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PITFALLS IN DETERMINING
TERMINAL VALUE
IN THE DCF MODEL
GILBERT E. MATTHEWS, CFA
American Society of Appraisers
Webinar –BV168-WEB
November 9, 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
2
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
ISSUES THAT IMPACT TERMINAL VALUE
An current assumption that need to be rethought
1. The perpetual growth rate and firm mortality
Errors often made in current practice
2. The relationship between capital expenditures and
depreciation
3. The appropriate treatment of amortization
4. Projections, normalization, and steady state growth
Current investment banking practice
5. The trend toward using lower long-term growth rates
6. The relevance of multiples for terminal value
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
1.
Rethinking the Perpetual
Growth Rate Assumption
4
THE PERPETUAL GROWTH ASSUMPTION
Many traditional assumptions such as constant growth
rates in perpetuity are relied upon in determining
terminal value
In the customary DCF valuation, it is assumed that a
mature company will survive and will continue to grow
at a constant rate in perpetuity
There are some companies for which perpetual growth is
usually not assumed, e.g.:
ocompanies in extractive industries with diminishing reserves
ocompanies dependent on patent protection
5
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
REEXAMINING THE PERPETUAL GROWTH ASSUMPTION
The assumption that a mature company will grow at a
constant rate in perpetuity should be reexamined
The assumption is questionable due both to corporate
mortality and also to decelerating growth rates
These changes may be due to poor management (a
company-specific factor) but also may result from economic
changes, obsolescence, and/or disruptive innovation (which
are not company-specific)
The constant perpetual growth assumption results in
overstated values
6
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DISRUPTIVE INNOVATION
“Disruptive innovation” disrupts an existing market and
value network, displacing established market leading firms,
products, and alliances
A prime example is Amazon's impact on retailing
The most influential business theory of recent years is [the] theory
of disruptive innovation.
. . . Think of classified ads (Craigslist), long-distance calls (Skype),
record stores (iTunes), taxis (Uber) and newspapers (Twitter).
The Economist, June 17, 2017, p. 53.
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
QUESTIONING THE ASSUMPTION
Prof. James Morris perceptively wrote:
[R]elatively little attention is given to expected [corporate] 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.
Morris, James R., "Life and Death of Businesses: A Review of Research on Firm
Mortality,” 4 J. of Bus. Val. and Econ. Loss Analysis, Art. 3 (2009), p. 1
8
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DECLINE IN TENURE OF TOP 500 COMPANIES
In 1958, companies in the S&P 500 had been 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
remained in the 2015 Fortune 500
9
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
WHAT CAUSES THIS ATTRITION?
What are the reasons for this attrition?
1. Some companies are absorbed in mergers and acquisitions
2. Some larger companies are displaced by smaller faster-growing
rivals
3. Some companies grow at slower rates or suffer reverses due to
disruptive innovation, obsolescence, or economic changes
4. Some companies have financial difficulties that adversely affect
their growth and profitability
5. Some companies are restructured in bankruptcy or go out of
business
10
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SOME COMPANIES ARE DROPPED FROM INDICES
DUE TO MERGERS AND ACQUISITIONS
Examples of healthy companies dropped from S&P 500
because they were acquired, 2001-2012
Allegheny Energy: merged with FirstEnergy
Anheuser-Busch:acquired by InBev
Bell South: acquired by AT&T
Genzyme: acquired by Sanofi
May Dept. Stores: acquired by Macy’s
McAfee: acquired by Intel
Pepsi Bottling Group: acquired by PepsiCo
Sun Microsystems: acquired by Oracle
Toys “R” Us: taken private in LBO
Wendy’s: merger with TriArc
Wyeth: acquired by Pfizer
11
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SOME COMPANIES ARE DROPPED FROM INDICES
BECAUSE OF POOR PERFORMANCE
Examples of companies dropped from S&P 500 for poor
performance, 2001-2012
American Airlines: restructured in bankruptcy
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
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
12
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DOES MORTALITY RISK DECLINE AS OVER TIME?
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”
Many other studies have concluded that the corporate
mortality risk decreases with time
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
A CONTRARY CONCLUSION
A contrary conclusion was reached in a 2015 study of public
companies by Daepp, Hamilton, West, and Bettencourt
They used Compustat data to examine the lifespans of more
than 25,000 public companies and concluded that the
mortality rate of public companies is not a function of time
However, their definition of lifespan included mergers and
acquisitions, which were the terminal events for about half
of the companies
14
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SMALLER FIRMS HAVE
GREATER MORTALITY RISK
According to the U.S. Small Business Administration, 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
It is undisputed that the mortality rate is a function of a company’s
size
There is a high correlation between corporate mortality and size
measured either by equity value or number of employees
The following chart is based on equity value of public companies
and includes only “unfavorable” mortality, excluding companies
that were acquired
15
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
CHART: SMALLER FIRMS HAVE
GREATER MORTALITY RISK
Decile 1 = Largest Firms
Decile 10 = Smallest Firms
(by market value of equity)
Source: Morris, “Life and Death of Businesses,” p. 3, citing Maggie Queen and Richard Roll,
“Firm Mortality: Using Market Indicators to Predict Survival,” 43 Fin. Analysts J. 9 (1987)
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
IMPACT OF FINITE LIFE ASSUMPTION
Morris calculated the valuation error resulting from an infinite
life assumption vs. a finite life assumption
k = discount rate
g = perpetual growth rate
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
IMPACT OF MORTALITY RISK
If the risk of failure in any given year is 0.25% and is constant year
to year, the cumulative risk of failure within 25 years is 6%
If the risk of failure in any given year is 2% and is constant year to
year, the cumulative risk of failure within 25 years is 40%
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Cumulative Risk of Failure with Constant Annual Risk
Risk per year 0.25% 0.5% 1.0% 2.0%
Cumulative risk: 10 years 2.5% 4.9% 9.6% 18.3%
Cumulative risk: 15 years 3.7% 7.2% 14.0% 26.1%
Cumulative risk: 25 years 6.1% 11.8% 22.2% 39.7%
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
IMPACT OF MORTALITY RISK (2)
We also calculated the cumulative risk of failure assuming that the
annual risk decreases over time
We examined the impact assuming that the annual risk declines 5% per
year after the first ten years
If the risk of failure in the first 10 years is 2% annually and
declines 5% each year, the cumulative risk of failure within 25
years is 33½%
19
Cumulative Risk of Failure Assuming that Risk
Declines 5% per Year after Year 10
Risk per year 0.25% 0.5% 1.0% 2.0%
Risk in year 15 0.19% 0.39% 0.77% 1.55%
Risk in year 25 0.12% 0.23% 0.46% 0.93%
Cumulative risk: 15 years 3.5% 6.9% 13.4% 25.1%
Cumulative risk: 25 years 4.9% 9.6% 18.4% 33.5%
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 increases at lower discount rates
20
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DAMODARAN’SFORMULA
Prof. Aswath Damodaran proposes a simple formula for
adjusting enterprise 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
21
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DAMODARAN: DETERMINING
THE PROBABILITY OF DISTRESS
Damodaran 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 generally limited to companies with published
bond ratings
22
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DCF VALUATIONS SHOULD BEADJUSTED
FOR MORTALITY RISK
Prof. Sherrill Shaffer (2007) points out:
[Since] most of the value of a stream of discounted cash flows
stems from the distant future, . . . the correct adjustment for
the risk of failure may imply quite different values of equity
than those given by the standard model.
The risk of corporate decline and mortality is not reflected
in customary CAPM calculations
Although company-specific risk may include risk based on a
company’s financial condition, it seldom include risks of factors
such as technological change, competition and obsolescence
23
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?
Shaffer believes that the Gordon growth formula should be
adjusted to reflect risk of failure.
Shaffer proposes adjusting the Gordon growth formula for “p,”
which he defines as the probability that “the asset may
irreversibly default (i.e., the issuing company may fail) in any
given year”
24
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DISCOUNT RATES AND GROWTH RATES
ADJUSTED FOR RISK OF FAILURE
Shaffer (2006) adjusts the growth model to account for p
He solves his formula to determine “R” (the discount rate
adjusted for p):
r= discount rate
g= growth rate
He also solves it for “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 pis 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
THE SAHA – MALKIEL ARTICLE
“VALUATIO N 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.
27
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
SAHA–MALKIEL FRAMEWORK
Saha and Malkiel develop a framework for calculating present
value “when cash flows have a finite probability of cessation
at each period” and “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”
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
PV =
FCF (1 + g) (1 – p)
r –g + p (1 + g)
SAHA–MALKIEL FORMULAS
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
29
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
For companies with a low mortality risk, the impact may be
immaterial
Adjustments for firm mortality or for the risk of decelerating
growth should be considered
Venture capitalists commonly account for the substantial
possibility that a start-up company may not succeed by using
discount rates of 35% or more
30
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
If mortality risk is supported by data, it becomes defensible in
litigation
To the extent that mortality risk may be part of company-specific risk,
analysts should take care to avoid double-counting
31
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
STUDIES SHOULD EXCLUDE
ACQUISITIONS OF HEALTHY COMPANIES
Studies of corporate mortality have frequently included
acquisitions of healthy companies
Since these companies, at the time of their acquisition, are normally
continuing to grow, their inclusion is inappropriate and distorts the data
These transactions have been described as “favorable mortality”
They should be distinguished from acquisitions of troubled companies
affected by adversity, whose acquisition price is impacted by their poor
prospects and weak financial condition
To be useful for adjusting terminal value for mortality risk,
future studies should focus on “unfavorable mortality”
32
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
MORTALITY RISK CAN BEQUANTIFIED WITH
DATA, UNLIKE COMPANY-SPECIFIC RISK
Delaware courts are highly skeptical of company-specific risk
because it is subjective and not supported by data
Vice Chancellor Strine (now Chief Justice) wrote:
The calculation of a company specific risk is highly subjective and often is
justified as a way of taking into account competitive and other factors that
endanger the subject company’s ability to achieve its projected cash flows. In
other words, it is often a back-door method of reducing estimated cash flows
rather than adjusting them directly. To judges, the company specific risk premium
often seems like the device experts employ to bring their final results into line
with their clients’ objectives, when other valuation inputs fail to do the trick.
Del. Open MRI Radiology Assocs. v. Kessler, 898 A.2d 290, 339 (Del. Ch. 2006)
33
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
2.
The Relationship Between
Depreciation and
Capital Expenditures
34
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
[I]n corporate finance and valuation, once a practice has
become established, it becomes difficult to challenge,
even if the original reasons for it have long disappeared.
Aswath Damodaran, “The Small Cap Premium: Where is the Beef,”
34 Bus. Val. Rev. 152 (2015)
35
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
THIS ERROR OVERSTATES VALUATIONS
In fact, due to growth and inflation, capex must be greater
than depreciation in a growth model
The understatement of capex is a common error in
calculations of terminal value
Some analyses even have capex < depreciation in perpetuity!
Understating future capex in relation to projected
depreciation necessarily results in overstated terminal values
36
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 less than depreciation[!]: 6%
oThe same or very similar: 55%
oCapex more than depreciation: 38%
37
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
38
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 (2023) is 112.7% of depreciation [1,276.3 ÷1,132.8]
Sample calculations of the 15-year relationship between capital expenditures and depreciation using
straight line, double declining balance, and sum-of-the-digits depreciation are shown on Slides 67–69.
39
5-Yea r Straight Line Depreciation with 5% Growth
Year Purchased Capital Expenditures Depreciated in 2023
%Amount
2018 1,000.0 10% 100.0
2019 1,050.0 20% 210.0
2020 1,102.5 20% 220.5
2021 1,157.6 20% 231.5
2022 1,215.5 20% 243.1
2023 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
40
5-Yea r Double Declining Depreciation with 2% to 5% Growth
2% Growth 3% Growth 4% Growth 5% Growth
Year Capex
Depreciated
in 2023 Capex
Depreciated
in 2023 Capex
Depreciated
in 2023 Capex
Depreciated
in 2023
2018 1,000 57.6 1,000 57.6 1,000 57.6 1,000 57.6
2019 1,020 117.5 1,030 118.7 1,040 119.8 1,050 121.0
2020 1,040 119.9 1,061 122.2 1,082 124.6 1,103 127.0
2021 1,061 203.8 1,093 209.8 1,125 216.0 1,158 222.3
2022 1,082 346.4 1,126 360.2 1,170 374.4 1,216 389.0
2023 1,104 220.8 1,159 231.9 1,217 243.3 1,276 255.3
Depreciation in
2023 1,065.9 1,100.3 1,135.7 1,172.1
Capex in 2023 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
41
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)
42
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 OFTEN HAVE ACCEPTED
CAPEX ≤ DEPRECIATION
Many federal and Delaware court decisions have accepted
DCF valuations in which depreciation = capex
In most of these cases, neither side used a projection when
capex ≥ depreciation
A few federal and Delaware court decisions have even
accepted DCF valuations in which depreciation ≥ capex
Two Delaware decisions have accepted DCF valuations where
projected capex were less than half of projected depreciation!
43
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
3.
The Appropriate
Treatment of Amortization
in DCF Valuations
44
AMORTIZATION
Amortization and depreciation are both non-cash charges that
reduce reported income
Most amortizable intangible assets are created through either
acquisitions or creation of intellectual property
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
45
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
AMORTIZATION HAS ALIMITED 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
46
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
THE VALUE OF AMORTIZATION ISTHE 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
47
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
AMORTIZATION MUST BESEPARATED
FROM DEPRECIATION IN D&A
Companies customarily lump depreciation and amortization
(“D&A”) as a single line item in their income and cash flow
statements
For public companies, information re amortization can often be
found in footnotes or in the Management Discussion and Analysis
Because of the different analytical treatment of amortization
and depreciation, it is important that valuators determine
how much of the projected D&A is amortization
48
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
49
SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
BENEFITS OF LIMITED-LIFE ITEMS SHOULD
BEINCLUDED IN TERMINAL VALUE
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
50
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
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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 capitalized
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
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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
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
4.
Projections,
Normalization, and
Steady State Growth
54
DUE DILIGENCE
The analyst should conduct due diligence to determine the
reasonableness of the projection and the underlying
assumptions
Terminal value is a direct function of the final year of the
projection underlying the DCF analysis
A small change in the final year projection can materially
impact the valuation
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
NORMALIZATION
Normalizing adjustments should be made to adjust inputs that
will not grow in parallel with revenues and free cash flow
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 if
they 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
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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 the company is still growing at a faster rate in the final year
of the projection than its expected longer-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”
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
5.
Trend Toward Using
Lower Long-Term
Growth Rates
58
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 published in BVR,*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
____________________________
*These articles, as well as other selected articles, are listed in the
Bibliography appended to this presentation
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
DATA FROM STUDIES
Midpoints of Growth Rates in Growth Models for Fairness Opinions
Cash Acquisitions:
Sept. 2007–Aug. 2008
Cash Acquisitions:
Sept. 2010–Aug. 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% 69.0% 20 16.4%
1% 12.0% 46.0% 13 10.7%
>1% and <2% 23.9% 34.5% 16 13.1%
2% 713.7% 13 19.4% 19 15.1%
>2% and <3% 917.6% 11 16.4% 14 11.1%
3% 12 23.5% 16 23.9% 28 22.2%
>3% and <4% 47.8% 57.5% 64.8%
4% 47.8% 57.5% 32.4%
More than 4% 12 23.5% 46.0% 75.7%
Tot a l 51 100.0% 67 100.0% 122 100.0%
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
6.
The Relevance of Multiples
to Terminal Value
61
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
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
INVESTMENT BANKS USE MULTIPLES MORE
OFTEN THAN GROWTH MODELS
My 2012 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 2016 study of valuation methods used for fairness opinions
in U.S. stock-for-stock mergers (2009–2014) shows:
63
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 causes an
overstatement of terminal value
If an exit multiple is used for terminal value, it should be
normalized to reflect a “reversion to the norm” as the
company’s growth tends toward its long-term growth rate
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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
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Sample Calculations of Relationship between
Capital Expenditures and Depreciation
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
67
3% Growth –15 Year Straight Line Depreciation
Year Capital
Expenditures 2028 2029 2030 2031 2032 2033 2034
2018 1,000.0 50.0
2019 1,030.0 103.0 51.5
2020 1,060.9 106.1 106.1 53.0
2021 1,092.7 109.3 109.3 109.3 54.6
2022 1,125.5 112.6 112.6 112.6 112.6 56.3
2023 1,159.3 115.9 115.9 115.9 115.9 115.9 58.0
2024 1,194.1 119.4 119.4 119.4 119.4 119.4 119.4 59.7
2025 1,229.9 123.0 123.0 123.0 123.0 123.0 123.0 123.0
2026 1,266.8 126.7 126.7 126.7 126.7 126.7 126.7 126.7
2027 1,304.8 130.5 130.5 130.5 130.5 130.5 130.5 130.5
2028 1,343.9 67.2 134.4 134.4 134.4 134.4 134.4 134.4
2029 1,384.2 69.2 138.4 138.4 138.4 138.4 138.4
2030 1,425.8 71.3 142.6 142.6 142.6 142.6
2031 1,468.5 73.4 146.9 146.9 146.9
2032 1,512.6 75.6 151.3 151.3
2033 1,558.0 77.9 155.8
2034 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
68
3% Growth –15 Year Double Declining Depreciation
Year Capital
Expenditures 2028 2029 2030 2031 2032 2033 2034
2018 1,000.0 32.8
2019 1,030.0 67.5 33.8
2020 1,060.9 69.5 69.5 34.8
2021 1,092.7 71.6 71.6 71.6 35.8
2022 1,125.5 73.8 73.8 73.8 73.8 36.9
2023 1,159.3 85.5 76.0 76.0 76.0 76.0 38.0
2024 1,194.1 110.0 88.0 78.3 78.3 78.3 78.3 39.1
2025 1,229.9 141.7 113.3 90.7 80.6 80.6 80.6 80.6
2026 1,266.8 182.4 145.9 116.7 93.4 83.0 83.0 83.0
2027 1,304.8 234.9 187.9 150.3 120.2 96.2 85.5 85.5
2028 1,343.9 134.4 241.9 193.5 154.8 123.9 99.1 88.1
2029 1,384.2 138.4 249.2 199.3 159.5 127.6 102.1
2030 1,425.8 142.6 256.6 205.3 164.2 131.4
2031 1,468.5 146.9 264.3 211.5 169.2
2032 1,512.6 151.3 272.3 217.8
2033 1,558.0 155.8 280.4
2034 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
69
3% Growth –15 Year Sum-of-the-Digits Depreciation
Year Capital
Expenditures 2028 2029 2030 2031 2032 2033 2034
2018 1,000.0 9.1
2019 1,030.0 28.1 9.4
2020 1,060.9 48.2 28.9 9.6
2021 1,092.7 69.5 49.7 29.8 9.9
2022 1,125.5 92.1 71.6 51.2 30.7 10.2
2023 1,159.3 115.9 94.8 73.8 52.7 31.6 10.5
2024 1,194.1 141.1 119.4 97.7 76.0 54.3 32.6 10.9
2025 1,229.9 167.7 145.3 123.0 100.6 78.3 55.9 33.5
2026 1,266.8 195.8 172.7 149.7 126.7 103.6 80.6 57.6
2027 1,304.8 225.4 201.6 177.9 154.2 130.5 106.8 83.0
2028 1,343.9 122.2 232.1 207.7 183.3 158.8 134.4 110.0
2029 1,384.2 125.8 239.1 213.9 188.8 163.6 138.4
2030 1,425.8 129.6 246.3 220.3 194.4 168.5
2031 1,468.5 133.5 253.7 227.0 200.3
2032 1,512.6 137.5 261.3 233.8
2033 1,558.0 141.6 269.1
2034 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, Rajshree, 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, Rajshree, 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)
Audretsch, David, “New Firm Survival and the Technological Regime,” 73 Review of Economics and Statistics 441 (1991
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)
Chava, Sudheer, and Robert A. Jarrow, “Bankruptcy Prediction with Industry Effects,” 8 Review of Finance 4 (2004)
Damodaran, Aswath, Investment Valuation, 3rd ed. (Wiley, 2012), pp. 318-320
Daepp, Madeleine I.G., Marcus J. Hamilton, Geoffrey B. West, and Luís M. A. Bettencourt, “The Mortality of Companies,”
12 Journal of The Royal Society Interface (2015), available at
rsif.royalsocietypublishing.org/content/12/106/20150120
Duffie, Darrell and Ke Wang, “Multi-Period Corporate Failure Prediction with Stochastic Covariates,” National Bureau of
Economic Research, Working Paper 10743 (2004)
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography: Growth Rates & Firm Mortality (p. 2)
Dunne, Timothy, Mark Roberts, and Larry Samuelson, “Patterns of Firm Entry and Exit in U.S. Manufacturing
Industries,” XIX Rand Journal of Economics 495 (1988)
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 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
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 120 (2016)
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)
Morris, "Firm Mortality and Business Valuation," Valuation Strategies (September/October 2009)
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SUTTER SECURITIES INCORPORATED GILBERT E. MATTHEWS GIL@SUTTERSF.COM
Selected Bibliography: Growth Rates & Firm Mortality (p. 3)
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)
Reeves, Martin, Simon Levin and Daichi Ueda, “The Biology of Corporate Survival,” Harvard Business Review (Jan.-Feb.
2016), pp. 46-55
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)
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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)
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