<< . .

. 52
( : 66)



. . >>

[2] Equal to Pre-Discount Shares Sold in dollars * (1-Discount). B7 equals B14 only when the discount 0%.
[3] Earnings and Revenue stability are assumed at the averages from Table 7-5, G60 and H60, respectively, for all FMVs. In the
Management Planning data, a correlation analysis revealed that ¬rm size and the stability measures are uncorrelated. Therefore, we
assume the same levels for all FMVs.
[4] Total Discount max(discount, 0), because Disc 0 indicates the model is outside of its range of reasonability.
[5] In our regression of the Management Planning, Inc. data, this was a marketable minority interest value. This is an illiquid control
value and is higher by 12% to 25% than the marketable minority value. The regression coef¬cient relating to market capitalization in
B8 is so small that the difference is immaterial, and it is easier to work with the value available.




PART 4 Putting It All Together
372
T A B L E 10-4E

Calculation of Component #1”Delay to Sale”$375,000 Firm [1]


A B C D

4 Coef¬cients Co. Data Discount
5 Intercept 0.1342 NA 13.4%
Revenues2 [2]
6 5.33E 18 1.955E 12 0.0%
7 Value of block-post-discount [2] 4.26E 09 $368,041 0.2%
8 FMV-marketable minority 100% interest 5.97E 10 $375,000 0.0%
9 Earnings stability (assumed) 0.1376 0.4200 5.8%
10 Revenue stability (assumed) 0.1789 0.6900 12.3%
11 Average years to sell 0.1339 0.5000 6.7%
12 Total Discount [4] 1.9%
14 Value of block-pre-discount [5] $375,000
16 Selling price $375,000
17 Adjusted net income $ 69,913
18 Assumed pre-tax margin 5%
19 Sales $1,398,256
Sales2
20 1.96E 12

[1] Based on Abrams regression of Management Planning, Inc. data-Regression #2, Table 7-10
[2] Equal to Pre-Discount Shares Sold in dollars * (1-Discount). B7 equals B14 only when the discount 0%.
[3] Earnings and Revenue stability are assumed at the averages from Table 7-5, G60 and H60, respectively, for all FMVs. In the
Management Planning data, a correlation analysis revealed that ¬rm size and the stability measures are uncorrelated. Therefore, we
assume the same levels for all FMVs.
[4] Total Discount max(discount, 0), because Disc 0 indicates the model is outside of its range of reasonability.
[5] In our regression of the Management Planning, Inc. data, this was a marketable minority interest value. This is an illiquid control
value and is higher by 12% to 25% than the marketable minority value. The regression coef¬cient relating to market capitalization in
B8 is so small that the difference is immaterial, and it is easier to work with the value available.




T A B L E 10-4F

Calculation of Component #1”Delay to Sale”$750,000 Firm [1]


A B C D

4 Coef¬cients Co. Data Discount
5 Intercept 0.1342 NA 13.4%
Revenues2 [2]
6 5.33E 18 1.955E 12 0.0%
7 Value of block-post-discount [2] 4.26E 09 $686,724 0.3%
8 FMV-marketable minority 100% interest 5.97E 10 $750,000 0.0%
9 Earnings stability (assumed) 0.1376 0.4200 5.8%
10 Revenue stability (assumed) 0.1789 0.6900 12.3%
11 Average years to sell 0.1339 1.0000 13.7%
12 Total Discount [4] 8.4%
14 Value of block-pre-discount [5] $ 750,000
16 Selling price $ 750,000
17 Adjusted net income $ 69,913
18 Assumed pre-tax margin 5%
19 Sales $1,398,256
Sales2
20 1.96E 12

[1] Based on Abrams regression of Management Planning, Inc. data-Regression #2, Table 7-10
[2] Equal to Pre-Discount Shares Sold in dollars * (1-Discount). B7 equals B14 only when the discount 0%.
[3] Earnings and Revenue stability are assumed at the averages from Table 7-5, G60 and H60, respectively, for all FMVs. In the
Management Planning data, a correlation analysis revealed that ¬rm size and the stability measures are uncorrelated. Therefore, we
assume the same levels for all FMVs.
[4] Total Discount max(discount, 0), because Disc 0 indicates the model is outside of its range of reasonability.
[5] In our regression of the Management Planning, Inc. data, this was a marketable minority interest value. This is an illiquid control
value and is higher by 12% to 25% than the marketable minority value. The regression coef¬cient relating to market capitalization in
B8 is so small that the difference is immaterial, and it is easier to work with the value available.




CHAPTER 10 Empirical Testing of Abrams™ Valuation Theory 373
T A B L E 10-4G

Calculation of Component #1”Delay to Sale”$10 Million Firm [1]


A B C D

4 Coef¬cients Co. Data Discount
5 Intercept 0.1342 NA 13.4%
Revenues2 [2]
6 5.33E 18 2.560E 14 0.1%
7 Value of block-post-discount [2] 4.26E 09 $ 9,489,650 4.0%
8 FMV-marketable minority 100% interest 5.97E 10 $10,000,000 0.6%
9 Earnings stability (assumed) 0.1376 0.4200 5.8%
10 Revenue stability (assumed) 0.1789 0.6900 12.3%
11 Average years to sell 0.1339 1.0000 13.4%
12 Total Discount [4] 5.1%
14 Value of block-pre-discount [5] $10,000,000
16 Selling price $10,000,000
17 Divide by P / E multiple assumed at $ 800,000
12.5 net inc
18 Assumed pre-tax margin 5%
19 Sales $16,000,000
Sales2
20 2.56E 14


[1] Based on Abrams regression of Management Planning, Inc. data-Regression #2, Table 7-10
[2] Equal to Pre-Discount Shares Sold in dollars * (1-Discount). B7 equals B14 only when the discount 0%.
[3] Earnings and Revenue stability are assumed at the averages from Table 7-5, G60 and H60, respectively, for all FMVs. In the
Management Planning data, a correlation analysis revealed that ¬rm size and the stability measures are uncorrelated. Therefore, we
assume the same levels for all FMVs.
[4] Total Discount max(discount, 0), because Disc 0 indicates the model is outside of its range of reasonability.
[5] In our regression of the Management Planning, Inc. data, this was a marketable minority interest value. This is an illiquid control
value and is higher by 12% to 25% than the marketable minority value. The regression coef¬cient relating to market capitalization in
B8 is so small that the difference is immaterial, and it is easier to work with the value available.




T A B L E 10-6A

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 0.0% 0.0% 100.0% Delay to sale
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 4.9% 5.3% 94.7% Transactions costs”buyers
12 3B 14.3% 1.2% 98.8% Transactions costs”sellers
13 Percent remaining 89.9% Total % remaining components 1 2 3A 3B
14 Final discount 10.1% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $ 75,000
19 Discount rate r [3] 32.6%
20 Constant growth rate g (Table 10-2, row 24) 2.5%
21 Intermediate calculation: x (1 g)/(1 r) 0.7728
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I8 and I9 2% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




PART 4 Putting It All Together
374
T A B L E 10-6B

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 0.0% 0.0% 100.0% Delay to sale
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 4.5% 4.9% 95.1% Transactions costs”buyers
12 3B 14.0% 1.3% 98.7% Transactions costs”sellers
13 Percent remaining 89.8% Total % remaining components 1 2 3A 3B
14 Final discount 10.2% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $ 125,000
19 Discount rate r [3] 31.7%
20 Constant growth rate g (Table 11-2, row 24) 3.0%
21 Intermediate calculation: x (1 g)/(1 r) 0.7822
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I10 and I11 2% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




T A B L E 10-6C

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 0.0% 0.0% 100.0% Delay to sale
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 4.3% 4.7% 95.3% Transactions costs”buyers
12 3B 13.8% 1.3% 98.7% Transactions costs”sellers
13 Percent remaining 89.8% Total % remaining components 1 2 3A 3B
14 Final discount 10.2% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $ 175,000
19 Discount rate r [3] 31.0%
20 Constant growth rate g (Table 10-2, row 24) 3.0%
21 Intermediate calculation: x (1 g)/(1 r) 0.7860
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I12 and I13 2% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




CHAPTER 10 Empirical Testing of Abrams™ Valuation Theory 375
T A B L E 10-6D

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 0.0% 0.0% 100.0% Delay to sale
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 4.1% 4.5% 95.5% Transactions costs”buyers
12 3B 13.6% 1.6% 98.4% Transactions costs”sellers
13 Percent remaining 89.5% Total % remaining components 1 2 3A 3B
14 Final discount 10.5% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $ 225,000
19 Discount rate r [3] 30.6%
20 Constant growth rate g (Table 10-2, row 24) 4.5%
21 Intermediate calculation: x (1 g)/(1 r) 0.8003
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I4 and I5 2% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




T A B L E 10-6E

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 1.9% 1.9% 98.1% Delay to sale
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 4.7% 5.3% 94.7% Transactions costs”buyers
12 3B 14.2% 1.9% 98.1% Transactions costs”sellers
13 Percent remaining 87.6% Total % remaining components 1 2 3A 3B
14 Final discount 12.4% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $ 375,000
19 Discount rate r [3] 29.6%
20 Constant growth rate g (Table 11-2, row 24) 5.0%
21 Intermediate calculation: x (1 g)/(1 r) 0.8100
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I6 and I7 1% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




PART 4 Putting It All Together
376
T A B L E 10-6F

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 8.4% 8.4% 91.6% Delay to sale
10 2 9.0% 9.0% 91.0% Buyer™s monopsony power”thin markets
11 3A 4.2% 4.8% 95.2% Transactions costs”buyers
12 3B 13.7% 2.3% 97.7% Transactions costs”sellers
13 Percent remaining 81.4% Total % remaining components 1 2 3A 3B
14 Final discount 18.6% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $ 750,000
19 Discount rate r [3] 28.3%
20 Constant growth rate g (Table 11-2, row 24) 6.0%
21 Intermediate calculation: x (1 g)/(1 r) 0.8259
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I8 and I9 2% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




T A B L E 10-6G

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 5.1% 5.1% 94.9% Delay to sale
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 4.4% 1.5% 98.5% Transactions costs”sellers
13 Percent remaining 85.0% Total % remaining components 1 2 3A 3B
14 Final discount 15.0% Discount 1 total % remaining
16 Section 2: Assumptions and Intermediate Calculations:
18 FMV-equity of co. (before discounts) $10,000,000
19 Discount rate r [3] 23.5%
20 Constant growth rate g (Table 10-2, row 24) 8.0%
21 Intermediate calculation: x (1 g)/(1 r) 0.8743
22 Avg # years between sales j 10

[1] Pure Discounts: For Component #1, Table 10-4, cell D12; For Component #2, 9% per Schwert article. For Component #3A and #3B, Table 10-5, cells I20 and I21 2% for public
brokerage costs.
[2] PV of Perpetual Discount Formula: 1 (1 x j)/((1 (1 z)*x j)), per equation [7-9], used for Component #3B.
PV of Perpetual Discount Formula: 1 (1 z)*(1 x j)/((1 (1 z)*x j)), per equation [7-9a], used for Component #3A.
Components #1 and #2 simply transfer the pure discount.
[3] The formula is: 0.5352 (.0186 ln FMV), based on Table 10-1, B34 and B35.




CHAPTER 10 Empirical Testing of Abrams™ Valuation Theory 377
1. As ¬rm size increases, our assumed growth rate, g, increases. By
our analysis of the partial derivatives in the Mathematical
Appendix to Chapter 7, that causes an increase in DLOM.
2. As ¬rm size increases, the log size discount rate, r, decreases. By
our analysis of the partial derivatives in the Mathematical
Appendix to Chapter 7, that also causes an increase in DLOM.
3. As mentioned earlier, for ¬rm sizes under $375,000, we assumed
the delay to sale to be 0.33 years or less, which lead to a zero
discount for component #1. For the $375,000 and $750,000 ¬rms,
we assumed a one-half-year and one-year delay to sale, which
led to a component #1 pure discount of 1.9% (Table 10-6E, B9)
and 8.4% (Table 10-6F, B9), respectively. The latter accounts for
the vast majority of the much higher DLOM for the $750,000
mean selling price ¬rms. Had that been zero, like all of the
others except the $375,000 ¬rm, DLOM for the $750,000 ¬rms
would have been 13.1%”much closer to DLOM for the smaller
¬rms.
4. We assumed a 1% broker™s fee for publicly traded stocks for the
$375,000 and $750,000 ¬rms, while we assumed a 2% fee for the
¬rms under that size. This increased the pure discount for
components #3A and #3B by 1% for those two size categories,
and therefore increased DLOM.
5. Transactions costs decrease as size increases. Buyers™ transactions
costs are 7.7% (Table 10-5, I6) for $25,000 ¬rms and 5.2% for
$750,000 ¬rms (I18), for a difference of 2.5%. Sellers™ transactions
costs are 17.1% (I7) for $25,000 ¬rms and 14.7% (I19) for
$750,000 ¬rms, for a difference of 2.4%.
Items 1 through 4 above cause DLOM to increase with size, while
item 5 causes DLOM to decrease with size. Looking at Table 10-2, it is
clear that the ¬rst four items dominate, which causes DLOM to increase
with size. This is not a result that I would have predicted before. I would
have thought that overall, DLOM decreases with size.
As mentioned earlier in this chapter, had we used a different model,
it would have been possible to assign a pure discount for the delay to
sale of perhaps 3“5% using another model. This would have narrowed

<< . .

. 52
( : 66)



. . >>