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					Capital Budgeting with Risk
    Discount Rates, Expected Returns, and a Project‟s
       Internal Rate of Return-- some clarification

   The Capital Asset Pricing Model, and the SML in particular
    give us an estimate of the normal rate of return that is expected
    on assets with varying amounts of (beta) risk.
   The expected return we get from the SML should be used as
    the discount rate in valuing investment opportunities and
    proposed projects. This discount rate is also referred to as the
    cost of capital for the project, or the hurdle rate.
   Once we have forecasted the cash flows from a proposed
    project or investment, we can compute the project‟s Internal
    Rate of Return.
                 IRR and NPV
 Typically, a project will have a positive NPV
  if the IRR exceeds the project‟s cost of capital
  or hurdle rate.

 That  is, the NPV is positive if the IRR plots
  above the Security Market Line on a
  risk/return graph.
           Project A would have a positive NPV,
         while Project B would have a negative NPV
     Expected Return
                            *IRRA             SML

project cost
of capital

          Rf                 *IRRB

                          Project          Beta
         Two Complexities in Choosing Discount
                Rates for Projects or Divisions.
 If the firm has no debt in the capital structure and the project
  being evaluated has the same (Beta) risk as the firm‟s existing
  projects, then the expected return on the firm‟s equity is the
  appropriate discount rate for the project.
 If the project beta differs from the firm beta then use the project
        How can this be estimated?
   If the firm has debt in the capital structure, adjustments are
        Interest is tax deductible. Either allow for in cash flows or alter
         discount rate to reflect.
        Financial leverage increases equity betas relative to the firm‟s beta
          • Is an equity-beta or firm-beta estimated by
            regression techniques using stock return data?
               Project vs. Firm Risk (Unlevered Firm)
      Expected Return
project cost                                          SML
of capital

  firm cost
  of capital


                              Firm         Project
                              Beta         Beta
            The Weighted Average Cost Of
                  Capital (WACC)
• When a firm has both debt and equity in its capital
  structure, the most frequent recommendation is to
  work with the weighted average cost of capital
                      S          B                 (13.5)
         WACC            rS       rB (1  TC )
                    SB        SB
• where
   – S is the market value of the firm‟s stock
   – B is the market value of the firm‟s debt
   – rS is the required rate of return on the firm‟s stock
   – rB is the required before tax rate of return on the firm‟s debt
   – TC is the firm‟s marginal tax rate
         The costs of debt and equity.
 The before tax cost of debt can be calculated as the yield to
  maturity on the firm‟s existing debt.
 Can also be found from yields on companies with
  comparable financial risk.
 The after tax cost of debt is the before tax cost of debt
  multiplied by (1-Tc), where Tc is the firm‟s effective
  marginal tax rate.
• The cost of equity can be calculated using the Security
  Market Line (SML) from the CAPM.
                    rS= Rf+ b (E[RM]- Rf)
• This can be using the firm‟s own beta, or that of another
  firm that comprises a good surrogate for the project.
                 WACC Example
   Gamma airlines is financed with 60% debt and 40%
    equity. Currently the YTM on Gamma bonds is 9%, and
    Gamma has estimated its cost of equity to be 14.5%.
    Gamma‟s corporate tax rate is 40%. What is Gamma‟s
               WACC = .40(14.5%) + .60(9%)(1-.40)
                               = 9.04%.
   Issues:
      What if the risk of the project at hand differs from that

       of Gamma‟s past projects?
      What if risk of this project is similar to that of Delta

       Airlines‟ projects, and the 14.5% cost of equity figure
       was actually obtained for Delta. However, Delta‟s
       capital structure differs from Gamma‟s.
             Betas and Leverage
   We noted earlier that the beta of a portfolio is the
    average of the component betas. Also, we can
    think of the firm‟s assets as a portfolio of the debt
    and equity claims. From these insights it follows
    (see pgs 565-566) that:

                         S                    B(1  TC )             See
        Assets                               S  B(1  T )  Debt
                                    Equity  
                    S  B(1  T )                                     (13.3) for
                               C                         C           no tax

• Where S is the market value of the stock (equity), B is the
  market value of debt (borrowings), and Tc is the tax rate.
              Adjusting beta for different
                  capital structures
   In this analysis it is often assumed that the debt has a
    zero beta (a big simplification). Then:

                              S         
             bAssets                    bEquity
                         S  B(1  TC ) 

Example: Gamma airlines‟ equity beta is observed to be 1.31. It‟s
equity is worth 25.0 million while its debt is worth 15.0 million and
its tax rate is 40%. What is the beta of the underlying assets?
                           25      
         bAssets                   131  0.96
                     25  15(1.4) 
                Points to Note Regarding
                  Betas and Leverage
   If the firm uses no debt (B=0) the equity beta and the asset
    beta are equal.
   If the firm uses debt, the equity beta is increased relative to
    the asset beta:

            b Equity               1  B (1  TC ) 
                        b Assets                  
                                           S       
 implies:
        (1) equity holders will require a higher rate of return,
        (2) when surrogate firms are used to estimate beta,
        allowances for differing capital structures will be
     Why does Beta increase with
        financial leverage?
 Leverage Increases   the volatility of the equity
  cash flow:
 Numerical Illustration:

Outcome         Good         Bad         % Ch.
EBI             125          100         -20%
Interest         50           50           0%
Income           75           50         -33.3%
Aside on Leverage and Risk
          A stock/margin example
 Suppose you buy XOM at $70 per share with
 no leverage (margin).
     If stock price rises 10% to $77, your return is 10%

 Now,suppose you buy XOM at $70 with 50%
 margin (you pay $35 and borrow $35 at 5%).
     If stock price is $77:
       • You payback 35*1.05=36.75, and keep difference,
         40.25. Your return is 15% (40.25/35-1)
             Stock/margin continued
 But this is a double-edged sword…
 Suppose you buy XOM at $70 per share with no
  leverage (margin).
       If stock price falls 10% to $63, your return is -10%

   Now, suppose you buy XOM at $70 with 50% margin
    (you pay $35 and borrow $35 at 5%).
       If stock price is $63:
         • You payback 35*1.05=36.75, and keep difference, 26.25. Your
           return is -25% (26.25/35-1)
     Stock/margin example illustrated
                                                            Margin Example
Buy stock at Price = $70, r=5%
          Return     Return                  1
Price     Margin=0 Margin=.5
       50 -0.28571 -0.62143
       55 -0.21429 -0.47857                0.6
       60 -0.14286 -0.33571
       65 -0.07143 -0.19286                0.4
       70          0      -0.05            0.2

       75 0.071429 0.092857
       80 0.142857 0.235714                  0                                       Margin=.5
       85 0.214286 0.378571
       90 0.285714 0.521429
       95 0.357143 0.664286                -0.4
      100 0.428571 0.807143

                                                  50   60   70       80   90   100
                                                            stock price
Back to Notes
         How to use the tools developed here to select
            discount rates for capital budgeting.
   The cost of capital for each project (or division) should
    reflect the systematic risk of that project and the capital
    structure of the firm (or division) taking the project. So,
      Select a publicly traded company that is comparable in

        terms of the risk of the underlying business.
      Obtain the unlevered (asset) beta of the comparable.

      Obtain the corresponding project equity beta for your

        firm, reflecting your firm‟s capital structure.
      Obtain the cost of equity and cost of debt for this

        project at your firm.
      Calculate the WACC for the project and perform NPV

How to use the tools, continued…
   Why is this so hard?
       Because your comparable need not have the same capital
        structure as your own firm.
       What we‟re going to do is start with a levered comparable,
        figure out the beta of the equivalent unlevered firm, and
       find the corresponding equity beta for your project at your
        capital structure
       Then, figure out the WACC and solve NPV...
       It‟s just ugly.
           Example: BK Industries
 BK Industries is a conglomerate company with
  operations in marine power, pleasure boating,
  defense, and fishing tackle. BK‟s equity beta is
  1.0. BK has and will maintain a debt/equity ratio
  of 1.0.
    Can we use the company cost of capital to

     value an investment in text editing?
 Latec Inc. is a firm that makes only text editing
  systems. Latec‟s equity beta is 1.35. Latec has a
  debt to equity ratio of 0.75, and a marginal tax rate
  of 45%.
Delevered Betas with debt/equity ratios
   The formulas for obtaining asset betas from equity betas and
    vice versa provided earlier required dollars values for debt (B)
    and equity (S). What if you are only given the leverage ratio,
    L = B/S? The formulas are restated as:

                              1        
            bAssets                    bEquity
                        1  L(1  TC ) 

         bEquity  bAssets (1  L(1  TC ))
Step 1: Delever Latec‟s Beta to obtain the
        Beta of text-editing assets:

   Latec has L =0.75, TC = .45, and an equity beta of
                           1          
        bAssets                      135  0.955
                   1  0.75(1  0.45) 
  Step 2: Relever the asset Beta to
   reflect BK‟s capital structure:

Recalling that BK will keep its debt/equity
ratio equal to one, we can get:

   bEquity  0.9551  1(1.45)  148

•This is the beta for a BK equity position in a text
 editing asset.
•Why is this equity beta greater than Latec‟s?
            BK Industries, Cont.
    Assume that the risk free rate is 8% and that BK‟s
     cost of debt is also 8%. The market risk premium
     is 7%. The required return on BK‟s equity is:

rS  RF  bEquity ( RM  RF )  8%  148 * 7%  18.36%
The weighted average cost of capital for the text editing
venture (using the fact that B/S = 1 here) is:
              S          B
 WACC            rS         rB (1  TC )
           SB         SB
 = (0.5) *18 .36 %  (0.5) * 8%(1  0.45 )  11 .38 %
              Finally, we can evaluate the NPV of the text editing
               venture using the WACC that reflects the risk
               associated with this particular business. Using the cash
               flow estimates obtained earlier:

                  3.980     5.419       6.685       5.990       22.465
NPV  26.0                                              
                (1.1138 ) (1.1138 ) 2 (1.1138 ) 3 (1.1138 ) 4 (1.1138 ) 5
 $3.778 Million

  • The NPV is positive, so proceed with the text editing business.
  • Notice that the selected discount rate of 11.38% reflects:
      The risk (beta) of text editing businesses, not BK‟s existing
      BK‟s capital structure, not that of the surrogate firm.
Why the firm (or division‟s) capital
 In the long run, each individual project is
  funded from a “pool” of capital. That pool
  includes both debt and equity.
 If we evaluated projects based on the specific
  financing used then those that were debt
  financed would tend to look better than those
  that are equity financed. But are they really
  better projects?
       Some practical observations
    (useful on cases and in real applications)
 Leverage is some times measured as,
     the debt to equity ratio (which we denoted L)
     the debt to total capital (equity + debt) ratio,
      which is the weighting on debt (W).
     You can convert these measures as
       • L = W/(1-W)
       • W = L/(1+L)
     The debt and equity numbers used should, in
      principle, be based on market values.
       • In practice, the market value of equity is typically
         used, along with the book value of debt.
           Summary: Risk, Return, and Discount Rates
   Some risk can be diversified, some cannot.
   „Beta‟ coefficients provide a measure of non-
    diversifiable risk.
   We expect that non-diversifiable risk will earn a risk
    premium in equilibrium but that diversifiable risk will
   The CAPM (and particularly the SML) is a simple model
    capturing important insights regarding risk and
   Discount rates for projects should reflect the systematic
    risk of the project (not necessarily that of the firm) and
    the capital structure of the firm or division (not
    necessarily the financing of the project).

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