E) beta equity = business risk + financial risk beta equity = beta assets + (D/E) beta assets M&M 1963 I. The overall market value of the firm is an increasing function of leverage II. The cost of equity is a function of capital structure and corporate taxes. M&M 1963: Proposition I VL= [PVCF to s/h + PVCF to b/h] = EBIT(1-T)/ke + rTD/r VL = VU + tax shield M&M 1963: Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B invest today buy aSL = a(VL - D) buy aSU = a VU borrow (1-T)aD receive the payoff a(1-T)(EBIT - rD) a(1-T)(EBIT - rD) M&M 1963: Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B invest today buy aSL = a(VL - D) buy aSU = a VU borrow (1-T)aD receive the payoff a(1-T)(EBIT - rD) a(1-T)(EBIT - rD) M&M 1963: Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B invest today buy aSL = a(VL - D) buy aSU = a VU borrow (1-T)aD receive the payoff a(1-T)(EBIT - rD) a(1-T)(EBIT - rD) M&M 1963: Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B invest today buy aSL = a(VL - D) buy aSU = a VU borrow (1-T)aD receive the payoff a(1-T)(EBIT - rD) a(1-T)(EBIT - rD) M&M 1963: Proposition I Alternative proof Assume two firms: L is levered VL = SL + D U is unlevered VU = SU portfolio A portfolio B invest today buy aSL = a(VL - D) buy aSU = a VU borrow (1-T)aD receive the payoff a(1-T)(EBIT - rD) a(1-T)(EBIT - rD) Since the payoffs are equal, a(VL - D) = aVU - a(1-T)D That is VL = VU + (D)(T) (D)(T) = tax shield Exemplification: NoDebt Inc. and MoreDebt S.A. have identical EBIT of $69,230.77 in perpetuity. NoDebt has 15,000 shares outstanding selling at $30 each and no debt. MoreDebt has 20,000 shares outstanding and $200,000 in perpetual debt. The corporate tax rate is 35%, and the interest on debt is 5%. Mr. R buys 800 shares in MoreDebt SA, while Mr. P borrows $5,200 (at 5%) and uses his own savings to buy 600 shares in NoDebt. Who will have a higher cash flow at the end of the year? CF (Mr. R) = (0.04)[$69,230.77 – (0.05)(200,000)](0.65) = $1,540 CF (Mr. P) = (0.04)($69,230.77)(0.65) – (0.05)(5,200) = $1,540 What is the price per share for More Debt Inc.? Since the payoff for the two portfolios is equal, 600 shares in NoDebt should have the same market value as 800 shares in MoreDebt and a 5,200 loan. $18,000 = (X)800 + 5,200; x = $16/share Total MV (NoDebt) = (30)(15,000) = $450,000 Total MV (MoreDebt) = (16)(20,000) + 200,000 = $520,000 Notice that $520,000 = $450,000 + (0.35)(200,000) What is the cost of equity and the WACC for each of the two firms? WACC(NoDebt) = Ke(NoDebt) = (69,230.77)(0.65)/450,000 = 0.1 Ke(More Debt) = (69,230.77- 10,000)(0.65)/320,000 = 0.1203 Notice that 0.1203 = 0.1 + (0.1 – 0.05)(0.65)(0.625) WACC(MoreDebt) = (0.1203)(0.6154) + (0.05)(0.65)(0.3846) = 8.65% M&M 1963: Proposition II II. The cost of equity is a function of capital structure and corporate taxes. ke = wacc + (wacc - r)(1-T)(D/E) Capital structure with corporate and personal taxes (Miller 1976) Stockholders receive: (EBIT- rD)(1-Tc)(1-Ts) Tc = corporate tax Ts = personal tax on equity income Bondholders receive: rD(1-Td) Td = personal tax on ordinary income Capital structure with corporate and personal taxes (Miller 1976) VL = PV of (EBIT- rD)(1-Tc)(1-Ts) + rD(1-Td) VL = VU + [1 - (1-Tc)(1-Ts)/(1-Td)]D VL = VU + tax shield Capital structure with corporate and personal taxes (Miller 1976) The tax shield can be negative, positive or zero, depending on the differences between personal and corporate tax rates. Summary VL = VU + Debt tax shield - Cost of bankruptcy - Agency costs Discussion Debt clearly makes residual cash flow more volatile. Debt generates tax shields. The net effect is unclear Since wacc is calculated as an average of a relatively high cost of equity and relatively low cost of debt, it is not clear what happens to the overall market value of the firm. Discussion (con’t) In an ideal world, capital structure should have no impact on total firm value (M&M 1958) In the real world, however, capital structure appears to have some influence on total market value. Discussion (con’t) The real question: How much impact has debt financing? If impact is small, then we’re back to M&M Discussion (con’t) Choosing the right investment projects is the main determinant of firm value Financing the projects is only a matter of fine tuning Conclusion The range of optimal capital structure is a matter of managerial opinion NPV implications Even though the impact of debt financing might be small, one has to account for it when calculating NPV