Minority interest discounts: a quantitative approach for real estate limited partnerships.
This article addresses one element of the valuation process: the discount for lack of control, most often referred to as the minority interest discount. It presents a quantitative, market-based method intended specifically for small real estate limited partnerships.(2) Let us briefly examine the discounting process, look at the foundations for estimating the minority interest discount, and finally, outline a quantitative procedure for developing the value estimate.
The flow chart in figure 1 shows a simplified model of the discounting process.(3) The model shows discounting from full net asset value, first because of the minority interest(4) holder's inherent lack of ability to influence management, and then because the subject partnership is private, and its interests cannot be traded publicly (unlike the underlying real estate, or units of public limited partnerships). The first discount, due to lack of control, is addressed in this article; its application gives a "minority-marketable" value for the subject interest. The second discount is due to lack of marketability, and its proper analysis is perhaps even more challenging than the analysis for lack of control.(5) Sequential application of the two discounts then gives the minority "limited-market" value of the interest.
This process could be handled in one step, with one estimated discount, if data concerning transfer of interests in private limited partnerships were available. Unfortunately, such data is not compiled. Even if it were, financial history and other intimate partnership information would not likely be forthcoming or verifiable, not to mention possible difficulties in dealing with conditions of sale.
In this article, we use a sales comparison approach to estimate the discounts, and to do so need reliable transaction and other financial data. This is available from public sources, but only for public companies and partnerships. The discounting process is therefore constructed here with the public minority-marketable intermediate value to accommodate the realities of the market data.(6)
THE MINORITY INTEREST DISCOUNT
The analytical portion of this article concerns only the minority interest discount. The process will be based on an expanded top half of figure 1, shown here as figure 2.
The diagram in figure 2 relates equities (stock corporations) and real estate partnerships, and shows how discount elements are developed and applied. The minority interest discounting process for real estate limited partnerships is shown on the right side of the diagram, and for equities is shown on the left.
Minority interest discount data are taken from transactions involving minority interests in public real estate limited partnerships. These transactions take place in the limited partnership secondary market. Because this market is not as efficient as the stock exchanges, the discount includes a small element of lack of marketability, the trading market discount. This discount is then subtracted from the indication from comparable public limited partnerships to give the net minority interest (control) discount.
The appraiser's task is then to compare the characteristics of the subject interest and subject partnership that influence marketability, with related characteristics, or elements of comparison, in the study data. The foundation for isolating these elements of comparison is Revenue Ruling 59-60.(7) A real estate limited partnership is a special case of the generalized business valuation problem addressed by the ruling, and its requirements have been set forth in a recent court case.(8) Provisions are also covered in some detail by Martin Shenkman and Cal Feingold.(9) Appraisers should understand the entire ruling, and discuss its application to the full appraisal process in the report.
Market Data Selection
The first question is how to obtain market data. If information on transactions involving interests in private real estate partnerships were available, it would give both discounts in one step, as was discussed in the overview of the discounting process. Fortunately, data from trades of minority interests in public real estate limited partnerships is available, and can be readily applied to the subject limited partnership.(10)
Trading of units in public real estate partnerships takes place in the limited partnership secondary market. This is an informal market consisting of about 15 independent broker-dealers that match up buyers and sellers of public limited partnership interests. A good discussion of the history of this market was presented by Mark Thompson and Eggert Dagbjartsson,(11) by Steve Kam, et al.,(12) and by numerous others. An authority on the secondary market, also referenced by Thompson, is The Partnership Spectrum, published by Partnership Profiles.(13) The May/June issue each year features secondary market discounts, and in 1996 contained transaction data for 167 partnerships. This periodical contains much useful information, general market analysis, discussion of trends, and some overall compilation. Partnership Profiles also publishes a special addendum with compiled Securities and Exchange Commission (SEC) reporting and other data on nearly all the partnerships involved. The work is so comprehensive that the appraiser's data gathering effort is much reduced and his or her focus becomes data selection, and most important, application of the data to the subject interest.
The following hypothetical case, whose salient parameters are summarized here for the sake of brevity, may be helpful. The case concerns an estate, where the deceased was a limited partner in Shelter Enterprises, Ltd. The subject interest is a 30% share in two apartment complexes located in Los Angeles and Las Vegas. The real estate was appraised for $9.7 million as of the date of death, and because there is a mortgage as well as other small assets and liabilities, the net asset value (NAV) of the partnership is $6.2 million.(14) The subject interest's pro rata share is $1.86 million.
Name: Shelter Enterprises, Ltd. Properties: Two apartment projects in California and Nevada. Net asset value: $6.2 million. Term: 1966-2016 (20 years remaining) Distributions: $338,000 to limited partners over past 12 months, or 5.5% of NAV. This rate has been declining during the recession, but is now expected to increase slowly. Allocations: Cash flow, profit and loss, and proceeds of sale all in proportion to a partner's percent interest, no preferences. Control: 75% vote to amend, terminate, or extend. Can remove general partner only for gross negligence.
Elements of Comparison
Numerous elements can be selected from the public limited partnership database. Those which are usually the most relevant for analysis are the following, shown for a typical partnership:
Name: Perpetual Income Fund Property: Four apartment projects in Florida, Minnesota, and Michigan Net asset value: $43 million, $1,437 per unit Leverage: None Trading:(15) 26 transactions, 10.2% spread Average price:(16) $1,020 per unit = 29% discount Term: No plans to wind up or sell assets Distributions: $100 per unit = 7.0% of NAV, and has been reasonably stable
Market Data Analysis
Limited partnership data analysis can be approached in several different ways, but it should be a quantitative analysis to the greatest extent possible. Appraisers can choose from a range of procedures. For example, an appraiser could select a few comparable public limited partnerships, observe the discounts, and then try to reconcile the discounts to the subject. Even ranking by discount or return would not improve matters much. The range of discounts is likely to be quite wide and the significance of individual elements cannot be ascertained. Such a simple procedure is really not a good idea, because too many variables exist to produce an accurate and well-considered result.
The other extreme is to use multiple linear regression to directly calculate the discount indicated by the secondary market data. Unfortunately, formula methods can remove an intuitive sense for the result, which the conventional sales comparison approach allows.(17) To avoid regression methods is actually rather difficult because the significance of the elements of comparison varies significantly with different groups of partnerships. It is not possible to fully understand how to adjust for each of the elements without some good method of data crunching. Fortunately, current spreadsheet programs have handy regression capabilities.
We take a step-by-step look at an analytical method that is really a middle ground between the purely mathematic and the more intuitive sales comparison. This method takes advantage of the quantitative understanding that can be gained by applying a regression model, but then presents results in an adjustment grid that allows for some intuitive understanding of the result. This method evaluates the grid data and reconciles the discount in the same way that the sales comparison analysis does. The process steps are described next.
Step 1. Selection of Market Data
An appraiser selects market data from sales of limited interests reported in The Partnership Spectrum. He or she selects a fairly large number of partnerships initially, perhaps 30 to 40, because it is difficult to tell at this stage which of the elements of comparison will be most important. The appraiser should try to select only those that have independent appraisals of the real estate rather than those for which the general partner provided the value estimates. The appraiser should select those with property types similar to the subject when possible, such as apartments, office buildings, and triple-net leases. Property type may turn out not to be the most important element, and the appraiser's selection should also include those with other similar elements. Selecting for the comparison elements of dividend rate and the remaining term of the partnership is particularly important.
Step 2. First Regression
The basic multiple regression equation is:
y = a + [b.sub.1][x.sub.1] + [b.sub.2][x.sub.2] + [b.sub.3][x.sub.3] + [b.sub.4][x.sub.4] + ... + [b.sub.n][x.sub.n]
where y is the discount due to lack of control, a is the constant, and [b.sub.i] is the coefficient for the independent variable, [x.sub.i]. Detailed explanations of the mathematics are found in many good references,(18) and will be considered further in step 3.
The important thing at this stage of the process is to take a first cut at selecting the independent variables (elements of comparison). The elements that have the greatest effect on the minority interest discount include distribution rate and trends, remaining term of the partnership, degree of asset diversification, and the type of properties held. The size of the partnership and other elements, which can be examined as part of the regression analysis, may also influence the discount.(19)
Distribution rates exhibit an inverse correlation with discount; that is, a buyer of an interest that provides lower distributions will demand a greater discount to compensate. Distribution trends indicate the degree to which cash returns to the limited partners have been affected by economic instability or operational and management problems. Distribution trends relate both to historical and expected future cash flow patterns. The historical trend is reported, but the likelihood of future distributions is more difficult to analyze because it requires an understanding of the financial condition of each of the partnerships in the database. For example, historical distributions might be distorted by payments from reserves or asset sales. Upcoming balloon mortgage payments can have a big negative impact, as can a deferred need for tenant improvements, for example.(20)
If the remaining term of the partnership is short, the likelihood that the limited partners will realize the NAV of their shares is obviously increased. Shares of partnerships likely to wind up within a few years transfer at lower discounts than those with no such expectation. The general partner sometimes announces an intention to sell some or all of the partnership assets, and these should be used as comparables if the subject partnership has a short remaining life. If there is no indication that it will wind up in the near term, then it may be compared to most partnerships.
Degree of asset diversification refers to both geography and number of properties owned. The fewer the number of properties or the more localized the geography, the more susceptible operations may be to the vagaries of markets and local economies, and the perceived risk may be greater.
[TABULAR DATA FOR TABLE 1 OMITTED]
Asset type refers to the underlying asset base of the partnerships. All hold principally real estate assets, and market factors affecting the values of differing property types have been accounted for as part of the process of valuing the properties themselves. However, secondary market buyers often apply an additional discount for property types that are currently out of favor.(21) Dummy variables can be used to characterize asset type and diversification for each partnership.
Step 3. Second Regression
Running a second regression is not absolutely necessary, but makes for a much better analysis. First, reduce the database to the most useful comparable partnerships(22) based on the results of the first regression, and then regress the new data set. The multiple linear regression output is shown in table 1. This was taken from the second regression for the 18 partnerships that were selected for our case study. (The first regression was done similarly, but with a larger database of 33 partnerships.)
The [R.sup.2] term is the coefficient of determination, and indicates that in theory the regression explains 77% of the variation in the percentage discount.(23) The t-statistics indicate the reliability of the b-coefficients as a predictor of the influence of each of the x-variables; the larger the t-statistic, the more reliable the estimate. The b-coefficients indicate the sensitivity of the discount to each of the x-variables; a 1% increase in the distribution rate will decrease the discount by 0.835%.
Step 4. Adjustment Grid
There is no analytical reason why the regression formula cannot be used to calculate the subject discount as shown. However, the adjustment grid of the sales comparison approach makes a nice, conventional presentation, and the results can be much more easily understood. A grid is particularly useful if elements not picked up in the regression analysis might be important for the reconciliation. These might involve an unusual property type, geographic region, or anything else not well represented in the data. An appraiser should select a group of six to nine partnerships just as he or she would [TABULAR DATA FOR TABLE 2 OMITTED] select comparable sales - to best represent the elements that influence value.
Table 2 shows three hypothetical partnerships for the sake of illustration. The adjustments are calculated from the second regression table by multiplying the difference between the comparable and subject values for each x-variable by its b-coefficient.(24) The result works exactly like a sales comparison grid. The indicated discount is reconciled to the subject, and also with respect to any elements which have not been quantified. The process quantifies nearly all the influences on value, and can produce a narrow range of discount indications.
Most of the elements have been successfully bracketed except for the size of the partnership. This is typically difficult to bracket, because family limited partnerships are generally smaller than public limited partnerships. In this case, we only adjusted the comparables as if the subject size were only $7.2 million, since this was the smallest public partnership in the sample.(25) Distribution rate and trend are the most significant elements for this analysis; none of the comparables has a short remaining term, and although size varies a great deal, its coefficient is small, as is its t-statistic. The dependent variable was selected as the discount percentage for consistency with the discussion in the text.(26)
The reconciliation is handled just as it would be for a real estate approach, but with different elements. For example, the first comparable was included because it is relatively small and leveraged. Its average trade is taken from only three transactions and the spread is fairly wide, so the weight is reduced somewhat. Gross adjustments are fairly similar. Because size has only a limited effect, the greatest weight is given to the third comparable, since many trades occurred in a reasonably narrow range. The reconciled discount is 38%. This reconciliation was too short; the report should discuss all the elements and comparables, including relevant details of the partnerships' operations, properties owned, reasoning behind selected dummy variable elements (the distribution trend that might be affected by deferred maintenance or notes coming due), and other points of comparison.
Step 5. Other Elements to Consider
Some matters may not be represented in the limited partnership database, and cannot be readily quantified. For example, the public limited partnership data are made up of transactions involving small interests. A small subject interest is usually similar with respect to degree of control, but as the interest gets larger, this may change, and the effect cannot be captured in the regression analysis. An appraiser must understand the provisions of the limited partnership agreement relating to control, such as voting provisions, the likelihood that the subject percentage could be combined with another to increase the degree of control (a "swing vote"), and specific rights of the general and limited partners. The best way to handle these matters is to carefully go through the provisions of Revenue Ruling 59-60 and make sure to discuss all relevant factors.
The discount should not be reconciled outside the indicated range, even if provisions in the agreement are obviously more onerous than those typically found in public limited partnerships. Such elements can exhibit strong nonlinearities, which would not be understood in any quantitative way without usable data for guidance. Fortunately, most of the influences can be quantified and going outside the available data is not required.
Step 6. Marketability Influence
The discount for lack of control derived from limited partnership data has a problem: It incorporates a marketability element [ILLUSTRATION FOR FIGURE 2 OMITTED]. Several methods are available to extract the discount, including analysis of data extracted from marketability discount studies and analysis of trading spreads. The most direct method uses a regression analysis of the discount differential between reasonably similar REITs and larger public limited partnerships.
The database for this regression includes New York Stock Exchange (NYSE) traded REITs and limited partnerships. An appraiser should select the limited partnerships and real estate investment trusts to be as similar as possible with respect to size, asset diversification and dividends paid, and the other important elements of comparison. The regression formula is the same as for the partnership analysis, where y is the discount percentage. A dummy x-variable is used to represent the trading market: 1 for the limited partnership secondary market, and 0 for the NYSE. Our regressions show a b-coefficient of 0.05-0.07, meaning that there is a 5%-7% difference in discount due to the inefficiency of the secondary market compared with the NYSE, a fully liquid trading market.
The difference is shown in figure 2 as the trading market discount between the two markets. This discount is then subtracted from the discount previously estimated, to give the net minority interest (control) discount applicable to the subject interest. This is a function of characteristic market efficiency, not related to the subject partnership, and the result can range from about 50/0-7%; 6% is selected for the case. The concluded minority interest discount is then 38% less 6% = 32%.
Application of Discounts Net asset value of subject interest: $1,860,000 Discount for lack of control at 32%: - 595,000 Minority-marketable value: $1,265,000
The next step in the appraisal process is to estimate the discount due to lack of marketability. The required analytical process is substantially different from the one just presented; some approaches will be familiar to real estate appraisers, but most of the material will not. Marketability analysis is developed within the fields of business valuation and finance, and good references are available, as noted earlier.(27) Marketability analysis is not presented here due to space constraints, but may be the subject of a follow-up article.
This article considers in detail only the first half of the discounting process. The process applies to small partnerships that hold real estate as their principal asset, and is illustrated with a simplified case. The discount for lack of control was developed from market transactions for public limited partnerships. The analytic process uses multiple linear regression to identify significant elements of comparison, and to quantify adjustments to the subject. The article then presents selected comparables in a grid similar to that used in the sales comparison approach, discusses the quantified and nonquantified elements, and reconciles the indications. A marketability discount element (the trading market discount) is subtracted from the reconciled discount, and the result is the minority interest discount for the subject interest. This applied to the subject's pro rata share of partnership NAV, gives a minority-marketable value. The next step deals with the operation of markets; the appraiser then applies the marketability discount to this minority-marketable value to give a market value estimate for the interest. This analysis is subject specific, and conforms to the intent of recent requests by several courts for better and more relevant valuations.
1. The need for a thorough and well-supported analysis should be self-evident to any appraiser, but it has also been requested in no uncertain terms by the courts. See Judge Wright's opinion in Estate of Edgar A. Berg v. Commissioner, 91 TCM 1383 (1991) [Opinion, Section IV]. The subject of experts is also addressed by Judge Laro in Bernard Mandelbaum, et al. v. Commissioner, TCM 1995-255 [Opinion, Issue 1d.].
2. In addition to real estate assets, such small partnerships may also have operating capital and some other minor current assets and liabilities as well as long-term liabilities such as property mortgages. These partnerships are a special case of an asset-holding company, and the procedures recommended in this article apply only to such entities. More complex real estate partnerships, and those holding other principal assets, are excluded from consideration for the sake of brevity.
3. Lance S. Hall, "Valuation of Fractional Interests: A Business Appraiser's Perspective," The Appraisal Journal (April 1989): 175. This same general structure was presented by Lance Hall, and has been used in various forms by other writers.
4. The reference to minority interest is typically meant to denote lack of control, not necessarily less than a 50% interest in the subject entity. A larger interest may have no more control than a smaller one. However, it is up to the appraiser to carefully consider any control elements that may influence value, regardless of the interest's fraction of the whole.
5. The analysis of this discount is entirely within the province of the disciplines of business valuation and finance. Its elements are not as familiar to real estate appraisers as are the elements of the minority interest discount. Numerous articles and other references are available, and should be a starting point for any appraiser seriously contemplating practice in this area. A comprehensive reference is Shannon P. Pratt, et al., Valuing a Business, The Analysis and Appraisal of Closely Held Companies, 3d ed. (Chicago, Illinois: Irwin Professional Publishing, 1996): Chapter 15. This chapter provides a complete overview, and includes many other references. An entire text devoted to the subject is Z. Christopher Mercer, Quantifying Marketability Discounts (Memphis, Tennessee: Peabody Publishing, 1997). Mercer presents some important analytical techniques not found elsewhere, in addition to a thorough overall treatment of the subject.
6. The data set for estimating the minority interest discount is taken from the trading of public limited partnership interests; for the marketability discount the data set is taken from identical stock interests in public companies trading in two different types of markets. Because the appraisal process switches gears at the minority-marketable point, the need for tracking parallels between partnerships and equities in the appraisal is important.
7. See Internal Revenue Service Revenue Ruling 59-60, 1959-1 CB 237. This ruling deals specifically with the stock of closely held corporations for estate and gift tax purposes, but has wide application for business appraisal. It is a touchstone in business valuation and is the best available reference for the valuation of other security interests, including interests in private limited partnerships.
8. See Bernard Mandelbaum, et al. v. Commissioner, TCM 1995-255. In his opinion, Judge Laro develops his own discount analysis, largely by following the breakdown of influencing elements from Ruling 59-60.
9. Martin M. Shenkman and Cal R. Feingold, "Minority, Marketability Discounts Affect Valuation of Partnership Interest," The Real Estate Finance Journal (Summer 1993): 18-25.
10. Some practitioners advocate using real estate investment trusts (REITs) as a database for partnership valuation, but this author does not, for a variety of reasons. REITs are typically large, are diverse in their holdings, are structured differently, and are open-ended. To make a case for satisfying Revenue Ruling 59-60, Section 401(h) is difficult trader these conditions.
11. Mark S. Thompson and Eggert Dagbjartsson, "Market Discounting of Partial Ownership Interests," The Appraisal Journal (October 1994): 535-541. This article also presents a good treatment of partnership characteristics and elements affecting control and liquidity.
12. Steve Kam, et al., "The Market Pricing of Syndicated LPs and the Valuation of FLPs," Trusts & Estates (February 1996): 35-45. The authors present an analysis of partnership trading data based on a multiple linear regression model.
13. Partnership Profiles, "Secondary Spectrum," The Partnership Spectrum (Dallas, Texas: Partnership Profiles, May/June 1996).
14. We assume readers are familiar with the net asset value method of estimating partnership value, where an appraiser estimates the market value of its assets (in this case, a fee interest in the real estate); makes adjustments for non-real estate items such as current assets and liabilities, real estate financing, and any other minor balance sheet items; and obtains a NAV for the partnership.
15. Trading price spread is calculated as: [(high price - low price) + (average price)].
16. This is the weighted average of the individual trades as provided by Partnership Profiles, and is expressed as price per unit for convenience. The discount is calculated as [1 - (price per unit) divided by net asset value per unit)].
17. The sales comparison adjustment grid provides a data format that shows the elements of comparison and their adjustments to the subject. This format is relatively easy to explain and follow, compared with a purely mathematical approach, which for many people does not inspire understanding or confidence in the conclusion.
18. Appraisal Institute, The Appraisal of Real Estate, 11th ed. (Chicago, Illinois: Appraisal Institute, 1996), mathematics appendix. Spreadsheet programs can be particularly helpful; however, a reasonable understanding of the regression process is necessary to evaluate the results.
19. See Kam, et al., 36, 41-44. The authors present an analysis of partnership trading data based on a multiple linear regression model, developing a list of influencing elements similar to those identified here.
20. The "financial condition" rating developed and published by Partnership Profiles is very useful in this respect. This rating is based on an evaluation of working capital, operating surplus or deficit amounts, and the likelihood that the partnership will be able to meet its financial obligations.
21. For example, office properties had been "out," and mini-storage properties had been "in" at the beginning of 1995. Office properties recovered by 1997, and strip retail replaced it in the "out" category.
22. "Most useful" is used here to indicate those partnerships that either 1) possess characteristics that should be represented in the adjustment grid (such as the only partnership in the first regression database with properties in the subject district, or are similar in some other unusual respect), or 2) are those for which the regression model is able to predict the actual discount with the least error.
23. The [R.sup.2] indication given by the Lotus 1-2-3 program can be overstated for small samples. This is not too important for this analysis, but readers interested in pursuing the subject should see Gene Dilmore, "Of Regression Analysis, Business Valuation, Lotus 1-2-3, Hewlett-Packard, and William of Ockham," Business Valuation Review (June 1995): 75-82.
24. For example, comparable 1 has a distribution rate of 4.1%, so its adjustment to the subject for this element is (4.1% - 5.5%) x (-0.835) = 1.1%. (Actually -1.17% here, slightly greater than the grid's -1.1% due to rounding of the x- and b-factors used here.)
25. It is not good form to adjust outside the data set because nonlinearities may be present that would not be revealed for points outside.
26. An appraiser should be careful about some unusual conditions that this introduces into the process. First, a superior comparable element (e.g., a greater distribution rate) will decrease the discount indication for that comparable, and require a positive adjustment, backward from conventional sales comparison analysis. Also, the adjustments are expressed not as a percentage of the discount indication, but as arithmetic adjustments to it.
27. See Pratt, Chapter 15, and Mercer's entire text.
Fishman, Jay E., et al. Guide to Business Valuations, 7th ed. Fort Worth, Texas: Practitioners Publishing Co., 1997.
Hall, Lance S. "Minority Interests in Closely Held Real Estate: Lessons from Estate of Berg," Journal of Real Estate Taxation (Winter 1993): 170-177.
Hall, Lance S., and Timothy C. Polacek. "Strategies for Obtaining the Largest Valuation Discounts," Estate Planning (January/February 1994): 38-44.
Hanford, Lloyd D. Jr. "The Market Value of Partial Interests in Real Property," The Appraisal Journal (October 1989): 460-465.
Hitchner, James R., and Kevin J. Rudd, "The Use of Discounts in Estate and Gift Tax Valuations," Trusts & Estates (August 1992): 49-60.
Internal Revenue Service. "Standard Federal Tax Reports," IRS Valuation Guide for Income, Estate and Gift Taxes, v, 81, no, 4 (1994).
Johnson, Bruce A., and James R. Park. "Study of Discounts for Limited Partnership Units Traded in a Secondary Market," Business Valuation Review (September 1995): 99-101.
Sirmans, C. F., et al. "A Survey of Appraisers Regarding Factors in Discounting Partial Interests," The Appraisal Journal (October 1993): 600-607.
Thompson, Mark S., and Eric S. Spunt. "Widespread Overvaluation of Fractional Ownership Positions," Trusts and Estates (June 1993): 62-66.
Dennis A. Webb, MAI, is the owner of Primus Valuations in Santa Monica, California. He was co-owner of a National Association of Securities Dealers (NASD) broker-dealer firm and a general securities principal, gaining experience with real estate partnerships and investment marketing before beginning his real estate appraisal career. Mr. Webb received his BS in engineering from the University of California, Los Angeles, and was a design engineer before his transition into the investment and marketing fields. His work on undivided interests in real estate has previously appeared in another publication. Contact: 3435 Ocean Park Blvd., Suite 206; Santa Monica, CA 90405. (310) 454-8114. Fax 823-4617. firstname.lastname@example.org.
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|Author:||Webb, Dennis A.|
|Date:||Apr 1, 1999|
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