Content uploaded by Gilbert Matthews
Author content
All content in this area was uploaded by Gilbert Matthews on Mar 31, 2020
Content may be subject to copyright.
Cautionary Notes on Determining
Terminal Value in the DCF Model
Gilbert E. Matthews, CFA
Organismo Italiano di Valutazione
Organismo Italiano di Valutazione
5th Annual International Conference
16 January 2017
SUTTER SECURITIES GIL@SUTTERSF.COM
1 -415-352-6336
TERMINAL VALUE
Terminal value is the dominant component of most DCF
valuations
With 5-year projections, terminal value usually accounts for
70% or more of the aggregate value
This presentation will examine several factors that impact
terminal value and discuss how to address them
The final year of the projection
The trend toward using lower long-term growth rates
The “perpetual” growth rate and firm mortality
The use of multiples for terminal value
The relationship between capital expenditures and depreciation
The appropriate treatment of amortization
2
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
The Final Year of
the Projection
3
DUE DILIGENCE
Terminal value is a direct function of the final year of the
projection underlying the DCF analysis
The analyst should conduct due diligence to determine the
reasonableness of the projection and the underlying
assumptions
Normalizing adjustments should be made to adjust inputs
that will not grow in parallel with revenues and free cash
flow
4
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
NORMALIZATION
Some normalizing adjustments depend on the purpose of
the valuation, e.g.:
If the company is being valued as a going-concern under its
current management, no normalizing adjustments are needed
for such items as excess compensation or management perks
because these would be expected to continue
If a company is being valued at financial control value,
normalizing adjustments for excess compensation and
management perks would be appropriate because these
would be changed by a buyer
5
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
STEADY STATE
In applying a growth model, the analyst should consider
whether the company has reached a “steady state” of growth
by the final year of the projection
If in the final year of the projection, the company is still
growing at a faster rate than its expected long-term growth
rate, the use of a multi-stage model is necessary
Some companies, such as mining and oil & gas production,
may have negative long-term growth rates in their “steady
state”
6
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Trend Toward Using
Lower Long-Term
Growth Rates
7
TREND TOWARD USING LOWER GROWTH RATES
Common practice for determining terminal value has been to
assume that a company’s perpetual growth rate should be
close to the expected long-term growth of the economy
In two recent studies,* I have examined the discount rates
used by investment bankers in connection with publicly-
disclosed fairness opinions
Data from these studies indicate that since the 2008
recession, investment bankers have tended to use lower
growth rates to calculate terminal value
____________________________
* Cited articles, as well as other selected articles, are listed in the
Bibliography appended to this presentation
8
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
TREND TOWARD LOWER GROWTH RATES
Midpoints of Growth Rates in Growth Models for Fairness Opinions
Cash Acquisitions:
9/2007–8/2008
Cash Acquisitions:
9/2010–8/2011
Stock-for-Stock
Mergers: 2009–14
Median 3.0% 2.5% 2.0%
Mean 3.4% 2.9% 2.0%
Number Percent Number Percent Number Percent
Less than 1% 0 0.0% 6 9.0% 20 16.4%
1% 1 2.0% 4 6.0% 13 10.7%
>1% and <2% 2 3.9% 3 4.5% 16 13.1%
2% 7 13.7% 13 19.4% 19 15.1%
>2% and <3% 9 17.6% 11 16.4% 14 11.1%
3% 12 23.5% 16 23.9% 28 22.2%
>3% and <4% 4 7.8% 5 7.5% 6 4.8%
4% 4 7.8% 5 7.5% 3 2.4%
More than 4% 12 23.5% 4 6.0% 7 5.7%
Total 51 100.0% 67 100.0% 122 100.0%
9
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
The “Perpetual”
Growth Rate and
Firm Mortality
10
THE PERPETUAL GROWTH ASSUMPTION
In the customary DCF valuation, it is assumed that a mature
company will survive and will grow at a constant rate in
perpetuity
This assumption is invalid for two reasons:
The impact of corporate mortality
The impact of decelerating company growth due to economic
changes and/or obsolescence
The constant perpetual growth assumption can result in
overstated values
11
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
CHANGES IN TENURE OF TOP 500 COMPANIES
Companies in the 1958 S&P 500 were in the index for an
average of 61 years (based on seven year rolling averages)
By 1980, the average tenure had declined to about 25 years
Now the average tenure is about 18 years
Over the decade to 2012, about half the S&P 500 was
replaced
Only 61 companies that were in the 1955 Fortune 500 remain
in the 2015 Fortune 500
12
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
COMPANIES ARE DROPPED FROM INDICES
FOR VARIOUS REASONS
Examples of companies dropped from S&P 500: 2001-2012
American Airlines: restructured in bankruptcy
Anheuser-Busch: acquired by InBev
Bear Stearns: insolvent, taken over by JP Morgan
Eastman Kodak: restructured in bankruptcy
Enron: bankrupt, ceased operations
Global Crossing: restructured in bankruptcy
Lehman Brothers: bankrupt, ceased operations
May Dept. Stores: acquired by Macy’s
Maytag: acquired after material reduction in sales
NY Times: slow growth
Palm: sales decline and financial problems
Radio Shack: financial problems
Sears: restructured in bankruptcy
Toys “R” Us: taken private in LBO
Wendy’s: merger
13
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
WHAT CAUSES THIS ATTRITION?
What are the reasons for this attrition?
Some companies are absorbed in mergers and acquisitions
Some companies grow at slower rates and are replaced by faster-
growing companies
Some companies have financial problems that slow or reverse
their growth
Some companies are restructured in bankruptcy
Some companies cease operations and die
14
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
YOUNG FIRMS HAVE THE GREATEST
MORTALITY RISK
According to the U.S. Bureau of Labor Statistics, about 50%
of all new businesses are still operating after 5 years, and
about two-thirds of the survivors are still in business after
another 5 years
As firms grow older and larger, the risk of failure in any
given period declines
For companies that mature and become listed, Loderer,
Neusser and Waelchli conclude that the frequency of
corporate failure falls “from about 3% in early years [after
listing] to 0.3% before companies get to be 75”
15
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
THE MORRIS ARTICLE
"LIFE AND DEATH OF BUSINESSES: A REVIEW OF RESEARCH ON FIRM MORTALITY”
Prof. James Morris (2009a) notes:
[R]elatively little attention is given to expected life in the
valuation literature and in the valuation methods used by
practitioners. . . . The constant growth model is as accurate as
the assumptions on which it is based: an infinite horizon and
growth that is expected to be the same rate every period forever.
If the firm’s circumstances do not fit these assumptions, the
model can lead to an inaccurate valuation. How inaccurate
depends on how far the assumptions depart from reality.
This thoughtful article discusses firm survival and mortality,
examines available data, and addresses the impact of a
constant growth assumption on corporate valuation
16
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
IMPACT OF FINITE LIFE ASSUMPTION
Morris calculated the impact of a finite life assumption vs. an
infinite life assumption
k = discount rate
g = growth rate
17
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
BUSINESS MORTALITY DATA
He examined U.S. government data as to business mortality
18
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
STUDIES OF SURVIVAL RATES
Morris also reviewed prior studies of survival rates
19
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
IMPACT OF MORTALITY RISK
If the risk of failure in any given year is 1% and is constant year to
year, the cumulative risk of failure within 15 years is 14%
If the risk of failure in any given year is 0.6% and is constant year
to year, the cumulative risk of failure within 25 years is 14%
If the risk of failure in any given year is 1% and is constant year to
year, the cumulative risk of failure within 25 years is 22%
20
Cumulative Risk of Failure
Per year 0.4% 0.6% 0.8% 1.0%
10 years 3.9% 5.8% 7.3% 9.6%
15 years 5.8% 8.6% 10.8% 14.0%
20 years 7.7% 11.3% 14.2% 18.2%
25 years 9.5% 14.0% 17.4% 22.2%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
FIRM MORTALITY IS
INVERSELY RELATED TO SIZE
Morris points out that firm mortality is a function of size
Decile 1 = Largest Firms
Decile 10 = Smallest Firms
(by market value of equity)
21
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
EFFECT OF GROWTH AND DISCOUNT RATES
This magnitude of the impact of firm mortality on firm value
is a function not only of the mortality risk, but also of the
growth rate and the discount rate
The impact on value increases at higher growth rates
The impact on value decreases at higher discount rates
22
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
THE GORDON GROWTH FORMULA
The standard formula for calculating terminal value using the
Gordon growth model is
PV = present value of future cash flows
CF = free cash flow in final year of projection
r= discount rate
g= long-term growth rate
23
CF (1 + r)
r - g
PV =
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
ADJUSTING THE GROWTH FORMULA
FOR RISK OF FAILURE
How can the Gordon growth formula be adjusted to reflect the
risk of failure?
Prof. Sherrill Shaffer (2006) proposes adjusting the formula for
the probability (p) that “the asset may irreversibly default (i.e.,
the issuing company may fail) in any given year”:
24
CF (1 + r) (1 - p)
r + p - g (1 - p)
PV =
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DISCOUNT RATES AND GROWTH RATES
ADJUSTED FOR RISK OF FAILURE
She solves this formula to determine
R– the discount rate adjusted for p, and
G– the growth rate adjusted for p
25
p (1 + r)
2
1 + g - p (r + g + 2)
R =
rg (1 - p)
r + p
G =
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
HOW CAN THE RISK OF FAILURE
BEDETERMINED?
Shaffer (2007) wrote:
The simplest way to estimate p is to use historical average
business failure rates, which are widely available. . . .
Recognizing that different industries sometimes exhibit
very different failure rates, sector-specific failure rates
may be more appropriate. . . .
A more detailed and forward-looking approach would
involve statistical models predicting firm-specific probabilities
of failure, based on current financial data for each firm and
calibrated using historical linkages between financial ratios
and subsequent failure.
26
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DAMODARAN’SFORMULA
Prof. Aswath Damodaran proposes a formula for adjusting
terminal value for the risk of financial distress
AV = PV x (1-p) + DSV x p
AV = adjusted value
PV = unadjusted present value based on DCF
DSV = distressed sales value
p= probability of distress
27
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DAMODARAN: DETERMINING
THE PROBABILITY OF DISTRESS
Damodaran also posits that statistical techniques can be
applied to historical data to determine the probability of
distress as a function of observable variables
He notes that factors such as high debt ratios and negative cash
flows increase the risk of failure
He also points out that bond ratings and the historical
relationship between ratings and defaults can be used to
estimate the mortality risk
This approach is necessarily limited to companies with
published bond ratings
28
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
THE SAHA – MALKIEL ARTICLE
“VALUATION OF CASH FLOWS WITH TIME-VARYING CESSATION RISK”
Atanu Saha and Burton Malkiel (2012) point out:
Because CAPM-based discount rates only account for
market risk, valuation models may greatly underestimate
the discount rate . . . in settings where the idiosyncratic risk
of the cash flows matters. This is especially so in cases
where there is a significant probability that the future
stream of cash flows may completely cease. This is a risk
that the CAPM ignores because that model assumes it is a
risk that can be diversified away. . . . [W]e believe that an
additional adjustment to the discount rate is warranted to
account for cash flow cessation probability, in settings
where such a possibility is not immaterial.
29
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SAHA–MALKIEL FRAMEWORK
They develop a framework for calculating present value
“when cash flows have a finite probability of cessation at
each period”
They “present a simple formula for the cessation risk-
adjusted discount”
They “then extend the analytical framework to allow for the
possibility of a time-varying cessation risk”
30
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SAHA–MALKIEL FORMULAS
The Saha–Malkiel formula with a constant “cessation risk” is
the same as Shaffer’s formula
They then create a formula based on the assumption that the
cessation risk declines as the firm ages
This complex formula is a further helpful step for adjusting
valuations to reflect mortality risk
31
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
VALUATORS SHOULD CONSIDER
WHETHER TO ADJUST FOR MORTALITY RISK
Today’s general practice of using a perpetual growth rate
calculating terminal value needs to be reexamined
Adjustments for firm mortality or for the risk of decelerating
growth should be considered
For companies with a low mortality risk, the impact may be
immaterial
Venture capitalists commonly account for the substantial
possibility that a start-up company may not succeed by using
discount rates of 35% or more
32
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
FURTHER EMPIRICAL RESEARCH ISNEEDED
The valuation community – and the academic community –
should consider how to quantify the risks not only of mortality
but also of declining (or negative) long-term growth
How can these risks be reflected in higher discount rates and/or
lower long-term growth rates?
Further empirical research into firm decline and mortality is
necessary to develop the appropriate risk premiums
33
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Using Multiples to
Calculate Terminal Value
34
TERMINAL VALUE ISSOMETIMES
CALCULATED USING MULTIPLES
The use of exit multiples for determining terminal value is
criticized by academics and other commentators for
intermixing two different valuation approaches
Shannon Pratt explains:
The market multiple brings a major element of the market
approach into the income approach.*
Nonetheless, multiples (primarily of EBITDA) are commonly
used by investment bankers to calculate terminal value
_________________________________
* Shannon P. Pratt, Valuing a Business, 5th Ed. (McGraw Hill, 2008), p. 220
35
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
INVESTMENT BANKS USE MULTIPLES MORE
OFTEN THAN GROWTH MODELS
My study of valuation methods used for fairness opinions in U.S.
cash acquisitions showed that 65½% used multiples and only
41% used a growth model (6½% used both)
My forthcoming study of valuation methods used for fairness
opinions in U.S. stock-for-stock mergers (2009–2014) shows:
36
Financial
Institutions
Other
Companies Total
Multiples only 93% 59½% 72%
Growth model only 5% 37½% 25%
Both 2% 3% 3%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
MULTIPLES SHOULD BENORMALIZED
A common error in using multiples for determining terminal
value is to assume that multiples in the terminal year will be at
the currently prevailing level
When the current multiples reflect optimistic growth
expectations, the use of current multiples to calculate terminal
value causes overstatement of terminal value
If an exit multiple is used for terminal value, it should be
normalized to reflect the “reversion to the norm” as the
company’s growth tends toward its long-term growth rate
37
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SANITY CHECKS ON TERMINAL VALUES
The practitioner who determines terminal value using
multiples of EBITDA should calculate the implied growth rate
and consider whether the result is reasonable
Similarly, the practitioner who uses a growth model should
examine the implied multiples of EBITDA and net income
based on the calculated terminal value
If the multiple-based terminal value implies a unrealistic
growth rate (or if a growth model’s implied multiples of
terminal value are materially inconsistent with projected
future multiples), the practitioner should reexamine the
underlying assumptions
38
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
The Relationship Between
Depreciation and
Capital Expenditures
39
A COMMON ERROR
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
A common error is to assumes that capex = depreciation
Many analyses even have capex < depreciation in perpetuity!
Understating capex necessarily results in overstated terminal
values
40
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
MOST PRACTITIONERS ASSUME THAT
DEPRECIATION = CAPEX
A 2015 survey by Jim Hitchner published in his bi-monthly
Financial Valuation and Litigation Expert, valuators in a
webinar audience were asked:
How do you typically handle depreciation
and cap ex when calculating cash flows?
The responses were:
oCapex greater than depreciation[!]: 6%
oThe same or very similar: 55%
oCapex less than depreciation: 38%
41
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
FCF FOR TERMINAL VALUE
SHOULD BENORMALIZED
The analyst must always review 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 less expensive or more efficient,
the ratio of capex to depreciation may decrease
oIf a single-facility company built and equipped a factory, depreciation
could exceed capex until major new investments are required
42
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
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]
43
5 Year Straight Line Depreciation with 5% Growth
Year Purchased Capital Expenditures
Depreciated in 2022
% Amount
2017 1,000.0 10% 100.0
2018 1,050.0 20% 210.0
2019 1,102.5 20% 220.5
2020 1,157.6 20% 231.5
2021 1,215.5 20% 243.1
2022 1,276.3 10% 127.6
1,132.8
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
5-YEAR DOUBLE DECLINING DEPRECIATION
Five-year double declining depreciation to zero residual value
44
5 Year Double Declining Depreciation with 2% to 5% Growth
2% Growth 3% Growth 4% Growth 5% Growth
Year Capex
Depreciated
in 2022 Capex
Depreciated
in 2022 Capex
Depreciated
in 2022 Capex
Depreciated
in 2022
2017 1,000 57.6 1,000 57.6 1,000 57.6 1,000 57.6
2018 1,020 117.5 1,030 118.7 1,040 119.8 1,050 121.0
2019 1,040 119.9 1,061 122.2 1,082 124.6 1,103 127.0
2020 1,061 203.8 1,093 209.8 1,125 216.0 1,158 222.3
2021 1,082 346.4 1,126 360.2 1,170 374.4 1,216 389.0
2022 1,104 220.8 1,159 231.9 1,217 243.3 1,276 255.3
Depreciation in
2022 1,065.9 1,100.3 1,135.7 1,172.1
Capex in 2022 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%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
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
45
0%
10%
20%
30%
40%
50%
2% 3% 4% 5%
Growth Rate
Straight Line
Depreciation
Double Declining
Depreciation
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
A SUMMARY TABLE
The table below summarizes the relationships between
capex and depreciation for different lives, growth rates,
and depreciation methods (zero residual value)
46
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%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
COURTS GENERALLY HAVE ACCEPTED
CAPEX ≥ DEPRECIATION
Unfortunately, some federal and Delaware court
decisions have accepted DCF valuations in which
depreciation equaled capital expenditures
Other federal and Delaware court decisions have
accepted DCF valuations in which depreciation exceeded
capital expenditures
Two Delaware decisions have accepted DCF valuations
where capital expenditures were less than half of
depreciation!
47
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
The Appropriate
Treatment of Amortization
in DCF Valuations
48
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 reduces only net income
Most amortizable intangible assets are created through either
acquisitions or creation of intellectual property
49
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
AMORTIZATION HAS A LIMITED LIFE
An important difference between amortization and
depreciation must be recognized by valuators when
calculating terminal value: amortization has a limited life
A common error is to project growth in amortization in
perpetuity
Amortizable intangible assets such as goodwill are not
systematically replaced in the ordinary course of business
Since amortization, unlike depreciation, does not grow in
perpetuity, it must be separately valued in terminal value
calculations
50
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
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, it is important that valuators determine
how much of the projected D&A is amortization
51
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
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
An appropriate manner to value amortization subsequent
to the projection period is to determine the risk-adjusted
present value of the future tax benefits of the remaining
amortization
52
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
OTHER NORMALIZING ADJUSTMENTS
FCF must be also be normalized to exclude any other items
that are not 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 positive or negative cash flows
from limited-life items after the projection period should be
included in terminal value
The value of tax-loss carryforwards is the risk-adjusted 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
53
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
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+ PVT+ 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;
PVT = 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
54
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
ERRONEOUS TREATMENT OF AMORTIZATION
BY EXPERTS IN COURT
An example of the erroneous treatment of amortization in a
DCF analysis is a 2007 Delaware decision in which 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 projected 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
55
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SUMMARY – D&A, CAPEX & TERMINAL VALUE
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
56
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
I would like to thank
I would like to thank I would like to thank
I would like to thank
Prof. Mauro Bini
Prof. Mauro BiniProf. Mauro Bini
Prof. Mauro Bini
for the opportunity
for the opportunity for the opportunity
for the opportunity
to share my ideas with you
to share my ideas with youto share my ideas with you
to share my ideas with you
at this 5
at this 5at this 5
at this 5th
thth
th Annual International
Annual International Annual International
Annual International
Conference of the OIV
Conference of the OIVConference of the OIV
Conference of the OIV
Your questions and comments are welcome
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM 57
Sample Calculations of Relationship between
Capital Expenditures and Depreciation
58
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
59
3% Growth – 10 Year Straight Line Depreciation
Year Capital
Expenditures 2027 2028 2029 2030 2031 2032 2033
2017 1,000.0 50.0
2018 1,030.0 103.0 51.5
2019 1,060.9 106.1 106.1 53.0
2020 1,092.7 109.3 109.3 109.3 54.6
2021 1,125.5 112.6 112.6 112.6 112.6 56.3
2022 1,159.3 115.9 115.9 115.9 115.9 115.9 58.0
2023 1,194.1 119.4 119.4 119.4 119.4 119.4 119.4 59.7
2024 1,229.9 123.0 123.0 123.0 123.0 123.0 123.0 123.0
2025 1,266.8 126.7 126.7 126.7 126.7 126.7 126.7 126.7
2026 1,304.8 130.5 130.5 130.5 130.5 130.5 130.5 130.5
2027 1,343.9 67.2 134.4 134.4 134.4 134.4 134.4 134.4
2028 1,384.2 69.2 138.4 138.4 138.4 138.4 138.4
2029 1,425.8 71.3 142.6 142.6 142.6 142.6
2030 1,468.5 73.4 146.9 146.9 146.9
2031 1,512.6 75.6 151.3 151.3
2032 1,558.0 77.9 155.8
2033 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%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
60
3% Growth – 10 Year Double Declining Depreciation
Year Capital
Expenditures 2027 2028 2029 2030 2031 2032 2033
2017 1,000.0 32.8
2018 1,030.0 67.5 33.8
2019 1,060.9 69.5 69.5 34.8
2020 1,092.7 71.6 71.6 71.6 35.8
2021 1,125.5 73.8 73.8 73.8 73.8 36.9
2022 1,159.3 85.5 76.0 76.0 76.0 76.0 38.0
2023 1,194.1 110.0 88.0 78.3 78.3 78.3 78.3 39.1
2024 1,229.9 141.7 113.3 90.7 80.6 80.6 80.6 80.6
2025 1,266.8 182.4 145.9 116.7 93.4 83.0 83.0 83.0
2026 1,304.8 234.9 187.9 150.3 120.2 96.2 85.5 85.5
2027 1,343.9 134.4 241.9 193.5 154.8 123.9 99.1 88.1
2028 1,384.2 138.4 249.2 199.3 159.5 127.6 102.1
2029 1,425.8 142.6 256.6 205.3 164.2 131.4
2030 1,468.5 146.9 264.3 211.5 169.2
2031 1,512.6 151.3 272.3 217.8
2032 1,558.0 155.8 280.4
2033 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%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
61
3% Growth – 10 Year Sum-of-the-Digits Depreciation
Year Capital
Expenditures 2027 2028 2029 2030 2031 2032 2033
2017 1,000.0 9.1
2018 1,030.0 28.1 9.4
2019 1,060.9 48.2 28.9 9.6
2020 1,092.7 69.5 49.7 29.8 9.9
2021 1,125.5 92.1 71.6 51.2 30.7 10.2
2022 1,159.3 115.9 94.8 73.8 52.7 31.6 10.5
2023 1,194.1 141.1 119.4 97.7 76.0 54.3 32.6 10.9
2024 1,229.9 167.7 145.3 123.0 100.6 78.3 55.9 33.5
2025 1,266.8 195.8 172.7 149.7 126.7 103.6 80.6 57.6
2026 1,304.8 225.4 201.6 177.9 154.2 130.5 106.8 83.0
2027 1,343.9 122.2 232.1 207.7 183.3 158.8 134.4 110.0
2028 1,384.2 125.8 239.1 213.9 188.8 163.6 138.4
2029 1,425.8 129.6 246.3 220.3 194.4 168.5
2030 1,468.5 133.5 253.7 227.0 200.3
2031 1,512.6 137.5 261.3 233.8
2032 1,558.0 141.6 269.1
2033 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%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography
Growth Rates & Firm Mortality (p. 1)
Agarwal, Rajshree, “Survival of Firms over the Product Life Cycle,” 63 Southern Economic
Journal 971 (1997)
Agarwal, R., and David B. Audretsch, “Does Entry Size Matter? The Impact of the Life
Cycle and Technology on Firm Survival,” 49 Journal of Industrial Economics 21 (2001)
Agarwal, R., and Michael Gort, “Firm and Product Life Cycles and Firm Survival,” 92
American Economic Review 184 (2002)
Agarwal, Vineet, and Richard Taffler, “Comparing the performance of market-based and
accounting-based bankruptcy prediction models,” 32 Journal of Banking & Finance
1541 (2008)
Altman, Edward I., and Edith Hotchkiss, Corporate Financial Distress and Bankruptcy
,
3rd ed. (Wiley, 2006)
Bhattacharya, Utpal, Alexander Borisov and Xiaoyun Yu, “Firm Mortality and Natal
Financial Care”, 50 Journal of Financial and Quantitative Analysis 61 (2015)
Cassia, Lucio, Andrea Plati and Silvio Vismara, “Equity Valuation Using DCF: A Theoretical
Analysis of the Long Term Hypotheses,” 4 Investment Management and Financial
Innovations 91 (2007)
62
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography
Growth Rates & Firm Mortality (p. 2)
Chava, Sudheer, and Robert A. Jarrow
, “Bankruptcy Prediction with Industry Effects,”
8 Review of Finance 4 (2004)
Damodan, Aswath, Investment Valuation, 3rd ed. (Wiley, 2012), pp. 318-320
Duffie, Darrell and Ke Wang, “Multi-Period Corporate Failure Prediction with Stochastic
Covariates,” National Bureau of Economic Research, Working Paper 10743 (2004)
Foster, Richard N., “Creative Destruction Whips Through Corporate America,” Innosight
Executive Briefing, Winter 2012, available at www.innosight.com/insight/creative-
destruction-whips-through-corporate-america-an-innosight-executive-briefing-on-
corporate-strategy/
Gittelson, Kim, “Can a Company Live Forever,” BBC News, Jan 19, 2012, available at
http://www.bbc.com/news/business-16611040
Jennergren, L. Peter, “Firm valuation with bankruptcy risk,” 8 Journal of Business Valuation
and Economic Loss Analysis 91 (2013)
Loderer, Claudio F., Klaus Neusser and Urs Waelchli, “Firm Age and Survival,” SSRN (2011),
available at www.ssrn.com/abstract=1430408
63
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography
Growth Rates & Firm Mortality (p. 3)
Matthews, Gilbert E., “Valuation Methods in Fairness Opinions: An Empirical Study of Cash
Transactions,” 31 Business Valuation Review 55 (2012)
Matthews, “Stock-for-Stock Mergers: An Empirical Study of Fairness Determinations in
Fairness Opinions,” 35 Business Valuation Review (forthcoming)
Morris, James R., "Growth in the Constant Growth Model," 25 Business Valuation Review
153 (2006)
Morris, "Life and Death of Businesses: A Review of Research on Firm Mortality,” 4 Journal
of Business Valuation and Economic Loss Analysis (2009) (“2009a”)
Morris, "Firm Mortality and Business Valuation," Valuation Strategies
(September/October 2009)
Perry, Mark J., “Fortune 500 firms in 1955 v. 2015; Only 12% remain, thanks to the creative
destruction that fuels economic prosperity,” American Enterprise Institute, Oct. 12,
2015, available at www.aei.org/publication/fortune-500-firms-in-1955-vs-2015-only-
12-remain-thanks-to-the-creative-destruction-that-fuels-economic-growth/
Petersen, Christian, and Thomas Plenborg, “The implementation and application of firm
valuation models,” 20 Journal of Applied Business Research 1 (2009)
64
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography
Growth Rates & Firm Mortality (p. 4)
Reis, Pedro Nogueira , and Mário Gomes Augusto, “Determinants of Firm Terminal
Value: The Perspective of North American and European Financial Analysts,” 13
International Business & Economics Research Journal 793 (2014)
Reis and Augusto, “What Is a Firm’s Life Expectancy? Empirical Evidence in the Context
of Portuguese Companies,” 10 Journal of Business Valuation and Economic Loss
Analysis 45 (2015)
Saha, Atanu, and Burton K. Malkiel, “Valuation of Cash Flows with Time-Varying
Cessation Risk,” 7 Journal of Business Valuation and Economic Loss Analysis (2012)
Shaffer, Sherrill, “Corporate Failure and Equity Valuation,” 62 Financial Analysts Journal
71 (2006)
Shaffer, “Equity duration and convexity when firms can fail or stagnate,” 4 Finance
Research Letters 233 (2007)
Shumway, Tyler, “Forecasting Bankruptcy More Accurately: A Simple Hazard Model,”
74 Journal of Business 101 (2001)
Vassalou, Maria, and Yuhang Xing, “Default Risk in Equity Returns,” 59 Journal of
Finance 831 (2004)
65
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography
Capex, Depreciation & Amortization
Armentrout, Brant H., “A Sanity Test When Estimating Capital Expenditures,” 22
Business Valuation Review 136 (2003)
Coffey, John F., “The Capex Adjustment,” Value Examiner, Nov./Dec. 2009
Lee, Brian H., Daniel L. McConaughy, Mary Ann K. Travers and Steven R. Whitehead,
“The Long-term Relationships between Capital Expenditures and Depreciation and
Long-term Net Working Capital to Sales across Industries,” 31 Business Valuation
Review 87 (2012)
Lee, M. Mark, “The Ratio of Depreciation and Capital Expenditures in DCF Terminal
Values,” Financial Valuation and Litigation Expert, Aug.-Sept. 2007, pp. 7-8
McConaughy, Daniel L., and Lorena Bordi, “The Long Term Relationships between
Capital Expenditures and Depreciation Across Industries: Important Data for
Capitalized Income Based Valuations,” 23 Business Valuation Review 14 (2004)
Matthews, Gilbert E., “CapX = Depreciation Is Unrealistic Assumption for Most Terminal
Values,” Business Valuation Update, March 2002
Matthews, “Capital Expenditures, Depreciation and Amortization in the Gordon Growth
Model,” 33 Business Valuation Review 113 (2014)
66
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
