# Compounding at 10_

Document Sample

```					               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
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
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)

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
Mechanisms of Market Efficiency       3-70

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
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
• 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
• 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
• 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
• 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
become dim?
•   Does corp. have obligation to
disclose a specific alternative to an
announced plan when the alternative
comes under active consideration
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
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,
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
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
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
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-
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
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
statement.‖ - page 152
Time Warner         3-125

9. Why does Judge Winter
think the motive to
artificially maintain the
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
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

• 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
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
• 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
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
• They may have identified similar
• 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?
•   Average over some period
•   Last Trade before deal effect
•   What if no public market?
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?
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
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
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
• 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
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
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
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

• \$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
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
• 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
• (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,
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
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
• That there is a ―minority discount‖
from the value of the entire company in
Harris v. Rapid-American 3-207
3. What rationale supports WMA‘s
values it found for Rapid-American‘s
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
• 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
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
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
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
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.―

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