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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