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7 $100 million 1.00% 0.10% 0.06% 0.00% 0.16% 1.32% 0.00% 1.32%
8 $10 million 1.50% 0.23% 0.20% 0.00% 0.25% 2.18% 0.00% 2.18%
9 $1 million 4.00% 0.30% 0.70% 0.00% 0.70% 5.70% 0.00% 5.70%

11 Seller
Tax Deal
12 Deal Size Legal [2] Acctg Appraisal Appraisal [3] Internal Mgt [4] Subtotal Inv Bank Total

13 $1 billion 0.10% 0.01% 0.00% 0.02% 0.05% 0.18% 0.75% 0.93%
14 $100 million 1.00% 0.05% 0.00% 0.05% 0.10% 1.20% 1.10% 2.30%
15 $10 million 1.50% 0.08% 0.00% 0.20% 0.15% 1.93% 2.75% 4.68%
16 $1 million 4.00% 0.10% 0.00% 0.75% 0.42% 5.27% 10.00% 15.27%

18 Total
Tax Deal
19 Deal Size Legal [2] Acctg Appraisal Appraisal [3] Internal Mgt [4] Subtotal Inv Bank Total

20 $1 billion 0.20% 0.03% 0.02% 0.02% 0.14% 0.41% 0.75% 1.16%
21 $100 million 2.00% 0.15% 0.06% 0.05% 0.26% 2.52% 1.10% 3.62%
22 $10 million 3.00% 0.30% 0.20% 0.20% 0.40% 4.10% 2.75% 6.85%
23 $1 million 8.00% 0.40% 0.70% 0.75% 1.12% 10.97% 10.00% 20.97%

25 Summary For Regression Analysis-Buyer Summary For Regression Analysis-Seller

26 Sales Price Log10 Price Subtotal Sales Price Log10 Price Subtotal

27 $1,000,000,000 9.0 0.23% $1,000,000,000 9.0 0.18%
28 $100,000,000 8.0 1.32% $100,000,000 8.0 1.20%
29 $10,000,000 7.0 2.18% $10,000,000 7.0 1.93%
30 $1,000,000 6.0 5.70% $1,000,000 6.0 5.27%
259
T A B L E 7-11 (continued)

Estimates of Transaction Costs [1]


A B C D E F G H

32 SUMMARY OUTPUT: Buyer Subtotal Fees as a Function of Log10 FMV
34 Regression Statistics

35 Multiple R 0.9417624
36 R square 0.88691642
37 Adjusted R square 0.83037464
38 Standard error 0.00975177
39 Observations 4

41 ANOVA

42 df SS MS F Signi¬cance F
43 Regression 1 0.001491696 0.0014917 15.68603437 0.058237596
44 Residual 2 0.000190194 9.5097E 05
45 Total 3 0.00168189

47 Coef¬cients Standard Error t Stat P-value Lower 95% Upper 95%

48 Intercept 0.1531 0.033069874 4.62959125 0.043626277 0.010811717 0.295388283
49 Log10 price 0.0172725 0.004361126 3.96055986 0.058237596 0.036036923 0.001491923

51 SUMMARY OUTPUT: Seller Subtotal Fees as a Function of Log10 FMV
53 Regression Statistics

54 Multiple R 0.93697224
55 R square 0.87791699
56 Adjusted R square 0.81687548
57 Standard error 0.00943065
58 Observations 4

60 ANOVA

61 df SS MS F Signi¬cance F

62 Regression 1 0.00127912 0.00127912 14.38229564 0.063027755
63 Residual 2 0.000177874 8.8937E 05
64 Total 3 0.001456994

66 Coef¬cients Standard Error t Stat P-value Lower 95% Upper 95%

67 Intercept 0.14139 0.031980886 4.42107833 0.04754262 0.00378726 0.27899274
68 Log10 price 0.0159945 0.004217514 3.79239972 0.063027755 0.034141012 0.002152012




also 0.9% (B57), which gives us the same con¬dence intervals around the
y-estimate of 1.8%.
Rows 73 and 74 show a sample calculation of transactions costs for
the buyer and seller, respectively. We estimate FMV before discounts for
our subject company of $5 million (B73, B74). The base 10 logarithm of 5
million is 6.69897 (C73, C74).61 In D73 and D74, we insert the x-coef¬cient
from the regression, which is 0.0172725 (from B49) for the buyer and
0.0159945 (from B68) for the seller. We multiply column C column


61. In other words, 106.69897 5 million.




PART 3 Adjusting for Control and Marketability
260
T A B L E 7-11 (continued)

Estimates of Transaction Costs [1]


A B C D E F G H I J

70 Sample Forecast of Transactions Costs For $5 Million Subject Company:

72 FMV log10 FMV X-Coeff. log FMV Coef Regr. Constant Forecast Subtotal Inv Bank [5] Forecast Total

73 Buyer $5,000,000 6.698970004 0.0172725 0.115707959 0.1531 3.7% 0.0% 3.7%
74 Seller $5,000,000 6.698970004 0.0159945 0.107146676 0.14139 3.4% 5.0% 8.4%

Notes:
[1] Based on interviews with investment banker Gordon Gregory, attorney David Boatwright, Esq; and Douglas Obenshain, CPA. Costs include buy and sell side. These are estimates of average costs. Actual costs vary with the complexity
of the transaction.
[2] Legal fees will vary with the complexity of the transaction. An extremely complex $1 billion sale could have legal fees of as much as $5 million each for the buyer and the seller, though this is rare. Complexity increases with: stock deals
(or asset deals with a very large number of assets), seller carries paper , contingent payments, escrow, tax-free (which is treated as a pooling-of-interests), etc.
[3] We are assuming the seller pays for the deal appraisal. Individual sales may vary. Sometimes both sides hire a single appraiser and split the fees, and sometimes each side has its own appraiser.
[4] Internal management costs are the most speculative of all. We estimate 6,000 hours (3 people fulltime for 1 year) at an average $150/hr. internal cost for the $1 billion sale, 2,000 hours @ $80 for the $100 million sale, 500 hours at $50
for the $10 million sale, and 200 hours @$35 for the $1 million sale for the buyer, and 60% of that for the seller. Actual results may vary considerably from these estimates.
[5] Ideally calculated by another regression, but this is sight-estimated. Can often use the Lehman Bros. Formula”5% for 1st $1 million, 4%, for 2nd, etc., leveling off at 1% for each $1 million.
261
D column E. F73 and F74 are repetitions of the regression constants
from B48 and B67, respectively. We then add column E to column F to
obtain the forecast subtotal transactions costs in G73 and G74. Finally, we
add in investment banking fees of 5%62 for the seller (the buyer doesn™t
pay for the investment banker or business broker) to arrive at totals of
3.7% (I73) and 8.4% (I74) for the buyer and seller, respectively.

Component #3 Is Different than #1 and #2. Component #3, trans-
actions costs, is different than the ¬rst two components of DLOM. For
component #3, we need to calculate explicitly the present value of the
occurrence of transactions costs every time the company sells. The reason
is that, unlike the ¬rst two components, transactions costs are actually
out-of-pocket costs that leave the system.63 They are paid to attorneys,
accountants, appraisers, and investment bankers or business brokers. Ad-
ditionally, internal management of both the buyer and the seller spend
signi¬cant time on the sale to make it happen, and they often have to
spend time on failed acquisitions before being successful.
We also need to distinguish between the buyer™s transactions costs
and the seller™s costs. The reason for this is that the buyer™s transactions
costs are always relevant, whereas the seller™s transactions costs for the
immediate transaction reduce the net proceeds to the seller but do not
reduce FMV. However, before the buyer is willing to buy, he or she should
be saying, ˜˜It™s true, I don™t care about the seller™s costs. That™s his or her
problem. However, 10 years or so down the road when it™s my turn to
be the seller, I do care about that. To the extent that seller™s costs exceed
the brokerage cost of selling publicly traded stock, in 10 years my buyer
will pay me less because of those costs, and therefore I must pay my
seller less because of my costs as a seller in Year 10. Additionally, the
process goes on forever, because in Year 20, my buyer becomes a seller
and faces the same problem.™™ Thus, we need to quantify the present value
of a periodic perpetuity of buyer™s transactions costs beginning with the
immediate sale and sellers™ transactions costs that begin with the second
sale of the business.64 In the next section we will develop the mathematics
necessary to do this.

Developing Formulas to Calculate DLOM Component #3. This
section contains some dif¬cult mathematics, but ultimately we will arrive
at some very usable formulas that are not that dif¬cult. It is not necessary
to follow all of the mathematics that gets us there, but it is worthwhile
to skim through the math to get a feel for what it means. In the Mathe-


62. We could run another regression to forecast investment banking fees. This was sight estimated.
One could also use a formula such as the Lehman Brothers formula to forecast investment
banking fees.
63. I thank R. K. Hiatt for the brilliant insight that the ¬rst two components of DLOM do not have
this characteristic and thus do not require this additional present value calculation.
64. One might think that the buyers™ transactions costs are not relevant the ¬rst time, because the
buyer has to put in due diligence time whether or not a transaction results. In individual
instances that is true, but in the aggregate, if buyers would not receive compensation for
their due diligence time, they would cease to buy private ¬rms until the prices declined
enough to compensate them.




PART 3 Adjusting for Control and Marketability
262
matical Appendix we develop the formulas below step by step. In order
to avoid presenting volumes of burdensome math in the body of the
chapter, we present only occasional snapshots of the math”just enough
to present the conclusions and convey some of the logic behind it.
For simplicity, suppose that, on average, business owners hold the
business for 10 years and then sell. Every time an owner sells, he or she
incurs a transactions cost of z. The net present value (NPV) of the cash
¬‚ows to the business owner is:65
NPV NPV1 (1 z)NPV11 (7-1)
10

Equation (7-1) states that the NPV of cash ¬‚ows at Year 0 to the
owner is the sum of the NPV of the ¬rst 10 years™ cash ¬‚ows and (1
z) times the NPV of all cash ¬‚ows from Year 11 to in¬nity. If transactions
costs are 10% every time a business sells, then z 10% and 1 z
66
90%. The ¬rst owner would have 10 years of cash ¬‚ows undiminished
by transactions costs and then pay transactions costs of 10% of the NPV
at Year 10 of all future cash ¬‚ows.
The second owner operates the business for 10 years and then sells
at Year 20. He or she pays transactions costs of z at Year 20. The NPV of
cash ¬‚ows to the second owner is:
NPV11 NPV11 (1 z)NPV21 (7-2)
20

Substituting (7-2) into equation (7-1), the NPV of cash ¬‚ows to the
¬rst owner is:
NPV NPV1 (1 z)[NPV11 (1 z)NPV21 ] (7-3)
10 20

This expression simpli¬es to:
z)2 NPV21
NPV NPV1 (1 z)NPV11 (1 (7-4)
10 20

We can continue on in this fashion ad in¬nitum. The ¬nal expression
for NPV is:
z)i 1
NPV (1 NPV[10(i (7-5)
1) 1] 10i
i1

The NPV is a geometric sequence. Using a Gordon model, i.e., as-
suming constant, perpetual growth, in the Mathematical Appendix, we
show that equation (7-5) solves to:
10
1 g
1
1 r
1 r
NPVTC (7-6)
10
r g 1 g
1 (1 z)
1 r

where NPVTC is the NPV of the cash ¬‚ows with the NPV of the trans-
actions costs that occur every 10 years removed, g is the constant growth


65. Read the hyphen in the following equation™s subscript text as the word ˜˜to,™™ i.e., the NPV from
one time period to another.
66. z is actually an incremental transaction cost, as we will explain later in the chapter.




CHAPTER 7 Adjusting for Levels of Control and Marketability 263
rate of cash ¬‚ows, r is the discount rate, and cash ¬‚ows are midyear.67
The end-of-year formula is the same, replacing the 1 r in the nu-
merator with the number 1.
The NPV of the cash ¬‚ows without removing the NPV of transactions
costs every 10 years is simply the Gordon model multiple of ( 1 r)/
(r g), which is identical with the ¬rst term on the right-hand side of
equation (7-6). The discount for lack of marketability for transactions costs
is equal to:

NPVTC
DLOM 1 (7-7)
NPV

The fraction in equation (7-7) is simply the term in the large braces
in equation (7-6). Thus, DLOM simpli¬es to:
10
1 g
1
1 r x 10

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