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13.3% is signi¬cantly higher than the American VRP, which in the Lease,
McConnell, and Mikkelson study is 5.4% and in the Houlihan Lokey
Howard & Zukin study (which follows the section on Megginson) is 3.2%.
The purpose of this section is to determine how much of the 13.3% VRP
is for the power of the vote versus the higher expected cash ¬‚ows to the
SV shareholders.
The analysis that follows shows that of the 13.3% VRP, 11.9% is due
to higher expected cash ¬‚ows to the SV shareholders and 1.4% is being
paid purely for the right to vote.
The rest of this section is a detailed explanation of Table 7-3, which
is my quantitative analysis of the Megginson results. The reader who
wants to save time can safely skip the rest of this section and continue
with the Houlihan Lokey Howard & Zukin (Much and Fagan) study.

My Analysis of the Megginson Results. We assume that the average
holding period on the London Stock Exchange during the 1955“1982 pe-
riod was ¬ve years. The table begins with expected cash ¬‚ows to the
shareholders in rows 6 to 13, which we show in two different scenarios.
In scenario #1 (Columns A“F), the ¬rm will not be acquired during the
shareholder™s tenure. In scenario #2 (Columns H“M), the ¬rm will be
acquired during the shareholder™s tenure.
The assumptions of the model are as follows:
1. Using large capitalization NYSE ¬rm data from the SBBI
yearbooks,18 for the years 1955“1982, total returns were 10.48%
(B30), which we use as our discount rate. This broke down to a
dividend yield of 3.94% (B27) and capital gains return of 6.54%
(B29).
2. The voting rights premium is 13.3% (B28), per Megginson
(1990).
3. When ¬rms were acquired, we assume a 20% acquisition
premium to the RV shares.19 The ¬nal results are insensitive to
the magnitude of this assumption.
4. The SV shares receive a premium that is 27.6% (B32) higher than
the RV shares in the event of an acquisition.
The RV shareholder cash ¬‚ows appear in cells C6 to C12. The share-
holder invests $1.00 (C6) at time zero. In Year 1, he or she receives divi-
dends of 3.94% $1.00 $0.0394 (C7). As the shares rise in price by
6.54% (B29) annually, applying the constant dividend yield is equivalent


18. London Stock Exchange data were unavailable to us. We use NYSE data as a proxy for the LSE
data. According to Professor Megginson, the NYSE data should be a good proxy for the
LSE.
19. These data did not appear in the article and are no longer available.




PART 3 Adjusting for Control and Marketability
214
T A B L E 7-3

Analysis of Megginson Results


A B C D E F H I J K L M

4 Scenario #1: SV Shares-No Acquisition Scenario #2: SV Shares-Acquisition

5 Yr SV RV PV Factor [1] NPV SV NPV RV Yr SV RV PV Factor [1] NPV SV NPV RV
6 0 1.1330 1.0000 1.0000 1.1330 1.0000 0 1.1330 1.0000 1.0000 1.1330 1.0000
7 1 0.0394 0.0394 0.9051 0.0357 0.0357 1 0.0394 0.0394 0.9051 0.0357 0.0357
8 2 0.0420 0.0420 0.8193 0.0344 0.0344 2 0.0394 0.0394 0.8193 0.0323 0.0323
9 3 0.0447 0.0447 0.7416 0.0332 0.0332 3 0.0394 0.0394 0.7416 0.0292 0.0292
10 4 0.0476 0.0476 0.6712 0.0320 0.0320 4 0.0394 0.0394 0.6712 0.0264 0.0264
11 5 0.0508 0.0508 0.6075 0.0308 0.0308 5 0.0394 0.0394 0.6075 0.0239 0.0239
12 5 1.5552 1.3727 0.6075 0.9449 0.8340 5 2.101819 1.647194 0.6075 1.2770 1.0008
13 Total 0.0221 0.0000 Total 0.2915 0.1483


15 Summary of NPVs SENSITIVITY ANALYSIS: NPV of RV-SV

16 No Acq Acquisition Total
17 SV 0.0221 0.2915 Capital RV-SV
18 RV 0.0000 0.1483 Apprec
19 Probabilities [2] 94.95% 5.05% 100.00% 0.00% 0.0461
20 Probability Wtd NPVs 2.00% 0.0371
21 SV 0.0210 0.0147 0.0062 4.00% 0.0273
22 RV 0.0000 0.0075 0.0075 6.54% 0.0137
23 RV-SV 0.0137 8.00% 0.0053
24 RV-SV (in percent) 1.4% 10.48% 0.0100
26 Assumptions
27 Dividend yield [3] 3.94%
28 Voting rights prem 0.133
29 Cap apprec g [3] 6.54%
30 Disc rate r [3] 10.48%
31 Acq prem-RV [4] 20%
32 SV/RV acq prem 27.6%

[1] Present value factors are end-of-year. Using midyear factors makes no difference in the ¬nal result to four decimal places.
[2] Probability of acquisition 5 year holding period/[152 Firms/(43 Acquisitions/28 Years)], or 5 Years / 98.98 years
[3] Derived from SBBI-1999 for 1955-1982. We use the US data as a proxy for UK data, as the latter were unavailable.
[4] This is an assumption, as the data were unavailable. However, the ¬nal results are insensitive to the assumption.
215
to having dividends rise by the same capital appreciation percentage of
6.54%. Thus, $0.0394 (1 0.0654) $0.0420 (C8). As we go down
the column, each year™s dividend is 6.54% higher than the previous
year™s. The ¬nal dividend is $0.0508 (C11). Finally, at the end of Year
5, the shareholder sells for $1.3727 (C12), which is the original invest-
ment of $1.00, with ¬ve years of compound growth at the 6.54% or
1.06545
$1.00 $1.3727.
The SV share cash ¬‚ows begin with a $1.133 investment (B6). The SV
shareholders receive the same dividend stream as the RV shareholders,
so B7 through B11 is the same as those rows in column C. At the end of
Year 5, the SV shareholder sells at the voting rights premium of 13.3%,
i.e., $1.3727 1.133 $1.5552 [C12 (1 B28) B12].
We discount the forecast cash ¬‚ows at the average return of 10.48%
(B30). The end-of-year present value factors at 10.48% appear in D6 to
D12. Multiplying the SV and RV forecast cash ¬‚ows by the present value
factors leads to present values of the SV and RV forecast cash ¬‚ows in
E6 through E12 and F6 through F12, respectively. The totals are the net
present values of the investments, which are $.0221 (E13) and 0 (F13)
for SV and RV.
The analysis of scenario #2 is structured identically to that of scenario
#1. The forecast cash ¬‚ows in I6 through J11, which are the initial in-
vestments and the dividends, are identical to their counterparts in col-
umns B and C. The only differences are in Year 5, where we assume
the ¬rms are acquired. The acquisition amount for the RV shares is com-
posed of two parts. The ¬rst is the ¬ve years of growth at 6.54% (B29), or
1.06545 $1.3727, which is the same as C12. We then multiply that by 1
plus the assumed acquisition premium for RV shares of 20% (B31), or
$1.3727 1.2 $1.647194 (J12). The actual premium is unknown; how-
ever, a sensitivity analysis showed our ¬nal results are insensitive to this
assumption within a fairly wide range around our assumption.
The SV buyout occurs at the SV-over-RV premium of 27.6% (B32), or
$1.647194 1.276 $2.101819 (I12). The present values of the cash ¬‚ows
are $0.2915 (L13) and $0.1483 (M13) for SV and RV shares when there is
an acquisition.20
We now proceed to the summary of the net present values (NPVs)
and begin with the no-acquisition scenario. In B17 and B18, we transfer
the NPVs of $0.0221 and zero from E13 and F13 for the SV and RV
shares. We then multiply those conditional FMVs by the probability of
not being acquired in our assumed ¬ve-year holding period, which is
94.95% (B19) and is calculated in footnote [2] to Table 7-3. The probability-
weighted NPVs for the SV and RV shares are $0.0210 and 0 (B21, B22).
Next we transfer the acquisition scenario NPVs of $0.2915 and
$0.1483 for SV and RV shares from L13 and M13 to C17 and C18, re-
spectively. We multiply those NPVs by the probability of acquisition of
5.05% (C19), which is 1 minus the 94.95% in B19, to obtain the probability-



20. Actually, the present values are slightly higher, as the acquisitions could take place before Year
5. However, this simpli¬cation has no material impact on the outcome of the analysis.




PART 3 Adjusting for Control and Marketability
216
weighted NPVs of $0.0147 (C21) and $0.0075 (C22) for the SV and RV
shares.
We add columns B and C to obtain the probability-weighted NPVs
of SV shares of $0.0062 (D21) and $0.0075 (D22). The RV minus SV NPV
difference is $0.0137 (D23), or approximately 1.4% (D24) of the RV share
price.
Let™s do a recap of this table, as it is very detailed. At the 10.48%
(B30) discount rate, the RV shares are priced exactly right, assuming there
will be no acquisition, i.e., they have a zero present value (F13), while
they actually have a small, positive weighted average NPV of $0.0075
(D22) after including the 5% probability of an acquisition premium. Thus,
RV shares are a good buy based on expected cash ¬‚ows for one with a
10.48% hurdle rate.
The SV shares, on the other hand, are a bad buy on a pure discounted
cash ¬‚ow basis. In the absence of an acquisition, which is a 95% proba-
bility for a ¬ve-year holding period, the NPV is $0.0221 (E13, trans-
ferred to B17). The positive NPV of $0.2915 (L13, transferred to C17) in
the event of an acquisition, which is only a 5% probability, is insuf¬cient
to outweigh the negative NPV absent the acquisition. Overall, the SV
shares have a negative NPV of $0.0062 (D21). On a pure basis of NPV
of forecast cash ¬‚ows, the RV shares have a $0.0137 (D23) NPV differential
over the SV shares. The investor in SV shares passed up $0.014 (rounded)
of NPV to buy the vote, or 1.4% (D24) of the $1.00 RV price. We subtract
this from the average SV price of $1.133, and $1.119, or 11.9% of the 13.3%
voting rights premium is justi¬ed by higher expected cash ¬‚ows, while
1.4% of it appears to be paid for the right to vote and the marginal power
that goes with it.
In the middle-right section of the table, we present a sensitivity anal-
ysis of the SV-RV NPV differential. The SV-RV NPV differential rises as
the fraction of the total return shifts more towards dividend yield and
away from capital appreciation. For example, if capital appreciation ac-
counted for none of the 10.48% yield, then the portion of the $0.133 voting
rights premium attributable to the power of the vote rises to $0.0461 (I19)
versus the base case.
The intuition for this result is that when returns are weighted more
heavily towards dividends, the SV shares receive a lower effective divi-
dend yield. This is because the SV shares receive the same absolute div-
idends as the RV shares but paid a higher price per share to receive them.
Also, both SV and RV share prices grow more slowly, and the absolute
cash value of the 27.6% SV-over-RV premium upon acquisition is less than
when returns are primarily in the form of capital gains.
Table 7-3A is identical to Table 7-3, but it is for the Lease, McConnell,
and Mikkelson study. The net VRP is 1.1% (D24).

The Houlihan Lokey Howard & Zukin (HLHZ) Study
Much and Fagan (2000), of HLHZ, describe their own update of the Lease,
McConnell, and Mikkelson study. The HLHZ study consists of 18 dual-
class ¬rms with identical dividend rights and liquidity preference. While
this is professional rather than academic research, we include it here be-
cause it is an update of academic research and ¬ts in better topically.



CHAPTER 7 Adjusting for Levels of Control and Marketability 217
218
T A B L E 7-3A

Analysis of American VRP Results


A B C D E F H I J K L M

4 Scenario #1: SV Shares-No Acquisition Scenario #2: SV Shares-Acquisition

5 Yr SV RV PV Factor [1] PV SV NPV RV Yr SV RV PV Factor [1] PV SV NPV RV
6 0 1.0544 1.0000 1.0000 1.0544 1.0000 0 1.0544 1.0000 1.0000 1.0544 1.0000
7 1 0.0394 0.0394 0.9051 0.0357 0.0357 1 0.0394 0.0394 0.9051 0.0357 0.0357
8 2 0.0420 0.0420 0.8193 0.0344 0.0344 2 0.0394 0.0394 0.8193 0.0323 0.0323
9 3 0.0447 0.0447 0.7416 0.0332 0.0332 3 0.0394 0.0394 0.7416 0.0292 0.0292
10 4 0.0476 0.0476 0.6712 0.0320 0.0320 4 0.0394 0.0394 0.6712 0.0264 0.0264
11 5 0.0508 0.0508 0.6075 0.0308 0.0308 5 0.0394 0.0394 0.6075 0.0239 0.0239
12 5 1.4473 1.3727 0.6075 0.8793 0.8340 5 1.921726 1.921726 0.6075 1.1675 1.1675
13 Total 0.0090 0.0000 Total 0.2607 0.3151
15 Summary of NPVs SENSITIVITY ANALYSIS: NPV of RV-SV

16 No Acq Acquisition Total Discount RV-SV
17 SV 0.0090 0.2607 Rate
18 RV 0.0000 0.3151 8% 0.0061
19 Probabilities [2] 94.95% 5.05% 100.00% 10.48% 0.0113
20 Probability Wtd NPVs 12% 0.0142
21 SV 0.0086 0.0132 0.0046 14% 0.0176
22 RV 0.0000 0.0159 0.0159
23 RV-SV 00.0113 Capital RV-SV
24 RV-SV (in percent) 1.1% Apprec
25 0.00% 0.0230
26 Assumptions 2.00% 0.0230
27 Dividend yield [3] 3.94% 4.00% 0.0162
28 Voting rights prem [5] 0.0544 6.54% 0.0113
29 Cap apprec g [3] 6.54% 8.00% 0.0083
30 Disc rate r [3] 10.48% 10.48% 0.0027
31 Acq perm-both [4] 40%
32 SV/RV acq prem 0.0%

[1] Present value factors are end-of-year. Using midyear factors makes no difference in the ¬nal result to four decimal places.
[2] Probability of acquisition is from the British data. However, increasing cell C19 to 25% causes D24 to rise to only 2%.
[3] Derived from SBBI-1999 for 1955-1982.
[4] This is an assumption, as the data were unavailable. However, the ¬nal results are insensitive to the assumption.
The HLHZ study presents the VRP over a very short period of time
ending with December 31, 1994.21 In this respect it is very different than
the two previous studies, which present VRP averages over many years.
The Lease, McConnell, and Mikkelson VRP results are the averages over
38 years, while the Megginson results are averages over 28 years. In con-
trast, the HLHZ study covers a short snippet of time.
The 260-day moving average mean and median voting rights pre-
miums were 3.2% and 2.7%, respectively, while they were 1.5% and 1.15%
for 60-day moving averages. The longer the time period, the more reliable
is the result, unless there are clear trends that render older data obsolete,
which is not the case here. Therefore, the 260-day moving average of 3.2%
is the best measure of the VRP in this study. These are lower premiums
than those in the Lease, McConnell, and Mikkelson study, although the
mean VRP was monotonically increasing with the length of the moving-
average time period (the authors also presented data for 120- and 180-
day moving averages. Given the reported results, it is possible that ex-
panding the time horizon would have led to a larger VRP.
The authors point out anecdotally that the voting rights premium
can be affected by other factors. They mentioned that until the fourth
quarter of 1994, the Class A stock of Paci¬care Health Systems, Inc. was
included in the S&P 400 index. During this time, the Class A voting shares
consistently traded at a 1.5“2.5% premium over the nonvoting shares.

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