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Week Seven – Part II

Week Seven – Part II. Capital Structure Decisions. Topics in Chapter. MM models, with and without corporate taxes Miller model, with corporate and personal taxes. Who are Modigliani and Miller (MM)?.

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Week Seven – Part II

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  1. Week Seven – Part II Capital Structure Decisions

  2. Topics in Chapter • MM models, with and without corporate taxes • Miller model, with corporate and personal taxes

  3. Who are Modigliani and Miller (MM)? • They published theoretical papers that changed the way people thought about financial leverage. • They won Nobel prizes in economics because of their work. • MM’s papers were published in 1958 and 1963. Miller had a separate paper in 1977. The papers differed in their assumptions about taxes.

  4. What assumptions underlie the MM and Miller Models? • Firms can be grouped into homogeneous classes based on business risk. • Investors have identical expectations about firms’ future earnings. • There are no transactions costs. (More...)

  5. All debt is riskless, and both individuals and corporations can borrow unlimited amounts of money at the risk-free rate. • All cash flows are perpetuities. This implies perpetual debt is issued, firms have zero growth, and expected EBIT is constant over time. (More...)

  6. MM’s first paper (1958) assumed zero taxes. Later papers added taxes. • No agency or financial distress costs. • These assumptions were necessary for MM to prove their propositions on the basis of investor arbitrage.

  7. MM with Zero Taxes (1958) Proposition I: VL = VU. Proposition II: rsL = rsU + (rsU - rd)(D/S).

  8. Given the following data, find V, S, rs, and WACC for Firms U and L. • Firms U and L are in same risk class. • EBITU,L = $500,000. • Firm U has no debt; rsU = 14%. • Firm L has $1,000,000 debt at rd = 8%. • The basic MM assumptions hold. • There are no corporate or personal taxes.

  9. EBIT rsU $500,000 0.14 VU = = = $3,571,429. VL = VU = $3,571,429. 1. Find VU and VL.

  10. 2. Find the market value of Firm L’s debt and equity. VL = D + S = $3,571,429 $3,571,429 = $1,000,000 + S S = $2,571,429.

  11. rsL = rsU + (rsU - rd)(D/S) = 14.0% + (14.0% - 8.0%)() = 14.0% + 2.33% = 16.33%. $1,000,000 $2,571,429 3. Find rsL.

  12. WACC = wdrd + wcers = (D/V)rd + (S/V)rs = ()(8.0%) +()(16.33%) = 2.24% + 11.76% = 14.00%. $1,000,000 $3,571,429 $2,571,429 $3,571,429 4. Proposition I implies WACC = rsU. Verify for L using WACC formula.

  13. Without taxes Cost of Capital (%) 26 20 14 8 rs WACC rd Debt/Value Ratio (%) 0 20 40 60 80 100 MM Relationships Between Capital Costs and Leverage (D/V)

  14. The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost. • Although rd remains constant, rs increases with leverage. The increase in rs is exactly sufficient to keep the WACC constant.

  15. Value of Firm, V (%) 4 3 2 1 VL VU Firm value ($3.6 million) 0 0.5 1.0 1.5 2.0 2.5 Debt (millions of $) Graph value versus leverage. With zero taxes, MM argue that value is unaffected by leverage.

  16. V, S, rs, and WACC for Firms U and L (40% Corporate Tax Rate) With corporate taxes added, the MM propositions become: Proposition I: VL = VU + TD. Proposition II:rsL = rsU + (rsU - rd)(1 - T)(D/S).

  17. Notes About the New Propositions • 1. When corporate taxes are added,VL ≠ VU. VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. • 2. rsL increases with leverage at a slower rate when corporate taxes are considered.

  18. EBIT(1 - T) rsU $500,000(0.6) 0.14 VU = = = $2,142,857. 1. Find VU and VL. Note: Represents a 40% decline from the no taxes situation. VL = VU + TD = $2,142,857 + 0.4($1,000,000) = $2,142,857 + $400,000 = $2,542,857.

  19. 2. Find market value of Firm L’s debt and equity. VL = D + S = $2,542,857 $2,542,857 = $1,000,000 + S S = $1,542,857.

  20. = 14.0% + (14.0% - 8.0%)(0.6)( ) = 14.0% + 2.33% = 16.33%. $1,000,000 $1,542,857 3. Find rsL. rsL = rsU + (rsU - rd)(1 - T)(D/S)

  21. WACCL = (D/V)rd(1 - T) + (S/V)rs = ()(8.0%)(0.6) +()(16.33%) = 1.89% + 9.91% = 11.80%. When corporate taxes are considered, the WACC is lower for L than for U. $1,000,000 $2,542,857 $1,542,857 $2,542,857 4. Find Firm L’s WACC.

  22. Cost of Capital (%) rs 26 20 14 8 WACC rd(1 - T) Debt/Value Ratio (%) 0 20 40 60 80 100 MM: Capital Costs vs. Leverage with Corporate Taxes

  23. Value of Firm, V (%) 4 3 2 1 VL TD VU Debt (Millions of $) 0 0.5 1.0 1.5 2.0 2.5 MM: Value vs. Debt with Corporate Taxes Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used.

  24. Miller’s Proposition I: VL = VU + [1 - ]D. Tc = corporate tax rate. Td = personal tax rate on debt income. Ts = personal tax rate on stock income. (1 - Tc)(1 - Ts) (1 - Td) Miller Model with Personal Taxes (Td = 30% and Ts = 12%)

  25. VL = VU + [1 - ]D = VU + (1 - 0.75)D = VU + 0.25D. (1 - 0.40)(1 - 0.12) (1 - 0.30) Tc = 40%, Td = 30%, and Ts = 12%. Value rises with debt; each $100 increase in debt raises L’s value by $25.

  26. Miller vs. MM Model with Corporate taxes • If only corporate taxes, then VL = VU + TcD = VU + 0.40D. • Here $100 of debt raises value by $40. Thus, personal taxes lowers the gain from leverage, but the net effect depends on tax rates. (More...)

  27. If Ts declines, while Tc and Td remain constant, the slope coefficient (which shows the benefit of debt) is decreased. • A company with a low payout ratio gets lower benefits under the Miller model than a company with a high payout, because a low payout decreases Ts.

  28. Why do personal taxes lower value of debt? • Corporate tax laws favor debt over equity financing because interest expense is tax deductible while dividends are not. (More...)

  29. However, personal tax laws favor equity over debt because stocks provide both tax deferral and a lower capital gains tax rate. • This lowers the relative cost of equity vis-a-vis MM’s no-personal-tax world and decreases the spread between debt and equity costs. • Thus, some of the advantage of debt financing is lost, so debt financing is less valuable to firms.

  30. What does capital structure theory prescribe for corporate managers? • MM, No Taxes: Capital structure is irrelevant--no impact on value or WACC. • MM, Corporate Taxes: Value increases, so firms should use (almost) 100% debt financing. • Miller, Personal Taxes: Value increases, but less than under MM, so again firms should use (almost) 100% debt financing.

  31. Do firms follow the recommendationsof capital structure theory? • Firms don’t follow MM/Miller to 100% debt. Debt ratios average about 40%. • However, debt ratios did increase after MM. Many think debt ratios were too low, and MM led to changes in financial policies.

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