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Intangible Asset Remaining Useful Life Analysis for Bankruptcy Purposes

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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.

Impact of RUL on Valuation

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.

Determinants to RUL

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

  • permits
  • patents
  • non-compete agreements
  • copyrights
  • trademarks and trade names
  • certificates of need
2. Contractual Determinants
  • contracts (supplier or customer)
  • leases
  • licenses (FCC, etc.)
  • permits
  • franchises
3. Functional Determinants
  • customer files and documentation
  • computer software
  • automated databases
  • patented or unpatented technology
  • trade secrets
  • systems and procedures
4. Technological Determinants
  • proprietary technology
  • technical documentation
  • engineering drawings
  • technological know-how
  • training materials and documentation
5. Economic Determinants
  • development or exploitation rights
  • proprietary technology
  • trademark and trade name licenses
  • product formulations
  • advertising and promotional materials
6. Analytical Determinants
  • customer relationships
  • subscriber lists
  • patient relationships
  • core deposit accounts
  • distribution networks
  • loan or credit card portfolios

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.

RUL Analysis Methods

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.

Survivor Curve Analysis

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:

  1. average service life,
  2. total life, and
  3. average remaining life.

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 =



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 =



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 =



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

Construction of an Illustrative Survivor Curve

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:

  1. In Figure 2, we are looking at the "experience band" of historical engineering drawing placement and retirement data for the years 1993-2000.
  2. 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.
  3. 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).
  4. 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."

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

  1. 34.19 percent of the observation period population of engineering drawings survived at the beginning of the five- to six-year age interval.
  2. 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.
  3. 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.

Constructed Survivor Curve

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.

Statistical Curve-fitting Procedure

The following procedures summarize the statistical curve-fitting process.

  1. 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).
  2. 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).

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

  1. Iowa-type curves,
  2. exponential curve (the exponential function is a special case of this type of survivor curve),
  3. Weibull distribution (the Iowa-type curves themselves are a special case of this type of survivor curve),
  4. Gompertz-Makeham curves,
  5. J curves, and
  6. polynomial equations.

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?"

Summary and Conclusion

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:

  • physical life,
  • functional life,
  • technological life,
  • economic life,
  • contract life,
  • statutory/judicial life,
  • legal/regulatory life, and
  • actuarial mortality life.

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.



Journal Date: 
Thursday, March 1, 2001

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