Compounding at 10_

Document Sample
Compounding at 10_ Powered By Docstoc
					               finan



Chapter 3: Valuing Firm Output and
         Pricing Securities

   How do you assign values to
 investments and opportunities and
    how do you compare them?
                      Valuation Issues                       3-2

• Identifying the stream of future benefits
• Valuing them at the owner‘s opportunity cost.
• Compounding interest to show future amounts at the
  opportunity cost.
• Discounting future sums to present value using opportunity
  cost.
•     Discounting a single future period.
•     Discounting for a period several years removed
• Discounting future streams - annuities
•     Application - valuing corporate bonds: Annuity plus a final
  payment
• Valuing Perpetuities (stock)
• Valuing earnings with growth
• Valuing Projects
•     Determining the weighted cost of capital for a firm.
•     Determining Net Present Value using the cost of capital.
                 Compounding at 10%                  3-3

• Year 1:$1.00 x 1.1 = $1.10;
• Year 2$1.10 x 1.1 = $1.21;
• Year 3:$1.21 x 1.1 = $1.33;
• Year 4:$1.33 x 1.1 = $1.46;
• Year 5:$1.46 x 1.1 = $1.61.
•
• Formula:
• V = s(1+r)
• Where:
• V = future value
• s = a sum to be received at the end of a period
• r = interest rate
• Calculator: enter 1+r in memory
• Enter sum; ―x‖, MR, =. Repeat as necessary for additional
  periods.
Table 3-2 Future Values of $1.00 Invested Today,                                     3-4
               Compounded Annually
•                   Interest Rate, r_________________         ____________________
     • Number of     2%      4%       6%      8%      10%      12%       14%
•      Years, n
     • 1           1.0200   1.0400 1.0600 1.0800 1.1000       1.1200     1.1400
     • 2           1.0404   1.0816 1.1236 1.1664 1.2100       1.2544     1.2996
     • 3           1.0612   1.1249 1.1910 1.2597 1.3310       1.4049     1.4815
     • 4           1.0824   1.1699 1.2625 1.3605 1.4641       1.5735     1.6890
     • 5           1.1041   1.2167 1.3382 1.4693 1.6105       1.7623     1.9254
     • 6           1.1262   1.2653 1.4185 1.5869 1.7716       1.9738     2.1950
     • 7           1.1487   1.3159 1.5036 1.7138 1.9487       2.2107     2.5023
     • 8           1.1717   1.3686 1.5938 1.8509 2.1436       2.4760     2.8526
     • 9           1.1951   1.4233 1.6895 1.9990 2.3579       2.7731     3.2519
     • 10          1.2190   1.4802 1.7908 2.1589 2.5937       3.1058     3.7072
     • 15          1.3459   1.8009 2.3966 3.1722 4.1722       4.4736     7.1379
     • 20          1.4859   2.1911 3.2071 4.6610 6.7275       9.6463     13.7435
     • 25          1.6406   2.6658 4.2919 6.8485 10.8347      17.0001    26.4619
     • 30          1.8114   3.2434 5.7435 10.0627 17.4494     29.9599    50.9502
     • 35          1.9999   3.9461 7.6861 14.7853 28.1024     52.7996    98.1002
     • 40          2.2080   4.8010 10.2857 21.7245 45.2593    93.0510    188.8835
     • 50          2.6916   7.1067 18.4202 46.9016 117.3909   289.0022   700.2330
                 Quick Check Question 3.1                3-5



• How long will it take for your money to double at 8%
• Use rule of 72
  72      = 9 years
  8

Check Table 3-2:

8% column at 9 years = 1.999
                 Quick Check Question 3.1                3-6



• How long will it take for your money to double at 6%
• Use rule of 72
  72      = 12 years
  6

Check Table 3-2:

6% column at 12 years = 2.012
               Quick Check Question 3.2                  3- 7

• Franklin invests a penny at 6% in 1750. What is value in
  2000?
• Relevant Period: 250 years
• Interest Rate: 6%
• Formula: V = $0.01 (1 + .06)250
• Use Table 3-2 for 50 years @ 6% = $0.18422
• Calculation: V = $0.18422
• V = $0.01 ($0.18422)5 = $21,216.
•
• Alternative Means:
• If your money doubles according to the Rule of 72s, at 6%
  interest, it will double every 12 years.
• Thus, in 252 years it would double 21 times (252/12 = 21).
• This can be expressed as 1(2)21 = $20,971.
       Compounding Quarterly vs. Annually                         3- 8

•                                Quarterly         Annual
•                                Compounding -10% Compounding -10.38%
•   Beginning Balance             $1,000.00        $1,000.00
•   Quarter 1:
•   Interest: .025 x $1,000           25.00             0.00
•   Ending Balance                 1,025.00         1,000.00
•   Quarter 2:
•   Interest: .025 x $1,025.00        25.62             0.00
•   Ending Balance                 1,050.62         1,000.00
•   Quarter 3:
•   Interest: .025 x $1,050.62        26.27              0.00
•   Ending Balance                 1,076.89          1,000.00
•   Quarter 4:
•   Interest: 0.25 x $1,076.89         26.91
•           .1038 x $1,000.000    ________             103.80
•   Ending Balance                 $1,103.80        $1,103.80
                Quick Check Question 3.3                    3-9



• If interest is earned monthly what is your effective annual
  interest rate?
• If interest compounds monthly, you earn 1/12 of 10%.
•      .10 = .0083, or .83% monthly
        12

•   Effective annual rate = (1 + .10 )12 - 1
•                                12
•
•   Thus: (1.0083)12 -1 = 1.104669 - 1 = $104.67 interest

•   Effective annual rate of 10.46%.
•
         Basic Discounting to Present Value                     3- 10

• PV =         Sum_____
            1 + interest rate
•   Where PV = present value, S = sum, and r = interest rate:
•           PV = 1.00
                   1+r
•   Thus, where the interest rate is 10%:
•          PV = $1.00 = $0.909
                 1.10
•   To test: what would $0.909 be worth @ 10% in one year?
•         $0.909 x 1 + r = $0.909 x 1.1 = $0.99999
•
• To discount to one more year:
•        PV = $0.909 = $0.826
                  1.10
• Usually expressed as: PV = S      Or more generally PV = S _
                             (1+r)2                      (1+r)n
• Where n = number of periods
           Table 3-4 Present Values of $1.00                          3-11

•               Interest Rate, r     _________________________________
    •   Number of      2%      4%   6%      8%     10%     12%    14%
        Years, n
    •   1           0.9804 0.9615   0.9434   0.9259   0.9091 0.8929 0.8772
    •   2           0.9612 0.9246   0.8900   0.8573   0.8264 0.7972 0.7695
    •   3           0.9423 0.8890   0.8396   0.7938   0.7513 0.7118 0.6750
    •   4           0.9239 0.8548   0.7921   0.7350   0.6830 0.6355 0.5921
    •   5           0.9057 0.8219   0.7473   0.6806   0.62090.5674 0.5194
    •   6           0.8880 0.7903   0.7050   0.5835   0.5645 0.5066 0.4556
    •   7           0.8706 0.7599   0.6651   0.5835   0.5132 0.4523 0.3996
    •   8           0.8535 0.7307   0.6274   0.5403   0.4665 0.4039 0.3506
    •   9           0.8368 0.7026   0.5919   0.5002   0.4241 0.3606 0.3075
    •   10          0.8203 0.6756   0.5584   0.4632   0.3855 0.3220 0.2697
    •   15          0.7430 0.5553   0.4173   0.3152   0.2394 0.1827 0.1401
    •   20          0.6730 0.4564   0.3118   0.2145   0.1486 0.1037 0.0728
    •   30          0.5521 0.3083   0.1741   0.0994   0.0573 0.0334 0.0196
    •   35          0.5000 0.2534   0.1301   0.0676   0.0356 0.0189 0.0102
    •   40          0.4529 0.2083   0.0972   0.0460   0.0221 0.0107 0.0053
    •   50          0.3715 0.1407   0.0543   0.0213   0.0085 0.0035 0.0014
              Quick Check Question 3.4                 3-12



• Brother gets a $10,000 bond maturing in 8 years and says
  he received $10,000. If the rate on 8 year government
  bonds is currently 7%. What is his bond really worth
  today?
              Quick Check Question 3.4                3-13



• Discounting a $10,000 savings bond due in 8 years @ 7%

• Solution: PV =      $10,000
                     (1 + .07)8
•
• PV =    $10,000   =   $5,820.3829
           1.7181
         Quick Check Question 3.5       3-14



Law School receives a pledge of
$1,000,000.00 bequest from a person with a
20 year life expectancy. How should it
report the gift?
            Quick Check Question 3.5             3-15

Two choices
$1,000,000 Or PV of $1M paid in 20 years.
According to Table 3-4 at 7% value is $258,000

Which way should you report it?
Calculating the Discounted Present Value of a Bond   3-16

• $1,000 principle amount 10 year bond
  paying 10% interest a year. What is its
  current present value? Bond terminology:
• Principle is the amount paid by the issuer to
  the holder at maturity. For bonds without
  original issue discount this is the same
  amount paid for the bond at issue.
• Interest the payment made each year
  calculated as a percentage of the principle
  amount
• Bond interest is usually paid semiannually
  but for simplicity we will assume annual.
  Interest payment date often called coupon
  date
Calculating the Discounted Present Value of a Bond   3-17



•   Year 1:    $100 ÷ 1.1000      =      $90.91
•   Year 2:    $100 ÷ 1.2100      =      $82.64
•   Year 3:    $100 ÷ 1.3310      =      $75.13
•   Year 4:    $100 ÷ 1.4641      =      $68.30
•   Year 5:    $100 ÷ 1.6105      =      $62.09
•   Year 6:    $100 ÷ 1.7716      =      $56.45
•   Year 7:    $100 ÷ 1.9487      =      $51.32
•   Year 8:    $100 ÷ 2.1436      =      $46.65
•   9 years $100 ÷ 2.3579         =      $42.41
•   10 years $100 ÷ 2.5937        =      $38.55
•   Total of interest payments:          614.45
•   Principal $1,000 ÷ 2.5937            385.55
•   Discounted Present Value          $1,000.00
          Table 3-5 Present Value of an Annuity                            3- 18
•   Present Value of an Annuity Payable at the End of Each Period for n
    Periods
•                            Discount Rate, r
    No. Yrs. 2%      4%        6%      8%         10%    12%      14%
•   1     0.9804 0.9615     0.9434 0.9259       0.9091 0.8929    0.8772
•   2     1.9416 1.8861     1.8834 1.7833       1.7355 1.6901    1.6467
•   3     2.8839 2.7751     2.6730 2.5771       2.4869 2.4018    2.3216
•   4     3.8077 3.6299     3.4651 3.3121       3.1699 3.0373    2.9137
•   5     4.7135 4.4518     4.2124 3.9927       3.7908 3.6048    3.4331
•   6     5.6014 5.2421     4.9173 4.6229       4.3553 4.1114    3.8887
•   7     6.4720 6.0021     5.5824 5.2064       4.8684 4.5638    4.2883
•   8     7.3255 6.7327     6.2098 5.7466       5.3349 4.9676    4.6389
•   9     8.1622 7.4353     6.8017 6.2469       5.7590 5.3282    4.9464
•   10     8.9826 8.1109    7.3601 6.7101       6.14465.6502    5.2161
•   15    12.8493 11.1184    9.7122 8.5595       7.6061 6.8109   6.1422
•   20    16.3514 13.5903   11.4699 9.8181       8.5136 7.4694   6.6231
•   30    22.3965 17.2920   13.7648 11.2578      9.4269 8.0552   7.0027
•   35    24.9986 18.6646   14.4982 11.6546      9.6442 8.1755   7.0700
•   40    27.3555 19.7928   15.0463 11.9246      9.7791 8.2438   7.1050
•   50    31.4236 21.4822   15.7619 12.2335      9.9148 8.3045   7.1327
           Quick Check Question 3.6      3-19




• If the market rate on comparable bonds (10
  year 10%) drops to 8% what is the present
  value fo the bond now? The bond pays $100
  interest annually & $1,000 at maturity.
                Quick Check Question 3.6                 3-20



• The bond pays $100 interest annually & $1,000 at maturity.

• 10 annual payments of $100:

•   Use the annuity table in Table 3-5:
•   10 years @ 8% = 6.7101 x $100                = $671.01

• The principal payment is a lump sum after
  10 years, discounted at 8% in Table 3-3:
•      $1,000 x .4632                           = $463.10

•   Value of the bond in today's market:        $1,134.11
            Quick Check Question 3.6         3-21




• As interest rates fall prices (present value)
  on issued bonds go up
• As interest rates rise prices (present value)
  falls.
• Why?
                  Value of a Perpetuity                3-22




• Present Value of a Perpetuity = Payment      =   P
•                                Discount Rate     r

     PV = 1        = $10.00
        .10
 Valuing a Perpetuity Intended to be Sold                3-23



• Assume collection of dividend & sale at close of one year:
•
• PV of Dividend: =    $1.00 = $1.00           =    $0.909
                       1+r       1 + .10
•
• Value of the sale:=   $10.00 = $10.00        =    $9.090
                        1+r        1 + .10
• Total:                                            $9.99999
 Valuing a Perpetuity Intended to be Sold      3-24




• Thus if dividends held constant and
  discount rate constant stock prices would
  never change.
• If dividends held constant price of stocks
  would be related to changes in doscount
  rate applied
• In the real world both are variables.
            Quick Check Question 3.7      3-25




• What is the value of a share of preferred
  stock carrying an $8.00 annual dividend,
  discounted at 7%, assuming it is neither
  redeemable by the company ("callable") nor
  subject to forced redemption by the holder?
•
          Quick Check Question 3.7   3-26




Discount Rate of 7%
PV =   $8.00 = $114.29
         .07

Discount rate of 8%,
PV =   $8.00 = $100.00
        .08
Discount rate of 10%
PV = $8.00 = $80.00
       .10
           Price – Earnings Multiples   3-27

• P-E multiples based on (1) current
  market price & (2) last 4 quarters‘ net
  income
• Regularly reported in financial press,
  e.g., Wall St. Journal:
             Price – Earnings Multiples                 3-28

 YTD     52 Week                         Yld  Vol
Net  Hi      Lo  Stock (Sym)      Div % PE 100s     Last
4.2  57.91 42.90 CocaCola KO .80 1.8 27 39470       45.67
                  (for Friday, Jan. 17, 2003)
            Price – Earnings Multiples       3-29

              (for Friday, Jan. 17, 2003)
Problems with P/E:
• Uses historical earnings, not expected
  earnings & not cash flows
• P/E ratio includes both cap rate and growth
  rate, bundled (described next)
• Seems to assume same cap & growth rate
  will apply to all future periods (i.e. managers
  will continue to invest in projects that make
  the same rate of return).
• Based on Net Income, not cash flows.
Valuing Perpetuities with Constant Growth              3-30



• The Value of a Perpetuity with Constant Growth is:
•
• PV =       P
           r –g

• Where g = constant growth rate
Valuing a Perpetuity with Constant Growth 3-31

• Assumptions:
•
• Earnings (A)                   = $1.00 per year
• Capitalization Rate (r)        = .10
• Growth Rate (g)                = .04 per year
•
• Calculation:

      PV =    $1.00     =     $1.00   =      $16.67
             .10 -.04          .06
• With no growth
  PV =    $1.00     =       $10.00
           .10
 Valuing a Perpetuity with Initial Growth     3-32

• Most companies do not sustain the same
  growth rate. There is usually a period of
  high growth until industry maturity when
  growth levels off and remains nearly
  constant.
 Valuing a Perpetuity with Initial Growth               3-33

• Assume: Initial Earnings $1.00, growing at 4% for 5 years.
• Stable earnings thereafter, discounted @ 10%
• Year Dividend x Discount Factor         = Present Value
         ( x 1.04)      @ 10%                   (P / 1.1)n
• 1      1.00          0.9091                   $0.9091
• 2      1.04          0.8264                    0.8595
• 3      1.0816        0.7513                    0.8126
• 4      1.1249        0.6830                    0.7683
• 5      1.17          0.6209                    0.7264
•       Subtotal:                                4.0759
• 6 Perpetuity of $1.17 = $11.70 x 0.5645 =      6.6046
                     .10
• Total Present Value:                         $10.6805
    Valuing Investments with Different Timing of                  3-34
                        Returns
        Project A:                         Project B:
•   End of Year      Return                End of Year   Return
•   1                $200,000              1             $100,000
•   2                 150,000              2              100,000
•   3                 150,000              3              325,000
•   Total:           $500,000              Total:        $525,000

Discounted present values @ 10%, using Table 3-4:

•      Project A:                           Project B:
• End of Return x            NPV      End of Return    x          NPV
  Year                                Year
• 1       $200,000 x .9091 $181,920   1     $100,000 x .9091    $90,910
• 2        150,000 x .8264 123,960    2      100,000 x .8264     82,640
• 3        150,000 x .7513 112,695    3      325,000 x .7513    244,172
• Totals:                 $418,575                             $417,722
      Net Present Value Defined   3-35




•    PV of Funds to be Received
    — PV of Funds Invested
     NPV of Project
    Quick Check Question 3.8           3-36

A factory costs $400,000. You calculate
that it will produce net cash after
operating expenses of $100,000 in year
1, $200,000 in year 2, and $300,000 in
year 3, after which it will shut down with
zero salvage value. Calculate its Net
present Value.
           Quick Check Question 3.8    3-37

Year Pymnt x Discnt Fctr   Prsnt
                @ 10%      Value
1   $100,000     .909      $90,900
2    200,000     .8264     165,280
3    300,000 .   7513      225,390
  Total                    $481,570
• Less: Cost of Capital:   (400,000)
• Net Present Value:       $81,570
                 Summary                  3-38



1. Compounding of interest or returns.
2. Discounting future payments to present
   value.
3. Valuing Annuities (and bonds)
4. Valuing perpetuities.
5. Valuing perpetuities with growth.
6. Valuing perpetuities with changing growth.
6. Testing the present value of projects.
                           Equations                            3-39

• 1 .Compounding of interest or returns.      V = P(1+r)n
•
• 2. Discounting future payments to
      present value.                          PV = P__
                                                  (1+r)n
•
•   3. Valuing Annuities                  PV = P     -       P__
                                               r         r (1 + r)n
•
•   4. Valuing Perpetuities                   PV =          P
                                                           r
•
•   5. Valuing Perpetuities with Growth       PV =     P
                                                     r-g
• 7. Net Present Value = PV (income) – PV (investments)
                    Determining the Right
                    Discount Rate           3-40



• So far we have assumed a discount or
  interest rate. Where does it come from?
• It has two parts: Risk Free Rate and
  Compensation for Risk.
• Risk Free Rate: Compensation for delaying
  other uses of the money. Inflation plus a
  risk free market rate of return. T-Bill 3.7%
  could be 3% inflation plus 0.7% return
• Compensation for risk?
    Table 3-6. Returns to Asset Classes, 1926-1997              3- 41

•                               Table 3-6
                              Returns to Asset Classes
•                                      Std. Deviation Risk Premium
                     Nominal    Real        of          over
     Asset Class     Return     Return Annual Returns T- Bills
•    Short-term
•    Treasury Bills    3.8%      0.7%       3.2%         0%
•    Intermediate-Term
•    T- Bonds          5.3%      2.2%      5.7%          1.5%
•    Long-Term
•    Treasury Bonds    5.2%      2.1       9.2%          1.4%
•    Corporate Bonds 5.7%        2.6%      8.7%          1.9%
•    Large-Co. Stocks 11%        7.9%     20.3%          7.2%
•    Small-Co. Stocks 12.7%      9.6%     33.9%          8.9%
•
Dow-Jones Average, May 2000 – 2005   3-42
                The Coin Flipping Game                3-43

      • Outcome             Probability   Weighted
                                          Outcome
• Original Bet: $1.00
      • $0                     0.5          $0
      • $2.00                  0.5          $1.00
      • Expected outcome:      1.0          $1.00

      • Outcome             Probability   Weighted
                                          Outcome
• Original Bet: $25,000
      • $0                     0.5          $0
      • $50,000                0.5          $25,000
      • Expected outcome:      1.0          $25,000
                        Figure 3-1                     44
• Utility
•           120

•           100




•           40




•            0 10,000   35,000       60,000   Wealth
Percentage Gains & Losses in Figure 3-1           3- 45

    Money:

    Start:      $35,000
    • Win       +25,000 = $60,000 - a 71% gain
    • Lose      - 25,000 = $10,000 - a 71% loss

•    Utility:
•
    • Start:    100
    • Win:      +20 =    120     - a 20% gain
    • Lose      -60 =     40     - a 60% loss
                          Figure 3-2              3-46
• Utility
•           160


•
•           100




•           40




•            0 10,000 35,000    75,000   Wealth
Percentage Gains & Losses in Figure 3-2           3- 47

    Money:

    Start:      $35,000
    • Win       +40,000 = $75,000 - a 115% gain
    • Lose      - 25,000 = $10,000 - a 71% loss

•    Utility:
•
    • Start:    100
    • Win:      +60 =   160     - a 60% gain
    • Lose      -60 =    40     - a 60% loss
            Figure 3-3 – Outcome Probabilities                     3- 48

•   Firm A                                   Firm B
•   Probability                              Probability
•   1.0                                       1.0
•   .9                                         .9
•   .8                                         .8
•   .7                                         .7
•   .6                                         .6
•   .5                                         .5
•   .4                                         .4
•   .3                                         .3
•   .2                                         .2
•   .1                                         .1
•       0     50   100 150 200 250 Firm Value     0 50 100 150 200 250
                      Expected Values                       3-49


•          Firm A                              Firm B
•   Outcome Probability   Product   Outcome Probability   Product
•     $0         0           0       0           .1       $ 0
•   $ 50        .1          $5      $ 50         .2        $10
•   $100        .8         $80      $100         .4        $40
•   $150        .1         $15      $150         .2        $30
•   $200         0           0      $200         .1        $20
•   Total                 $100      Total                 $100
                             Table 3-7                       3-50
•                               Firm A
•                 Deviation      Deviation    Probability times
• Outcome x Prob. from Mean      Squared     Deviation Squared
•   0          0        0           0                0
•   50         .1     -50        2,500              250
•   100        .8        0           0                0
•   150        .1     +50        2,500              250
•   Variance                                        500
                            • Firm B
•                 Deviation      Deviation    Probability times
• Outcome x Prob. from Mean      Squared     Deviation Squared
•   0          .1    -100        10,000             1,000
•   50         .2     -50         2,500               500
•   100        .4       0             0                  0
•   150        .2     +50         2,500                500
•   200        .1    +100        10,000             1,000
•   Variance                                        3,000
                           Table 3-7 Extended                                     3-51
•                                Firm A
•                         Deviation Deviation Probability times     Standard Deviation
    Outcome x Probability from Mean Squared Deviation Squared       (sq. rt. variance)
•    0             0        0             0             0                   -
    50            .1      -50         2,500           250                   -
    100           .8        0             0             0                   -
    150           .1      +50         2,500           250                   -
    Variance                                          500
    Standard Deviation                                                    22.36
•                                 Firm B
•                         Deviation Deviation   Probability times Standard Deviation
    Outcome x Probability from Mean Squared     Deviation Squared (sq. rt. variance)
•    0           .1       -100         10,000           1,000               -
•   50           .2        -50          2,500             500               -
    100          .4          0              0               0               -
    150          .2        +50          2,500             500               -
    200          .1       +100         10,000           1,000               -
    Variance                                            3,000
    Standard Deviation                                                    54.77
        Returns to Diversification – Slide 1                         52


•                    Returns to                Returns to
                   Umbrella Maker           Beach Resort
• Rainy Season     $0.50 x .5 = $0.25      ($0.25) x .5 = ($0.125)
• Sunny Season    ($0.25) x .5 = (0.125)    $0.50 x .5 = $0.25
• Expected Return               $0.125                     $0.125
       Returns to Diversification – Slide 2   3-53
• Returns




                1          2




•            Umbrellas   Resorts
•             1 Rain     2 Shine
             Returns to Diversification 54
• Systemic Risk – General Market risk to whole
  economy. All investments are subject to it
  but to different extents. Beta represents the
  extent of the effect of systemic risk on a
  particular company‘s stock.
• Unsystemic Risk – Risk to a particular
  industry or investment. This can be
  eliminated by diversification
    Table 3-9 Effects of Increasing Diversification                3-55
                       on Volatility
Number of Stocks    Average Volatility of  Ratio of Portfolio Volatility
  in Portfolio     Annual Portfolio Returns To Volatility of a Single
                                                 Stock
•          (1)              (2)                   (3)____________
•         1                49.24%                1.00
          2                37.36                 0.76
          4                29.69                 0.60
          6                26.64                 0.54
          8                24.98                 0.51
         10                23.93                 0.49
         20                21.68                 0.44
         30                20.87                 0.42
         40                20.46                 0.42
         50                20.20                 0.41
        100                19.69                 0.40
        200                19.42                 0.39
        300                19.34                 0.39
        400                19.29                 0.39
        500                19.27                 0.39
        1,000              19.21                 0.39 - Market Risk
 Table 3-10 Return on Treasuries + Stocks               3-56

%Treasury Rate of Weighted % Common Rate of Weighted   Total
  Bonds Return Return      Stocks   Return Return     Return
• 100       5%     5%         0       0%      0       5%
• 75        5%     3.75%    25       10%      2.5%    6.25%
• 50        5%     2.5%     50       10%      5%      7.5%
• 25        5%     1.25%    75       10%      7.5%    8.75%
• 0         5%     0%      100       10%     10%     10%

• (Assuming 5% return on Treasuries & 10% on stocks)
  Table 3-11 Return to Stocks + Borrowing                  57


                   Return on % Borrowed Interest Interest Net
• %Stocks % Return Equity    Funds       Rate    Expense Return
• 100       10%      10%        0          5%      0      10%
• 125       10%      12.5%     25%         5%     1.25% 11.25%
• 150       10%      15%       50%         5%     2.5%    12.5%
• 175       10%      17.5%     75%         5%     3.75% 13.75%
• 200       10%       20%     100%         5%     5%      15%

• (Assuming borrowing @ 5% & 10% return on stocks)
    Summary of Portfolio Choices and Results 3-58
•    % Stocks Weighted % T – Bonds Weighted % Borrowed Interest   Total
•             Return               Return              Expense    Retun
•    0          0     100            5%      0            0     5%
•    25%        2.5%   75            3.75%   0            0     6.25%
•    50%        5%     50            2.5%    0            0     7.5%
•    75%        7.5%   25            1.25%   0            0     8.75%
•    100%       10%     0            0       0            0     10%
•    125%       12.5%   0            0      25           1.25% 11.25
•    150%       15%     0            0      50           2.5%   12.5%
•    175%       17.5%   0            0      75           3.75% 13.75%
•    200%       20%     0            0     100           5%    15%
      Two Different ways to get the same rate of
     return                                3-59
Buy a single risky stock with expected 15% return
     –     Faces both systemic and non-systemic risk. Expected annual
           volatility of 49.21% rather than diversified portfolio volatility of
           19.21% (Table 3-9)
     –     Market does not pay a premium for this high risk (volatility)
           because there are two less risky ways to get the same result.
1.       Buy a portfolio of stocks with a Beta of 2 (gets a 15%
         return (Figure 3-4)
2.       Buy a market portfolio with leverage 15% return (Table 3-
         11)
    Capital Asset Pricing Model Cap M                     3-60

R = Return on investment
S = Systemic Return
U = Unsystemic Return

R = S+U
    The Cap M theory holds that companies do not have to
    pay for unsystemic risk because that can be eliminated
    through portfolio diversification and/or leverage so U is
    fixed at 0

Different companies respond to Systemic Risk differently so
     S needs to be modified by this ratio called Beta
             Figure 3-4 Capital Market Line         3-61
Expected
Return on
Investment




 Market Rate (10%)




Risk-Free Rate (5%)




                      0   .5   1.0    1.5        2.0
                                            Risk (beta)
             Figure 3-4 Capital Market Line              3-62
Expected
Return on
Investment




                           • Company A
 Market Rate (10%)

                                         • Company B

Risk-Free Rate (5%)




                      0   .5     1.0       1.5        2.0
                                                 Risk (beta)
    Expected Cost of Capital under CAPM             3-63



• Risk Free Rate + (Equity Premium)(beta)

• Assume Risk-Free Rate of 5% and Equity Premium of 5%
     (10% - 5%)

• Assume a company with a beta of 1.5

• Risk-Free Rate:                  5%
• + Equity Premium: 5% x beta: 1.5 7.5%
• Cost of Equity Capital          12.5%
      Leverage and Capital Structure                    3-64



• Covered in more detail in next Chapter
• Basic Example

Firm A                         Firm B
Debt        $300,000           Debt        $0
Equity      $700,000           Equity      $1,000,000
            $1,000,000                     $1,000,000

Because Beta is calculated based on market as a whole it is a
  function of average form of capital structure. It helps us
  calculate the cost of capital of the equity of the firm but
  capital structure can be changed so we may want the cost
  of capital of an unleveraged (all equity firm)
             Calculating an Unlevered Beta                      3-65



•   Unlevered beta =
•   Levered beta/ [1+ (1-tax rate)(debt/equity)]
•   Example:
•   levered beta = 1.2
•   Tax rate: .4
•   Capital structure: 30% debt, 70% equity
•   Unlevered beta =          1.2______ =        1.2_______ =
•                      1+ (1-.40)( 30/70)   1 + (.60)(.42)
•   =    1.2___ = .95
•       1.257
           Calculating an Unlevered Beta                    3-66



• Beta goes down since leverage creates volatility.
• When would you want to use this?
• When you are buying an entire company and could redo
  the capital structure (mix of equity and debt). You are
  trying to figure out what to pay for the whole compnay.
    Expected Cost of Capital under CAPM                 3-67



• Risk Free Rate + (Equity Premium)(unleveraged beta)

• Assume Risk-Free Rate of 5% and Equity Premium of 5%
     (10% - 5%)

• Assume a company with a beta of .95

• Risk-Free Rate:                  5%
• + Equity Premium: 5% x beta: .95 4.75%
• Cost of Equity Capital           9.75%
                       Forms of ECMH                      3-68



• Weak Form: Nothing in past stock prices predicts future
  prices. Based on the Random Walk Findings

•   Semi-Strong Form: Stock prices reflect all publicly
    available information.

•   Strong Form: Stock prices reflect all information.
        Necessary Conditions for ECMH       3-69


1.   Zero Transaction Costs in Securities (as
  commissions falla nd internet brokerage
  rises this is getting close)
2. All available information is costlessly
  available to all market participants.
3. Agreement on the implications of current
  information for stock prices.
4.Sufficient capital to engage in risky
  arbitrage? (this is necessary to cause the
  market adjustments to information)
       Mechanisms of Market Efficiency       3-70



Efficient Markets Paradox (Grossman &
  Stiglitz):
• Traders must believe that markets are
  inefficient.
• Inefficiency creates opportunity to find
  bargains.
• Bargains create opportunity to earn
  extraordinary returns.
                   Anomalies in ECMH                      3-71

•   Evidence:
•   1. Trend chasing can sometimes be profitable.
•   2. Low p/e (“value”) stocks outperform the market.
•   3. High risk stocks are overpriced
•   4. Convertible debt can sell below conversion value
•   5. Closed End Mutual Funds trade below asset value
•   6. Japanese bubble of 1980s
•   7. 1987 Crash of U.S. Market
•   8. Late 1990s bubble and 2001 U. S. Market Crash
•   9. January Effect
•
• Explanations:
• A. Irrational behavior by some investors swamps
      capacity of sophisticated investors to correct.
• B. Small changes in expected interest & growth rates    can
  cause large changes in prices.
Nikkei 225: 1985 – 2005   3-72
          Examples of Pricing Anomalies                 3-73

• 3Com: (maker of modems, switches & computer components)
•   Mkt. Value of $19 billion in early 2000
•   Owned 95% of Palm, Inc., with $332 Billion mkt. value.
•
• Healthdyne: (maker of infant monitors & medical devices)
•   Dec. 31, 1996 - stock traded at $8.88
•   Early 1997 -rejected takeover bid of $15
•   Nov. 1997 - sold for $24.
•
• Royal Dutch Shell - 60/40 sharing agreement
  Royal Dutch should be worth 150% of Shell
•        Early 1990s, Royal Dutch traded at 5-7% discount
•        Late 1990s, Royal Dutch traded at up to 20% premium
        Psychological Bases for Investor Errors                3-74


1.   Investors make a series of systematic calculation errors that
   prevent rational investment choices.
    a.    Investors fear risk more than they value rewards.
    b.    Investors suffer from an “anchoring bias” and
              calculate gains & losses from a reference point,
              rather than looking long-term.
2. Investors suffer from the “availability bias” in which they
       calculate based only on recent and easily recalled events
       rather than looking at a larger data set.
    a.    Investors suffer from a “framing bias” in which their
              answer to a question depends on how it is framed.
3. Experimental economists have found an “endowment
       effect,” in which individuals will refuse to sell an item they
       own, where they would refuse to buy that item at that price.
      Challenges to ECMH and Responses                           3-75

1. Arbitrage is risky, not risk-free.
•      There are particular explanations where arbitrage fails. -
       e.g., insufficient public shares for short sales of Palm, Inc.
2. There may be insufficient funds to correct overall
       market bubbles.
•      Some market crashes can be explained by new
       information, e.g., interest rate changes.
•      It‟s unrealistic to assume public trades foolishly, when
       80% of trading is by informed professionals.
3. ―Value‖ investing, that buys low p/e stocks, performs
   better than indexes over the long run.
•      “Value” stocks may be depressed for a reason, such as
       setbacks that make them riskier.
•      Many bargains don‟t persist, but revert to mean returns.
               Wachter‘s Reconciliation                       3-76
• 1.   Anomalies exist, and may persist for some time before
       correction.
• 2.   Grossman & Stiglitz‟s “Efficient Market Paradox” – it takes
       inefficiencies to generate profits to motive searches for
       trading opportunities, and restore efficient pricing.
• 3.   Markets can be (relatively) efficient without always
       being correct – the only question then is how long it takes
       prices to be corrected.
• 4.   Fama & French: beta doesn‟t capture all elements of risk;
       some are explained by other factors.
• 5.   These other factors mean that CAPM doesn‟t necessarily
       capture the cost of equity capital accurately.
• 6.   Variations in growth rates of expected earnings can
       dramatically affect estimates of firm value.
• 7.   The risk premium on stocks appears to vary with the
       business cycle.
• 8.   No new theory has been offered; behavioralists test their
       theories against CAPM / ECMH.
        Implications for Lawyers      3-77

• How do you price an IPO? Google Dutch
  Auction.
• Should managers be able to use takeover
  defenses if the markets are efficient? Why
  do takeovers occur?Inefficient?
• Should short term drops in share prices be
  evidence of misrepresentation in securities
  offerings?
• Should share prices movements after an
  IPO prove that unerwriter valuatiosn were
  fraudulent?
                               3-78




The Use of ECMH in the Courts and to Make
             Legal Arguments
                  ECMH in the Courts   3-79

• Fraud on the Market assumes ECMH Semi
  Strong Form. All public information is reflected
  in price. Thus even if I don‟t “know” the
  information it affects me in the price.
       West v. Prudential Securities, Inc.   3-80




• Facts: Hoffman, a Prudential broker, lied to his
  customers that Jerfferson was going to be
  taken over shortly. Those who bought shares
  during the 8 month period of the “lie” alledge
  they bought over priced shares as a result of
  his lie. Opinion assumes he told the customers
  it was “inside” information. Lie was never made
  public.
• Judge: Easterbrook (law and economics
  school)
       West v. Prudential Securities, Inc.    3-81




• Issue: Can a class be certified? To do so P
  must show causation of loss.
• Basic v. Levinson: Case involved false public
  announcements and a securities fraud claim.
  An issue is whether P has to show actual
  reliance on the false public information. “Fraud
  on the Market” theory accepted by 4 of the 6
  Justices. Theory is that false public information
  affects all prices in the security due to ECMH.
  Does Basic apply to false private information?
       West v. Prudential Securities, Inc.   3-82




• Analysis: Since there was no public
  announcement and no evidence how the tips to
  the custoemrs here could have caused stock
  price rise there was no fraud on the market and
  hence no causation of the loss claimed.
• P‟s expert argued that purchases initiated by
  the false information drove up the price.
  (Almost a but for causation argument). He
  argues lie increased demand which increased
  price.
       West v. Prudential Securities, Inc.   3-83



• But Easterbrook says that demand in securities
  is elastic as so many fungible stocks (CAPM)
  so trades can only increase price to the extent
  trades convey information.
• These retail customers could not convey
  information by trading (not professionals and
  volume too small)
      West v. Prudential Securities, Inc.   3-84



• Which form of ECMH could have helped
  Plaintiffs?
      West v. Prudential Securities, Inc.   3-85



• Which form of ECMH could have helped
  Plaintiffs? Strong Form: Prices reflect all
  even private information. This form is not
  accepted much any more.
       West v. Prudential Securities, Inc.   3-86



• QUESTION: Easterbrook presumes Jefferson‟s
  stock is efficiently priced and suggests P bears
  the burden of proving it is not. Does Behavioral
  Economics suggest a different presumption?
       West v. Prudential Securities, Inc.    3-87



• Behavioral Economics would suggest that a
  large enough trading volume will cause
  irrational actors to follow the herd and drive
  prices up. How do you prove this with
  testimony in courts?
• Q. Why did you (who are now suing Prudential
  and trying to prove an irrational herd following
  price change) buy Jefferson Stock?
• A. I was following the herd.
 When is the market for a stock efficient? 3-88
• ECMH assumes public information is
  disseminated and understood.
• Thus when a sufficient number of analysts
  follow a stock.
• Information will be shared and multiple
  analysts will ensure agreement on
  significance.
• Born out by fewer earnings surporises for
  well followed stocks.
  How many are enough?
  Time Warner Securities Litigation      3-89

• You may have read the Time Warner
  Paramount Case in Corporations.
• It dealt with the issue of whether a board
  could just say no to an offer.
• If company is not for sale are there Revlon
  duties?
• This case arises later when TW tries to raise
  money for the cash tender offer and merger.
• Doe sthe poor trading of TW prove the
  earlier decision wrong? Does it prove the
  board was wrong in their business judgment
  that it was better than the Paramount deal?
       Elements of a 10b-5 Claim            3-90

•   Material Misstatement or omission
•   Scienter (knowing or reckless)
•   In connection with sale of securities
•   Relied on by P
•   Caused damage
    Elements of a 10b-5 Claim              3-91

Two issues in this case
• Were there materialy misleading statements
  or omissions.
• Was scienter pled sufficiently
  – one way to plead is motive and opportunity to
    commit fraud.
      Elements of a 10b-5 Claim       3-92

•   Is corp. responsible for statements in
    the press attributed to unnamed
    corporate personnel?
•   Does corp. have duty to update
    optimistic predictions about a
    business plan when the prospects
    become dim?
•   Does corp. have obligation to
    disclose a specific alternative to an
    announced plan when the alternative
    comes under active consideration
•   Did Plaintiffs adequately plead
    scienter?
      Elements of a 10b-5 Claim                 3-93

•   Is corp. responsible for statements in the press
    attributed to unnamed corporate personnel?
    No.
•   Does corp. have duty to update optimistic
    predictions about a business plan when the
    prospects become dim? Not when
    projections were not specific.
•   Does corp. have obligation to disclose a specific
    alternative to an announced plan when the
    alternative comes under active consideration?
    Yes
•                                    Yes,
    Did Plaintiffs adequately plead scienter?
    Motive was lessening the dilution
             Time Warner           3-94
―A duty to disclose arises whenever secret
   information renders prior public statements
   materially misleading, not merely when that
   information completely negates the public
   statements.‖
―We do not hold that whenever a corporation
   speaks, it must disclose every piece of
   information in its possession that could affect
   the price of its stock.‖
―Rather, we hold that when a corporation is
   pursuing a specific business goal and
   announces that goal as well as an intended
   approach for reaching it, it may come under an
   obligation to disclose other approaches to
   reaching the goal when those approaches are
   under active and serious consideration.‖
             Time Warner           3-95

Question of motive.
―The unresolved issue is whether the effects of the
   artificial raising of the stock price by the
   combination of the glowing reports of potential
   strategic alliances and the nondisclosure of the
   active consideration of a rights offering could
   reasonably have been expected by the company
   not to have been completely dissipated by the
   announcement of the rights offering, thereby
   enabling the company to set the rights offering
   price somewhat higher than would have been
   possible without the misleading statements....‖
            Time Warner         3-96

Question of motive.
This statement implies markets may not fully
   react ot the correction of prior fraudulent
   statements.
But ECMH says they should. This is Winter‘s
   point in dissent.
         Time Warner      3-97

1. Does the majority suggest that all
   statements made must be
   updated when new information
   would make them no longer
   completely true?
            Time Warner         3-98

1. Not exactly. ―It is important to appreciate
   the limits of our disagreement with the
   District Court. We do not hold that
   whenever a corporation speaks, it must
   disclose every piece of information in its
   possession that could affect the price of
   its stock. Rather, we hold that when a
   corporation is pursuing a specific
   business goal and announces that goal as
   well as an intended approach for reaching
   it, it may come under an obligation to
   disclose other approaches to reaching the
   goal when those approaches are under
   active and serious consideration.‖
             Time Warner        3-99

2.   Note that the Court concludes that
     consideration of a possible stock
     offering rather than strategic alliances
     would be material to investors. ―An
     offering of new shares, in contrast [to
     a strategic alliance], would dilute the
     ownership rights of existing
     shareholders, likely decrease
     dividends, and drive down the price of
     the stock.‖ If you represented Time-
     Warner, what arguments could you
     make that this wasn‘t so?
•
                   Time Warner                     3-100
2.   First, new equity investments will help reduce interest payments and
     will thus free up cash to pay dividends. This was a company with
     over $1.1 billion in interest expense in 1990, with net losses of $227
     million.
Losses per common share were over $13.00. No dividends were paid on
     the common in 1990.
Second, notice that dilution of ownership rights, in terms of percentage
     ownership, always occurs when new shares are issued. As Winter‘s
     dissent states, in a public corporation, ―investors who do not care
     about control also do not care about dilution.‖
Thus dilution of ownership is not always bad. The question is whether
     you have positive net present value projects that will earn more than
     the cost of capital. Interest savings are a form of earnings.
Third, Winter‘s dissent points out that strategic partners would have
     diluted Time-Warner‘s earnings - they would want a share of them in
     exchange for their investments.
This isn‘t to say that investors aren‘t interested in whether the company is
     planning to issue more stock, or that it might not affect stock prices.
        Dilution   3-101


100 shares pre offer =
 original shareholders
 own 100%
200 shares post offer =
 original shareholders
 own 50%
        Dilution   3-102


Original company worth
  $100 so original
  shareholders own $100
After new money company
  becomes worth $300 so
  original shareholders
  own $150 of value
   Example of Real Dilution   3-103


Original company worth
  $100 so original
  shareholders own $100
After new money company
  becomes worth $150 so
  original shareholders
  own $75 of value where
  they owned $100 before.
              Dilution   3-104

Three theories on why new offerings
    drive down price:
It dilutes share value by increasing
    total shares in issue: refuted
    above.
It signals best time to sell so price is
    not going up so people sell.
 It conveys bad information (like in
    this case the alliances are off).
       Time Warner                 3-105

3. Note the dilution example in footnote
   5 of the majority‘s opinion:
   ―Presumably, announcement of a
   rights offering will tend to reduce a
   stock price by the extent to which the
   offering, if fully subscribed, dilutes
   the position of the original
   shareholders.
      Time Warner                3-106

For example, if a company, with 1,000
  outstanding shares selling at $100 a
  share raises $100,000 of new capital
  by a rights offering that issues 2,000
  shares at a price of $50 a share, the
  original shareholders will own one-
  third (1,000 shares of 3,000
  outstanding) of a company that
  should be worth $200,000, and the
  share price after the rights offering
  should be $66.67 ($200,000/3,000).‖
      Time Warner               3-107

3. Do you see any logical flaws in
   employing this example in Time-
   Warner?
   Time Warner   3-108



3. Why should a
 company be
 willing to sell new
 shares for $50?
       Time Warner                       3-109
3. A. The new project to be financed is a negative
   net present value project.
   B. The offering reveals new information about
   the company - that it isn‘t worth as much as
   investors previously thought. (The failure to find
   strategic partners may have meant that Time-
   Warner‘s businesses weren‘t worth what
   management thought, and as much as
   management‘s asking price.) In this case, the
   harm isn‘t issuance of new shares, but revelation
   that the company is worth less than investors
   previously believed. This could have resulted
   from the disappointment of hopes that strategic
   partnerships would create new value (i.e., be
   positive net present value projects) for Time-
   Warner.
   Time Warner   3-110


4. How does Judge
  Winter distinguish
  types of dilution
  compared to the
  majority‘s
  approach?
    Time Warner        3-111

4. His characterization of
  the first rights offering is
  that it ―created a
  disproportionate dilutive
  effect on non-exercising
  shareholders as a means
  of coercing shareholders
  to exercise the rights.‖
     Time Warner            3-112

4. Why is it disproportionate and
   coercive?
   Rights weren‘t transferable so
   shareholders were forced to
   exercise if they believed the
   purchase price would be below
   the fair value of the shares. (If
   the offering were under-priced,
   the rights, if marketable, would
   have traded for the amount of
   that bargain.)
       Time Warner                3-113

5. Is there anything in particular about
   the Time-Warner Rights Offering that
   might make the above example
   realistic?
      Time Warner                 3-114

5. Rights Offer terms sent a negative
   message. Companies do not want to
   invest in TW at current valuations and
   lenders do not want to put in new
   debt. As Winter‘s dissent says, ―It
   thus indicated that the only source of
   capital available for the debt
   payments were the locked-in
   shareholders of Time Warner who
   might lose all if the company
   defaulted on the debt.‖
      Time Warner                3-115

5. Rights offering seemed to be
   purposely dilutive so as to coerce
   acceptance (remember this was the
   only way to get money to pay off
   debt).
       Time Warner                3-116

6. Plaintiff‘s scienter theory argued in
   part that management concealed
   plans for the rights offering because it
   didn‘t want to scare off potential
   strategic partners. How does the
   court react to this argument?
       Time Warner              3-117

6. Trial Court Rejected and Majority
   Agrees. Winter suggests that it might
   even be favorable news for an
   investor (new source of capital).
     Time Warner              3-118

7. Plaintiff‘s scienter theory argues
   that management was motivated
   to maintain an artificially high
   market price so the asking price
   in the rights offering could be
   higher. What assumptions
   underlie this argument?
•
     Time Warner             3-119

7. That markets can be fooled and
   misprice a stock. Is that
   inconsistent with ECMH?
No. It can happen when the
   information reflected in a stock
   price is false.
But once the dilutive rights offering
   is announced, (true information is
   released) what happens to price?
     Time Warner          3-120

7. ECMH says markets should adjust
   rapidly to the new information,
   and correct for the
   misinformation.
     Time Warner          3-121


8. How does the court
   reconcile plaintiff‘s theory
   with ECMH?
       Time Warner                       3-122
8. ―In such circumstances, we consider the
   pleading sufficient to survive dismissal because,
   however efficiently markets may be thought to
   work when disclosures are proper, it is not
   beyond doubt that they may not fully correct for
   prior misleading information once a necessary
   disclosure has been made. Though, in many
   circumstances, a truthful correction might be
   expected promptly to alert the market to errors in
   prior statements, ... it is possible, in some
   circumstances, that the embellishments of a
   deliberately false statement and the manner of
   its dissemination might leave its effects
   lingering in the market for some time, despite a
   correcting statement.‖ - page 152
       Time Warner                    3-123

8. The court‘s real answer is that the issue is
   whether defendants believed in ECMH; if
   they didn‘t, they might (naively) think the
   market might not correct sufficiently when
   the truth was revealed:
   ―In a case like the pending one, however,
   the issue is not whether the misleading
   aspect of the prior statement in fact
   lingered; it is only whether the plaintiff can
   show that the defendants had a motive not
   to promptly correct the misleading aspect
   of the prior statement.‖ - page 152
     Time Warner           3-124

8. ―In a case like the pending
   one, however, the issue is not
   whether the misleading aspect
   of the prior statement in fact
   lingered; it is only whether the
   plaintiff can show that the
   defendants had a motive not to
   promptly correct the
   misleading aspect of the prior
   statement.‖ - page 152
    Time Warner         3-125


9. Why does Judge Winter
   think the motive to
   artificially maintain the
   market price in advance of
   the rights offering is
   implausible?
       Time Warner               3-126

9. Because TW intended the offering to
   be below the pre-announcement
   market price, in order to coerce
   shareholders to exercise.
10.And management would have
   expected a negative reaction to the
   announcement of the coercive rights
   offering.
• And because management knew that
   in their registration statement filing
   for the rights offering, management
   would have to disclose the failure of
   the strategic partners approach.
     Time Warner            3-127

• And because the notion that
  markets quickly reflect widely
  disseminated news is widely
  accepted by Securities Laws:
 – Texas-Gulf Sulpher
 – Basic v. Levinson
 – Securities Act waiting period for
   Registration Statements
 – Plaintiffs own pleading (to prove
   reliance)
                         3-128




Valuation Issues in the Courts
               Old Attitudes Toward Markets                        3-129

• Chicago Corp. v. Munds, 172 A.2d 452, 455. (Del. Ch. 1934):

• "When it is said that the appraisal which the market puts upon
  the value of the stock of an active corporation as evidenced by
  its daily quotations is an accurate, fair reflection of its intrinsic
  worth, no more than a moment's reflection is needed to refute
  it."

• Smith v. Van Gorkom, 488 A.2d 858, 875-76 (1985):

• "Using market price as a basis for concluding that the premium
  adequately reflected the true value of the Company was a
  clearly faulty, indeed fallacious, premise.... Most chief
  executives think that the market undervalues their companies'
  stock."
        Changing Attitudes Toward Markets?                      3-130



• Appelbaum v. Avaya, 2002 Del. LEXIS 699:

•        “The corporation owes its cashed-out stockholders
    payment representing the “fair value” of their fractional
    interests. The cashed-out stockholders will receive fair value if
    Avaya compensates them with payment based on the price of
    Avaya stock averaged over a ten-day period preceding the
    Proposed Transaction. While market price is not employed in
    all valuation contexts, our jurisprudence recognizes that in
    many circumstances a property interest is best valued by the
    amount a buyer will pay for it. The Vice Chancellor correctly
    concluded that a well-informed, liquid trading market will
    provide a measure of fair value superior to any estimate the
    court could impose.”
               Del. Gen. Corp. L. § 262(h)                       3-131


•
•          “(h) After determining the stockholders entitled to an
    appraisal, the Court shall appraise the shares, determining their
    fair value exclusive of any element of value arising from the
    accomplishment or expectation of the merger or consolidation,
    together with a fair rate of interest, if any, to be paid upon the
    amount determined to be the fair value. In determining such
    fair value, the Court shall take into account all relevant factors.”
    Cede & Co. v. Technicolor – Basic Facts                   3-132


•    June 30, 1978 - $7.75
•    June 30, 1979 - $10.33
•    June 30, 1980 - $24.67 (peak of silver bubble)
•    July 7, 1981 - $18.63 (after announcement of 1-Hour Photo)
•    1981-82 – earnings drop
•    June 30, 1982 - $10.37
•    June – Sept. 1982 Trading Range - $9.00 to $11.00
•    Negotiated buyout price - $23
•    MAF tender offer got all but 17.81% of shares
•    Cinerama dissents from merger for its 4.4%
•    Appraised value by Chancery Court: $21.60
Cede & Co. v. Technicolor – Basic Facts    3-133

 What is the Fair Value of Technicolor‘s
 stock?
• Chancellor Allen decides $20.48, plus
  $1.12 adjustment for long-term debt =
  $21.60.
 Cede & Co. v. Technicolor – Basic Facts 3-134
There are three parts to a discounted cash
  flow valuation analysis:
• An estimation of expected cash flows for the
  firm;
• Determination of a residual or terminal value
  for periods beyond the cash flow
  projections; and
• Selection of the appropriate discount rate.
   Methodology of Experts – Earnings Estimates               3-
                              135


• Technicolor: Alfred Rappaport (Northwestern)
• Calculated an initial period of projected growing earnings
  (“Value Growth Duration” (“VGR”) during which earnings are in
  excess of cost of capital.
• For a residual value thereafter, Rappaport assumed constant
  cash flows. (i.e. no equity value growth)

• Cinerama: John Torkelson (Princeton Venture Research)
• Also calculated cash flows for first five years.
• Then assumed earnings continued to grow @ 5% in perpetuity.
                     Cost of Capital                        3-136



• Rapaport:
• Used beta of 1.7, based on December, 1982 beta for
  Technicolor
• Added 4% small capitalization premium for 22.7% cost of
  capital

• Torkelson:
• Used average of two costs of capital:
   – MAF‟s cost of 9.96%
   – Cost for all manufacturing companies of 15%
   – Average = 12.5%
 Rappaport‘s cost of capital without a small   3-137
                    cap premium


• Cost of capital          22.7%
• Small cap premium        - 4%
• Cost of capital          18.7%
      Technicolor Questions                  3-138

1. What are the incentives of each expert in a case
   such as this?
      Technicolor Questions              3-139
1.What are the incentives of each expert in a
  case such as this?
In fn. 17 Chancellor Allen describes them:
  ―... the incentive of the contending parties is
  to arrive at estimates of value that are at the
  outer margins of plausibility – that
  essentially define a bargaining range.‖
  ―If one substitutes the higher discount rate
  used by respondent‘s principal expert
  [Rappaport] for the lower rate used by
  petitioner‘s expert [Torkelson] and makes
  no other adjustment to either DCF model the
  differences reduces from $49.61 a share to
  $20.86.
     Technicolor Questions             3-140

2. What are the three parts of discounted cash
   flow analysis described by the court?
• An estimation of expected cash flows for
   the firm.
• Determination of a residual or terminal
   value for periods beyond the cash flow
   projections.
• Selection of the appropriate discount rate.
     Technicolor Questions                3-141

3. Why do you suppose experts focus on the
   first 5 - 7 years before calculating a
   terminal value?
      Technicolor Questions                   3-142

3. Why do you suppose experts focus on the first 5
   - 7 years before calculating a terminal value?
• It‘s customary to calculate expected cash flows
   out to a ―valuation horizon‖ - chosen somewhat
   arbitrarily.
• Beyond 5 years, it‘s terribly difficult to project
   cash flows - too many variables will intrude.
• As the court suggests, the assumption is that if a
   business is growing now, it will mature and
   growth either stop or slow down as competitors
   appear.
• The terminal value assumes a no-growth state in
   most models - that earnings will be stable, and
   that the company will only earn its cost of capital
   on older businesses.
    Technicolor Questions            3-143

4. Why did the court prefer the September
   1982 beta to the December 1982 beta?
     Technicolor Questions                  3-144

4. Why did the court prefer the September 1982
   beta to the December 1982 beta?
• Recall that beta is the relationship between the
   variance of the company‘s stock and the
   variance of the market.
• When the takeover at a premium was announced,
   Technicolor‘s stock price would have jumped
   relative to the overall market. This would
   increase the beta observed for that period.
• Because that jump was temporary and caused
   by an unusual event, it wasn‘t representative of
   the way the market normally valued Technicolor.
    Technicolor Questions               3-145

5. What do Rappaport‘s calculations suggest
   about the cost of capital without a small
   cap premium?
• His cost of capital (22.7%) included a 4%
   small cap premium, so the cost of capital
   would have been 18.7%
    Technicolor Questions               3-146

6. What is the small cap premium? What
   does the court think of applying it to
   Technicolor?
Table 3-6. Returns to Asset Classes, 1926-1997                    3- 147

•                                 Table 3-6
                                Returns to Asset Classes
•                                        Std. Deviation Risk Premium
                        Nominal   Real        of          over
    Asset Class         Return    Return Annual Returns T- Bills
•   Short-term
•   Treasury Bills       3.8%      0.7%       3.2%         0%
•   Intermediate-Term
•   T- Bonds            5.3%       2.2%      5.7%          1.5%
•   Long-Term
•   Treasury Bonds       5.2%      2.1       9.2%          1.4%
•   Corporate Bonds      5.7%      2.6%      8.7%          1.9%
•   Large-Co. Stocks    11%        7.9%     20.3%          7.2%
•   Small-Co. Stocks    12.7%      9.6%     33.9%          8.9%
•
     Technicolor Questions              3-148

6. What is the small cap premium? What
   does the court think of applying it to
   Technicolor?
• Although some think the phenomenon is
   observable there is no theory to explain its
   existence
• In any event Technicolor as an industry
   leader is not a small cap company.
     Technicolor Questions             3-149

7. Why does the court use a lower cost of
   capital for One Hour Photo (14.13%) than
   for the rest of Technicolor (15.28%)? What
   would cause it to make such a decision?
     Technicolor Questions             3-150

7. Why does the court use a lower cost of
   capital for One Hour Photo (14.13%) than
   for the rest of Technicolor (15.28%)? What
   would cause it to make such a decision?
• Presumably One Hour Photo is considered
   a lower risk business.
• They may have identified similar
   businesses and used their betas.
• This shows complexity in valuing
   conglomerates which have a blended beta
   of businesses and hence different costs of
   capital.
     Technicolor Questions             3-151

8. If experts determine the beta for
   Technicolor and then use CAPM to
   determine cost of capital, to what should
   they apply it?
     Technicolor Questions                3-152

8. ―Professor Rappaport used the Capital
   Asset Pricing Model (CAPM) to estimate
   Technicolor's costs of capital as of
   January 24, 1983. That model estimates
   the cost of company debt (on an after tax
   basis for a company expected to be able to
   utilize the tax deductibility of interest
   payments) by estimating the expected
   future cost of borrowing; it estimates the
   future cost of equity through a multi-factor
   equation and then proportionately weighs
   and combines the cost of equity and the
   cost of debt to determine a cost of capital.‖
     Technicolor Questions              3-153

8. Thus he used the unlevered cost of capital
   for the company, by estimating the cost of
   debt and, separately, using CAPM, the cost
   of equity capital.
• If he uses a weighted average cost of
   capital reached this way, it‘s lower than the
   cost of equity capital, because of the
   interest tax benefit of debt.
• And the weighted average cost of capital
   will always be lower than the cost of
   equity.
     Technicolor Questions              3-154

8. He then uses this as a discount rate
   applied to his valuations of cash flow
   during the value growth period and the
   residual value to get a present value.
• Note that this can reduce his valuation of
   the common stock of Technicolor because
   although he uses a lower discount rate he
   subtracts the value of debt from enterprise
   value.
            Technicolor Questions                          3-155
•   If experts determine the beta for Technicolor and then use CAPM to
    determine cost of capital, to what should they apply it?
•       ―Professor Rappaport used the Capital Asset Pricing Model
    (CAPM) to estimate Technicolor's costs of capital as of January 24,
    1983. That model estimates the cost of company debt (on an after
    tax basis for a company expected to be able to utilize the tax
    deductibility of interest payments) by estimating the expected future
    cost of borrowing; it estimates the future cost of equity through a
    multi-factor equation and then proportionately weighs and combines
    the cost of equity and the cost of debt to determine a cost of
    capital.‖
•   Thus he used the unlevered cost of capital for the company, by
    estimating the cost of debt and, separately, using CAPM, the cost of
    equity capital.
•   If he uses a weighted average cost of capital reached this way, it‘s
    lower than the cost of equity capital, because of the interest tax
    benefit of debt.
•   And the weighted average cost of capital will always be lower than
    the cost of equity.
•   Note that this can reduce his valuation of the common stock of
    Technicolor.
    Trial Court‘s Valuation of New Boston Garden          3- 156




•                    Value        Weight        Result
• Market Value:    $ 26.50 X       10% =       $ 2.65
• Earnings Value:   $ 52.60 X      40% =       $ 21.04
• Net Asset Value: $103.16 X       50% =       $ 51.58

                     Total Value Per Share:     $ 75.27
        This is the Delaware Block Method supposedly discarded
        in Delaware by Weinberger
    Market Value of New Boston Garden   3- 157

•   Market Value What is it?
•   Last trade before vote
•   Average over some period
•   Last Trade before deal effect
•   What if no public market?
•   What does ECMH have to say about this?
Boston Garden‘s Earnings Value – Slide 1   3-158

• Court accepted a 5 year average of past
  earnings $5.26 and then applied a
  multiplier of 10 to get $52.60
Boston Garden‘s Earnings Value – Slide 2   3-159

1. What does the average earnings for the
   past 5 years tell us about expected future
   earnings? Would it make a difference if
   there was a trend, either up or down?
Answer: Past predicts the future!
Boston Garden‘s Earnings Value                             3-160

• Suppose average earnings are $5.26, determined as follows:
• Year 1:           $3.26
  Year 2:            4.26
  Year 3:            5.26
  Year 4:            6.26
  Year 5:            7.26
  Total:           $26.30 / 5 = $5.26 capitalized @ 10% = $52.60
• Growth Rate:
• From year 1 to year 2:   30.7% growth rate ($1.00/$3.26)
  From year 2 to year 3:   23.5% growth rate ($1.00/4.26)
  From year 3 to year 4:   19% growth rate ($1.00/5.26)
  From year 4 to year 5:   16% growth rate ($1.00/6.26)
  From year 5 to year 6:   13.8% growth rate ($1.00/7.26)
• Discounted Present value of $7.26 perpetuity @ 10% = $72.60
• (Note this assumes no further growth.)
Boston Garden‘s Earnings Value           3-161

• Suppose we use Rappaport‟s CAPM
  Model of five years of growth plus terminal
  value times capitalization rate.
Calculating Earnings with 5 Yrs Growth @ $1.00                   3-162

• Going forward:
• Earnings growing @ $1.00 per year:
  Year 1: $8.26      x       0.909                =             $7.51
• Year 2: 9.26       x       0.826                =              7.65
• Year 3: 10.26      x       0.751                =              7.71
• Year 4: 11.26      x       0.683                =              7.69
• Year 5: 12.26      x       0.621                =              7.61
  Total present value of growth era:                            38.17

• Terminal value: $12.26/ .10               =      $122.60
• Discounted to PV after 6th year: $122.60 x 0.564        =    $69.15
                                                              $107.32

• Alternative: a perpetuity with growth:
• Assume present earnings of       $7.26                 =    $103.71
                                 .10 - .03
    Calculating Earnings Value   3-163


2. When a court uses a multiple of
 earnings to determine earnings
 value, does this resemble any of
 the valuation techniques available
 in modern finance? If it differs, in
 what ways does it differ?
    Calculating Earnings Value   3-164


2. The multiplier is the reciprocal of
 dividing by the capitalization rate
 It‘s the Price-Earnings Multiple
 from newspaper quotes.
 It masks the growth rate and the
 real cost of capital.
 It also ignores how different capital
 structures influence beta.
    Calculating Earnings Value   3-165


3. The trial court included income
 received from payments made by
 new teams admitted to the NHL in
 income. Why? Wasn‘t this
 extraordinary income that should
 be excluded, as the court‘s
 discussion of the Delaware
 approach suggests?
    Calculating Earnings Value   3-166


3. Why is extraordinary income
  excluded?
• Extraordinary means non-recurring
  (present does not predict the
  future) and thus should not be
  multiplied.
    Calculating Earnings Value   3-167


3. In this case court concludes this
 income is not extraordinary. It ahd
 been received in the past and likely
 in the future.
      Calculating Asset Value   3-168

4. The trial court accepted the
   defendant‘s expert‘s valuation of
   $1,116,000 for the good will of the
   Boston Bruins, the ―net player
   investment,‖ and the value of the AHL
   franchise as part of the asset
   valuation. Are these tangible assets?
   How does good will add value to a
   business? If you represent the
   defendant, how would you argue this
   to the court?
      Calculating Asset Value   3-169


4. These are intangibles.
• Good will represents what you
   paid over fair market value of
   tangible assets for a business.
• It only shows up on a balance
   sheet after an acquisition.
       Calculating Asset Value   3-170

4. Defendant Arguments:
• As intangibles they are too
   speculative. This is why goodwill is
   not just put on a balance sheet.
• Good wilI depends exclusively on the
   ability of the business to earn profits.
• ―Net player investment‖ has to be an
   intangible. Players aren‘t chattels.
• Value of the AHL franchise must also
   depend on profitability of team.
       Calculating Asset Value   3-171

5. The court held that it was not error to
   appraise the asset value of the
   concessions, while their earning
   power was already included in the
   calculation of earnings value. The
   concessions were valued at $4.2
   million, roughly equal to the purchase
   price of the Boston Garden. Do you
   suppose they represented comparable
   tangible assets? If not, are they likely
   to duplicate the earnings valuation of
   the business?
      Calculating Asset Value   3-172


5. This shows the problem with
   valuing assets separate from their
   earning power.
• What do you do with intangibles
   that exist solely based on their
   earning power?
      Calculating Asset Value   3-173


6. What is the court doing to
   determine the asset value of the
   Bruin‘s franchise?
      Calculating Asset Value   3-174


6. There is reference to comparable
   sales, based on admission of new
   teams to the NHL, and the court
   indicates that the $9.6 million
   asset value seems low, but the
   court accepted the defendant‘s
   expert opinion rather than the
   plaintiff‘s $18,000,000 valuation.
   Not clear on what basis.
      Calculating Asset Value   3-175


7. If the company was valued more
   for its assets than its earnings
   because of tax reasons, why didn‘t
   the market value it higher than the
   $26.50 price the court determined
   for market value?
      Calculating Asset Value   3-176


7. It is not clear sometimes the market
   doesn‘t take into account tax benefits.
• Is the company losing money for tax
   purposes, while producing a positive
   cash flow?
• The company had $5 million in excess
   liquid assets.
• If so, it‘s worth more to a tax-paying
   business than investors.
     Calculating Asset Value   3-177


8. The court uses the net book value
   of the Boston Garden Arena as its
   asset value. Is this a useful
   approach?
        Calculating Asset Value        3-178

8. Because the arena was purchased in 1973, the
   year of the merger, ordinarily the book value
   would correspond to an arm‘s length purchase
   price (market value).
• The longer the passage of time between
   purchase and valuation, the less likely book
   value will correspond to market value.
• But because the company had an extremely
   favorable lease on the property before the
   purchase, the purchase price for the asset was
   less than it would otherwise have been.
• Because the trial judge didn‘t explain how he
   handled this issue, it‘s remanded for further
   findings.
      Calculating Asset Value   3-179


9. Why did the court say that in a
   family corporation earnings were
   of little significance?
      Calculating Asset Value   3-180

9. Court gives no explanation.
• One theory is that controlling
   shareholders can extract through high
   salaries, good trips, and the psychic
   benefits of rubbing elbows with star
   athletes.
• The other possibility is that ownership
   of valuable physical assets (Boston
   Garden Arena) is simply a real estate
   play, with the family holding the asset
   for appreciation.
      Calculating Asset Value   3-181


10. What is the significance of the
  court‘s statement that Garden
  Arena had approximately $5
  million in excess liquid assets?
      Calculating Asset Value   3-182


10.Tax Law likely has an answer.
• The family doesn‘t need dividend
  income, taxed at ordinary income
  rates (35%) (double taxation).
• So it accumulates income and
  appreciating real estate assets for
  eventual sale at lower capital
  gains rates (15%).
     Calculating Asset Value   3-183


11. Can you discern a principled way
  in which courts can decide how
  much weight to assign to each
  valuation method?
      Calculating Asset Value   3-184


11. Case law does not disclose a rule
  or system of deciding this. It is
  one of the major problems with
  the block method.
     Calculating Asset Value   3-185


12. How can there be such large
  differences (from $26.50 to
  $103.16) in the valuation of the
  same company, depending on
  which valuation method is used?
      Calculating Asset Value   3-186


12. No real answer.
• $26.50 represents a shallow
  market‘s guess at future value
  streams of this business. Is this
  an efficient market? If not its
  price is not reliable?
• Purchase Value of assets not
  necessarily prove their value to
  generate income streams.
      Calculating Asset Value   3-187


13. Is the dissenting shareholder
  getting what his minority interest
  is worth, or a pro rata share of the
  value of the entire business?
NOTE minority interest discount is
  discussed in the next section.
       Calculating Asset Value     3-188

13. The attempt to value the whole business in
   valuing income and assets suggests a
   share of the whole; but giving some weight
   to market value suggests the value of a
   minority interest.
• In Sarrouf v. New England Patriots Football
   Club, Inc., 397 Mass. 542, 492 N.E.2d 1122
   (1986), the court suggested that the
   minority shareholder was entitled to the
   pro rata value of the entire enterprise,
   which suggests throwing out market value
   of shares and earnings value.
     Calculating Asset Value   3-189


14. If the company wasn‘t being
  managed to produce earnings,
  what was it producing for
  shareholders?
       Calculating Asset Value     3-190

14. For the majority shareholders it may have
   produced high salaries that reduced net
   income.
• This reduces taxable income for the
   corporation, and thus means no double
   taxation of the majority shareholders.
• Note there was a mortgage of $3,437,065
   on the arena even though the company
   had $5 million in excess liquid assets. The
   mortgage created interest expense that
   reduced taxable income. (This should be
   offset by interest income on the $5,000,000
   in excess liquid assets, but perhaps not.)
        Calculating Asset Value         3-191

14. Majority shareholders get the psychic benefits of
    being owners of a major sports franchise. See
    Sarrouf v. New England Patriots Football Club,
    Inc., 397 Mass. 542, 492 N.E.2d 1122 (1986):
• ―[The trial judge] concluded that earnings or
    prospective earnings play little part in the
    valuation because ‗there exists a class of
    extremely wealthy individuals willing to purchase
    National Football League franchises at prices not
    directly related to the earnings or prospective
    earnings of the football team [in order to
    become] a member of an exclusive club - NFL
    Franchise-owners.‘‖
      Calculating Asset Value   3-192


15. If the company wasn‘t being
  managed to produce earnings,
  and its asset value is twice its
  earnings value, why not rely
  exclusively on asset values?
         Calculating Asset Value           3-193

15. The court doesn‘t address this. Most courts
    don‘t wonder about the disparity.
• This kind of disparity suggests the possible
    improvement in corporate values if this business
    were owned by someone else seeking to
    maximize profits.
• From the shareholders‘ perspective, failing to
    sell it looks like a breach of duty by the directors.
• Or the difference in values represents the value
    of the current mismanagement, which might be
    the value of a derivative claim.
• To weight these two values - earnings & market -
    produces a value less than the enterprise could
    be worth.
     Control Premium and Minority Discount    3-194


• Control Premium: amount paid over the current
  market price for obtaining control of a company.
• Minority Discount: Reduction fo a price for
  shares being a minority (lacking control)
• Marketability or Illiquidity Discount: Reduction
  from price because no public market in which to
  sell
• To what extent should any of these be used to
  determine “fair” value in an appraisal
  proceeding.
Revised Model Bus. Corp. Act § 13.01(4)                3-195



• “(4) 'Fair Value,‟ means the value of the corporation‟s
  shares determined:
    – (i)      immediately before the effectuation of the
      corporate action to which the shareholder objects;
    – (ii)     using customary and current valuation
      concepts and techniques generally employed for
      similar businesses in the context of the transaction
      requiring appraisal; and
    – (iii)    without discounting for lack of
      marketability or minority interest except, if
      appropriate, for amendments to the articles pursuant
      to section 13.02(a)(5).“
         Commentary to RMBCA § 13.01(4)                           3-196



•        “Subsection (iii) of the definition of „fair value‟ establishes
    that valuation discounts for lack of marketability or minority
    status are inappropriate in most appraisal actions, both
    because most transactions that trigger appraisal rights affect
    the corporation as a whole and because such discounts give
    the majority the opportunity to take advantage of minority
    shareholders who have been forced against their will to accept
    the appraisal-triggering transaction. Subsection (iii), in
    conjunction with the lead-in language to the definition, is also
    designed to adopt the more modern view that appraisal should
    generally award a shareholder his or her proportional interest in
    the corporation after valuing the corporation as a whole, rather
    than the value of the shareholder‟s shares when valued alone.“
         Summary of RMBCA § 13.02(b)                         3-197


• (1) No appraisal rights for shares listed on exchange or
      NASDAQ or with 2,000 or more beneficial owners
• (3) Unless shareholders receive anything other than
      exchange-listed or widely-traded shares
• (4) (i)     (A) Unless the transaction is caused by a person
      owning 20% or more of the company‟s shares,
      except pursuant to a takeout merger following within one
      year of a tender offer at the same price & kind of
      consideration, or
•             (B) Unless the control person has had the power to
      control election of 25% of the directors, or
•      (ii) Unless the transaction is caused by a senior executive
      or director who will receive benefits not generally available
      to other shareholders.
         Comments to RMBCA § 13.02(b)                          3-198




•        “The premise of the market exception is that the market
    must be liquid and the valuation assigned to the relevant shares
    must be „reliable.‟ Section 13.02(b)(1) is designed to assure
    liquidity. For purposes of these provisions, section 13.02(b)(4)
    is designed to assure reliability by recognizing that the market
    price of, or consideration for, shares of a corporation that
    proposes to engage in a section 13.02(a) transaction may be
    subject to influences where a corporation‟s management,
    controlling shareholders or directors have conflicting interests
    that could, if not dealt with appropriately, adversely affect the
    consideration that otherwise could have been expected.“
                     Del. G.C.L. § 262(b)                         3-199

• (b) Appraisal rights shall be available for the shares of any
  class or series of stock … in a merger…:
•      (1) Provided, however, that no appraisal rights under this
  section shall be available for the shares of any class or series
  of stock . . . Which … were either (i) listed on a national
  securities exchange … or (ii) held of record by more than 2,000
  holders . . . .
•       (2) Notwithstanding paragraph (1) of this subsection,
  appraisal rights … shall be available for the shares of any class
  or series of stock . . . If the holders thereof are required . . . to
  accept for such stock anything except:
•               a. Shares of stock of the corporation surviving or
  resulting from such merger . . .;
•               b. Shares of stock of any other corporation [listed
  or traded in an equivalent manner];
•               c. Cash in lieu of fractional shares . . . .
                          Del. G.C.L. § 262(a)       3-200



•      (a) Any stockholder of a corporation of this State who holds
    shares of stock on the date of the making of a demand
    pursuant to subsection (d) of this section with respect to such
    shares, who continuously holds such shares through the
    effective date of the merger or consolidation, who has
    otherwise complied with subsection (d) of this section and who
    has neither vote in favor of the merger or consolidation nor
    consented thereto in writing pursuant to § 228 of this title shall
    be entitled to an appraisal by the Court of Chancery of the fair
    value of his shares of stock under the circumstances described
    in subsections (b) and (c) of this section. * * *
       Harris v. Rapid-American – the Deal                           3-201
•                                   Riklis

•                  Controls                  Controls

•                  Kenton (new Rapid)          AFC

•                             (1) bought 46.5%
•                                    of         which owns:
•   (2) (merger)                   Rapid       100%      McCrory
•
•                                                    100% Schenley
•                   (3) $28    cash-out
•                                                       100% McGregor
•                     Rapid Public Shareholders
           Harris v. Rapid-American 3-202
• Harris claimed that WMA‘s valuation technique only
  compared the value of the subsidiaries with the market
  value of publicly traded shares, which are discounted
  because they are a minority interest.
• Rapid argued that Cavalier prohibits adjustments to value,
  and that the addition of a control premium would reflect
  liquidation value, or a sale to a third party, which isn't
  involved here.
• Rejected: Cavalier only prohibits adjustments in the
  shareholders‘ valuation, not in the valuation of the
  company itself.
• Tri-Continental Corp. v. Battye recognized that adjustments
  at the corporate level from market values of underlying
  assets were sometimes appropriate (as in the case of
  closed-end investment companies).
• Cavalier, in approving of Tri-Continental, approved
  adjustments of value at the corporate level but not at the
  shareholder level.
      Harris v. Rapid-American 3-203
1.Why did both appraisers choose to
  value the subsidiaries rather than
  Rapid as a whole?
       Harris v. Rapid-American 3-204
• Rapid was a conglomorate. No two are
  alike so there are no comparables.
• CAPM would suggest value earnings of
  each and then use the appropriate
  discount rate to value them.
       Harris v. Rapid-American 3-205
2. What did the Chancery Court mean
  when it criticized the SRC report as
  valuing Harris‘ shares ―as freely
  trading minority shareholders‖?
       Harris v. Rapid-American 3-206
2. What did the Chancery Court mean
  when it criticized the SRC report as
  valuing Harris‘ shares ―as freely
  trading minority shareholders‖?
• That there is a ―minority discount‖
  from the value of the entire company in
  trading markets where small amounts
  are traded.
       Harris v. Rapid-American 3-207
3. What rationale supports WMA‘s
  addition of a control premium to the
  values it found for Rapid-American‘s
  subsidiaries? If Rapid had liquidated
  the subsidiaries and become the direct
  owner of their assets and businesses,
  does this mean the control premium
  would disappear?
           Harris v. Rapid-American 3-208
3. The rationale is that when the subsidiaries are valued by comparing
   them with the public market price of similar companies in their
   industries, the market price measure is simply a measure of the value
   of a small minority interest.
• Simply multiplying that price by the number of shares outstanding
   doesn't produce the total value of the firm, because someone willing to
   purchase the entire firm would be willing to pay a control premium.
• Similarly, if someone now controls the firm, that owner values the
   control block at a higher per share price, because control carries with
   it the ability to set the investment and distribution policies of the firm
   for the convenience of the controlling shareholder.
• If Rapid were not a conglomerate, the same analysis would apply to
   Rapid as an operating firm, and the premium would be applied to value
   Rapid as a whole, under this reasoning.
• Note that the result of this is to add a ―control premium‖ value for each
   subsidiary to the ―fair value‖ of Rapid, which, in effect, gives
   dissenting shareholders their pro rata share of the value of the entire
   firm.
• In effect this eliminates the control premium that the majority
   shareholder may have paid for its interest in the company, or at least
   forces it to share that value (for which it may have paid) with the
   dissenters.
      Harris v. Rapid-American 3-209
4. If a control premium means that a
  controlling block of shares is worth
  more per share than a minority block,
  how can a 100% ownership carry a
  control premium?
• A.
        Harris v. Rapid-American 3-210
4. In a real sense, it can't. But the
  measures of value that experts used all
  refer to markets, and in those markets
  only minority interests in firms are
  traded on a daily basis. Markets also
  produce information about the size of
  control premiums when firms are taken
  over, of course.
         Harris v. Rapid-American 3-211
5. Tri-Continental Corp. v. Battye, 74 A.2d 71 (Del. 1950),
   involved a discount of the asset value of a closed-end
   mutual fund. Closed-end mutual funds are organized like
   business corporations, in that they issue shares that are
   subsequently traded in markets, in contrast to open-end
   funds, which continuously redeem and reissue shares.
   Closed-end funds‘ shares typically trade at prices that
   deviate from their ―net asset value,‖ which is their pro rata
   share of the investments owned by the funds. Where the
   investments are publicly traded securities, determining net
   asset value is a simple task; one performed daily by open-
   end funds. These deviations from net asset value for
   closed-end companies‘ shares generally are discounts
   from net asset value. Thus the value of a closed-end
   fund‘s assets in its hands is less than the value of the
   same assets in the market, and the Tri-Continental court
   recognized that this factor should be taken into account in
   an appraisal proceeding. How does this relate to a
   discussion of whether a shareholder in Rapid-American
   should be accorded a control premium?
        Harris v. Rapid-American 3-212
5. If Rapid had held a controlling but not 100%
  interest in its subsidiaries, the answer to this
  question would proceed as follows.
• If the minority shares in each subsidiary were
  actively traded in efficient markets, determining
  market value of the subsidiaries would be easy:
  one would simply refer to the market value per
  share, and multiply by the number of shares.
• This undervalues the company, because minority
  interests carry a discount reflecting the
  disadvantages under which minority shareholders
  operate.
• The control block is simply worth more per share,
  because of its ability to control investment and
  distribution policies, and to hold out for a higher
  price should anyone else want to buy control of
  the firm.
       Harris v. Rapid-American 3-213
6. What does the court mean when it
  says that Harris was not claiming a
  control premium at the shareholder
  level?
       Harris v. Rapid-American 3-214
6. Harris is saying that the aggregate
  value of Rapid is worth more than the
  market value of Rapid shares, and that
  he is entitled to a pro rata share of its
  aggregate value. In that respect, he‘s
  claiming a share of the control
  premium that previously belonged to
  Riklis, as if the company were being
  liquidated and its value being
  distributed pro rata.
        Harris v. Rapid-American 3-215
7. Bell v. Kirby Lumber Corp., 413 A.2d 137 (Del.
  1980) involved a company where use of liquidation
  values was rejected by the Delaware Supreme
  Court, on the theory that the firm was to be valued
  as a going concern, with the expectation that it
  would consider, despite the fact that its liquidation
  value, according to asset appraisals, was over
  $600, while its value based on its income was
  approximately $150. Note that WMA‘s valuation
  added a control premium, but the court stated that
  this didn‘t involve a liquidation valuation, because
  WMA didn‘t assume that an acquirer was going to
  liquidate Rapid-American. From the perspective
  of the present shareholders of Rapid-American,
  isn‘t a sale of their entire interest to a new buyer
  equivalent to a liquidation?
       Harris v. Rapid-American 3-216
7. Kirby Lumber wasn't being liquidated,
  and neither is Rapid. In both cases, a
  majority shareholder simply froze out
  the minority investors.
• In Bell v. Kirby Lumber the liquidation
  value was much higher than the
  previous market value of the minority
  interest, and higher than its value
  based on historic earnings (the
  Delaware Block was in effect).
        Harris v. Rapid-American 3-217
7. The higher liquidation value was based on what
  appraisers thought the company could obtain if it
  sold its assets (timber). In short, this was a
  ―control premium.‖ Its huge size must have meant
  that Kirby Lumber had not been harvesting lumber
  at the optimal rate.
• From the perspective of minority shareholders in
  Rapid, the analysis is exactly the same. Inclusion
  of a control premium at the subsidiary level is the
  same as inclusion of a control premium for Rapid
  itself. Control premiums, of course, only occur
  when control is sold. In short, the control
  premium appears to be identical to liquidation
  value, despite the language in Cavalier Oil Corp. v.
  Harnett that the firm be viewed as a ―going
  concern.―