Intellectual properties are a specific category of general commercial intangible assets. Intellectual property is distinguished from general intangible assets by (1) special legal recognition/protection and (2) enhanced economic commercialization opportunities. Intellectual properties receive special legal recognition under either federal or state statutes. Because of this legal recognition, it is relatively easy to transfer (e.g., license) limited intellectual property (IP) ownership rights. Therefore, an IP has income earning potential to both the IP owner (e.g., licensor) and IP operator (e.g., licensee). Accordingly, IPs typically have greater commercialization potential than general intangible assets.

There are four types of IPs: copyrights, patents, trademarks and trade secrets. These four types of IP are often subject to valuation (or other economic analysis) in a commercial bankruptcy context. An IP may be the collateral for secured lender or DIP financing. An IP may provide immediate cash flow opportunities for the DIP in the form of sale/leaseback or license/ exploitation transactions. Trade secrets are one of the four types of intellectual properties.

A bankruptcy-related valuation analysis estimates a defined standard (or type) of value for the use or exchange of (1) an IP, (2) a collection of IPs or (3) certain specified legal rights in an IP. A valuation analysis would also estimate the fair, arm's-length license fee or royalty rate for the license of specified rights in an IP.

All of these analyses involve some procedures for estimating the remaining useful life (RUL) of the subject IP value, value decrement, lost historical/future income, transfer price or royalty rate. All of the generally accepted IP valuation approaches consider (implicitly or explicitly) the IP RUL.

This discussion will present a methodology for estimating IP RUL. The suggested methodology is properly referred to in the professional appraisal literature as the analytical method. However, it is frequently called the survivor curve method in the analyst's vernacular. Using the analytical method, the IP RUL is estimated indirectly by examining the history of the creation and retirement of the tangible documentation related to the subject IP. The analytical method can be used to estimate (1) the expected total life of a new IP, (2) the expected average RUL of an in-use IP and (3) the expected RUL of an individual trade secret functioning within a group of commercial IPs.

IP Documentation

This application of the analytical method works particularly well with regard to IP documentation. While IPs are often confidential, owner/operators typically document their IP for various legal and commercial purposes. Such purposes include product packaging, advertising/promotion, publication/distribution, product production management/scheduling, product/service quality control, employee training and so on. While this documentation is sometimes maintained in secrecy, it typically does exist.

Examples of product/process IP documentation include: food product recipes, product chemical formulations, product engineering drawings, production process schematics, process flow charts, plant layouts and designs, distribution system drawings/mylars, computer software programs, clothing and other product patterns, blueprints, laboratory notebooks, system flowcharts and diagrams, employee manuals, user/procedure manuals, customer file contents and so on. Each of these types of documentation are the tangible embodiment of the owner/operator's IP. In addition, each of these types of documents contains IP content and represents IP legal rights.

IP Document Placement and Retirement

Each of these types of product/ process/procedure documentation are created at a specific point in time. For purposes of the analytical method, we will call that document creation date a "placement." Each of these types of product/process/procedure documentation can be retired or replaced at a specific point in time. Whether the seasoned document is (1) simply no longer used or (2) permanently replaced with a new document, we will call that event a "retirement."

The basis of the analytical method is the statistical analysis of IP document placements and retirements. A document placement represents an event when a particular IP came into use by the owner/operator. A document retirement represents an event when the owner/operator discontinued the current use of a particular IP. By analyzing the historical placements and retirements of IP documentation, we can estimate the expected IP RUL.

By analyzing the placements and retirements of supporting documentation, we can assess the owner/operator's actual use of the IP. When the owner/operator retires the document, the IP is no longer in use. (For this reason, a retirement should represent a discontinuation of that document and not simply an update or minor modification.) When the IP is retired, it is no longer generating economic income for the owner/operator.

The analytical method is indifferent as to why the IP document is retired. That is, it is not important whether the IP became functionally or technologically obsolete, fell out of consumer favor, was declared illegal and so on. The only consideration in the analytical method is that the IP document is either in use or it is not in use (retired).

Accordingly, the analytical method is a very objective methodology for estimating IP RUL. In addition, it is an unbiased methodology in that it equally considers all reasons why the IP documentation was retired.

The Analytical Method

The theory of survivor curves was developed at Iowa State University in the early 1900s. Survivor curves are used to predict the mortality or decay of a group of similar assets (e.g., intellectual properties) as the assets age. Survivor curve theory is similar to the mortality table theory used by actuaries to estimate the human life span.

The analytical method is the process of predicting the behavior of a group of assets by fitting a "test group" of the actual asset placements/retirements to various survivor curves. Thus, by selecting the survivor curve that best "describes" the past actual decay of the test group of assets, the future behavior of each asset in the group can be estimated.

The Survivor Curve

Graph 1 presents a typical survivor curve. The x-axis represents the age of the assets, and the y-axis represents the percentage of the original group of assets that are still surviving at a given age. For example, at age equal to zero years, 100 percent of the group is surviving.

As time passes, the assets within the group retire. Therefore, the percentage of the group still surviving decreases. This creates the downward sloping characteristic of the survivor curve. A survivor curve can be any mathematical function of age that can accurately (and logically) depict the asset group's mortality.

The age at which 50 percent of the original group still survives is defined as the group's "average life." That is, a new asset (i.e., an asset that is created at any given time) would have an expected life of the average life of the group. In reality, assets are "active" (i.e., assets are in current use) across a wide range of possible time units. However, the expected life (i.e., the mean time that the asset is in current use) is the average life for the group.

There are three basic types of survivor curves: left mode, symmetric and right mode.

A left-mode survivor curve depicts a group that retires (1) at a faster rate before the average life is reached and (2) at a slower rate after the average life is reached. In other words, if a left-mode survivor curve accurately predicts a group's behavior, it could be interpreted as "the group's older assets will continue to operate longer than its newer assets and will tend to have a longer relative life."

A symmetrical survivor curve predicts that the assets within a group will retire at a similar rate at any given relative age on either side of the group's average life.

A right-mode survivor curve is the opposite of the left-mode survivor curve. An asset that has reached the group's average life tends to decay faster than an asset that has yet to reach the average life. In other words, if a right-mode survivor curve accurately predicts a group's behavior, it could be interpreted that "the group's newer assets will continue to operate longer than its older assets and will tend to have a longer relative expected life."

Graph 2 illustrates the "curve structure" of left-mode, symmetrical and right-mode survivors plotted on the same graph.

The ultimate purpose of an RUL analysis is to assign a specific "remaining life" to each asset (e.g., each IP document) within the group. RUL is defined as the amount of time before an asset will retire. An asset is "retired" when (1) it is no longer in active use and (2) no further economic benefit is expected from it. An example of how RUL could be interpreted would be to state that, "document number 123456 is expected to remain in active use for two and a half more years." In that case, two and a half years is the RUL of document number 123456.

The Probable Life Curve

An important procedure in estimating RUL is to calculate the "probable life" for each asset within the group. Probable life is the age at which an asset would retire, given that it has already reached its current age. By subtracting the current age of an asset from its probable life, the asset RUL can be estimated. That is,
RUL = Probable life minus current age
The mathematical definition of the probable life of a given asset is the area under the survivor curve (i.e., using calculus, the integral) to the right of the current age of that asset. Every survivor curve has a corresponding probable life curve. For any asset (e.g., an IP document) that is already x years old, this relationship can be summarized in this form:

Graph 3 illustrates the relationship between (1) percent surviving and (2) probable life. The probable life of an asset at age x years is the area under the curve that is inside the shaded area (i.e., to the right of x years).

By solving for the probable life in the equation above for all possible asset ages, a probable life curve can be constructed. A typical survivor curve and its corresponding probable life curve are illustrated on Graph 4.

To determine the probable life of an asset that is already z years old using Graph 4, first locate z years on the x-axis and find the corresponding point on the survivor curve. Then draw a line parallel to the x-axis to the point of intersection with the probable life curve. The probable life is obtained by moving down the y-axis to the number of years on the x-axis.

Graph 4 illustrates the probable life (point PL) of an asset that is already z years old.

The RUL of the particular asset (e.g., the particular IP document) can then be estimated by using the formula presented above.

There are several sets (or series) of survivor curve mathematical functions that are generally used in the analytical method. These survivor curve mathematical functions include: (1) Iowa State University modified Pearson-type frequency functions, (2) Weibull distribution functions, (3) Gompertz-Makeham distribution functions, (4) H-curves (a single parametic series of curves derived by truncating a normal probability distribution) and (5) polynomial (least squares regression fitting) functions. All of these mathematical functions should be considered when selecting the best fitting survivor curve relative to a specific set of assets.

In summary, by selecting a survivor curve that best explains the past decay performance of a group of assets, the future decay of the asset group can be predicted. From the predicted decay curve, the RUL of each individual asset within the group can be estimated.

RUL Analysis Procedures

The procedure used to select the most appropriate survivor curve is called "curve fitting." The basic concept is to find the standardized survivor curve that best explains the actual age/life decay pattern of the subject asset group. The following procedures are involved in selecting a best fit survivor curve.

1. Select a sample population of retired assets (i.e., trade secret document no longer in active use): a random selection of the most recent retired assets is generated. The data needed from the selected sample of retired assets are: (1) the placement date and (2) the retirement date of each retired asset. Again, a placement is the initial creation of the trade secret document. A retirement is the final discontinuation of the use of the trade secret document. This information is usually obtained from a computer database, inspection of the subject intellectual property inventory or discussion with the owner/ operator management.

2. Select an active asset (i.e., trade secret document in current use) sample population: a random selection of all active assets is generated. The information needed for the actual asset sample is the asset placement (i.e., document creation) date. Again, this information is usually gathered from a computer database, inspection of the subject intellectual property inventory or discussions with the owner/operator management.

3. Create the survivor table. A survivor table is created by using the retired asset and active asset age/life data described above. A survivor table presents the percent surviving of the sample asset group at a given age. Table 1 presents a typical survivor table. The percent surviving at a given age x years is:

The retirement rate at any age is the ratio of (1) the number of assets that retired during the age interval divided by (2) the number of assets exposed to retirement at the beginning of the age interval. The number of assets exposed to retirement is simply the number of actual assets (i.e., in-use trade secret documents) at the beginning of the age interval.

For example, with regard to Table 1, let's assume that:

a. at age interval 5, the percent surviving is 78.448 percent;
b. at age interval 5, the retirement rate is 4.268 percent;
c. then, the percent surviving at age interval 6 is (78.444%) times (1 - 4.268%) = 75.099%.

4. Plot the actual survivor table. By selecting the pairs of coordinates (x,y), where x is the age (the first column in Table 1) and y is the percent surviving (the last column in Table 1), an "actual" survivor curve is plotted. This "actual" survivor curve is illustrated by the "P" markings on Graph 5.

5. Select the best fit standardized survivor curve: all standardized survivor curves are plotted on the same graph as the "actual" (i.e., actual survivor table) survivor data described above. These standardized curves are called the ideal curves. The difference between the actual percent surviving (from the actual survivor table) and the ideal percent surviving is the fitting error at each age.

By summing all the squares of the fitting errors for a curve, a ranking factor describing the "fit" of the curve can be ascertained. The errors are squared both (1) to remove the "canceling" effect of negative fitting errors and (2) to put more emphasis on large errors. This curve-fitting procedure is represented by the following formula:

where n is the number of entries in the survivor table selected for the curve-fitting procedure.

The method described above is called a stub period curve fitting. The stub period curve-fitting method is illustrated in Graph 5.

All potential standardized survivor curves are fitted over a logical range of average lives, and a ranking factor is assigned to each curve fitting. The best fit standardized survivor curve is the survivor curve at the specified average life that has the smallest ranking factor. This procedure is referred to as minimizing the sum of the squared errors.

As each standardized survivor curve is fitted, a correlation coefficient is determined. The correlation coefficient is a ranking from -1 to +1. The correlation coefficient describes how well the standardized survivor curve fits the actual survivor table. A correlation coefficient of +1 suggests that the standardized survivor curve at the average life being fitted accurately predicts the asset sample's actual past decay rate activity.

Once a best fit standardized survivor curve is selected, the RUL for all active assets is estimated using the RUL procedure described above. The RUL represents the remaining number of years that the owner/operator will expect to use (and receive economic benefit from) the IP document. Thus, it is the appropriate time period for an economic analysis of that IP.

Summary and Conclusion

Commercial IPs are routinely the subject of valuation within a bankruptcy context. Often, these IPs are the most valuable assets in the bankruptcy estate. Estimating the IP RUL is an important component of valuation approach. For many types of IP, it is often possible to estimate the RUL of the tangible documentation.

This discussion focused on the analytical method for estimating IP RUL. Unlike some other IP RUL methods, the analytical method (1) provides a specific quantitative conclusion and (2) is objective and unbiased with regard to data sources