Capital Expenditures, Depreciation and Amortization in the Gordon Growth Model

Abstract

This presentation discusses the fallacy of assuming that depreciation should equal capital expenditures and the appropriate treatment of amortization in a perpetual growth model.

Full text

CAPITAL EXPENDITURES,
DEPRECIATION AND AMORTIZATION
IN THE GORDON GROWTH MODEL
Gilbert E. Matthews, CFA
BVR Webinar, June 30, 2016
SUTTER SECURITIES INCORPORATED
1

-
This presentation is based on my article,
“Capital Expenditures, Depreciation and
Amortization in the Gordon Growth Model,”
Business Valuation Review, Winter 2014.
SUTTER SECURITIES GIL@SUTTERSF.COM (415) 352-6336
2

MOST PRACTITIONERS ASSUME THAT
DEPRECIATION = CAPEX
In a 2013 survey published by Jim Hitchner, valuators
were asked:
How do you typically handle depreciation
and cap ex when calculating cash flows?
The responses were:
oThe same or very similar – 68%
oCapex less than depreciation – 4%
oCapex greater than depreciation – 28%
3

TWO COMMON ERRORS
When calculating terminal value in the Gordon growth model,
it has been common practice for valuators to assume that
depreciation equals capital expenditures in perpetuity
In fact, due to growth and inflation, capex must be greater
than depreciation in a growth model
Another common error is to project growth in amortization
Amortization has a limited life and its impact on future
cash flow should appropriately analyzed
Both of these errors result in overstated values
4

THE GORDON GROWTH MODEL
The formula applied for calculating terminal value in the
Gordon growth model is:
TV = F(1+g)/(k-g)
TV = terminal value
F = normalized free cash flow (FCF) in the terminal year
g = expected long-term annual growth rate
k = the cost of capital
The formula is based on the assumption that FCF is expected
to grow at a constant rate in perpetuity
5

FCF FOR TERMINAL VALUE
SHOULD BENORMALIZED
The analyst should examine projected capex and depreciation
in the terminal year to determine whether normalizing
adjustments to FCF are needed
Although capital expenditures in any given year can be less
than depreciation, a growing company’s normalized capex
should exceed its depreciation
Equipment costs and evolving technology costs may affect the
relationship of the depreciation rate to the growth rate
oTo the extent that new equipment is cheaper to manufacture or more
efficient in use, the ratio of capex to depreciation may decrease
If a single-facility company built and equipped a factory, depreciation
could exceed capex until major new investments were required
6

5-YEAR STRAIGHT LINE DEPRECIATION
Example: a company depreciates its assets on a straight-line basis over a
five-year period to zero residual value and is growing at 5% annually
Capex in year 6 is 112.7% of depreciation [1,276.3 ÷ 1,132.8]
7
5 Year Straight Line Depreciation with 5% Growth
Year Purchased Capital Expenditures
Depreciated in 2021
% Amount
2016 1,000.0 10% 100.0
2017 1,050.0 20% 210.0
2021 1,102.5 20% 220.5
2019 1,157.6 20% 231.5
2020 1,215.5 20% 243.1
2021 1,276.3 10% 127.6
1,132.8

5-YEAR DOUBLE DECLINING DEPRECIATION
Five-year double declining depreciation to zero residual value
8
5 Year Double Declining Depreciation with 2% to 5% Growth
2% Growth 3% Growth 4% Growth 5% Growth
Year Capex
Depreciated
in 2021 Capex
Depreciated
in 2021 Capex
Depreciated
in 2021 Capex
Depreciated
in 2021
2016 1,000 57.6 1,000 57.6 1,000 57.6 1,000 57.6
2017 1,020 117.5 1,030 118.7 1,040 119.8 1,050 121.0
2018 1,040 119.9 1,061 122.2 1,082 124.6 1,103 127.0
2019 1,061 203.8 1,093 209.8 1,125 216.0 1,158 222.3
2020 1,082 346.4 1,126 360.2 1,170 374.4 1,216 389.0
2021 1,104 220.8 1,159 231.9 1,217 243.3 1,276 255.3
Depreciation in
2021 1,065.9 1,100.3 1,135.7 1,172.1
Capex in 2021 1,104.1 1,159.3 1,216.7 1,276.3
Difference 38.2 59.0 81.0 104.2
Capex as % of
Depreciation 103.6% 105.4% 107.1% 108.9%

EFFECT OF 15-YEAR DEPRECIATION
With a 15-year depreciable life, capex is always materially greater than
depreciation
Excess of Capital Expenditures over Depreciation,
Assuming 15-year Life with No Residual Value
9
0%
10%
20%
30%
40%
50%
2% 3% 4% 5%
Growth Rate
Straight Line
Depreciation
Double Declining
Depreciation

A SUMMARY TABLE

The table below summarizes the relationships between
capex and depreciation for different lives, growth rates,
and depreciation methods (zero residual value)
10
Excess of Capital Expenditures Over Depreciation
Depreciation Method Growth rate:
2% 3% 4% 5%
5 year life
Straight line 5.03% 7.56% 10.11% 12.67%
Double declining 3.58% 5.36% 7.13% 8.89%
Sum of the digits 3.66% 5.49% 7.31% 9.12%
10 year life
Straight line 10.22% 15.50% 20.87% 26.35%
Double declining 7.73% 11.62% 15.52% 19.43%
Sum of the digits 7.05% 10.60% 14.17% 17.76%
15 year life
Straight line 15.58% 23.79% 32.27% 40.99%
Double declining 11.95% 18.03% 24.16% 30.34%
Sum of the digits 10.48% 15.83% 21.24% 26.69%

SOME COURTS HAVE ACCEPTED
CAPEX GREATER THAN DEPRECIATION
Some U.S. and Delaware court decisions have accepted
DCF valuations in which depreciation exceeded capital
expenditures, e.g.:
Kleinwort Benson Ltd. v. Silgan Corp., 1995 Del. Ch. LEXIS 75
(June 15, 1995)
Estate of Simplot v. Commissioner, 112 T.C. 130, 164 (U.S. Tax
Ct., 1999), rev’d on other grounds, 249 F.3d 1191 (9th Cir., 2001)
Prescott Group Small Cap, L.P. v. Coleman Co., 2004 Del. Ch.
LEXIS 131 (Sept. 8, 2004)
Albert Trostel & Sons Co. v. Notz, 2010 U.S. Dist. LEXIS 108778
(E.D. Wisc., Sept 28, 2010)
11

SOME COURTS HAVE ACCEPTED
CAPEX EQUAL TO DEPRECIATION
However, other U.S. and Delaware court decisions have
accepted DCF valuations in which depreciation equaled
capital expenditures, e.g.:
Salomon Brothers Inc. v. Interstate Bakeries Corp., 1992 Del. Ch.
LEXIS 100 (May 1, 1992)
Cede & Co. v. Technicolor, Inc., 2003 Del. Ch. LEXIS 146 (July 11,
2003)
In re: Nanovation Technologies, Inc., 364 B.R. 308; 2007 Bankr.
LEXIS 1862 (Bankr. N.D. Ill., May 7, 2007).
In re Greater Southeast Community Hospital Corp., 2012 Bankr.
LEXIS 618 (Bankr. D.D.C., Feb. 21, 2012)
In re Orchard Enterprises, Inc., 2012 Del. Ch. LEXIS 165 (July 18,
2012)
12

SOME COURTS HAVE ACCEPTED
CAPEX LESS THAN DEPRECIATION!
Two Delaware decisions have accepted DCF valuations
where capital expenditures were less than half of
depreciation!
Depreciation was more than 4x
capital expenditures in
Lane v. Cancer Treatment Centers of America, Inc., 2004
Del. Ch. LEXIS 108 (July 30, 2004)

Depreciation was almost 2½ times capital expenditures in
In re Emerging Communications, Inc. Shareholders Litigation,
2004 Del. Ch. LEXIS 70 (May 3, 2004)
13

AMORTIZATION
Amortization and depreciation are both non-cash charges that
reduce reported income
Tax-deductible amortization is similar to depreciation in that it
reduces both reported net income and taxes
Non-tax-deductible amortization only reduces net income
Most amortizable intangible assets are created through
acquisitions or intellectual property
In taxable stock acquisitions, if a C Corp acquires another C Corp,
the acquiror may make an election under §338 of the Internal
Revenue Code and, under certain conditions, elect to create a
depreciable intangible asset (goodwill) by writing up the assets in
the same manner as in an asset purchase
14

AMORTIZATION HAS A LIMITED LIFE
There is an important difference between amortization and
depreciation that must be recognized by valuators when
calculating terminal value
Intangible assets such as goodwill are not systematically
replaced in the ordinary course of business
Therefore, amortization has a limited life
Since amortization, unlike depreciation, does not grow in
perpetuity, it should be separately valued in terminal value
calculations
15

AMORTIZATION MUST BESEPARATED
FROM DEPRECIATION IN D&A
Companies customarily report depreciation and amortization
(“D&A”) as a single line item in their income and cash flow
statements
Because of the substantive differences between amortization
and depreciation, valuators should determine how much of
the projected D&A is amortization
16

THE VALUE OF AMORTIZATION IS THE PRESENT
VALUE OF FUTURE TAX BENEFITS
Even though amortization should be excluded from the
computation of terminal value, any tax benefit it generates
has value and should be included in enterprise value
The appropriate manner to value amortization subsequent
to the projection period is to determine the present value
of the future tax benefits of the remaining amortization
17

OTHER NORMALIZING ADJUSTMENTS
FCF must be also be normalized to exclude any other items
that will not be growing over time or which have a finite
term, such as tax-loss carryforwards, limited-life royalties,
and non-compete agreements
The present value of future cash flows after the projection
period from amortization, tax-loss carryforwards, and other
limited-life items should be included in enterprise value
The value of tax-loss carryforwards is the present value of future
tax benefits
The value of future limited-life income streams is the present value
of the income net of taxes
The value of future limited-life obligations is the negative present
value of the expense net of taxes
18

A SIMPLE FORMULA
These adjustments are achieved by adding the present value
of these net cash flows after the terminal year to enterprise
value, as shown in the following equation:
EV = PVF+ PVTV + PVA
EV = enterprise value at the valuation date;
PVF = present value of free cash flows from the valuation date
through the terminal year of the projection;
PVTV= present value of terminal value based on normalized FCF
PVA= present value of net benefits (costs) of amortization,
tax-loss carryforwards, and limited-life income and
expense items after the terminal year of the projection
19

ERRONEOUS TREATMENT OF AMORTIZATION
BY EXPERTS IN COURT
An example of the erroneous treatment of amortization in a
DCF analysis is the 2007 Dr Pepper Bottling decision*
Annual tax-deductible amortization of $5.4 million was included
as a non-cash charge in the Court’s valuation model
Since amortization was part of the free cash flow that the
testifying experts used in their growth models, they effectively
assumed that the amortization was perpetual, leading to an
overstated valuation by the Court
________________________________
* Crescent/Mach I Partnership, L.P. v. Dr Pepper Bottling Co. of Texas, 2007 Del. Ch.
LEXIS 63 (May 2, 2007)
20

A SANITY CHECK
The practitioner who determines terminal value using a
growth model should examine the multiples of EBITDA and
net income that are implied by the calculated result
If the multiples of calculated terminal value are materially
inconsistent with projected multiples of guideline companies
and/or guideline transactions, the practitioner should
reexamine the assumptions used – the growth rate, the
discount rate, the relationship between capital expenditures
and depreciation, and other adjustments
21

CONCLUSION
As a general rule, capital expenditures should be greater
than depreciation in a terminal value calculation
The relationship is a function of depreciation rates,
company growth rates and technological innovation
Amortization of intangible assets, loss carryforwards, and
other limited-life assets (and liabilities) should be excluded
from normalized FCF in terminal value and should be
separately valued
Since data supplied by management often lumps
depreciation and amortization together, the valuator must
obtain the granular information necessary for an
appropriate analysis
22

Sample Calculations of Relationship between
Capital Expenditures and Depreciation
23

24
3% Growth – 10 Year Straight Line Depreciation
Year Capital
Expenditures 2026 2027 2028 2029 2030 2031 2032
2016 1,000.0 50.0
2017 1,030.0 103.0 51.5
2018 1,060.9 106.1 106.1 53.0
2019 1,092.7 109.3 109.3 109.3 54.6
2020 1,125.5 112.6 112.6 112.6 112.6 56.3
2021 1,159.3 115.9 115.9 115.9 115.9 115.9 58.0
2022 1,194.1 119.4 119.4 119.4 119.4 119.4 119.4 59.7
2023 1,229.9 123.0 123.0 123.0 123.0 123.0 123.0 123.0
2024 1,266.8 126.7 126.7 126.7 126.7 126.7 126.7 126.7
2025 1,304.8 130.5 130.5 130.5 130.5 130.5 130.5 130.5
2026 1,343.9 67.2 134.4 134.4 134.4 134.4 134.4 134.4
2027 1,384.2 69.2 138.4 138.4 138.4 138.4 138.4
2028 1,425.8 71.3 142.6 142.6 142.6 142.6
2029 1,468.5 73.4 146.9 146.9 146.9
2030 1,512.6 75.6 151.3 151.3
2031 1,558.0 77.9 155.8
2032 1,604.7 80.2
Annual Depreciation 1,163.6 1,198.5 1,234.4 1,271.5 1,309.6 1,348.9 1,389.4
Capital Expenditures 1,343.9 1,384.2 1,425.8 1,468.5 1,512.6 1,558.0 1,604.7
Capital Expenditures in Excess
of Depreciation 180.3 185.7 191.3 197.1 203.0 209.1 215.3
Difference in % 15.50% 15.50% 15.50% 15.50% 15.50% 15.50% 15.50%

25
3% Growth – 10 Year Double Declining Depreciation
Year Capital
Expenditures 2026 2027 2028 2029 2030 2031 2032
2016 1,000.0 32.8
2017 1,030.0 67.5 33.8
2018 1,060.9 69.5 69.5 34.8
2019 1,092.7 71.6 71.6 71.6 35.8
2020 1,125.5 73.8 73.8 73.8 73.8 36.9
2021 1,159.3 85.5 76.0 76.0 76.0 76.0 38.0
2022 1,194.1 110.0 88.0 78.3 78.3 78.3 78.3 39.1
2023 1,229.9 141.7 113.3 90.7 80.6 80.6 80.6 80.6
2024 1,266.8 182.4 145.9 116.7 93.4 83.0 83.0 83.0
2025 1,304.8 234.9 187.9 150.3 120.2 96.2 85.5 85.5
2026 1,343.9 134.4 241.9 193.5 154.8 123.9 99.1 88.1
2027 1,384.2 138.4 249.2 199.3 159.5 127.6 102.1
2028 1,425.8 142.6 256.6 205.3 164.2 131.4
2029 1,468.5 146.9 264.3 211.5 169.2
2030 1,512.6 151.3 272.3 217.8
2031 1,558.0 155.8 280.4
2032 1,604.7 160.5
Annual Depreciation 1,204.10 1,240.10 1,277.50 1,315.70 1,355.30 1,395.90 1,437.70
Capital Expenditures 1,343.90 1,384.20 1,425.80 1,468.50 1,512.60 1,558.00 1,604.70
Capital Expenditures in Excess
of Depreciation 139.80 144.10 148.30 152.80 157.30 162.10 167.00
Difference in % 11.62% 11.62% 11.62% 11.62% 11.62% 11.62% 11.62%

26
3% Growth – 10 Year Sum-of-the-Digits Depreciation
Year Capital
Expenditures 2026 2027 2028 2029 2030 2031 2032
2016 1,000.0 9.1
2017 1,030.0 28.1 9.4
2018 1,060.9 48.2 28.9 9.6
2019 1,092.7 69.5 49.7 29.8 9.9
2020 1,125.5 92.1 71.6 51.2 30.7 10.2
2021 1,159.3 115.9 94.8 73.8 52.7 31.6 10.5
2022 1,194.1 141.1 119.4 97.7 76.0 54.3 32.6 10.9
2023 1,229.9 167.7 145.3 123.0 100.6 78.3 55.9 33.5
2024 1,266.8 195.8 172.7 149.7 126.7 103.6 80.6 57.6
2025 1,304.8 225.4 201.6 177.9 154.2 130.5 106.8 83.0
2026 1,343.9 122.2 232.1 207.7 183.3 158.8 134.4 110.0
2027 1,384.2 125.8 239.1 213.9 188.8 163.6 138.4
2028 1,425.8 129.6 246.3 220.3 194.4 168.5
2029 1,468.5 133.5 253.7 227.0 200.3
2030 1,512.6 137.5 261.3 233.8
2031 1,558.0 141.6 269.1
2032 1,604.7 145.9
Annual Depreciation 1,215.1 1,251.6 1,289.1 1,327.8 1,367.6 1,408.6 1,450.9
Capital Expenditures 1,343.9 1,384.2 1,425.8 1,468.5 1,512.6 1,558.0 1,604.7
Capital Expenditures in Excess
of Depreciation 128.8 132.7 136.7 140.8 145.0 149.3 153.8
Difference in % 10.60% 10.60% 10.60% 10.60% 10.60% 10.60% 10.60%