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86 80 47.2014 5.07E-07 0.000024 0.4087 0.0000098
87 81 49.5614 4.23E-07 0.000021 0.3596 0.0000075
88 82 52.0395 3.52E-07 0.000018 0.3596 0.0000066
89 83 54.6415 2.93E-07 0.000016 0.3596 0.0000058
90 84 57.3736 2.45E-07 0.000014 0.3596 0.0000050
91 85 60.2422 2.04E-07 0.000012 0.3596 0.0000044
92 86 63.2544 1.7E-07 0.000011 0.3596 0.0000039
93 87 66.4171 1.42E-07 0.000009 0.3596 0.0000034
94 88 69.7379 1.18E-07 0.000008 0.3596 0.0000030
95 89 73.2248 9.83E-07 0.000007 0.3596 0.0000026
96 90 76.8861 8.19E-08 0.000006 0.3596 0.0000023
97 91 80.7304 6.82E-08 0.000006 0.3165 0.0000017
98 92 84.7669 5.69E-08 0.000005 0.3165 0.0000015
99 93 89.0052 4.74E-08 0.000004 0.3165 0.0000013
100 94 93.4555 3.95E-08 0.000004 0.3165 0.0000012
101 95 98.1283 3.29E-08 0.000003 0.3165 0.0000010
102 96 103.0347 2.74E-08 0.000003 0.3165 0.0000009
103 97 108.1864 2.29E-08 0.000002 0.3165 0.0000008
104 98 113.5957 1.9E-08 0.000002 0.3165 0.0000007
105 99 119.2755 1.59E-08 0.000002 0.3165 0.0000006
106 100 125.2393 1.32E-08 0.000002 0.3165 0.0000005

107 Totals $7.3030 $7.0030

108 Discount 1 (F107/D107) 4.1%
109 Discount-By Formula [1] 4.1%

111 Parameters Sensitivity Analysis

112 r 20% Avg Yrs Between Sales

113 g 5% 8 10 12
114 z 12% 18% 7.2% 5.1% 3.8%
115 x (1 g)/ 87.50% 20% 5.9% 4.1% 2.9%
(1 r)
116 j yrs to sale 10 22% 4.9% 3.3% 2.3%


[1] Formula For Discount: 1 ((1 x j)/((1 (1 z)*x j)))




PART 3 Adjusting for Control and Marketability
268
Table 7-13 is identical to Table 7-12, except that it demonstrates the
accuracy of equation (7-9a), which is the formula appropriate for buyers™
transactions costs. Buyers care about their own transactions costs from
the outset. Therefore, the continuum of buyers™ transactions costs begins
immediately. Thus, E7 to E16 equal 0.88 in Table 7-13, while they were
equal to 1.00 in Table 7-12.
The discount in Table 7-13 is considerably larger”15.6%, which we
calculate in F108 using the ˜˜brute force™™ method and in F109 using equa-
tion (7-9a). The spreadsheet formula appears in note [1] as it also does in
Table 7-12. Table 7-13 thus demonstrates the accuracy of equation
(7-9a).

Value Remaining Formula and the Total Discount. The fraction in
(7-9) is the percentage of value that remains after removing the perpetuity
of transactions costs. Equation (7-10) shows the equation for the value
remaining, denoted as VR:
xj
1
VR valuing remaining formula (7-10)
z)x j
1 (1
We can multiply all three value remaining ¬gures for each of the
three components, and the result is the value remaining for the ¬rm over-
all. The ¬nal discount is then one minus the value remaining for the ¬rm
overall.
Next we will demonstrate the ¬nal calculation of DLOM.

Table 7-14: Sample Calculation of DLOM
Table 7-14 is an example of calculating DLOM for a privately held
¬rm with a $5 million FMV on a marketable minority basis. Column B is
the pure discount of each component as calculated according to the meth-
odology in the previous tables. Component #1, the discount due to the
delay to sale, is equal to 13.4% (B9), which comes from Table 7-10, cell
D12. Component #2, monopsony power to the buyer, equals 9% (B10),
per our discussion of Schwert™s article earlier in this chapter. Component
#3A, buyers™ transactions costs, equals 3.7% (Table 7-11, I73) for private
buyers, minus the approximately 1% brokerage fee to buy a $5 million
interest in publicly traded stocks 2.7% (B11). Component #3B, sellers™
transactions costs, equals 8.4% (Table 7-11, I74) for private buyers minus
the approximate 1% brokerage fee to buy publicly traded stocks 7.4%
(B12). The reason that we subtract stock market transactions costs from
the private market transactions costs is that we are using public market
values as our basis of comparison, i.e., our point of reference.
Column C is the present value of the perpetual discount, which
means that for Components #3A and #3B, we quantify the in¬nite peri-
odic transactions costs. Using equations (7-9a) for the buyers and (7-9)
for the sellers, the 2.7% (B11) pure discount for buyers results in a net
present value of buyers™ transactions costs of 3.6% (C11), and the 7.4%
(B12) pure discount for sellers results in a net present value of sellers™
transactions costs of 2.4% (C12). Again, that excludes the seller™s costs
on the assumed sale to the hypothetical buyer at t 0. The ¬rst two



CHAPTER 7 Adjusting for Levels of Control and Marketability 269
T A B L E 7-13

Proof of Equation (7-9a)


A B C D E F G

4 (1 z) Int(Yr 1) Post Tx
5 Cash PV Cash Post-Trans PV Cash
6 Year Flow PVF Flow Costs Flow

7 1 1.0000 0.912871 0.912871 0.8800 0.8033264
8 2 1.0500 0.760726 0.798762 0.8800 0.7029106
9 3 1.1025 0.633938 0.698917 0.8800 0.6150468
10 4 1.1576 0.528282 0.611552 0.8800 0.5381659
11 5 1.2155 0.440235 0.535108 0.8800 0.4708952
12 6 1.2763 0.366862 0.468220 0.8800 0.4120333
13 7 1.3401 0.305719 0.409692 0.8800 0.3605291
14 8 1.4071 0.254766 0.358481 0.8800 0.3154630
15 9 1.4775 0.212305 0.313671 0.8800 0.2760301
16 10 1.5513 0.176921 0.274462 0.8800 0.2415264
17 11 1.6289 0.147434 0.240154 0.7744 0.1859753
18 12 1.7103 0.122861 0.210135 0.7744 0.1627284
19 13 1.7959 0.102385 0.183868 0.7744 0.1423873
20 14 1.8856 0.08532 0.160884 0.7744 0.1245889
21 15 1.9799 0.0711 0.140774 0.7744 0.1090153
22 16 2.0789 0.05925 0.123177 0.7744 0.0953884
23 17 2.1829 0.049375 0.107780 0.7744 0.0834648
24 18 2.2920 0.041146 0.094308 0.7744 0.0730317
25 19 2.4066 0.034288 0.082519 0.7744 0.0639028
26 20 2.5270 0.028574 0.072204 0.7744 0.0559149
27 21 2.6533 0.023811 0.063179 0.6815 0.0430545
28 22 2.7860 0.019843 0.055281 0.6815 0.0376727
29 23 2.9253 0.016536 0.048371 0.6815 0.0329636
30 24 3.0715 0.0138 0.042325 0.6815 0.0288431
31 25 3.2251 0.011483 0.037034 0.6815 0.0252378
32 26 3.3864 0.009569 0.032405 0.6815 0.0220830
33 27 3.5557 0.007974 0.028354 0.6815 0.0193227
34 28 3.7335 0.006645 0.024810 0.6815 0.0169073
35 29 3.9201 0.005538 0.021709 0.6815 0.0147939
36 30 4.1161 0.004615 0.018995 0.6815 0.0129447
37 31 4.3219 0.003846 0.016621 0.5997 0.0099674
38 32 4.5380 0.003205 0.014543 0.5997 0.0087215
39 33 4.7649 0.002671 0.012725 0.5997 0.0076313
40 34 5.0032 0.002226 0.011135 0.5997 0.0066774
41 35 5.2533 0.001855 0.009743 0.5997 0.0058427
42 36 5.5160 0.001545 0.008525 0.5997 0.0051124
43 37 5.7918 0.001288 0.007459 0.5997 0.0044733
44 38 6.0814 0.001073 0.006527 0.5997 0.0039142
45 39 6.3855 0.000894 0.005711 0.5997 0.0034249
46 40 6.7048 0.000745 0.004997 0.5997 0.0029968
47 41 7.0400 0.000621 0.004373 0.5277 0.0023075
48 42 7.3920 0.000518 0.003826 0.5277 0.0020191
49 43 7.7616 0.000431 0.003348 0.5277 0.0017667
50 44 8.1497 0.000359 0.002929 0.5277 0.0015459
51 45 8.5572 0.0003 0.002563 0.5277 0.0013526
52 46 8.9850 0.00025 0.002243 0.5277 0.0011835
53 47 9.4343 0.000208 0.001962 0.5277 0.0010356
54 48 9.9060 0.000173 0.001717 0.5277 0.0009062
55 49 10.4013 0.000144 0.001502 0.5277 0.0007929
56 50 10.9213 0.00012 0.001315 0.5277 0.0006938
57 51 11.4674 0.0001 0.001150 0.4644 0.0005342
58 52 12.0408 8.36E-05 0.001007 0.4644 0.0004674
59 53 12.6428 6.97E-05 0.000881 0.4644 0.0004090
60 54 13.2749 5.81E-05 0.000771 0.4644 0.0003579
61 55 13.9387 4.84E-05 0.000674 0.4644 0.0003131
62 56 14.6356 4.03E-05 0.000590 0.4644 0.0002740
63 57 15.3674 3.36E-05 0.000516 0.4644 0.0002397




PART 3 Adjusting for Control and Marketability
270
T A B L E 7-13 (continued)

Proof of Equation (7-9a)


A B C D E F G

4 (1 z) Int(Yr 1) Post Tx
5 Cash PV Cash Post-Trans PV Cash
6 Year Flow PVF Flow Costs Flow

64 58 16.1358 2.8E-05 0.000452 0.4644 0.0002098
65 59 16.9426 2.33E-05 0.000395 0.4644 0.0001836
66 60 17.7897 1.94E-05 0.000346 0.4644 0.0001606
67 61 18.6792 1.62E-05 0.000303 0.4087 0.0001237
68 62 19.6131 1.35E-05 0.000265 0.4087 0.0001082
69 63 20.5938 1.13E-05 0.000232 0.4087 0.0000947
70 64 21.6235 9.38E-06 0.000203 0.4087 0.0000829
71 65 22.7047 7.81E-06 0.000177 0.4087 0.0000725
72 66 23.8399 6.51E-06 0.000155 0.4087 0.0000634
73 67 25.0319 5.43E-06 0.000136 0.4087 0.0000555
74 68 26.2835 4.52E-06 0.000119 0.4087 0.0000486
75 69 27.5977 3.77E-06 0.000104 0.4087 0.0000425
76 70 28.9775 3.14E-06 0.000091 0.4087 0.0000372
77 71 30.4264 2.62E-06 0.000080 0.3596 0.0000286
78 72 31.9477 2.18E-06 0.000070 0.3596 0.0000251
79 73 33.5451 1.82E-06 0.000061 0.3596 0.0000219
80 74 35.2224 1.51E-06 0.000053 0.3596 0.0000192
81 75 36.9835 1.26E-06 0.000047 0.3596 0.0000168
82 76 38.8327 1.05E-06 0.000041 0.3596 0.0000147
83 77 40.7743 8.76E-07 0.000036 0.3596 0.0000128
84 78 42.8130 7.3E-07 0.000031 0.3596 0.0000112
85 79 44.9537 6.09E-07 0.000027 0.3596 0.0000098
86 80 47.2014 5.07E-07 0.000024 0.3596 0.0000086
87 81 49.5614 4.23E-07 0.000021 0.3165 0.0000066
88 82 52.0395 3.52E-07 0.000018 0.3165 0.0000058
89 83 54.6415 2.93E-07 0.000016 0.3165 0.0000051
90 84 57.3736 2.45E-07 0.000014 0.3165 0.0000044
91 85 60.2422 2.04E-07 0.000012 0.3165 0.0000039
92 86 63.2544 1.7E-07 0.000011 0.3165 0.0000034
93 87 66.4171 1.42E-07 0.000009 0.3165 0.0000030
94 88 69.7379 1.18E-07 0.000008 0.3165 0.0000026
95 89 73.2248 9.83E-07 0.000007 0.3165 0.0000023
96 90 76.8861 8.19E-08 0.000006 0.3165 0.0000020
97 91 80.7304 6.82E-08 0.000006 0.2785 0.0000015
98 92 84.7669 5.69E-08 0.000005 0.2785 0.0000013
99 93 89.0052 4.74E-08 0.000004 0.2785 0.0000012
100 94 93.4555 3.95E-08 0.000004 0.2785 0.0000010
101 95 98.1283 3.29E-08 0.000003 0.2785 0.0000009
102 96 103.0347 2.74E-08 0.000003 0.2785 0.0000008
103 97 108.1864 2.29E-08 0.000002 0.2785 0.0000007
104 98 113.5957 1.9E-08 0.000002 0.2785 0.0000006
105 99 119.2755 1.59E-08 0.000002 0.2785 0.0000005
106 100 125.2393 1.32E-08 0.000002 0.2785 0.0000005

107 Totals $7.3030 $6.1626

108 Discount 1 (F107/D107) 15.6%
109 Discount-By Formula [1] 15.6%

111 Parameters Sensitivity Analysis

112 r 20% Avg Yrs Between Sales

113 g 5% 8 10 12
114 z 12% 18% 18.3% 16.5% 15.3%
115 x (1 g)/ 87.50% 20% 17.2% 15.6% 14.6%
(1 r)
116 j yrs to sale 10 22% 16.3% 14.9% 14.0%


[1] Formula For Discount: 1 ((1 x j)/((1 (1 z)*x j)))




CHAPTER 7 Adjusting for Levels of Control and Marketability 271
T A B L E 7-14

Sample Calculation of DLOM


A B C D E F G

4 Section 1: Calculation of the Discount for Lack of Marketability
6 1 Col. [C]

7 Pure Discount PV of Perpetual Remaining
8 Component z [1] Discount [2] Value

9 1 13.4% 13.4% 86.6% Delay To sale-1 yr (Table 7-10, D12)
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 2.7% 3.6% 96.4% Transactions costs-buyers
12 3B 7.4% 2.4% 97.6% Transactions costs-sellers
13 Percent remaining 76.9% Total % remaining components 1 2 3A 3B
14 Final discount 23.1% Discount 1 Total % remaining

<<

. 58
( 100 .)



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