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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
   – 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.


   There is no “magic” in finance - you can’t get something for

   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 :
RE  RA  ( RA  RD ) x 
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 x1  
                             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
2.     and " financial" risk
              The M&M Propositions

Cost of capital
(%)                                       RE

                                          WACC = RA


                                          Debt-equity ration
    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
                                                       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


                                                       Total debt
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


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
                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 = 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
  (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
      VU                                      Case I
                                              M&M (no taxes)

                                                                  Case 2
                      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
cost of
                                                                  of debt goes up.

                                              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
                                              Case II             D*, the optimal amount of borrowing. At the same
                                              M&M (with taxes)
                                                                  time, the weighted average cost of capital, WACC,
                                              Debt-equity ratio
                                                                  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
   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
– The more the physical assets the more the debt level in capital
– Announcement of equity issues cause negative abnormal
– Announcement of debt for equity exchange increases stock
– Announcement of equity for debt exchange decreases stock
– 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
– 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
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
                          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

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