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Empirical analysis of the breakdown method of estimating physical depreciation.

The breakdown method of estimating physical depreciation entails estimating "all items of depreciation individually"(1) then adding the individual estimates together and deducting the sum from the estimated reproduction or replacement cost. While the breakdown method applies to depreciation from all causes, this study focuses on the implications of applying the method in estimating physical depreciation.

Three steps are involved in estimating physical depreciation by the breakdown method. The first step is to estimate curable physical depreciation by calculating the cost to cure deferred maintenance items. Next, the appraiser estimates incurable physical depreciation of short-lived components of the property improvements. Finally, incurable physical depreciation is estimated for long-lived property components.(2) Because short-lived and long-lived components are depreciated over differing lives, this method results in relatively rapid physical depreciation in the early years of property life and a decreasing rate of property depreciation as a property ages. Because the breakdown method is employed often in practice, it is important to know if markets exhibit the pattern of property depreciation over time implied by the breakdown method.

APPLIED APPRAISAL LITERATURE

Max Derbes relies on the breakdown method of estimating physical depreciation to derive a residual estimate of the productive life of long-lived components of property improvements.(3) His analysis supports the then-new concept of depreciating the "bone structure" over its physical life rather than over some shorter term, economic-life estimate. Concurrent with his paper, the idea of depreciating long-lived components over the physical life of the improvements was adopted by the Appraisal Institute with the publication of the ninth edition of The Appraisal of Real Estate in 1987. In contrast, the eighth edition demonstrated long-lived component depreciation over the economic life of the improvements in its breakdown method example.

An eight-step process for completing a valuation analysis by the cost approach was outlined by James Mason. Step three consists of estimating "the depreciation that has accrued from physical, functional, and external causes."(4) He notes that the crucial difference between the use of the breakdown method of computing physical depreciation and using the simpler age-life method is that the breakdown method employs estimates of physical life to compute building component depreciation whereas the age-life method utilizes a ratio of effective age to economic life. Mason also states that "the breakdown method is more appropriate in the absence of adequate market data to support the simple, broad-brush age-life ratio."(5) Further, he demonstrates how periodic renovation of short-lived components extends and renews a property's economic life throughout the structure's physical life.

Age-life depreciation is often used without market support, according to Thomas Holderness, who recommends that market data be used to derive depreciation estimates whenever possible.(6) He also points out that depreciation tables (generated by Marshall and Swift, a company that specializes in publishing construction cost manuals) are based on market studies, implying that their tables can provide market support for depreciation estimates, subject to adjustment to account for local markets. Marshall and Swift depreciation tables show a relatively constant rate of depreciation over a property's life, which is consistent with the pattern of property depreciation indicated by Mason for the simple age-life method. Because Marshall and Swift depreciation schedules only consider effective age and economic life, they are not amenable to calculating physical depreciation of the core structure by the breakdown method.

Richard Knitter takes a contrary position, holding that the cost approach is inappropriate for most appraisals because of the problematic issue of estimating depreciation and citing an anecdotal statement by a participant in the survey he conducted: "MAIs know that the cost approach is either the only approach or it is useless."(7) He also cites Richard Marchitelli, among others, who said that "to suggest...that depreciation can be extracted from an analysis of comparable sales is as embarrassing as it is impossible."(8)

Knitter's assertions seem to echo, at least in part, Kenneth Boyd's study of the cost approach in expropriation cases in Canada. Boyd notes that the cost approach is generally not accepted by Canada's courts, and in cases where it has been accepted it was carefully applied.(9) The Appraisal Institute of Canada recommends that the "observed condition" method be employed when estimating depreciation in the cost approach.(10) The observed condition method consists of noting the condition of each component of the property on the valuation date and then deducting the depreciation applicable to the component's observed condition from the estimated cost new. Hence, the observed condition method is equivalent to what is referred to as the breakdown method in the United States.

It is evident from the applied literature that appraisal practitioners recognize estimating depreciation to be the most problematic aspect of the cost approach. The process of accurately estimating depreciation is so difficult that Knitter, Boyd, and Marchitelli, among others, have concluded that the cost approach is inappropriate for solving many appraisal problems. If the cost approach is to be used, however, the literature seems to endorse the breakdown method as the method of choice. Therefore, an unanswered question remains, "Do property depreciation patterns resemble the pattern implied by the breakdown method, namely, rapid depreciation in the early years compared with a relatively slower rate of depreciation as properties age?"

EMPIRICAL LITERATURE

Two fairly recent empirical studies address the question of the form of the real property depreciation function over time. Roger Cannaday and Mark Sunderman analyzed data on 812 single-family home sales in Champaign, Illinois, during the period January 1976 through May 1984 to test whether the depreciation function is concave, convex, or straight line [ILLUSTRATION FOR FIGURE 1 OMITTED].(11)

Straight-line depreciation would imply that properties actually depreciate over their physical lives in a manner that is most consistent with simplified age-life methods. Convex depreciation implies that actual depreciation is most consistent with the breakdown method where short-lived items depreciate rapidly in a property's early years and the "bone structure" depreciates more slowly over an extended period of time. Concave depreciation is not consistent with either of the methods normally used in practice. Oddly enough, the Cannaday and Sunderman study found that depreciation of homes in the market that they studied best fit the concave form.

Cannaday and Sunderman note that their result differs from earlier studies, which found a convex form for the depreciation equation.(12) However, they also point out that their result is consistent with the findings of two other prior researchers. A concave depreciation function was discovered in a 1981 study of single-family homes and in a 1969 study of office buildings by Taubman and Rasche.(13)

In 1987, Stephen Malpezzi, Larry Ozanne, and Thomas Thibodeau estimated rates of depreciation for owner-occupied and renter-occupied properties in 59 metropolitan statistical areas, using data from the Annual Housing Survey, Bureau of the Census (1976-1978).(14) The study found that 81% of the renter-occupied property markets exhibited negative coefficients on the age term and positive coefficients on the age-squared term, indicating a reduction in the rate of depreciation as properties age (consistent with the breakdown method). The study also found this convex form of relationship to prevail in 85% of the owner-occupied property markets. Another important finding was that rates of depreciation could be vastly different from market to market.

Empirical studies of the form of the relationship between depreciation and property age are, at best, inconclusive. One recent study and one older study find that depreciation rates for single-family homes follow a concave functional form. This finding also held for a 1969 study of office buildings. In contrast, one recent study of rented and owner-occupied residences and two older studies of single-family residences support the idea that properties depreciate more rapidly in their early years and that the depreciation rate slows as properties age (i.e., a convex form). The empirical data indicates that depreciation rates differ by property type and location, implying that appraisers must have knowledge of how properties depreciate in their markets in order to conduct an adequate analysis of value by applying the cost approach.

FUNCTIONAL FORM AND THE BREAKDOWN METHOD

The convex form of the depreciation function implied by the breakdown method of estimating physical depreciation can be demonstrated by example. Consider an apartment complex with a replacement cost new of $4,298,408, including land valued at $670,000. (For illustrative purposes, curable physical depreciation is assumed to be zero.) Short-lived components include the roof cover, vinyl flooring, carpet, HVAC equipment, paved surfaces, and appliances, with a total value of $777,635 as itemized in table 1. The remaining cost new of the long-lived component of the improvements is therefore $2,850,773 ($4,298,408 - $670,000 - $777,635).

[TABULAR DATA FOR TABLE 1 OMITTED]

The aggregate effect of depreciation of the property's short-lived components over their various lives is a combined short-lived item depreciation curve that is convex in form [ILLUSTRATION FOR FIGURE 2 OMITTED]. When combined with the depreciation curve for the long-lived components, total physical depreciation also takes on a convex shape, which is indicative of the form of physical depreciation function implied by the breakdown method [ILLUSTRATION FOR FIGURE 3 OMITTED].

If the land component of value is assumed to increase in value over time, then a forecast of estimated property value will be even more convex in form as increases in land value offset decreases in property value due to physical depreciation. This effect will be more pronounced as a property ages because land value will represent a greater proportion of property value. Because of the influence of land value change, the form of curve representing total property value over time (assuming the breakdown method reflects reality) should resemble the top curve in figure 3, which was derived by assuming a 2.5% annual increase in the example's $670,000 beginning land value.

As the graphic representations show, the form of the property depreciation function over time, implied by the breakdown method, is convex. This is because the rate of physical depreciation is more rapid in early years as short-lived items age and less rapid in later years due to the relatively slow rate of decline in the value of the core structure.

DATA AND ANALYSIS

The data for this study consists of 1,124 observations of average one-bedroom apartment rents; 871 observations of average two-bedroom, one-bath apartment rents; and 470 observations of average two-bedroom, two-bath apartment rents across 15 central-city Seattle neighborhoods over 10.5 years from 1986 through mid-year 1996. The data is also categorized by property age group and square footage. Data were provided by Dupre + Scott Apartment Advisors, Inc., an apartment consulting and analysis firm in Seattle. Descriptive statistics for the data set are provided in table 2.

Data were reported by age cohorts, and each age group is well represented in the data set. How does one address the effect of possible unreported renovation of some of the properties in the data set? Although this is a valid concern on a property-by-property basis, because of the large number of properties in each age cohort (see table 2), renovation of some of the properties in the data set does not materially affect the results of this study. The statistical method employed in the analysis uncovers the relationship between [TABULAR DATA FOR TABLE 2 OMITTED] diminution in rent and property age for the typical property in each age cohort. Although some properties in each age cohort may be in better-than-average condition due to renovation, it is also likely that some properties may be in worse-than-average condition due to neglect. What matters here is the relationship between typical property rent and typical property age a relationship that can be uncovered by analyzing the data.

For each unit type, the 21- to 30-year age group is most frequent, whereas the 11- to 20-year age group is least frequent for 1 BR/1 BA units and 2 BR/1 BA units, and it is the next to least frequent for 2 BR/2 BA units. It is important to note that the sizeable number of rent observations in buildings 31-50 years old and those over 50 allows for modeling of depreciation over a fairly long time period. As expected, average unit size increases as bedroom and bath counts increase. Also, the data are well dispersed across the 15 Seattle core neighborhoods.

Three separate hedonic models are estimated, all with rent as a function of average unit size (SIZE), property age cohort (AGE), neighborhood location (NEIGH), and year of observation (DATE), as represented in equation 1:

RENT-f(SIZE, AGE, NEIGH, DATE) (1)

The estimation models are of the form

LN(RENT) = [[Alpha].sub.0] + [[Alpha].sub.1]SIZE + [summation of] [[Beta].sub.k][AGE.sub.k] where k=1 to k + [summation of] [[Gamma].sub.k][NEIGH.sub.k] where k=1 to k + [summation of] [[Delta].sub.k][DATE.sub.k] where k=1 to k + [Epsilon] (2)

(2) where [Alpha], [Beta], [Gamma], and [Delta] are coefficients on the independent variables and [Epsilon] represents random error. Use of the natural log of rent allows the estimated coefficients on AGE to be easily converted to percentage estimates. There are six age categories in the model. [AGE.sub.1], the base case, covers properties from 0 to 4 years of age. The remaining five categories are: [AGE.sub.2] (5-10); [AGE.sub.3] (11-20); [AGE.sub.4] (21-30); [AGE.sub.5] (31-50); and [AGE.sub.6] (over 50). Also, for estimation purposes, the base case neighborhood is Downtown, and the base case date is 1986.

Estimation models for the three unit types are shown in table 3. Model fit is good [TABULAR DATA FOR TABLE 3 OMITTED] in each instance with an adjusted [R.sup.2] of 0.884 for the 1 BR/1BA estimation model, 0.876 for the 2 BR/1 BA two estimation model, and 0.891 for the 2 BR/2 BA estimation model. F-statistics of 285.81, 206.75, and 129.42 indicate that all three models are highly significant. The SIZE variable is significant in each estimation model, as are all of the AGE variables. Most of the location (NEIGH) effects on rent are significantly different from the base Downtown location, and the models show a significant upward trend in rent over time for all three unit types.

The [Beta] coefficient estimates for the AGE variables can be converted to estimates of percentage decreases in rent by the formula PERCENT RENT DECREASE = ([e.sup.[Beta]] - 1) x 100. For example, the percentage rent decrease in 1 BR/1 BA units that are 5-10 years old ([AGE.sub.2]) compared with the base age of 0 to 4 years is equal to ([e.sup.-0.06536] - 1) x 100, or -6.3%. Table 4 shows percentage rent decreases for each age cohort by unit type as well as the percentage of value remaining for each age cohort compared with the nearly new base age cohort of 0-4 years. Note that rents decrease relatively rapidly in the early aging years and much more gradually in the later years consistent with the breakdown method of computing physical depreciation.

CONCLUSION

The study shows that apartment rents, hence property values, decline in Seattle as properties age. The statistical estimation models are highly significant, as are the coefficient estimates for the age cohorts determined by the data set. The pattern of decline in rents with property age is consistent with the implications of the breakdown method of estimating depreciation. That is, the form of the physical depreciation function appears to be convex, similar to the estimated property value curve shown in figure 3. This similarity is illustrated in figure 4, which plots the rent reduction percentages against the age cohorts from table 4. All three curves in table 4 are clearly convex in form.
TABLE 4 Percentage Reductions in Rent (Percentage of Like-New Rent
Remaining) as Properties Age

Age 1 BR/1 BA 2 BR/1 BA 2 BR/2 BA

5-10 years -6.3% (93.7%) -7.8% (92.2%) -9.1% (90.9%)
11-20 years -19.1% (80.9%) -20.5% (79.5%) -22.5% (77.5%)
21-30 years -24.2% (75.8%) -25.2% (74.8%) -25.2% (74.8%)
31-50 years -23.4% (76.6%) -25.8% (74.2%) -25.4% (74.6%)
Over 50 years -23.9% (76.1%) -30.4% (69.6%) -29.7% (70.3%)


The findings here are consistent with Derbes and Mason, and with the empirical findings of Hulten and Wykoff, Follain and Malpezzi, and of Malpezzi, Ozanne and Thibodeau. The result differs, however, from previously discussed empirical studies by Cannaday and Sunderman; Jones, Ferri and McGee; and by Taubman and Rasche. Differences in results could conceivably be attributed to a couple of factors. First, as Malpezzi, Ozanne and Thibodeau discovered, depreciation rates vary from location to location. Thus, there is no reason to expect consistent results. Second, an underlying problem in all of the empirical studies is an inability to uncouple the improvements from the land. Hence, if a certain age group of properties were to be predominantly similarly located and land price were changing dramatically in that location, the results could be affected by a dramatic change in land value for a given age cohort. This does not, however, appear to be occurring in this study because observations are well distributed geographically across property age cohorts.

This analysis shows that it is possible to discern a pattern of apartment property depreciation from market data. A thorough analysis of the Seattle core-neighborhood apartment market reveals that apartment rents, hence market values, decline relatively rapidly over the first 20 years of a property's life. The decline becomes more gradual as properties age, consistent with the implications of the breakdown method of estimating physical depreciation. Therefore, appraisers (at least in Seattle) should be able to uncover and apply reliable estimates of physical depreciation when estimating apartment market values by the cost approach. In addition, the sort of analysis shown here should be very beneficial in quantifying adjustments for property age differences within the sales comparison approach.

Several other intriguing observations can be derived from the estimation models. Note the substantial differences in apartment rents from neighborhood to neighborhood. For example, White Center 2 BR/2 BA rents are approximately 56% lower than Downtown rents after controlling for property age, size, and changing market conditions over time. However, the difference between these two locations is only half as much for 1 BR/1BA apartments. Conversely, Madison/Leschi rents are significantly higher than Downtown rents except for 2 BR/2 BA rents, which do not differ significantly. It is also interesting to observe the progression in rents over time. Rents have risen significantly in Seattle over the time period covered by the data, but the three unit types have not experienced the same rent growth rate. Rents for 2 BR/2 BA units have increased at an approximate 3.45% annual rate over the period, whereas the other two types of unit rents have increased at an approximate 4.33% annual rate. This leads to the question of whether or not apartment markets should be segmented by unit type. Although these other observations are interesting, an in-depth exploration of their implications is left for future study.

1. Appraisal Institute, The Appraisal of Real Estate, 11th ed. (Chicago, Illinois: Appraisal Institute, 1996), 379.

2. Bruce M. Closser, "Center City Breakdown," The Appraisal Journal (October 1988): 502-507.

3. Max J. Derbes, Jr., "Economic Life Concepts," The Appraisal Journal (April 1987): 216-224.

4. James J. Mason, "Under the Microscope: The Cost Approach," The Appraisal Journal (January 1993): 116-128.

5. Ibid., 123.

6. Thomas Holderness, "A New Look at Accrued Depreciation," The Real Estate Appraiser and Analyst (Fall 1988): 12-14.

7. Richard Knitter, "Depreciation Estimates," The Appraisal Journal (April 1993): 267-269.

8. Richard Marchitelli, "Rethinking the Cost Approach," The Appraisal Journal (July 1992): 424-426.

9. Kenneth J. Boyd, "The Cost Approach in Expropriation Cases," Canadian Appraiser (Spring 1987): 16-23.

10. Leopold Tremblay, "Cost Approach: Physical Depreciation Estimates Using the Observed Condition or Breakdown Method," Canadian Appraiser (Fall 1987): 26-30.

11. Roger E. Cannaday and Mark A. Sunderman, "Estimation of Depreciation for Single-Family Appraisals," AREUEA Journal (Summer 1986): 255-273.

12. C. R. Hulten and E C. Wykoff, "On the Feasibility of Equating Tax to Economic Depreciation," 1978 Compendium of Tax Research (Washington, D.C.: U.S. Government Printing Office, 1978): 91-128; J. R. Follain, Jr., and Stephen Malpezzi, Dissecting Housing Value and Rent: Estimates of Hedonic Indexes for Thirty-Nine Large SMSAs (Washington, D.C.: The Urban Institute, 1980): 89-98.

13. W. H. Jones, M. G. Ferri, and L. R. McGee, "A Competitive Testing Approach to Models of Depreciation in Housing," Journal of Economics and Business, v. 33, no. 3 (1981): 202-211; P. Taubman and R. H. Rasche, "Economic and Tax Depreciation of Office Buildings," National Tax Journal, v. 22, no. 3 (1969): 334-346.

14. Stephen Malpezzi, Larry Ozanne, and Thomas G. Thibodeau, "Microeconomic Estimates of Housing Depreciation," Land Economics (November 1987): 372-385.

REFERENCES

Cantwell, IV, Robert C. 'Curable Functional Obsolescence: Deficiency Requiring Substitution or Modernization," The Appraisal Journal (July 1988): 361-366.

Derbes, Jr., Max J. "Is the Cost Approach Obsolete?," The Appraisal Journal (October 1982): 581-590.

Epley, Donald R. "The Concept and Market Extraction of Effective Age for Residential Properties," The Journal of Real Estate Research, v. 5, no. 1 (1990): 41-52.

Listokin, David. "The Appraisal of Designated Historic Properties," The Appraisal Journal(April 1985): 200-216.

Lusht, Kenneth M. Real Estate Valuation: Principles & Applications. Chicago, Illinois: Irwin, 1997, chapter 12.

Mann, George R. "Replacement Allowance: Modified Sinking Fund Method," The Appraisal Journal (October 1990): 486-493.

Rand, S. J. "Cost Approach to Value," The Appraisal Journal (July 1986): 367-375.

Thayer, Ralph E. "Rethinking the Cost Approach to Valuation," The Appraisal Journal (April 1983): 278-289.

Treadwell, Donald H. "Intricacies of the Cost Approach in the Appraisal of Major Industrial Properties," The Appraisal Journal (January 1988): 70-79.

Marvin L. Wolverton, MAI, PhD, is the Alvin J. Wolff Professor of Real Estate and director of real estate research at Washington State University, Pullman. He has published previously in The Appraisal Journal and numerous other real estate journals. Contact: (509) 335-7658. remlw@mail.wsu.edu.
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Date:Apr 1, 1998
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