Intangible Asset Remaining Useful Life Analysis for Bankruptcy Purposes

Journal Issue

Mar 2001

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The estimation of remaining useful life (RUL) is an important component of intangible
asset valuation. The relevance of RUL analysis is obvious in the application of the
income approach to valuation. Whether a yield-capitalization method or a
direct-capitalization method is used, RUL analysis is necessary to determine the time
period over which income (however measured) is capitalized. RUL analysis is also
relevant to the cost approach and the sales-comparison approach to valuation. In the
cost approach, the estimation of RUL is one procedure for quantifying any external
obsolescence. And, in the sales-comparison approach, the estimation of RUL is one
factor in selecting and adjusting intangible asset guideline sale/license transactions.

The estimation of RUL is a particularly important procedure in intangible-asset
analyses for bankruptcy and reorganization purposes. This is true for intangible-asset
analyses performed for purposes of secured-lender collateral valuation, spin-off
opportunity identification, intangible-asset sale/leaseback, debtor-in-possession
financing, troubled-loan workout and proposed-plan-of-reorganization assessment. For
each of these analytical purposes, consideration of the intangible's RUL is a relevant
procedure.

This column will review the application of RUL analyses to all intangible
asset-valuation approaches. The principal "determinants" of an intangible's RUL will be
discussed. The causes of intangible-asset attrition or obsolescence will be explored.
The application of a particularly useful RUL estimation method—the analytical method—will
be discussed. The definitions and mechanics of analytical-method survivor-curve analysis
will be explained. The construction of a survivor curve and the associated curve
fitting procedure will be illustrated. Also, an illustrative example of the analytical
method will be presented.

<h3>Impact of RUL on Valuation</h3>

The estimation of RUL is a part of each intangible-asset valuation approach. In
the income approach, the RUL is used to estimate the projection period of economic
income for either yield capitalization or direct capitalization. In the cost approach,
RUL is used to estimate the total amount of obsolescence, if any, from the estimated
measure of "cost." This is the case whether "cost" is measured as reproduction,
replacement, creation or recreation cost. In the sales-comparison approach, RUL is
used to select, reject or to adjust "guideline" sale or license transactional data.

In the income approach, a longer RUL normally results in a higher value. This
is because the greater the intangible's life, the greater the total amount of
capitalized economic income. An intangible's value is particularly sensitive to the RUL
estimate when the remaining life is less than 10 years. An intangible's value is
not very sensitive to the RUL estimate when the remaining life is greater than 20
years.

In the cost approach, a longer RUL normally results in a higher value. A shorter
RUL normally results in a lower value. This is because an intangible with a long life
probably suffers from less obsolescence. On the other hand, an intangible with only
a two- or three-year RUL probably suffers from a significant amount of obsolescence.
After all, the intangible is about to become obsolete.

In the sales-comparison approach, the market should indicate an acceptance for the
intangible's RUL. If the subject's RUL is different from guideline sale/license
transactions, then adjustments to the transactional pricing multiples may be required.
If the subject's RUL is substantially different from the guideline sale/license
transactions, then this may indicate a lack of marketability of the subject intangible
(due to a lack of market demand for its age/life characteristics). For example,
if the subject has a two-year RUL, and all of the guideline sale/license transactions
relate to intangibles with at least a 10-year RUL, this may indicate that the
market does not demand a short-lived intangible.

<h3>Determinants to RUL</h3>

The following list presents several of the detriments, or factors, that influence
an intangible's RUL. This list includes examples of typical intangibles that are
influenced by the indicated determinant.

1. Legal Determinants
<ul>

<li>permits

</li><li>patents

</li><li>non-compete agreements

</li><li>copyrights

</li><li>trademarks and trade names

</li><li>certificates of need</li></ul>

2. Contractual Determinants
<ul>
<li>contracts (supplier or customer)

</li><li>leases

</li><li>licenses (FCC, etc.)

</li><li>permits

</li><li>franchises</li></ul>

3. Functional Determinants
<ul>
<li>customer files and documentation

</li><li>computer software

</li><li>automated databases

</li><li>patented or unpatented technology

</li><li>trade secrets

</li><li>systems and procedures</li></ul>

4. Technological Determinants
<ul>
<li>proprietary technology

</li><li>technical documentation

</li><li>engineering drawings

</li><li>technological know-how

</li><li>training materials and documentation</li></ul>

5. Economic Determinants
<ul>
<li>development or exploitation rights

</li><li>proprietary technology

</li><li>trademark and trade name licenses

</li><li>product formulations

</li><li>advertising and promotional materials</li></ul>

6. Analytical Determinants
<ul>
<li>customer relationships

</li><li>subscriber lists

</li><li>patient relationships

</li><li>core deposit accounts

</li><li>distribution networks

</li><li>loan or credit card portfolios</li></ul>

Each of these determinants should be considered in the intangible's RUL estimation.
Typically, for bankruptcy-related purposes, the determinant that indicates the shortest
RUL deserves primary consideration. For example, if an intangible has a remaining
contract life of 10 years, but an expected remaining functional life of four years,
the shorter indication of life (i.e., four years) is typically more relevant to
the bankruptcy valuation.

<h3>RUL Analysis Methods</h3>

There are several RUL analysis methods that relate to the above-listed life
determinants. The statutory method relates to the legal determinant and involves looking
to the statutorily defined legal life of a patent, copyright, trademark, etc. The
contractual method relates to the contractual determinant and involves looking to the
contractually defined term of the license, franchise, non-compete agreement, etc.

Economic life-cycle analysis and technology life-cycle analysis methods are often
used to estimate the RUL of certain intangibles. The description of these methods
deserves more space than is available in this column. This column will focus on the
analytical method. For the most part, each of the other RUL methods is based on
one life determinant—or one reason why the intangible has a finite, predictable life.
In contrast, the analytical method is influenced by several life determinants. In
other words, the analytical method RUL estimate is the synthesis of many different
reasons for the finite utility of an intangible. The analytical method is something
of an "all-purpose" RUL method and is, therefore, particularly applicable to
bankruptcy-related analyses.

There are two procedures related to the analytical method: (1) estimation of a
historical "attrition rate" (or retirement rate), and (2) development of a "survivor
curve," based on the historical attrition rate.

<h3>Survivor Curve Analysis</h3>

Figure I is a graphical representation of a "survivor curve" analysis as part of
the analytical method to RUL estimation (see original Journal article; cannot reproduce chart here).

The following life measurements are important components of survivor-curve analysis:
<ol>
<li>average service life,

</li><li>total life, and

</li><li>average remaining life.</li></ol>

The definitions of these life measurements are presented below:

1. Average service life (ASL)—the total number of years (or other defined time
periods—e.g., months, quarters, etc.) of service provided by the population of
intangibles divided by the number of individual intangibles (e.g., number of
engineering drawings) in the population.

Area Under the Complete Survivor Curve 
ASL = <hr width="30%"> 
Total Number of Individual Intangibles (at Age Zero)

The area under the survivor curve can be approximately calculated by adding the
height of the survivor curve (i.e., the percent surviving on the y axis of Figure
1) at each service age (i.e., 0, 1, 2, etc. years on the x axis of
Figure 1).

2. Total life (TL)—the maximum life of the last surviving individual intangible
from the population of intangibles. In the illustration in Figure 1, the TL is
approximately 30 years. This is the point where the survivor curve becomes asymptotic
to (or runs along) the X axis.

3. Average remaining life (ARL)—similar to the ASL, except that it is defined
as of a specific current age of a "seasoned" intangible (i.e., an intangible that
is already in service)—rather than at age zero (i.e., rather than for a brand new
intangible that is just about to be placed in service).

Area Under the Survivor Curve to the Right of a Particular Age
 ARL = <hr width="30%"> 
Number of Individual Intangibles Surviving at that Particular Age

Based on the survivor curve illustrated in Figure 1, the average service life
(or average life) of this hypothetical population of intangibles is approximately 12
years. This means that the average expected life of a brand new intangible (e.g.,
an engineering drawing) in this population (e.g., group of drawings) will be 12
years. The total life of this population (i.e., the age at which the very oldest
drawing retires) is approximately 30 years.

By comparing the survivor curve (for this population of intangibles) to its
corresponding probable life curve (that will be explained below), we can estimate the
RUL of an individual intangible (e.g., drawing) of any particular age. The average
life of brand new drawings is approximately 12 years. Now, let's use Figure 1
to estimate the RUL of an individual drawing that is already 14 years old. Given
(1) the average life of 12 years, (2) the average age of the subject drawing
of 14 years, and (3) the shape and slope of the survivor curve (that reaches
a total life of 30 years), the probable life of the subject intangible is 18
years. This means that the average remaining life or expected RUL of a 14-year-old
drawing within this population of drawings is approximately four years (i.e.,

18-year probable life minus 14-year actual age).

The following definitions are also important in survivor curve analysis:

Number of Individual Intangibles Retired During a Time Period
 1. Retirement Ratio = <hr width="30%"> 
Number of Individual Intangibles Exposed Ratio to Retirement (i.e., actually in service) at the Beginning of the Time Period

2. Survivor Ratio = 1 - Retirement Ratio

<h3>Construction of an Illustrative Survivor Curve</h3>

The following example illustrates the construction of a survivor curve. Figure 2
presents the "placements" and "retirements" of engineering drawings for the Illustrative
Manufacturing Co. The engineering drawings are the blueprints (including all associated
technical documentation) used in the manufacture of each product made by Illustrative (see original Journal article; cannot reproduce chart here).
The drawings are created by engineers and draftsmen. In addition, the drawings are
used by the technicians on the shop floor to actually manufacture and assemble the
proprietary high-tech Illustrative products.

Many of Illustrative's products are patented, and many of Illustrative's
manufacturing processes are patented. These engineering drawings encompass proprietary
technical know-how. Illustrative's management considers these drawings to be very
valuable intangible assets of the company.

From these hypothetical data regarding "placements" (that is, an individual engineering
drawing first created for the manufacture of a current product) and "retirements" (that
is, when the individual drawing is categorized as inactive because the associated product
is no longer in production), we will perform a survivor-curve analysis. The objective
of the survivor curve analysis is to estimate the RUL of the Illustrative engineering
drawings as of Dec. 31.

Figure 2 summarizes the empirical data regarding all of the engineering drawings
that were created ("placements") and taken out of active use ("returnments") at the
company during the observation period of 1993-2000. This observation period is
also called the "experience band."

In Figure 2, Illustrative had eight years of historical placement and retirement
data available. There is no formula to quantify the "right" number of historical
periods in the observation period. As with any statistical analysis, the more data
available (i.e., the longer the "experience band"), the greater the accuracy of
the analysis. However, there is no procedure to directly associate the number of
historical periods in the "experience band" to the analyst's level of confidence in the
RUL estimate.

The following observations regarding Figure 2 help us to construct the survivor curve
for the Illustrative engineering drawings:

<ol>
<li>In Figure 2, we are looking at the "experience band" of historical
engineering drawing placement and retirement data for the years 1993-2000.

</li><li>Because Illustrative has maintained actuarial data, the age of each "retired"
intangible (i.e., each drawing that has become inactive) is known. That is, we
know how old each drawing was when it was transferred from active (in use) status
to inactive (not in use) status.

</li><li>Going horizontally across for 1994 (i.e., row 1994), we see that,
of the 15 surviving drawings at the beginning of 1996 (column 1996), two
drawings were retired during 1996. That is, we know the age of these two drawings
to be two years when they retired (i.e., when they became inactive for whatever
reason).

</li><li>The survivor curve is constructed by combining elements of "like" age groups.
For example, lets consider the age group of 5-6 years old (i.e., the
highlighted areas in Figure 2). These are the engineering drawings that have
"survived" four years (i.e., are still in service) and are exposed to the fifth
year of service. In 1995 (column 1995), two drawings from 1990 (row
1990) have also survived four years (1991 to 1994). In addition, six
of the 1994 placements (row 1994) would be four years old in 1999
(column 1994) and would be exposed to their fifth years of "service."
</li></ol>

Based on the Illustrative engineering drawing age and life data, we know that:

<ol>
<li>34.19 percent of the observation period population of engineering drawings
survived at the beginning of the five- to six-year age interval.

</li><li>11.76 percent of the observation period population of engineering drawings
retired during the five- to six-year age interval. That is, of the 34.19
percent, 34.19% x 0.1176 = 4.03% will retire—or become inactive during
this age interval.

</li><li>34.19%-4.03% = 30.16% of the observation period population of
engineering drawings survived (i.e., still in "service") at the end-of-age
interval five to six years—in other words, at the beginning of age interval 6-7
years.</li></ol>

<h3>Constructed Survivor Curve</h3>

Figure 3 presents the Illustrated engineering drawing survivor curve that results
from plotting the data in the Survivor Curve column (from bottom to top) from
Figure 2 (see original Journal article; cannot reproduce chart here). This "actual survivor curve" is the curve that is represented by the
squares. The "fitted survivor curve" is the curve that is represented by the plus
(+) figures.

The actual survivor curve is often called the "stub curve." That is because the
actual survivor curve does not extend down to the X axis (i.e., to zero percent
surviving). The reason for this is because the data in the Survivor Curve column
in Figure 2 do not reach zero percent. This is because many of the engineering
drawings that Illustrative created during the eight-year observation period are still
in service at the end of the period.

The fitted-survivor curve is any curve (i.e., any mathematical function) that
best overlays the actual survivor curve. Since the fitted survivor curve is the
graphical representation of a standard mathematical function, the fitted curve becomes
asymptotic to the X axis. That is, it ultimately reaches zero percent surviving. The
standard mathematical function could be any equation (although it is typically a
quadratic equation) that results in a downward sloping decay pattern.

<h3>Statistical Curve-fitting Procedure</h3>

The following procedures summarize the statistical curve-fitting process.

<ol>
<li>Curve-fitting—Fit the actual survivor curve to the standard mathematical
function that best matches the actual curve's decay function (i.e., shape and
slope). These standard (or known) mathematical functions result in what are standard
(or known) survivor curves. The actual stub curve is compared to numerous standard
curves. The actual stub curve is usually fitted to the best-fitting standard curve
by the process of sum of ordinary least squares (or OLS).

</li><li>Extension of the Stub Curve—Extend the actual stub curve to match the fitted
standard curve. That is, extrapolate the actual stub curve to equal the remaining
portion of the standard curve. The extrapolated actual survivor curve will then reach
the zero percent surviving level (i.e., the X axis on the graph).</li></ol>

The actual survivor curves are typically fitted to the following types of standard
survivor curves:

<ol>

<li>Iowa-type curves,

</li><li>exponential curve (the exponential function is a special case of this type of
survivor curve),

</li><li>Weibull distribution (the Iowa-type curves themselves are a special case of
this type of survivor curve),

</li><li>Gompertz-Makeham curves,

</li><li>J curves, and

</li><li>polynomial equations.</li></ol>

It is noteworthy that each of these types (or families) of curves represents an
almost limitless number of standard curves. This is because each type (or family)
of curves can take on a wide range of shapes, slopes and sizes. It is also
noteworthy that the standard survivor curves are just the graphical representations of
mathematical equations.

Figure 1 also illustrates three other important components of the analytical method.
The first component is the estimation of the average life of the observed population
of intangibles. The average life of the population is exactly the point where each
curve passes through the 50 percent surviving line of the Y axis. At the point
where the survivor curve hits the 50 percent surviving line, the analyst drops a
line to the X axis. The age at which that line intersects with the X axis is the
average life of the population of intangibles.

If the question is, "What is the average life of all brand new Illustrative
engineering drawings?" the analyst can answer that question at this point in the
analytical method. However, if the question is, "What is the expected RUL of all
of the Illustrative drawings currently in use?" then the analyst has to perform
additional procedures. This is because the RUL of the population of active drawings
is a function of both (1) the average life of new drawings and (2) the average
age of the active drawings.

The second component is a set of frequency curves. Frequency curves plot the age
of each intangible in the population as a percentage of the population's average life.
For example, if an individual intangible is five years old and the average life of
all new intangibles is 10 years, then that intangible is plotted at 50 percent
of the average life. There is a unique frequency curve related to each survivor
curve. The frequency curves are used to construct the probable life curve. The
relationship of (1) an individual survivor curve and (2) its corresponding
unique-frequency curve is used to derive (3) a unique probable-life curve.

The third component is the series of probable-life curves. The probable-life curves
are used to answer the question, "What is the expected remaining life of an intangible
that is already X years old?" The probable-life curves are used to answer this RUL
question on either (1) a population-wide basis or (2) an individual intangible
basis. For example, the derived probable-life curve can answer this question: "What
is the expected remaining life of all Illustrated engineering drawings if the average
age of the current drawings is six years?" Likewise, the derived probable-life curve
can also answer this question: "What is the expected remaining life of Illustrative
drawing #1234 if its current age is 12 years?"

<h3>Summary and Conclusion</h3>

The estimation of an intangible's RUL will impact the results of any valuation
approach. For example, an intangible with an expected remaining life of three years
will have a lower depreciated replacement cost than the same intangible with an expected
remaining life of 15 years, all other factors held equal. The shorter-lived
intangible (1) will also generally fetch a lower market-derived transaction price
royalty rate and (2) will produce economic income for a shorter period of time
(than an identical longer-lived intangible).

These expected-life/value relationships hold true for a population (or group) of
intangibles, such as all of the Illustrative drawings. In addition, these
expected-life/value relationships also hold true for an individual intangible—such as
Illustrative drawing #1234.

There are numerous ways to measure an intangible's RUL, such as:
<ul>
<li>physical life,

</li><li>functional life,

</li><li>technological life,

</li><li>economic life,

</li><li>contract life,

</li><li>statutory/judicial life,

</li><li>legal/regulatory life, and

</li><li>actuarial mortality life.
</li></ul>
Generally, the shortest of these RUL measures is used in bankruptcy-related
analyses.

There are also numerous methods available to quantify the RUL of intangibles. This
column focused on the analytical method. If adequate historical age and life data are
available, the analytical method can be used to objectively quantify the RUL of an
intangible. The analytical method can be used to estimate the RUL of either (1)
an entire population of intangibles (e.g., all Illustrative drawings) or (2) an
individual intangible (e.g., Illustrative drawing #1234). Also, the analytical
method can be used to estimate the RUL of an intangible at any age (e.g.,

Illustrative drawing #1234 that is 14 years old versus Illustrative drawing
#4321 that is four years old).

Compared to other RUL methods, the analytical method provides a precise point life
estimate—as opposed to a range of possible life estimates. The analytical method is
mathematically replicable. Presumably, a second analyst could recreate the analysis of
the first analyst. The analytical method is objective rather than subjective. That
is, the method is influenced by empirical actuarial data and, presumably, not by
the biases of the analyst.

The analytical method is influenced by all factors affecting an intangible's life
characteristics. Most other RUL methods (e.g., technology life-cycle analysis,
economic life-cycle analysis, etc.) only encompass one influence on an intangible's
life. The analytical method is indifferent as to what factors caused the intangible
placements and retirements. The factors could be economic, social, political,
functional, technological, legal, etc. Therefore, the analytical method captures all
of an intangible's life influences in its analysis—and in its RUL estimate. Therefore,
the analytical method is particularly applicable to bankruptcy-related analyses.

<hr>

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<td valign="top" width="125">

Journal Authors

Robert F. Reilly

Journal Date

Thursday, March 1, 2001 - 12:00

Bankruptcy Rule

2001