Chapter 1 Introducing the Profit Vintages Method A … · Introducing the Profit Vintages Method A...

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Chapter 1

Introducing the Profit Vintages Method

A New Model for Valuing and Decomposing the Enterprise

I. Motivation

This book presents and explores a valuation model called the Profit Vintages

Method (“PVM”). The PVM is a new and useful way of describing and

understanding the firm and its component parts. It resolves certain problems

that have plagued the valuation field for many years, clarifies concepts that have

existed in an incoherent form, and yields new insights about the value and asset

composition of the firm.

The research that gave rise to the PVM did not begin with such a grand objective.

It began with a much more modest goal. In particular, we wanted to investigate

a question that arises in the valuation field every day – might one draw

inferences about the economic life of the firm’s intangible assets that are

analytically sound but that do not rely solely on the interview-based

impressionistic evidence that is usually offered up to address that question?1 We

found that the answer to this question is “yes,” and that this answer leads, if the

logic is followed to its conclusions, to the PVM.

The PVM rests ultimately on an identity that must be true under certain fairly

general conditions. We refer to this condition as the N=V condition.2 The

variable N stands for the economic life, or time horizon, over which the firm’s

investments in intangible assets pay off. Correspondingly, V stands for the

number of vintages, or prior instances, of past investments that must be “in

service,” or paying off, at any given time. In a steady state, which we define to

include constant growth, as well as “S-curve” growth patterns, N must equal V.

That is, the number of vintages of sunk intangible asset investments must equal

the number of years over which such investments yield returns (produce

revenue and profits).

1 Economic life is another term that we will discuss more carefully later. For now, define

economic life simply as the time period over which an investment in an asset pays off. 2 The reader will pardon the use of an equality rather than the identity symbol. For shorthand,

we use N=V, rather than N≡V, simply because the equality is more familiar to most readers.

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The PVM is, in principle, applicable to all of the firm’s assets, or to a single asset

category such as intangible assets. This book shows how the PVM applies to

both, but we focus the valuation analyst’s attention on the firm’s intangible asset

investments for two primary reasons. First, the firm, properly understood, is an

intangible asset. Indeed, in microeconomic theory the firm is understood as one

big “recipe” for combining capital and labor inputs in a specific way. Therefore,

the firm’s investments in organizational, technological, and customer-based

intangible assets are, relative to its investments in physical capital, its most

important investments and warrant particular attention.

Second, intangible assets require more complex valuation methods because they

are less directly observable and measurable than investments in physical assets.

We can directly observe the rate of obsolescence of physical assets because they

are physical. We can watch physical assets erode and become less productive.

Moreover, we know that physical capital is, per se, “dumb.” That is, by itself (i.e.,

without the aid of human rationality in the form of organizational, technological,

and relationship capital) the firm’s physical capital is nothing more than

undirected matter. It therefore cannot produce economic rents (profit in excess

of the cost of capital), its standalone value at the time of acquisition is equal to

cost, and its value at any time after acquisition is equal to the present value of the

remaining profit flow that is necessary in order for the physical asset to yield its

required return over its full lifetime (yield present value returns equal to cost, or

become NPV zero).3 Taken together, the observability of decay and the fact that

physical assets cannot generate rents on their own, mean that we can pinpoint

the profit stream associated with physical assets relatively easily.

Intangible assets, on the other hand, are not as easy to observe and evaluate. We

cannot directly observe the rate at which intangibles obsolesce. For example, we

cannot measure the economic life of intangible assets through direct observation.

And, because we cannot directly observe economic life (the time horizon over

which intangible asset investments pay off), it follows that we cannot directly

3 For readers that are questioning this assertion, consider for a moment a firm that can add to its

shareholder value by acquiring additional physical capital. The fact that paying for additional

physical capital adds to shareholder value means that the physical capital is net present value

positive (the profit that it generates is, in present value, greater than its cost of acquisition). The

question begged is why is this physical capital NPV>0? It must be because of the “recipe” that

the firm uses to combine these physical capital inputs with other inputs. This recipe is either

organizational, technological, or relationship-based. It must therefore be the case that the cause

of the economic rents (the positive NPV) is an intangible asset.

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observe the profit streams associated with a particular type or “vintage” (i.e.,

year of investment) of intangible asset.

This means that we cannot easily discern how much of the firm’s value is

composed of what valuation practitioners call “identifiable” intangible assets –

that is, intangible assets that are “in service” producing revenue and profit in any

given period – versus intangible assets that are “future intangibles” such as

goodwill or in-process R&D that require future investments. In other words, we

cannot easily discern how much of the firm’s value is associated with the

expectation of positive net present value future investments (i.e., goodwill),4 and how

much is associated with already made (or sunk) intangible asset investments.

In response to this problem, valuation practitioners have generally offered up

very impressionistic evidence when attempting to estimate the economic life of

intangible assets. Practitioners generally use interview methods and survey

techniques, not infrequently relying on competing or incoherent definitions of

economic life, in an attempt to gain an indistinct sense for the economic life of a

given firm’s intangible asset investments.

In part because of the imprecision in practitioners’ estimates of the economic life

of identifiable intangible assets, much confusion surrounds both the concept, and

in applied contexts the dollar value, of goodwill. This is because goodwill is

treated as the enterprise value that is “left over” after a firm’s identifiable assets

have been valued.

4 The reader may have already noted that the concept of net present value is crucially important

here. When we say that there is a positive net present value associated with a future investment,

we mean that while the investment hasn’t yet been made, the expected net, or difference,

between the cost of the investment and the profit stream expected from that investment, is

positive. As Miller and Modigliani have noted, the net present value, today, of the firm’s future

investments is what accountants call “goodwill.” By contrast, investments that have already been

made – for example, R&D that has already occurred – have a positive present value (we do not

say “net” present value because the investment has already been sunk, and there remains only

the benefit or profit flow). This distinction between already made investments and future

investments is the crux of the distinction, made by accountants and valuation practitioners,

between “identifiable” or “existing” intangibles and “future” intangibles or goodwill. And, if we

do not know the economic life (time horizon) over which sunk investments are expected to pay

off, then we simply cannot distinguish between existing (or identifiable) intangibles and

goodwill. For reference, see Merton H. Miller and Franco Modigliani, Dividend Policy, Growth,

and the Value of Shares, Journal of Business, Vol. 34, No. 4 (1961), pp. 411-433.

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Case law generally defines goodwill as “the expectation of future patronage.”5

Similarly, IRS regulations, such as Section 1060-1(b), define goodwill as “the

value of a trade or business attributable to the expectancy of continued customer

patronage.” However, some courts have also said that goodwill is “inextricably

related to” trademarks or trade names, and that such intangibles (trademarks or

trade names) are the “embodiment of goodwill.” In any case, such definitions do

practitioners little good, as they do not distinguish goodwill from other assets.

Indeed, all assets represent an expectation of future profits – i.e., an expectation of

future patronage. And, the efficacy of all of the firm’s assets is embodied in

trademark value.

Organizations that set accounting standards tend to take a more precise

approach. For example, the Financial Accounting Standards Board (“FASB”)

Statement of Financial Accounting Standards (“SFAS”) number 142, and

Accounting Standards Codification (“ASC”) number 805 define goodwill as the

enterprise’s value in excess of the value of identifiable intangibles. Identifiable

intangibles are those intangible assets that have identifiable cash flows and a

definite economic life. This essentially means that goodwill is the net present

value, today, of future investments in intangible assets. (Note that this definition

is essentially identical to that of Miller and Modigliani, cited earlier.)

Unfortunately, there is little in the way of guidance offered by courts, accounting

organizations, or valuation-related organizations such as the American Society of

Appraisers, regarding the proper approach to the estimation of the economic life

of identifiable intangibles. The estimation of the economic life of existing /

identifiable intangibles remains a sort of “black art” in the valuation field. It is

an area wherein experience, judgment, and ultimately subjectivity, prevail.

For investors, this creates a serious problem. Perhaps more than any other asset,

investors need to know how much of a firm’s value (which they either own or

are considering purchasing) consists of goodwill. The simple reason for this is

that goodwill is the enterprise’s most speculative asset. The fact that goodwill is

the value today of future investments means that these investments are less

defined and less understood than already sunk investments (i.e., existing assets).

Investors paying for a share of firms that have high goodwill value, relative to

the values of other assets, are paying now for future investments: 1) in the

expectation that these investments will earn more than their cost of capital, and

2) without any real knowledge of what some of these investments will be. In

5 {CITE CASE LAW}.

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other words, goodwill, being the value today of investments well into the future,

represents a bet that the enterprise will be able to make not yet defined

investments, and that these will be NPV positive.

Indeed, it may not be an overstatement to say that stock market mispricing, and

even bubbles, can be thought of as situations in which investors overestimate the

firm’s ability to continue to generate positive NPV investments in the future. We

focus on this possibility, and examine it empirically, in a later chapter.

The lack of clarity in the valuation profession regarding economic life also

creates serious problems for tax authorities. Multinational corporations use

“transfer pricing” structures to transfer identifiable intangible assets, such as

technology or trademark rights, between entities in different sovereign taxing

jurisdictions. These transactions are taxable at their fair market (or as defined by

the Organization for Economic Cooperation and Development, “arm’s length”)

values. Given that tax authorities are at an inherent informational disadvantage

relative to multinational corporations, it is sometimes possible for multinationals

to use interview-based fact finding methods to produce evidence for an

advantageous economic life. (For example, if the selling entity is in a high tax

jurisdiction and the purchasing entity is in a low tax jurisdiction, it may be

advantageous to “find” a short economic life, and thereby to generate a low

arm’s length value).

Finally, this creates a problem for economists. Intangible assets (or as economists

often refer to them, “know-how”) have always played an important role in

economic activity. Even in rustic societies successful production required know-

how about how most effectively to use the land, labor and tools at hand. With

the Renaissance and scientific and industrial revolutions, the importance of

knowledge resources increased dramatically. These new knowledge resources

encompassed not only technologies (the printing press, the wind mill, the steam

engine) but also non-technological areas of know-how (double-entry

bookkeeping, bills of exchange).

However, since the end of World War II, know-how has taken on economic

importance far out of proportion to anything it had in all prior economic history.

Developments in electronics, computing, pharmaceuticals, and a dozen other

areas dominate the economic landscape. Each year spending on R&D increases

and the trend shows no sign of slowing down. A single statistic illustrates: In

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the 16 years from 1992 through 2007, total US R&D spending exceeded what it

had been in the preceding four decades, even after accounting for inflation.6

In an early landmark article Nobel laureate Robert Solow showed that 85 percent

of growth in per capita productivity was due not to increases in the amount of

physical capital, but rather to technological improvements.7 Although

subsequent work tempered this conclusion, the central role of technological

change in economic growth remains unchallenged. A more recent landmark

analysis emphasized that it was the recipes for combining tangible resources,

rather than the tangible resources themselves, that was critical for an economy.

In the author’s words:

A hundred years ago all we could do to get visual stimulation from

iron oxide was to make it into pigment and spread it on … canvas

… Now we know how to spread iron oxide on long reels of plastic

tape and use it with … other assorted raw materials … to make

television sets and video tape recorders.8

The dramatic increase in the importance of intangible assets to economic growth

and wealth creation obviously means that intangibles are not a “sideshow” in

economic analysis. This means that proper measurement of the intangible asset

“stock” (which requires an estimate of economic life) is an important area of

focus in growth economics.9

For all of these reasons, devising a way to observe, rather than guess at, the

economic life of a firm’s intangibles is a valuable undertaking. This, in fact, is

exactly what the PVM does. As we show directly below, our basic insight is that

V is directly observable. And that fact, in a steady state, means that N is

observable as well.

6 US National Science Foundation, Division of Science Resources Statistics. Available on the web

at www.aaas.org/spp/rd. 7 Solow, Robert, “Technical Change and the Aggregate Production Function,” Review of Economics

and Statistics 39 No. 3 (August 1957) 312-320. 8 From Paul Romer, “Micro Foundations for Aggregate Technical Change”, a working paper that

became the basis for his seminal analysis: “Endogenous Technical Change”, Journal of Political

Economy, 98 No. 5 (October 1990, Part 2), S71-102. Quoted in Warsh, David, Knowledge and the

Wealth of Nations, New York, W.W. Norton, 2006, p. 291. That Romer’s references to “plastic

tape” and “video tape recorders” seem quaint to us today only confirms the importance of

technological change to our economy. 9 See for example, Corrado, Hulten, and Sichel, “Intangible Capital and Economic Growth,”

Review of Income and Wealth, September 2009.

http://www.aaas.org/spp/rd

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II. What is the Profit Vintages Method?

A. The PVM Starts with the N=V Condition

As noted, the Profit Vintages Method rests ultimately the N=V condition, which

is an equilibrium condition that must hold in a steady state. By “steady state,”

we mean a state in which the firm expects to grow at a constant rate, or at a

variable rate that follows a well-known function such as a logistic function (S-

curve).

We rely heavily on the concept of a steady state in this book, in large part

because valuation theory and practice both rely heavily on steady state concepts

in order to uncover key relationships that exist in equilibrium, and to simplify

analysis. For example, theoretical models such as the Gordon Model, the two-

stage model, and other “workhorse” valuation models in finance such as the H

Model or the three stage DDM10 all rely on steady state assumptions about the

firm’s expected cash flows. Second, following the theory, valuation practice also

invariably relies on steady state concepts. That is, virtually any cash flow

forecast assumes that the firm’s cash flow arrives at a steady state – that is, a state

of constant growth. In our experience, this steady state, or terminal value as it is

generally called, usually begins sometime after year 2 and before year 6 of a cash

flow forecast. In short, steady state assumptions are ubiquitous in valuation

theory, and the PVM is no exception.11

Any investment decision (for example, an investment in R&D) has a cash flow

profile that entails an initial outlay followed by a period of positive returns. This

is depicted in Exhibit 1-1 below, which assumes that the positive cash flow

associated with an intangible asset investment lasts for five years.

10 “DDM” stands for “dividend discount model.” 11 Importantly, as we show in a later chapter, the logic underpinning the N=V condition does hold

for periods of time in which a steady state does not inhere, although the mathematics of the N=V

condition are much more difficult and are idiosyncratic to each non-steady state.

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Exhibit 1-1: Example of an R&D Investment That Yields a Return Over N Years

Exhibit 1-1 is nothing new. It shows a year’s worth, or vintage, of the firm’s

intangible asset investments yielding a return over N (in this example 5) years.

In this book we often refer to intangible asset investments as “intangible

development costs,” or “IDCs.”

That return, or payoff, takes the form of “gross residual profit.” To understand

gross residual profit, we first define net residual profit. Net residual profit is the

firm’s operating profit, minus the required returns to the firm’s physical and

financial capital, minus cash taxes. It is what economists call “economic profit,”

and many finance practitioners refer to as “economic value added,” or “EVA.”

Gross residual profit is simply net residual profit before deduction of the firm’s

IDCs. That is, gross residual profit begins with net residual profit and simply

“adds back” the firm’s current period intangible asset investments (e.g., R&D,

marketing, sales efforts, etc.). Gross residual profit, which we call R, is thus net

residual profit (net economic profit) before deduction of intangible asset

investments that are, by definition, investments in future period returns. Thus,

gross residual profit is the firm’s total return to its previously sunk intangible

asset investments. We discuss the calculation of gross residual profit in much

more detail in a later chapter.

$ +

Time

1 2 3 4 5

$ -

Intan

gib

le Asset

Inv

estmen

t

Intangible Asset Return

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At any point in time, a firm’s gross residual profit (the current period return to

previously sunk intangible asset investments) must be composed of V layers, or

vintages, of returns to previously sunk intangible asset investments. What is

overlooked by valuation practitioners is that in a steady state, V must equal N.

The reason for this is quite simple. If investments pay off over N years, there

must be N vintages paying off at any point in time. Gross residual profit must be

composed of N vintages of prior IDC investments. N must equal V.

Exhibit 1-2, below, depicts the relationship between a firm’s gross residual profit

flow and its prior investments in intangibles. In essence, the exhibit illustrates

the N=V condition. We can see in Exhibit 1-2 that the number of vintages, or

layers, of return streams associated with intangible asset investments made in

previous years is exactly equal to the economic life of the firm’s IDCs. Again,

gross residual profit must be composed of V “layers,” or “vintages” of prior

intangible asset investment returns.

Exhibit 1-2: Number of Layers of Intangible Asset Investment

What this means is that if we know V, we know N. As it turns out, there is a way

to exactly determine (note we do not say “estimate”) V in a steady state.

Economic life, N, is knowable because the number of in service vintages, V, is

knowable.

The intuition for how we determine V can be seen with the aid of Exhibit 1-2. As

discussed in Chapter 2, we can use some straightforward mathematics to show

that in a steady state all V of the firm’s layers of returns to previously sunk IDCs

are of the same “thickness,” or “height.” That is, with steady state growth, in

$ +

N = 5 = Number of Years Over Which IDCs Yield a Return

IDC Return Layer - Vintage t= -5

IDC Return Layer - Vintage t =-4



1 2 3 4 5 6 7 8 9

$ -

N = V = 5 = Number of

Return Streams (Layers)

That Sum To Gross

Residual Profit, R

IDC

Investm

ent

t=-4

IDC

Investm

ent

t=-5

R


TimeIDC

Investm

ent

t=-1

IDC

Investm

ent

t=-2

IDC

Investm

ent

t=-3

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every period, all V of the firm’s previous IDC tranches produce the same flow of

dollars, which we call π.12 Because we can directly observe R (gross residual

profit), if we know the “height” of each layer (the number of dollars returned per

vintage of investment), we can simply divide R by π to obtain V. In terms of

Exhibit 1-2, once we have π, we simply figure out how many layers of returns

“fit” inside of R.

The determination of π is not as straightforward as the determination of V.

However, as it turns out, all we need to determine π is the rate of return to the

firm’s IDCs, which we call r*. We show in Chapter 2 that r* is actually

observable from the firm’s financial data, again assuming that the firm is in a

steady state.

While exhibits 1-1 and 1-2 focus on intangible asset returns, and thus residual

profit (profit after deduction of returns to the firm’s physical asset investments),

the logic of these exhibits (and the logic of the PVM) extends readily to all of the

firm’s investments. Simply replacing net residual profit in the foregoing

discussion with free cash flow to the enterprise (F), defined in the standard way,

and gross residual profit with gross free cash to the enterprise (C), reveals the

same relationships shown in exhibits 1-2 and 1-3.

In other words, we know that the firm’s enterprise free cash flow is the return,

net of the current period’s investments, to all of the firm’s prior asset investments

(including not only its intangible asset investments but also its investments in

physical capital).13 Thus, F is the total asset analogue to net residual profit

discussed earlier. This means that we can define gross enterprise free cash flow,

C, as F plus all of the firm’s current period investments (capital expenditures,

additions to working capital, R&D, and sales and marketing investments in

customer-based intangibles). Because C is the current period return to all prior

investments (whether tangible or intangible), the N=V condition holds in the

same way for C as it does for R.

The only difference between the PVM applied to the firm’s residual profit, and

applied to all of its profit, is that in the former, N is the weighted average

12 This may at first sound counterintuitive, since with growth the oldest tranches are associated

with the lowest levels of IDC investment. However, keep in mind that the payoffs from these

older tranches have also had the longest amount of time to grow as the firm grows. 13 Enterprise free cash flow is generally defined as NOPAT (operating profit less cash taxes) plus

depreciation and amortization, minus capital expenditures, plus changes in net working capital.

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economic life for intangible assets, while in the latter N is the weighted average

economic life for all of the firm’s assets including physical assets.

B. Overview of the Profit Vintages Method and its Key Equations

Now that we have a basic understanding of the N=V condition, we can provide a

high level overview of the PVM.14

We call this model the “profit vintages” model for reasons that can be seen from

Exhibit 1-2 above. Once we know economic life, N, which is also the number of

in service vintages, V, for a given asset category, we can show that the firm’s

value is equal to the present value of the returns (gross residual profit or gross

cash flow) to all N vintages of past investment, plus the net present value (if any)

of future investments. In other words, enterprise value is the present value of

the green “triangle” of gross cash flows shown in Exhibit 1-2, plus the net present

value of any future investments that the firm expects to make. Graphically, the

PVM is summarized in Exhibit I-3, below.

Exhibit I-3: Graphical Depiction of the PVM

Admittedly, Exhibit 1-3 looks more complex than the exhibits that have preceded

it. However, it tells an important story, and is worth a bit of investment by the

reader.15

14 Chapter 2, entitled “A Tour of the PVM,” explains the model and its primary implications in

much more detail.

$ +

N = 3 = Number of Years Over Which IDCs Yield a Return

R

IDC Excess Return t=-3 IDC Excess Return t=1 IDC Excess Return t=4

IDC Required Return t=-3 IDC Required Return t=1 IDC Required Return t=4





IDC

Inve

stme

nt

t=-3

IDC

Inve

stme

nt

t=-2

Intan

gible

Inve

stme

nt

t=-1

Intan

gible

Inve

stme

nt

t=1

Intan

gible

Inve

stme

nt

t=2

Intan

gible

Inve

stme

nt

t=3

Intan

gible

Inve

stme

nt

t=4

Intan

gible

Inve

stme

nt

t=5

Intan

gible

Inve

stme

nt

t=6 Time

$ -

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The best way to understand Exhibit 1-3 is to begin with the meaning of the colors

shown. Taken together, the white areas in the exhibit all have zero value today –

that is, no net present value. There are two categories of white “flows” shown in

the exhibit.

First, we have the firm’s historical investment costs and past profits. Obviously,

past profits have no value today. Similarly, past investment costs are not a cost

to the firm today – these investments may have created an expectation of profit

flows, today, that has a positive present value (i.e., they may have given rise to

one of the green colored flows in Exhibit 1-3, such as the identifiable intangible

asset returns), but the costs themselves do not enter into the firm’s present

enterprise value because they are sunk (they are in the past).

The second category of white colored flows that do not contribute to enterprise

value are offsetting positive and negative flows that occur in future periods.

These areas comprise investments (IDCs) and return streams that are offsetting

in present value terms. We show this in Exhibit 1-3 using the black diagonal

lines that connect one period’s IDCs with later periods’ profit streams. Note that

the lines all connect an intangible asset investment to its profit flows in later

periods. That is, the IDCs are connected to flows of returns that are labeled “IDC

required return t = X.” This means that the white return stream represents the

amount of profit necessary in order to return the IDC to the firm in nominal

dollars (the return of the IDC) and to provide a required return on the IDC

(profit) exactly equal to the cost of capital for that IDC. In other words, the white

profit areas are equal in present value to the IDC investment from a prior period,

and hence offsetting in the diagram. As with prior exhibits, we show the profit

streams being earned over N years.

Turning now to the green areas, it should be obvious to the reader that these

areas do have a present value. That is, these areas are the intangible asset

components of the firm’s enterprise value.

As with the white areas, there are two categories of intangible assets shown by

the green profit flows. The first category is represented by the stepwise

triangular box at the left, outlined in bright blue. This area, which we will often

15 A note to the reader before proceeding: Exhibit I-3 focuses only on the firm’s investments in

IDCs (intangible development costs). Again, however, the logic applies to any asset category,

including all of the firm’s assets.

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refer to in this book as “Area A,” includes both the future required returns and

any future excess returns to IDCs sunk by the firm during the N periods prior to

the current moment. In other words, Area A represents all of the returns to IDCs

that are currently in service (less than N years old).

Obviously, for a firm that earns economic rents, the returns to sunk IDCs of

vintages less than N years old will include both the required returns to those

IDCs and the economic rents expected to be earned on the investments. This is

shown in Exhibit 2-7 by the two tiers of return streams within each layer, or π,

inside Area A – one labeled “IDC Required Return,” and one labeled “IDC

Excess Return.”

The present value of Area A is, by definition, the value of what accountants call

“existing” or “identifiable” intangible assets. Again, these are “existing” in the

sense that these flows have been “unlocked” through investments already made.

They are “identifiable” because we know the nature of the IDCs that have been

sunk to produce the return streams that comprise Area A – in other words, we

know if the IDCs that give rise to Area A are marketing IDCs, R&D, or some

other kind of IDC. In short, we know what Area A is – it is cash flows caused by

technology, or customer-based intangibles, organizational intangibles, or some

combination of these. In addition, we know that the investments giving rise to

Area A are paying off over N years. Thus, the intangibles cannot live less than N

years, nor more than N years. They “exist” for the time horizon captured in Area

A.

The second category of intangible assets represented by the green profit flows is

goodwill, or again as Modigliani and Miller described them, “future investment

opportunities that are net present value positive today.” These areas are labeled

“IDC Excess Return t = X,” meaning that these are the economic rents, or

economic profits, attributable IDCs sunk at t = X, where X is some time period in

the future.

These green areas are the excess returns on, but not the returns of or the required

returns on, the IDCs sunk at t = X. As such, these areas, in present value, are the

net present value of an IDC investment and its corresponding total return stream

(the return of and return on that IDC).

In other words, because the horizontal white areas below these green areas

represent the required returns of and on IDCs sunk at t = X (and thus these white

areas directly below the green areas offset, in present value terms, their

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corresponding IDC investments) the green areas are the expected economic rents

associated with future IDCs. In standard finance terms, this is shareholder value,

or EVA, that the firm expects to “unlock” by making future investments. It has

value today as an expectation, but that value (that cash flow) is not yet

actualized.

Exhibit 1-4 simplifies Exhibit 1-3 by stripping away all of the clutter, so that we

see only the green areas shown in Exhibit 1-3. This exhibit shows us the two

categories of intangible assets that comprise the intangible asset component of

the firm’s total enterprise value – identifiable intangibles and goodwill. The

PVM says that the value of the enterprise is equal to the present value of the

green areas in Exhibit 1-4.

Exhibit I-4: Intangible Asset Enterprise Value Components

Exhibit 1-4 highlights the fact that not all future gross residual profit flows have

value today. Some of those flows (the white areas) do not contribute to

enterprise value, as they are offset by IDCs that the firm knows it will have to

expend in order to generate future generations of intangible assets, and thereby

to generate future economic rents.

Note the arrows in Exhibit 1-4 that extend to the right of the future IDC excess

returns. These denote the fact that the time horizon over which we discount the

firm’s expected economic rents on future IDCs is perpetual. This brings us to an

interesting point about the economic life of goodwill. Because goodwill is the

$ +

R

Future IDC Excess Return t=1 Future IDC Excess Return t=4



$ -

NPV Positive Future

IDCs = Goodwill

Returns to

Previously Sunk

IDCs:

Area "A" -

Identifiable

Intangibles

15

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present value of all economic rents expected from future investments in IDCs,

goodwill does not necessarily have a finite “economic life.” We discount the

firm’s expected economic rents from future IDCs for as long as the firm’s forecast

contains those rents – possibly into perpetuity.

However, it is important to keep in mind that the future IDC investments that

generate the expected future rents do have a finite life. Just as sunk IDC

investments have a finite life of N, the firm’s future investments in IDCs also

have a finite life. The firm’s future IDC vintages “roll over” as newer vintages

replace older vintages – in just the same way that the sunk IDC layers replaced

one another in the past. This is shown in Exhibit 1-3 by the future IDC excess

returns that last for N years, and are then replaced by future IDC excess returns

of another vintage.

When we think about the mechanics of a firm’s profit flows, we begin to see that

the PVM is a much richer, and more descriptive, way of understanding what the

firm’s investors actually own. Investors own cash flows associated with

investments already made (identifiable assets) and they own the net present

value (excess cash flows) associated with future investments.

The PVM is thus a way of both valuing the enterprise, and simultaneously

decomposing it into its primary component parts. The PVM is a new way of

thinking about the enterprise – a new apparatus for enterprise valuation – that

produces the same result as a standard discounted cash flow (“DCF”) model, but

it also produces more information than the standard DCF. The model tells us not

only how much the enterprise is worth, but also how much of the enterprise

consists of physical and financial assets, how much of it is identifiable intangible

assets, and how much is goodwill.

This contrasts sharply with current valuation models. At present, the field of

valuation treats enterprise valuation and enterprise value decomposition as two

separate exercises. To be sure, these exercises must reconcile, meaning that the

value of the enterprise must equal the sum of the values of its component parts.

However, enterprise valuation and decomposition are treated as entirely distinct

exercises in which the reconciliation item – or the “plug” as it is often called – is

goodwill.

The difference between this current standard and the PVM is that goodwill is no

longer a “plug.” In fact, goodwill value, and the values of all of the firm’s other

components, turn out to be “endogenous.” That is, the PVM demonstrates that

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the values of goodwill and identifiable intangibles are implied by the firm’s

financial variables, and that their values all “hang together” automatically. No

plug is necessary.

This is a very strong claim. If it is true, then the approach that has been taken for

at least the past two decades to critically important financial reporting exercises

such as purchase price allocation (for example, under SFAS 141) and goodwill

impairment (for example, under SFAS 141) misses key logical connections among

the firm’s asset categories.

Note that we are not saying that the results of the traditionally conducted

goodwill impairment and purchase price allocation exercises are necessarily

wrong. The fact that goodwill has been treated as a plug, and that practitioners

have not recognized that the value of identifiable intangibles and goodwill both

“fall out” of (are endogenous to) the firm’s financial forecast, does not mean that

the values resulting from the traditional method have necessarily been incorrect.

However, the PVM does tell us that the traditional approach misses something

fundamental about the firm. That is, the traditional approach is at least logically

incoherent, because it misses the logic, which by contrast the PVM recognizes,

that implies that the firm’s component parts are endogenous to its forecast and

enterprise value, rather than merely reconcilable.

As noted, in principle the PVM applies to a portfolio of assets of different

categories (e.g., the firm itself), as well as to an individual asset or asset category

(e.g. intangible assets). In this book, most of our emphasis will be on intangible

assets. Therefore, the PVM is used primarily to evaluate the firm’s intangible

asset portfolio, including its goodwill. We call this PVM(I). However, we also

illustrate the range of the PVM by applying it to the firm as a whole. We call this

application of the model PVM(T).

1. PVM(I)

In its most basic form, the PVM(I) can be summarized in a single formula for

enterprise value, as follows.

(Formula 1-1) V = C + P + VIA + G

Where V is enterprise value, C is the firm’s excess (non-operating) cash, P, is

physical assets, VIA is the value of identifiable, or existing, intangible assets, and

G is the value (if any) of the firm’s goodwill. Cash is worth its face value, and we

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discuss the value of P in later chapters. Thus, the key formulas of the PVM are

those for VIA and G. These are given below.

(Formula 1-2) VIA

( ) ( ( ) ( ) )

(Formula 1-3) G

( ) ( ( )

( )

)

The variables in the preceding formulas are defined as follows.

VIA = Again, this is the value of the firm’s existing intangible assets.

G = The value of the firm’s goodwill.

R = Gross Residual Profit in period 1 of the firm’s forecast.

I = Intangible asset investments in period 1 of the firm’s forecast. This

includes investments in R&D, sales, and marketing.

g = The Firm’s Steady State Growth Rate.

r The firm’s required rate of return to the firm’s capital base (this is the

firm’s weighted average cost of capital, or WACC).

N Economic life.

We derive, and discuss the intuition for, formulas 1-2 and 1-3 in Chapter 2.

The reader may have noted that upon addition of G and VIA, most of the terms

cancel, leaving the equation

. This is just the formula for the present

value of the firm’s net residual profit (gross residual profit less intangible asset

investment in each period). Astute readers will recognize this as the core

formula for the so-called “income method” of valuing intangible assets.

VIA and G are both functions of the following variables: R, I, g, r, and N. As we

show in the next section, N is itself a function of R, I, g, and r*. Thus, all of the

variables given above are either exogenous but easily and commonly derived

(such as r), or are native to the firm’s forecasts (such as R, I, r*, and g). Thus, as

we discussed earlier, the values of goodwill and identifiable intangibles are

endogenous to the firm’s forecast. With nothing more than a standard, well

developed, forecast, we can find the economic life of the firm’s identifiable assets,

the value of those assets, and the value of goodwill. Impressionistic, interview-

based, analysis of the economic life of the firm’s capital base is not, strictly

speaking, necessary.

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2. PVM(T)

Correspondingly, the basic PVM(T) can also be summarized in a single formula,

as follows.

(Formula 1-4) V = C + VA + G

Where V is enterprise value, C is the firm’s cash, VA is the value of identifiable, or

existing, assets including both intangible and physical assets, and G is the value

of the firm’s goodwill. Separate formulas, in turn, for VA and G are given below.

(Formula 1-5) VA

( ) ( ( ) ( ) )

(Formula 1-6) G

( ) ( ( )

( )

)

The variables in the preceding formulas are defined as follows.

VA = The value of the firm’s existing assets, or capital.

G = The value of the firm’s goodwill.

F = Gross Enterprise Cash Flow in period 1 of the firm’s forecast.16

K = Investments in all assets (including intangibles) in period 1 of the firm’s

forecast. This includes capital expenditures, increases (or decreases) in net

working capital, R&D, and sales and marketing investments.

g = The Firm’s Steady State Growth Rate.

r The firm’s required rate of return to the firm’s capital base (this is the

firm’s weighted average cost of capital, or WACC).

N Economic Life.

Once again, upon addition of G and VA most of the terms cancel, leaving the

equation

, which is just the formula for operating enterprise value. As

with the PVM(I), all of the variables given above are either exogenous but easily

derived (such as r), or are native to the firm’s forecasts (such as C, K, and g).

16 This is discussed in detail in later chapters. For now, we define gross enterprise cash flow as

net operating profit less cash taxes, plus depreciation and amortization, plus change in net

working capital, plus IDCs.

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III. Overview of the Primary Contributions of the PVM to Valuation Theory

This book is really nothing more than a tracing out and empirical testing of the

implications of the N=V condition and the PVM. The primary contributions that

we bring to the field of valuation are summarized below, and are covered more

thoroughly in subsequent chapters.

A. Economic Life

Certainly one the most fundamental contributions of this book is the technique

for determining the economic life of an asset or portfolio of assets. Economic life,

N, can be shown to be a function of four variables – all of which are directly

observable and exist in any firm’s forecast. For the firm’s intangible assets, these

are R, I, r*, and g. The variable r* stands for the firm’s realized rate of return to

its investments.

Given these variables, the formula for N (which is formally derived in a later

chapter) takes two equivalent forms.

(Formula 1-7) ( (

) )

( )

.

Formula 1-7 does, in fact, yield N as a function of R, I, g, and r*. However, it is

likely obvious to the reader that N is in both the exponent in the numerator of the

leftmost term, and in the denominator of the same term. Formula 1-7 cannot be

directly manipulated to produce N, but it can be solved for N in two ways. First,

the formula can be dropped into a spreadsheet and the value of N can be solved

for using, for example, the solver feature in Excel™.

Alternatively, N can be found using what mathematicians call Lambert’s W

function. Lambert’s W is what mathematicians call an “elementary function.”

This function was discovered by Johann Heinrich Lambert in 1758 as a way of

solving for X in an equation of the form Y = XeX.

Lambert’s W is much studied by mathematicians, and describes numerous

processes that occur in nature. For example, Lambert’s W has been shown to

describe the way in which the probability of heart failure corresponds to certain

breathing patterns for patients with chronic heart failure, the motion of a ballistic

projectile in the presence of air resistance, the relationships between voltage,

current, and resistance in a diode, and numerous other applications in statistical

mechanics, quantum chemistry, combinatorics, enzyme kinetics, the physiology

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of vision, the engineering of thin films, hydrology and the analysis of algorithms.

A few years ago, a brief, unsigned editorial in Focus, the newsletter of the

Mathematical Association of America, asked: "Time for a new elementary

function?" The function proposed for promotion to the core set was Lambert’s W.

Formula 1-7 is in the form Y = XeX, which means that we can solve it using

Lambert’s W. The solution is given below.

(Formula 1-8) (

(

))

( )

For any firm with a forecast steady state R, I, g, and a measurable r*, Formula 1-8

tells us the economic life of its intangible assets. Formula 1-2 can be evaluated

using software such as MATLAB, or with free solvers available on the internet.

To our knowledge, the use of Lambert’s W to solve for the economic life of the

firm’s intangible assets is its first application in the field of finance.

B. Observable Goodwill and Intangible Asset Values

As we have already discussed, knowing the economic life of the firm’s

identifiable assets means that we also know the value of goodwill. Given that

the economic life of the firm’s assets is endogenous to (implied by) its financial

forecast data, it follows that goodwill is also endogenous to the firm’s financial

forecast data.

Thus, we can take any firm that can be modeled using steady state assumptions,

and compute the value of its goodwill. This is extremely valuable for investors,

precisely because goodwill is the “speculative” portion of a firm’s value.

Goodwill is the portion of a firm’s value that investors expect to be “unlocked” in

future periods. In contrast to value associated with identifiable assets, which

have already been unlocked, goodwill is a bet by investors that the firm will

continue to have the ability to generate economic rents. When the value of

goodwill is high as a percentage of enterprise value, investors are betting

(speculating?) in a very bullish way about the firm’s future capabilities.

Correspondingly, when it is low relative to enterprise value, investors are

bearish on the firm’s future capabilities.

While companies are required under GAAP and IFRS to report the values of

identifiable intangibles and goodwill associated with acquisitions, they do not

have to report these values for their “organically grown” operations. This

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usually means that most of the dollar value associated with a firm’s identifiable

intangible assets and goodwill is not reported on the balance sheet.

One of the reasons that companies are not required to report the intangible asset

and goodwill values for their organically grown operations is that doing so using

traditional methods of determining the economic life of identifiable intangibles

would be very onerous. Certified Public Accountants would have to perform

lengthy interviews of the R&D, marketing, and sales personnel of every publicly

traded company in order to devise estimates of economic life. However, the

PVM shows us that such interviews are not necessary. Intangible asset values

and goodwill are “hidden,” or latent, in the firm’s forecast information.

C. Rates of Return to Investments

The formulas for the value of identifiable assets (for example, the value of

identifiable intangibles) and goodwill both depend upon N. In turn, N depends

upon r*.

The dependence of goodwill upon r* is intuitive. Goodwill, as Miller and

Modigliani first pointed out, is the current period’s capitalized expectation of

future periods’ positive net present value investments. It therefore depends

critically on the relationship between the expected rate of return on future

investments (IDCs, for example) and the required rate of return on those

investments. Future investments only have value today if they are expected to

be NPV positive. Thus, the existence of goodwill requires that r* > r.

Given this, the question is whether r* is observable. In the valuation field,

unfortunately, very little attention has been paid to r*. For example, the question

of whether r* can be inferred from the firm’s forecast data is, to our knowledge,

little studied. This is somewhat surprising, given that it is well understood by

valuation practitioners and theorists that value growth only occurs when the

firm is earning more than its cost of capital on its investments. In other words,

knowing whether a firm’s r* is greater than its r is crucial to knowing whether

enterprise value will grow in the future.

One very important contribution of this book is that we develop an approach to

estimating r* from a firm’s financial forecast (cash flow forecast). As with other

formulas presented in this chapter, the full derivation and underlying intuition is

offered later. For now, let the following suffice.

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First, the formula for r* is as follows.17

(Formula 1-9) (

).

Formula 1-9 is surprisingly simple. The basic intuition for this formula starts

with the recognition that a firm’s flow of profit in each period is equal to its stock

of assets times its realized rate of return to those assets. This leads to an

important and well known relationship between growth and rates of return.

That is, the firm’s profit growth (incremental profit in the period) is its new

capital (incremental capital added to the capital stock in the period) times the

rate of return to that capital. In most standard valuation texts, this relationship is

given in formula 1-10, below.

(Formula 1-10) ( )

( ).

This is the standard growth formula in valuation theory, relating growth in the

firm’s profit to the rate of return earned on net new capital (capital investment at

the margin). Formula 1-10 says that profit (NOPAT, or net operating profit less

cash taxes) grows at a rate equal to the rate of growth in the invested capital

stock (IC) times the marginal rate of return earned on that capital stock.18

Exactly the same logic applies to the firm’s net residual profit (R-I). Net residual

profit grows by an amount equal to the firm’s new IDC stock, times r*. This

relationship is described in Formula 1-11.

(Formula 1-11) ( ) ( ) ,

Where Δ equals the current period depreciation in the firm’s IDC stock. Thus,

the question is: what is Δ?

As we demonstrate in Chapter 2, it turns out that Δ is equal to Ie-g. This gives us

17 Note that this is the formula for PVM(I). The formula for PVM(T) is analogous, and is

presented fully in Chapter 2. 18 The astute reader will notice that formula 1-10 assumes that the firm’s average and marginal

ROIC are equal. More advanced treatments recognize that ROIC should be replaced with

ROMIC (return on marginal invested capital). However, the problem with this more precise

approach is that capital returns at the margin are harder to measure than average returns.

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(Formula 1-11) ( ) ( ) ( )

( ).

Formula 1-11 tells us that the rate of return to the firm’s IDCs is entirely a

function of parameters taken from the firm’s forecast. This is an important

finding, indeed a pivotal one for the PVM.

The fact that we can measure the steady state rate of return to the firm’s

intangible capital investments using its financial forecast data is important not

only to valuation theory, but to the fields of economics and finance generally.

Much econometric work has been directed at the question of the rate of return to

R&D, for example.19 The result in Formula 1-11 provides a means of comparing

firms’ rates of return to IDCs without having to resort to econometric techniques,

(at least for firms in a steady state).

The approach used to devise Formula 1-11 can also be applied in the context of

the PVM(T). The rate of return to the firm’s entire capital stock is given in

Formula 1-12.

(Formula 1-12) ( )

( ),

where r* in this case is the rate of return to all of the firm’s invested capital,

inclusive of its intangible capital.

Formula 1-12 is a clear departure from most of existing valuation theory and

practice. As is well known, the relationship between the firm’s rate of return to

invested capital (ROIC) and its cost of capital (WACC) is the key determinant of

whether enterprise value is growing. Firms that earn more than their cost of

capital (ROIC > WACC) are by definition increasing shareholder value. The

value of what they produce by combining inputs is greater than the cost of those

inputs, and this incremental value creation is captured by shareholders through

share price growth.

However, valuation theory also recognizes that, in practice, measured ROIC

generally involves a mismatch between numerator (NOPAT) and denominator

(IC). The measured invested capital in the denominator of ROIC generally omits

19 See Hall, Mairesse, and Mohnen, Measuring the Returns to R&D, National Bureau of Economic

Research Working Paper 15622, December 2009.

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intangible capital, resulting in an upward bias to ROIC. While some attempts

have been made to adjust for this, the reliability and generality of such

adjustments is unclear.20

Formula 1-12 offers the surprising conclusion that, in a steady state, a company’s

actual ROIC – i.e., its return on all of its capital inclusive of its intangible capital –

is a function solely of the firm’s measurable enterprise free cash flow, prior period

total capital investments, and growth rate. This means that the proper way to

account for the presence of intangible capital when measuring a firm’s return on

its total capital base is simply to estimate the ratio given in Formula 1-12.

This result also alleviates a longstanding concern in economics that accounting

rates of return cannot reliably measure economic rates of return, at least for firms

in a steady state. Fisher and McGowan (1983), in a famous article, demonstrate

that “only by the merest happenstance will the accounting rate of return on a

given investment … be equal to the economic rate of return that makes the

present value of the [profit] stream equal to the initial capital cost [internal rate of

return]. … Unless depreciation schedules are chosen in a particular way, so that

the value of the investment is calculated as the present value at the economic rate

of return of the stream of [profits] remaining in it – a choice that is exceptionally

unlikely to be made – the accounting rate of return will differ year to year and

will not in general equal the economic rate of return on the investment in any

year.”21 Formula 1-12, however, turns out to provide just such a measure of the

economic rate of return (r*), and it includes the returns to the firm’s intangible

capital investments as well as its returns to tangible and financial capital.

D. Valuation Models, Rates of Return, and the Competitive

Advantage Period

In practice, most enterprise valuations model a firm’s cash flows in two stages –

an “explicit forecast period” followed by a terminal value period. The former

takes into account all of the information that is known about the firm’s cash

flows, and is generally between two and five years in length. The latter period

represents a steady state that is generally assumed to extend into perpetuity.

20 See, for example, Aswath Damodaran on this point, at

http://people.stern.nyu.edu/adamodar/pdfiles/papers/returnmeasures.pdf. 21 See Franklin M. Fisher and John J. McGowan, “On the Misuse of Accounting Rates of Return to

Infer Monopoly Profits,” American Economic Review, Vol. 73, No. 1, March 1983, pp. 82-97.

http://people.stern.nyu.edu/adamodar/pdfiles/papers/returnmeasures.pdf

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In this kind of model setup, the terminal value should assume a growth rate that

represents a blend (technically, a present value weighted average) of the growth

rate over the very long run, and the growth rate during the “intermediate run”

that follows the explicit forecast period. Because the firm’s growth rate is equal

to the rate at which it invests in new capital times the rate of return on that new

capital, valuation models should incorporate a proper relationship between their

profitability assumptions (rate of return assumptions) and their growth rate

assumptions. Valuation models should assume intermediate and long run

growth rates that are consistent with formula 1-10, and consistent with the way

in which competitive dynamics influence rates of return.22

Valuation theorists have offered several models that describe a firm’s expected

future growth rates in a way that is consistent with the fact that competition

erodes rates of return (and therefore erodes growth rates). These include the H

Model (a two stage model) the three stage model, and more general multi-stage

models. Most of these models simply make assumptions about the time path of

growth rates, assuming it to behave in a certain way during the initial forecast

period, and transition to a long run steady state during a transitional period, and

then remain constant during the final stage of the company’s life cycle. In other

words, growth rates are modeled directly, rather than modeling both a firm’s

rate of investment in new capital and the rate of return earned on that new

capital.

The reason for modeling growth rates directly is that it is much easier than

modeling growth by first modeling the competitive dynamics surrounding r*,

then modeling the firm’s investments, and finally computing the growth rate as

r* × new capital in each period. Moreover, the fact that much (perhaps most) of

the firm’s new capital is intangible capital, which is hard to measure without a

way to estimate N, also complicates this formal approach.

We show in Chapter 3 that the PVM can easily be extended to a multi-stage

model. Because the centerpieces of the PVM are r* and N, and because we have

devised a way to measure both of these variables using income and cash flow

statement information, we also show that this multi-stage version of the PVM

22 Empirically, margins and rates of return for very profitable companies tend to revert

downward to the industry mean. Similarly, margins and rates of return for companies that earn

below average profits revert upward to the mean. Enterprise growth rates tend to exhibit the

same kind of mean reversion – not surprisingly, given the relationships described in formulas 1-

10 and 1-11. See Koller, Goedhart, and Wessels, Valuation: Measuring and Managing the Value

of Companies. (Wiley: 2010), University Edition, p. 97.

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allows us to relate profit growth directly to changes in the rate of return on

investments.

This, in our view, provides three distinct advantages over existing multi-stage

approaches that model growth rates directly.

First, it focuses attention directly on the underlying economic processes that

determine value growth. Per formulas 1-10 and 1-11, the rate of return on new

capital and the firm’s investment rate together govern value and value growth.

The rate of return on new investments is thus the key variable that competitive

processes act upon. Competition centers on the rate of return to invested capital,

and forces this rate of return toward an equilibrium level (the WACC) over time.

Therefore, when applying the multi-stage PVM, the analyst is forced to center his

or her attention on the same thing that markets focus on – that is, r*. The analysis

is thus explicit about the firm’s ability to earn monopoly rents, and for how long.

Second, the multi-stage PVM guarantees consistency between the assumed rate

of profit growth and the assumed rate of return to capital. Recall that enterprise

value is simply the present value of all future R-I (net residual profit).23 Starting

with Formula 1-11, a little algebra tells us that we find that we can obtain R-I for

future periods by multiplying I in each forecast period by:

Formula 1-13 ( ( )

( )).

Note that is just the rate of return, r*, adjusted by a factor involving g. As we

demonstrate in Chapter 3, this allows us to directly model changes in the rate of

return, r*, through time, then apply these rates of return to the firm’s investments

in IDCs in each period (I) in order to obtain forecast net residual profit. The logic

works identically in the PVM(T), allowing us to obtain future enterprise free cash

flows, F-K, in each period by multiplying each future period’s K by the same

factor shown in Formula 1-13, except that r* in that formula is the r* for the firm’s

total, rather than only intangible, capital investments. In such a model setup, we

are guaranteed that profit growth is logically consistent with the way in which

competitive dynamics affect the firm’s rate of return.

In many applied contexts this can be extremely useful. For example, we might

know that a company is going to introduce a new product that embodies a

23 Plus physical and financial capital.

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patented technology. The company may also have provided guidance that this

new product will expand margins by a certain amount, for a certain period of

time. Using the formulas for , we can infer the firm’s expected rate of return on

its investments (IDCs for example) from the firm’s margin guidance. We can

also compare these anticipated rates of return to rates of return earned by similar

firms in the industry, and examine the speed at which high rates of return revert

to the mean in the industry. Taken together, this information might allow us to

model the firm’s changing cash flows during the period for which guidance is

available, and thereafter using industry rate of return dynamics. Thus, by

forcing an explicit focus on r*, the multi-stage PVM contributes to more

disciplined thinking about competition, rates of return, and growth through

time. We provide an illustration of this in Chapter 3.

Finally, the multi-stage PVM allows us to make sense of, and measure

empirically, a concept that has existed in somewhat inchoate form in the

valuation literature for some time. The multi-stage PVM allows us to understand

and empirically measure something called the Competitive Advantage Period.

In Miller and Modigliani’s aforementioned 1961 paper, a concept was introduced

that later become known as the competitive advantage period or CAP. The

competitive advantage period is defined as the time horizon over which the firm

expects to earn returns in excess of its cost of capital. The Miller-Modigliani 1961

paper related the competitive advantage period to the valuation of an enterprise,

showing that a firm’s value is the present value of its “normal” or “routine”

profits, plus the value of economic profit over some competitive advantage

period.

Importantly, in the Miller-Modigliani paper, the competitive advantage period is

subjectively determined. In other words, Modigliani and Miller provide no

guidance regarding how to measure the competitive advantage period, and offer

no examination of the relationship between the firm’s other financial variables

and the competitive advantage period.

Mauboussin and Johnson later explored the notion of the CAP in a paper entitled

Competitive Advantage Period: The Neglected Value Driver.24 However, they also

failed to arrive at an objective measurement of the CAP period. In their paper,

Mauboussin and Johnson note that the CAP is determined by internal and

24 Michael Mauboussin and Paul Johnson, “Competitive Advantage Period: The Neglected Value

Driver,” Credit Suisse First Boston, Equity Research – Americas, January 14, 1997.

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external factors including management strategy, competitive position within the

industry, and government regulations. In other words, for Mauboussin and

Johnson, CAP is subjective.

The multi-stage version of the PVM allows us to make CAP explicit, and

demonstrates that it can be inferred from market valuations. In order to see this,

we provide a summary of the multi-stage PVM below.

The multi-stage PVM models a company’s future cash flows in three phases.

Phase 1 is an explicit forecast period covering a period of time, T1, that we obtain

from company information. T1 can, for example, derive from analyst’s forecasts,

or from other company guidance. During Phase 1, the company’s r* is constant

at a high (or low) rate relative to the industry average or required rate of return.

Phase 2 is a transitional stage of duration T2. Phase 2 connects the explicit

forecast period and a long run steady state. During Phase 2, the company’s rate

of return on new capital is declining (or rising) from its Phase 1 level to its long

run steady state level. As r* changes during Phase 2, the firm’s margins and rate

of growth in profits also change (because net residual profit is simply I × , and

is a function of r*). Finally, the firm’s long run steady state, Phase 3, is an

equilibrium stage that extends into perpetuity. In Phase 3, the firm arrives at

either the industry average r*, or at an r* equal to r.

The formulas for the multi-stage PVM are given directly below. A full derivation

is provided in Chapter 3.

(Formula 1-14) ,

where V is enterprise value, and VP1, VP2, and VP3 are as follows.

(Formula 1-15)

( ( ) )

.

(Formula 1-16)

( ) ( ( ) )

.

(Formula 1-17)

( )( )

.

(Formula 1-18)

.25

25 Note that is simply Formula 1-13 with r substituted for r*.

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The multi-stage PVM assumes that during the transitional period, P2, the firm’s

reverts to the level reflecting the industry mean (or WACC), i.e., it reverts to ,

following an exponential decay rate of δ. Mathematically, if we assume that

will revert to at the end of period 2, we have = e-δ(T2-T1). This allows us to

solve for the decay rate given in Formula 1-17.

The important thing about formulas 1-13 through 1-17 is that the only variable

that is not a given is T2, the duration of the transitional period. Everything else

in the multi-stage PVM is observable from forecast and/or market information.

This means that we can simply solve for T2 such that equals V

(the firm’s observable market enterprise value). In other words, because we have

all of the firm’s other key variables – i.e., its r*, r, its initial I, and the rate of

growth of its investments, I, and given the assumption that r* is competed

downward (or it rises) to the WACC following an exponential rate of decay (as

with most decay rates in nature), we can solve for T2 if we know V. There is a

market-implied T2.

If there is a market-implied T2, then there is market-implied Competitive

Advantage Period that is equal to T1 + T2. We have a way, then, to make the

concept of the Competitive Advantage Period both theoretically meaningful, and

empirically observable. Exhibit I-5, below, depicts this graphically.

30

DRAFT

Exhibit I-5: Multi-Stage PVM and the Competitive Advantage Period

Because the PVM provides us with an ability to infer r*, and to relate r* to net

residual profit, we can infer the competitive advantage period whenever we can

measure V. Alternatively, of course, if we assume a T2 in a multi-stage PVM,

then V is implied by our assumed parameters.

E. Relating Gross and Net Valuation Methods (Wasting Asset and

Ongoing Maintenance Methods) to One Another

There are two primary types, or categories, of valuation methods. In this book,

we call these “gross” and “net” methods. We also refer to these as “wasting

asset” and “ongoing maintenance” methods, respectively. Another important

contribution of the PVM is that it uncovers an important relationship, which has

gone largely unnoticed, between these two categories of methods.

A gross, or wasting asset, method values an asset assuming that the asset decays

in value to zero over a finite economic life, N. The intention of a wasting asset

method is to identify and value an identifiable asset, rather than the asset and all

of its progeny (future generations of the same asset category). Wasting asset

methods therefore treat an asset as a discrete, finite-lived, productive unit that

can generate cash flow over its economic life irrespective of whether the firm

r*

Time

T3 →T1 (Given)

T1 + T2 = CAP (Period During Which r * > r )

T2 (Inferred From V and PVM Equations)

r* (T1 )

r*= r

31

DRAFT

makes ongoing IDC or other investments in the future generations of the asset

category.

Because wasting asset methods seek to determine the value of the existing

generation of an asset category, without reference to future generations

(goodwill), these methods model the gross cash flows from an asset (cash flows

without reference to any ongoing investments in future generations of the asset

category) as a cash flow stream that declines to zero. Thus, the value of an asset

under a gross method is the present value of the declining stream of gross cash

flows from the asset.

By contrast, net methods value an asset in a very different way. As the name

implies, net methods discount the net cash flows (net of ongoing investments in

future generations) of an asset category, beginning with period 1, into perpetuity.

In one sense, net methods are based upon a more realistic depiction of the cash

flows that an asset owner can expect to receive, because net methods recognize

that asset ownership implies the right to “reinvest” in the asset category in order

to regenerate it through time, so long as reinvestment is NPV>0. Thus, net

methods recognize that an asset owner’s actual cash flow (what he or she can

consume) is the net cash flow (net of ongoing investments) in each period and,

given that investment, these net cash flows may continue indefinitely.

Thus, the difference between gross and net methods is that the latter (net

methods) are designed to capture any goodwill value associated with a given

asset or asset category, whereas the former (gross methods) capture only the

value of the existing generation of the asset category. This distinction should

already be familiar to the reader, having seen it in the formulas for VIA and G.

That is, gross methods are VIA methods. Net methods capture both VIA and G.

This brings to the relationship between the two methods. As we show in

Chapter 2, this means that whenever r* = r, net and gross methods provide

exactly the same answer – because there is no value today of future investments

in future generations (they are NPV=0).

F. Empirical Evaluation and Performance of the PVM

Models are built to be tested. Their purpose is to describe, explain, and predict.

The question, then, for any model is how well it accomplishes these purposes.

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DRAFT

Therefore, a final important contribution of this book is that it includes some

important and interesting tests that we have conducted of the PVM. As we relay

in Chapters 5 and 6, the long run behavior of N, r*, VIA and G, provides

interesting insights into stock market valuation in the real world, and long run

value equilibria. The G/V ratio – that is, the ratio of goodwill to market

enterprise value – is found to be mean reverting and predictive of future values.

We find that both N and r* are strongly mean reverting, and vary in interesting

and intuitive ways across industries.

IV. How to Use this Book

A. Overview of Remaining Chapters

The chapters that follow are ordered in such a way as to allow the reader to

move from theory to application. Chapters 2 and 3 provide the intuition and

derivation of the PVM, along with a careful examination of the underlying

relationships within the model. Chapter 3 completes the theory section of this

book. Chapter 4 begins the applied section by providing an example of a

valuation that employs the PVM. Chapters 5 and 6 are empirical in nature, and

evaluate the PVM’s ability to describe and explain firms’ values and value

composition through time. Chapter 7 is a description of the Excel™ models

included with this book (more on that directly below). Chapter 8 concludes.

B. Excel™ Models

We include a fully functioning Excel™ application with this book, which should

allow the reader to apply the PVM to his or her own valuation projects. The

Excel™ Application consists of five primary modules that handle and normalize

company data (Module 1), derive r* and r (Module 2), derive N and VIA or VA

(Module 3), compute G and G/V (Module 4), and provide graphs and summary

analytical information (Module 5).

While we have made every effort to ensure that the Application is accurate and

properly functioning, we encourage readers who identify errors (which are sure

to exist) to contact us at [email protected] with bugs and/or

bug fixes.

mailto:[email protected]

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