Debt to Equity Ratio Manufacturing

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Debt to Equity Ratio Manufacturing Powered By Docstoc
					CAPITAL BUDGETING WITH
LEVERAGE
Introduction
   Initial Assumptions
       The project has average risk.
           For convenience the betas or costs of capital used will be for the
            existing firm rather than being project specific.
       The firm’s debt-equity ratio is constant.
           This simplifies the application in that we don’t need to worry
            about changing costs of capital and fixes the adjustment of our
            risk measure for leverage.
       Corporate taxes are the only imperfection.
           No personal tax considerations or agency costs to quantify.
The Weighted Average Cost
of Capital Method
              E          D
  rwacc          rE        rD (1   c )
            E  D      E  D
 Because  the WACC incorporates the tax savings from
 debt, we can compute the levered value (V for enterprise
 value, L for leverage) of an investment, by discounting its
 future expected free cash flow using the WACC.
            FCF1         FCF2             FCF3
 V  L
                                                   
          1  rwacc   (1  rwacc )     (1  rwacc )
   0                               2                3
Valuing a Project with WACC

   Ralph Inc. is considering introducing a new type of
    chew toy for dogs.
     Ralph  expects the toys to become obsolete after five
      years when it will be discovered that chew toys only
      encourage dogs to eat shoes. However, the marketing
      group expects annual sales of $40 million for the first
      year, increasing by $10 million per year for the
      following four years.
     Manufacturing    costs and operating expenses (excluding
      depreciation) are expected to be 40% of sales and $7
      million, respectively, each year.
Valuing a Project with WACC

  Developing the product will require upfront R&D and
  marketing expenses of $8 million. The fixed assets
  necessary to produce the product will require an
  additional investment of $20.
    The equipment will be obsolete once production ceases and
    (for simplicity) will be depreciated via the straight-line
    method over the five year period.
  Ralphexpects no incremental net working capital
  requirements for the project.
  Ralph   has a target of 60% Equity financing.
  Ralph   pays a corporate tax rate of 35%.
   Expected Future Free Cash Flow

"Income Statement:" Year       0        1       2       3       4       5
Sales                               40.00   50.00   60.00   70.00   80.00
COGS                                16.00   20.00   24.00   28.00   32.00
Gross Profit                        24.00   30.00   36.00   42.00   48.00
Operating Expenses          8.00     7.00    7.00    7.00    7.00    7.00
Depreciation Exp                     4.00    4.00    4.00    4.00    4.00
EBIT                        -8.00   13.00   19.00   25.00   31.00   37.00
Tax (35%)                   -2.80    4.55    6.65    8.75   10.85   12.95
Unlevered NI                -5.20    8.45   12.35   16.25   20.15   24.05
Free Cash Flow:
Unlevered NI                -5.20    8.45   12.35   16.25   20.15   24.05
Plus Deprecition Exp         0.00    4.00    4.00    4.00    4.00    4.00
Less Net Cap Ex             20.00    0.00    0.00    0.00    0.00    0.00
Less Changes in NWC          0.00    0.00    0.00    0.00    0.00    0.00
Free Cash Flow             -25.20   12.45   16.35   20.25   24.15   28.05
   “Market Value” Balance Sheet


           Assets                     Liabilities              Cost of Capital
Excess Cash       $ 50.00    Debt                $ 390.00   Debt              5%
Existing Assets $ 850.00     Equity              $ 510.00   Equity          12%
                             Total Liabilities              Risk Free         4%
Total Assets      $ 900.00   and Equity          $ 900.00

      The firm is current at it’s target leverage:
        Equity   to Net Debt plus Equity ratio is:
               $510.00/($510.00 + $390.00 - $50.00) = 60.0%
   Valuing a Project with WACC
      Ralph intends to maintain a similar (net) debt-equity
       ratio for the foreseeable future, including any
       financing related to the project. Thus, Ralph’s WACC
       is:
            E          D                   510         340
rwacc          rE        rD (1   c )      (12%)      (5%)(1  0.35)
          E  D      E  D                 850         850
        8.5%
     Valuing a Project with WACC
        The value of the project, including the tax shield
         from debt, is calculated as the present value of its
         future free cash flows discounted at the WACC.
       12.45    16.35     20.25    24.15 28.05
V
0
 L
                   2
                             3
                                      4
                                         +   5
                                                $77.30 million
       1.085   1.085     1.085    1.085 1.085


            The   NPV (value added) of the project is $52.10 million
                  $77.30 million – $25.20 million = $52.10 million
                  It is important to remember the difference between value and
                   value added.
Summary of the WACC Method
1.   Determine the free cash flow of the investment.
2.   Compute the weighted average cost of capital.
3.   Compute the value of the investment, including the tax
     benefit of leverage, by discounting the free cash flow
     of the investment using the WACC.
4.   The WACC can be used throughout the firm as the
     companywide cost of capital for new investments that
     are of comparable risk to the rest of the firm and that
     will not alter the firm’s debt-equity ratio.
Implementing a Constant Debt-Equity Ratio

   By undertaking the project, Ralph adds new assets
    to the firm with an initial market value $77.30
    million.
     Therefore,to maintain the target debt-to-value ratio,
      Ralph must add $30.92 million in new debt.
       40%   × $77.30 = $30.92
       60%   × $77.30 = $46.38 (compare to $52.10)
Implementing a Constant Debt-Equity Ratio

    Ralph can add (net) debt in this amount either by
     reducing cash and/or by borrowing and increasing
     actual debt.
        Suppose Ralph decides to spend $25.20 million (cover the
         negative FCF in year 0) in cash to initiate the project.
            This increases net debt by $25.20 million
               Assets                   Liabilities               % of Total Value
    Excess Cash       $ 24.80    Debt              $ 390.00     Debt          39.4%
    Existing Assets $ 850.00     Equity            $ 562.10     Equity        60.6%
    New Project       $ 77.30
                                 Total Liabilities
    Total Assets     $ 952.10    and Equity          $ 952.10
  New Market Value Balance Sheet
     We need an increase in net debt of $30.92.
     Spend $25.20 million on the project and pay a
      $5.72 million dividend so $30.92 million in cash
      goes out (this further increases net debt and reduces
      equity by the required amount).
           Assets                  Liabilities               % of Total Value
Excess Cash       $ 19.08   Debt              $ 390.00     Debt          40.0%
Existing Assets $ 850.00    Equity            $ 556.38     Equity        60.0%
New Project       $ 77.30
                            Total Liabilities
Total Assets     $ 946.38   and Equity          $ 946.38
Implementing a Constant Debt-Equity Ratio

   The market value of Ralph’s equity increases by $46.38
    million.
       $556.38 − $510.00 = $46.38
   Adding the dividend of $5.72 million into the mix, the
    shareholders’ total gain is $52.10 million.
     $46.38 + 5.72 = $52.10
     Which is exactly the NPV calculated for the project

     Alternatively: without the dividend the equity increased by
      the project’s NPV of $52.10 = $562.10 - $510.00. This
      was too large an increase in equity given the increase in
      debt of $25.20 if Ralph is to maintain 60% equity.
Implementing a Constant Debt-Equity Ratio

   Debt Capacity
     The amount of debt at a particular date that is
     required to maintain the firm’s target debt-to-value
     ratio
     The   debt capacity at date t is calculated as:
      Dt  d  Vt L
       Where  d is the firm’s target debt-to-value ratio and VLt is
       the project’s levered continuation value on date t.
Implementing a Constant Debt-Equity Ratio

   Debt Capacity
     VLt    calculated as:
                              Value of FCF in year t  2 and beyond

                 FCFt  1                  V  L
    Vt   L
                                             t 1

                               1  rwacc
   Debt Capacity
      In order to maintain the target financing the amount
       of new debt must fall over the life of the project.
      This is true because the value of the project
       depends upon the future cash flow at each point in
       time. Since the project ends, value decreases.
                        year           0        1      2      3      4       5
Free Cash Flow                 $ (25.20) $ 12.45 $16.35 $20.25 $24.15 $ 28.05
Levered Value                  $ 77.30 $ 71.42 $61.14 $46.09 $25.85 $ -
Debt Capacity d = 40%          $ 30.92 $ 28.57 $24.46 $18.43 $10.34 $ -
   The Adjusted Present Value Method
      Adjusted Present Value (APV)
       A  valuation method to determine the levered value
         of an investment by first calculating its unlevered
         value and then adding the value of the interest tax
         shield and deducting any costs that arise from other
         market imperfections
V L  APV  V U  PV (Interest Tax Shield)
                PV (Financial Distress, Agency, and Issuance Costs)
The Unlevered Value of the Project
   The first step in the APV method is to calculate the
    value of the free cash flows using the project’s cost
    of capital if it were financed without leverage.
The Unlevered Value of the Project
   Unlevered Cost of Capital
     The    cost of capital of a firm, were it unlevered:
         for a firm that maintains a target leverage ratio, it
         can be estimated (recall the picture) as the weighted
         average cost of capital computed without taking into
         account taxes (pre-tax WACC).
              E          D
    rU           rE        rD  Pretax WACC
            E  D      E  D
          Thisis, strictly speaking, only true for firms that adjust their
           debt to maintain a target leverage ratio.
  The Unlevered Value of the Project
    For Ralph, the unlevered cost of capital is calculated
     as:
   rU  0.60  12.0%  0.40  5.0%  9.2%


      The project’s value without leverage is then
       calculated as:
       12.45    16.35     20.25    24.15 28.05
VU                 2
                             3
                                      4
                                         +   5
                                                $75.71 million
       1.092   1.092     1.092    1.092 1.092
Valuing the Interest Tax Shield
   The value of $75.71 million is the value of the
    unlevered project and does not include the value of
    the tax shield provided by the interest payments on
    debt.
    Interest paid in year t  rD  Dt  1
       The interest tax shield is equal to the interest paid multiplied
        by the corporate tax rate.
Interest Tax Shield
   From the debt capacity calculation we can find the
    interest associated with the project if the financing is
    kept at the target.
                        year           0          1         2         3         4          5
Free Cash Flow                 $ (25.20)   $ 12.45    $16.35    $20.25    $24.15    $ 28.05
Levered Value                  $ 77.30     $ 71.42    $61.14    $46.09    $25.85    $ -
Debt Capacity d = 40%          $ 30.92     $ 28.57    $24.46    $18.43    $10.34    $ -
Interest                       $ -         $ 1.55     $ 1.43    $ 1.22    $ 0.92    $ 0.52
Interest Tax Shield            $ -         $ 0.54     $ 0.50    $ 0.43    $ 0.32    $ 0.18
     Valuing the Interest Tax Shield
        The next step is to find the present value of the
         interest tax shield.
          When    the firm maintains a target leverage ratio, its
            future interest tax shields have similar risk to the project’s
            cash flows, so they should be discounted at the project’s
            unlevered cost of capital.
                              0.54    0.50     0.43     0.32     0.18
PV (interest tax shield)                2
                                                  3
                                                           4
                                                              +      5
                                                                        $1.59 million
                             1.092   1.092    1.092    1.092    1.092
   Valuing the Interest Tax Shield
      The total value of the project with leverage is the
       sum of the value of the interest tax shield and the
       value of the unlevered project.
V L  V U  PV (interest tax shield)  75.71  1.59  $77.30 million


        The   NPV of the project is $52.10 million
          $77.30      million – $25.20 million = $52.10 million
                  This is exactly the same value found using the WACC approach.
Summary of the APV Method
1.   Determine the investment’s value
     without leverage.
2.   Determine the present value of the interest
     tax shield.
     a.   Determine the expected interest tax shield.
     b.   Discount the interest tax shield.
3.   Add the unlevered value to the present value of
     the interest tax shield to determine the value of
     the investment with leverage.
Summary of the APV Method
   The APV method has some advantages.
     Itcan be easier to apply than the WACC method when
      the firm does not maintain a constant debt-equity ratio.
     TheAPV approach also explicitly values market
      imperfections and therefore allows managers to
      measure their contribution to value.
The Flow-to-Equity Method
   Flow-to-Equity
    A  valuation method that calculates the free cash flow
      available to equity holders taking into account all
      payments to and from debt holders.
       Free Cash Flow to Equity (FCFE), the free cash flow that
         remains after adjusting for interest payments, debt issuance
         and debt repayments
     The cash flows to equity holders are then discounted
      using the equity cost of capital.
     Free Cash Flow to Equity

Free Cash Flow to Equity
                        Year            0            1            2            3            4           5
Unlevered NI                   $   (5.20)   $    8.45    $   12.35    $   16.25    $   20.15    $ 24.05
Less After Tax Interest        $     -      $    1.00    $    0.93    $    0.79    $    0.60    $ 0.34
Plus Depr                      $     -      $    4.00    $    4.00    $    4.00    $    4.00    $ 4.00
Less Net Cap Ex                $   20.00    $     -      $     -      $     -      $     -      $ -
Less Change in NWC             $     -      $     -      $     -      $     -      $     -      $ -
Plus Net Borrowing             $   30.92    $   (2.35)   $   (4.11)   $   (6.02)   $   (8.09)   $ (10.34)
Free Cash Flow to Equity       $    5.72    $    9.09    $   11.31    $   13.43    $   15.46    $ 17.37
    Valuing the Equity Cash Flows
       Because the FCFE represent payments to equity holders,
        they should be discounted at the project’s equity cost of
        capital.
           Given that the risk and leverage of the project are the same
            as for Ralph Inc. overall, we can use Ralph’s equity cost of
            capital of 12.0% to discount the project’s FCFE.
                        9.09   11.31   13.43   15.46 17.37
NPV (FCFE )  5.72               2
                                          3
                                                  4
                                                     +      5
                                                               $52.10 million
                        1.12   1.12    1.12    1.12    1.12
           The value of the project’s FCFE represents the gain to shareholders
            from the project and it is identical to the NPV computed using the
            WACC and APV methods. (The debt is sold at a fair price.)
Project-Based Costs of Capital
   In the real world, a specific project may have
    different market risk than the average project for
    the firm.
   In addition, different projects will may also vary in
    the amount of leverage they will support.
Estimating the Unlevered Cost of Capital

   Suppose Ralph launches a new project that faces
    different market risks than its main business.
     The unlevered cost of capital for the new project can
      be estimated by looking at publicly traded, pure play
      firms that have similar business risks.
Estimating the Unlevered Cost of Capital

   Assume two firms are comparable to the chew toy
    project in terms of basic business risk and have the
    following characteristics:
                 Cost of Equity   Cost of Debt   Debt-to-Value
    Firm         Capital          Capital        Ratio


    Firm A             14%               6%            40%


    Firm B            15.5%            6.55%           50%
Estimating the Unlevered Cost of Capital

   Assuming that both firms maintain a target leverage
    ratio, the unlevered cost of capital for each
    competitor can be estimated by calculating their
    pretax WACC.
Firm A: rU  0.60  14.0%  0.40  6.0%  10.8%
Firm B: rU  0.50  15.5%  0.50  6.5%  11.0%
   Based on these comparable firms, we estimate an
    unlevered cost of capital for the project that is
    approximately 10.9%.
Estimating the Unlevered Cost
of Capital using Betas
   An alternative approach to estimating the
    unlevered cost of capital for the division is to
    “unlever” the betas of the comparable firms.
   If the risk free rate is 4% and the market risk
    premium is 6% (E(rM – rf)) the data above is
    consistent with firm A having an equity beta of 1.67
    and firm B an equity beta of 1.92.
   From the SML:
    rEA  rf   E ( RP)  4%  1.67(6%)  14%
                 A


    rEB  rf   E ( RP)  4%  1.92(6%)  15.5%
                 B
Estimating the Unlevered Cost
of Capital using Betas
   The comparable firms face costs of debt that are
    higher than the risk free rate so their debt betas
    are not zero:
     D  0.166  rDA  rf   D ( RP)  5%  0.34(6%)  6%
      A                        A


     D  0.083  rD  rf   D ( RP)  5%  0.42(6%)  6.5%
      B            B          B
Estimating the Unlevered Cost
of Capital using Betas
   We now find the unlevered or asset betas:
           EA        DA           0.6              0.4
      A
      A
               E  A
                A
                          D 
                           A
                                         1.67            0.34  1.14
        E  DA     E  DA      0.6  0.4        0.6  0.4
     U


           EB        DB           0.75                0.25
    U  B
     B
               E  B
                B
                          D 
                           B
                                           1.92               0.42  1.17
        E  DB     E  DB      0.75  0.25        0.75  0.25

 Or an average of these unlevered betas of 1.15.
 An unlevered beta of 1.15 gives an unlevered cost
  of equity capital of:
  rU  rf  U ( RP )  4%  1.15(6%)  10.9%
Project Leverage
and the Equity Cost of Capital
   A project’s equity cost of capital may differ from
    the firm’s equity cost of capital if the project uses a
    target leverage ratio that is different than the
    firm’s.
   The project’s equity cost of capital can be
    calculated as:
                D
    rE    rU    (rU  rD )
                E
Project Leverage
and the Equity Cost of Capital
   Now assume that Ralph plans to maintain an equal
    mix of debt and equity financing for its chew toy
    project, and it expects its borrowing cost to be 5%.
     Given  the unlevered cost of capital estimate of 10.9%,
      the chew toy division’s equity cost of capital is
      estimated to be:
                     0.50
      rE    10.9%       (10.9%  5%)  16.8%
                     0.50
Project Leverage
and the Equity Cost of Capital
   Alternatively, this can be found by “relevering” the
    unlevered beta estimate of 1.15 and using the SML
    we find the cost of levered equity:
                D                     0.5
     E  U  ( U   D )  1.154      (1.154  0.18)  2.13
                 E                    0.5
    rE  rf   E ( RP)  4%  2.13(6%)  16.8%
  Project Leverage
  and the Equity Cost of Capital
     The division’s WACC can now be estimated to be:
rWACC  0.50  16.8%  0.50  5.0%  (1  0.35)  10.0%

     An alternative method for calculating the chew toy
      division’s WACC is:
      rwacc  rU  d c rD
  rwacc  10.9%  0.50  0.35  5%  10.0%

				
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