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A survey of appraisers regarding factors in discounting partial interests.

The relationship between the value of a partial interest in a real property and the value of the whole may be expressed in one of the following ways:

1. The market value of all of the partial interests is equal to the market value of the whole.

2. The market value of all of the partial interests is greater than the value of the whole. In the commodity-bundling literature, entities sometimes sell their individual goods or partial interests at higher prices than those in packaged bundles. Such actions may be observed in the market for individual event tickets versus season tickets, a la carte menus versus dinner menus, and derivative securities versus their underlying pool of assets.

3. The market value of all of the partial interests is less than the value of the whole. The occurrence of plottage is well documented. The individual partial interests are valued at a discount.

These three classifications illustrate the difficulty faced by appraisers when valuing a partial interest in real estate. The subject has been debated for many years;(1) however, the real estate industry has generally accepted that partial interests are valued at discounts. The reasoning behind this conclusion is that the partial interests do not benefit from the same bundle of rights accorded to a 100% or controlling ownership position. Thus, partial interests have limited marketability and they do sell at a discount. Other factors affecting the marketability of partial interests include their limited value in use as collateral, absence of autonomous control, and possible restrictions imposed on transferring partial interests. Opinions vary regarding the size of the discount and the factors affecting its size. There are few empirical studies on the subject, and a search of the literature concerning the valuation of partial interests reveals a preponderance of personal opinions, a tendency to correlate discounts with those in the securities markets, an absence of compiled data, and semantical problems.

In the fall of 1988, a random sample of 1,000 real estate appraisers (SRPAs, SREAs, and MAIs) was surveyed regarding real property interests that were less than fee simple.(2) The questions were based on hypothetical scenarios as well as actual experiences in real estate transactions involving partial interests.(3) Approximately 14% (137) of the surveys were returned and usable.

This article examines the information from the survey, some key concepts, and the partial interest literature as well as the use of partial interests in several applications. The results of the hypothetical scenarios are discussed, as is the empirical model and its estimation, which is based on the experience part of the survey. It is hypothesized that the size of the discount applied to a partial interest is a function of the relation of the parties involved in the transaction, the attributes of the property, and the size of the interest.


The Dictionary of Real Estate Appraisal, second edition, defines a partial interest as the divided or undivided rights in real estate that are less than the whole.(4) Attempts to study this matter are limited; in his article "Valuation of Partial Interests,"(5) Healy states that there is no set procedure for valuing partial interests and that appraisers often rely on rules of thumb and court decisions. In his examination of an appraisal assignment that included the valuation of a partial interest involving data from approximately 100 sale transactions, 61% of the sales were conducted at a discount. Healy relates the discount directly to quantitative variables (e.g., property cash flow, age, location) and subjective factors. In his article "The Market Value of Partial Interests in Real Property,"(6) Hanford reasons that the valuation of partial interests is not an exact science, but rather requires skilled judgment. Proving that a discount is included in the value of a partial interest is difficult unless a comparison can be made with a market value appraisal of the 100% interest. In "Discounting Fractional Interests,"(7) Nelson focuses on various court cases involving the valuation of partial interests as well as a discussion of variables affecting the discount. The holding of a partial interest in real estate is similar to the holding of a minority interest in the stock of a closely held corporation. Discounts allowed to minority stockholders have been discussed in academic literature and serve as evidence that partial interests should trade at a discount. For instance, in their article "Quantitative Support for Large Minority Discounts in Closely Held Corporations,"(8) Harper and Lindquist explore the difference in the value of a minority shareholder interest when a market for that interest exists and when a market does not exist. Tax experts believe that a "tender offer premium"(9) is the best measure of the size of discount for minority interests. On the other hand, a discount of up to 75% might be warranted for a minority interest for which no market exists.

In "Most Courts Overvalue Closely Held Stocks,"(10) Moroney considers 146 purchases of restricted securities by investment companies. The discounts were market measured to range from 50% to 90%. In "Fixing Value of Minority Interest in a Business: Actual Sales Suggest Discount As High As 70%,"(11) Coolidge finds the discount to be as high as 70%.

Various courts have upheld this line of reasoning in valuing partial interests in real estate and have allowed the discounts attributed to partial interests to be as low as 5% and as high as 90%. Currently, Propstra v. U.S.(12) is the most commonly cited decision. The case involved the value of a half fractional interest in community property discounted (15%) in the valuation of an estate. The valuation was disputed by the Internal Revenue Service (IRS), which argued that it would be unlikely that the interest would sell apart from the other half interest (held by the spouse). The Court of Appeals granted the discount, precluding the consideration of post-death events in computing value. The relationship of the parties (and expected tendency for non-arm's-length activity) was ignored by the court.


The concept of partial interest applies to several valuation problems, including estate matters, internal buyout, partition, property taxation, condemnation, and others.

Estate matters

The estate of a deceased person presents a situation in which the valuation of partial interests is often necessary. Partial interests in inherited property have to be appraised at market value for federal estate taxes to be levied. Further, the value of the interest must be determined in the event a descendant wishes to sell his or her interest.

Internal buyout

Common forms of partial ownership such as corporations, general and limited partnerships, and equity syndications offer the opportunity for internal buyout when one or more of the owners wishes to sell his or her partial interest to another owner. Disagreements among partners and changing financial needs are often cited as reasons for liquidation, which then necessitates the valuation of the partial interests.


The law generally provides remedy, called partition,(13) to real estate co-owners wishing to move to a 100% fee simple position. A holder of a fractional interest has the right to become whole in ownership, and two methods of partition are generally available to achieve this goal. The preferable method results in former co-owners dividing a property, either economically, physically, or by agreement, such that smaller 100% fee simple interests in the original property are created. The second method creates a circumstance of forced sale at auction whereby the cash proceeds are divided fractionally pro rata.(14) It should be realized, however, that a sale in partition is a forced event, and thus does not reflect free market action.

Property taxation

Real estate is assessed for tax purposes by county assessors, who often must value the various interests in the property. Further, some areas require that the assessment be a particular percentage of market value.


When governments take private property for public use, the owners must be justly compensated for that property. Condemnation, the process of enforcing eminent domain, may also involve partial interests.

Other applications

The valuation of a life estate requires appraisal of the fee simple estate and the determination of the expected life of the life estate holder using actuarial tables. The value is then separated into the present value of the life estate and the value of the interest of the remainder.

When valuing property burdened with easements, each case must be individually examined. Value depends on whether the dominant or servient tenement's property is being appraised and the degree to which the encumbrance affects use.

Table 1 presents the results from a question in the survey regarding applications (i.e., the reason for the respondent's experience with a particular type of partial interest valuation). Note that about 70% of the data involve previously related parties (e.g., estates, buyouts, and partitions).


Section 2 of the survey(15) relates to a series of hypothetical scenarios involving the valuation of partial interests in real estate. Those scenarios and responses are discussed in the following sections.

Scenario 1

Respondents were requested to rank situations qualitatively, 1 (largest) to 4, by expected discount size: non-related parties, blood relatives, contracted parties, or married parties. Table 2, panel A presents the responses. Note that the range of the mean is small across categories, even though the related parties (i.e., blood, contract, married) are generally expected to receive smaller discounts in transacting undivided interests. Of interest, however, are the wider variances in responses to the non-related and married categories. It may be that situations involving blood relations (e.g., family property) are less likely discounted at settlement than other property.
TABLE 1 Purpose of the Valuation

 Number Percentage
Application of Responses of Responses

Estate matters 56 32%

Internal buyout 43 24%

Partition 28 16%

Income tax 15 9%

Condemnation 15 9%

Other 17 10%

Total 174(*) 100%

* Respondents could answer more than once.
TABLE 2 Responses to Hypothetical Scenarios Involving Ownership
Less than Fee Simple

Panel A
Scenario 1

Less Than Fee Simple Standard
Transactions Between: Mean Deviation

Non-related parties 2.44 1.46

Blood-related parties 2.46 0.90

Contracted partners 2.50 0.86

Married parties 2.71 1.27

Panel B
Scenario 2

Attribute in
Discount Size: Mean

Marketability 2.23

Size of interest 2.35

Voice in management 3.12

Voice in sales method 3.23

Market risks 3.55

Financing 3.67

Legal/time loss costs 4.14

Highest and best use 4.20

Other 5.92

Panel C
Scenario 3

 Size of Interest

 Interest 3/4 Interest
 (mean (mean
 discount discount
Type of Property percentage) percentage)

Build-to-suit bankable
lease 18.91% 12.51%

100-acre family farm 22.94% 16.86%

Single-family residence 24.08% 16.99%

1,000-acre swamp 33.10% 22.82%

Scenario 2

Respondents were asked to rank qualitatively, 1 (most important) to 9, the important attribute in discount size applied to less than fee values of real property: marketability, size of interest, voice in management, voice in sales method, market risks, financing, legal/time loss costs, highest and best use, or other.

It may be noted in Table 2, panel B that many of the considerations often mentioned in the traditional finance literature (e.g., lack of financing, costs of partition, market risks) are considered less important than size of the interest and voice. Overall marketability ranks first, as expected. This is upheld by some of the written comments received from practitioners. Further, Healy, Hanford, and Nelson support this conclusion.(16)

Scenario 3

Respondents were asked to contrast an opinion of the value of a one-tenth interest with a three-fourths interest in various properties. The results are presented in Table 2, panel C. Two basic observations can be inferred from this data. First, the discount size varied by type of property. Second, discount size declined as the size of the interest increased, implying a "control" premium.


Section 3 of the survey related to actual respondent experience in sales, litigation, and compromise/consultation. Respondents were asked to provide 1) size of discount, 2) size of property, 3) value of property, 4) relation of parties, 5) interest size, and 6) other information concerning partial interest appraisal assignments they may have had in the past.

Multiple regression analysis

A multiple regression equation was estimated using ordinary least squares for these data with the discount as the dependent variable and various factors potentially influencing the size of the discount as the independent variables. The estimated equation took the following form:

Discount = |a.sub.0~ + |b.sub.1~related + |b.sub.2~interest size + |b.sub.3~pptyvalue + |b.sub.4~landsize + |b.sub.5~bldgsize


discount = Size of discount assigned by appraiser, in percentage

related = 1 if parties are related, 0 if otherwise

interestsize = Size of the interest being appraised, in percentage

pptyvalue = Value of the total property, in dollars

landsize = Size of parcel being appraised, in square feet

bldgsize = Size of building being appraised, in square feet

Related parties are defined as blood relatives, contracted parties, and married parties. The related parties are expected to receive smaller discounts in transacting undivided interests. The size of the interest is expected to have an inverse effect on the dependent variable, because the partial interests do not benefit from the same bundle of rights that affect a 100% or controlling ownership position.

The value of the total property, the size of the lots, and the size of the buildings being appraised are also thought to affect the size of the discount.

Empirical results

Descriptive statistics for the variables used in this analysis are reported in Table 3.

Table 4 presents the results from the regression analysis. The F-statistic leads to the conclusion that the size of the discount is affected by the relationship of the parties involved, the size of the interest, the total property value, the size of the parcel, and the size of the building. Further, when these independent variables are considered, 87% of the variation in the TABULAR DATA OMITTED discount is explained--a strong result. After testing, the independent variable representing related parties is significant and of the predicted sign (negative). Non-related parties are offered a discount when purchasing a partial interest. As expected, the size of the partial interest also has a negative effect on the size of the discount. In addition, the coefficient is significant. This confirms the control premium mentioned in the previous section and cited by both Hanford and Healy.(17) There is a positive and significant relation between the total property value and the size of the discount, indicating that appraisers assign a higher discount to more expensive properties involved in partial interest valuation assignments. The remaining variables in the equation representing the size of the parcel being appraised (landsize) and the size of the building being appraised (bldgsize) are insignificant. Therefore, appraisers appear to believe that these variables are of less importance in partial interest valuation. It is interesting to note, however, that the intercept term is significant. This implies there are some other factors that influence the size of the discount that are not captured in the equation. For example, numerous respondents noted 15% as an unquestioned discount on partial interests, providing no justification for the discount.(18)
TABLE 4 Empirical Results (t-statistics in parentheses)

Independent Dependent Variable:
Variables Size of Discount (%)

intercept 13.947000

related -7.960000

interestsize -0.164000

pptyvalue 0.000003

landsize -1.852000

bldgsize -0.000100

|R.sup.2~ 87.26%

F 9.59%(*)

N 137.00%

* Significant at 5%.


The valuation of partial interests in real estate is an interesting topic that has been much debated by practitioners. We believe our survey to be the first of its kind to address the issue from both a practical and empirical standpoint. The respondents generally verified 1) that the dominant trading is by related parties (68% of the respondents experiences involved related parties), and 2) that there is an inverse relationship between size of discount and whether the parties were related and size of the interest being appraised. A positive relationship was found between the size of the discount and the value of the total property.

The response to the survey included generous comments (even a few phone calls). The issues covered are important and affect practitioners. A few observations about the survey results follow:

* Not one written response mentioned premiums. No cases were noted involving values or prices greater than pro rata. While the survey specifically asked for discounts, this appears odd.

* Numerous respondents noted 15% as an unquestioned discount on fractional interests valued in federal matters where interests of less than 100% are involved (perhaps the aftereffects of Propstra).

* The survey results provide a base from which to review a particular partial interest problem.

* To comply with the typical market value definition, related trading should be discarded. The response indicates that there should be few data remaining. If sufficient data remain, adjust for dissimilarities such as time, market risks, and so on.

Our original intention was to develop a decision-making tool. We have found that appraisers do not use any "set" percentage discount to apply to the valuation of partial interests. Therefore, no rules were developed regarding the discounting of partial interests. Each case must be individually examined.

1. L. Hanford, "The Market Value of Partial Interests in Real Property," The Appraisal Journal (October 1989): 460-465; M. Healy, Jr., "Valuation of Partial Interests," The Appraisal Journal (July 1988): 293-298; R. Nelson, "Discounting Fractional Interests," The Appraisal Journal (October 1969): 522-528.

2. Partial funding for this survey was received from the Society of Real Estate Appraisers. Some of the respondents to our survey were also designated as SRAs and RMs of the American Institute of Real Estate Appraisers.

3. A copy of the survey is included in the Appendix.

4. American Inst. of Real Estate Appraisers, The Dictionary of Real Estate Appraisal, 2d ed. (Chicago: American Inst. of Real Estate Appraisers, 1989), 220.

5. Healy, "Valuation of Partial Interests."

6. Hanford, "The Market Value of Partial Interests in Real Estate."

7. Nelson, "Discounting Fractional Interests."

8. J. Harper and P. Lindquist, "Quantitative Support for Large Minority Discounts in Closely Held Corporations," The Real Estate Appraiser and Analyst (Winter 1983): 270-277.

9. In a takeover, a tender offer premium is that value paid to the target firm's shareholders that is over and above the stock's fair market value.

10. R. Moroney, "Most Courts Overvalue Closely Held Stocks," Taxes (March 1973): 144-156.

11. C. Coolidge, "Fixing Value of Minority Interest in a Business: Actual Sales Suggest Discount As High As 70%," Estate Planning (Spring 1975): 138-141.

12. 680 F. 2d. 1248 (USCA, 9th Cir. 1981).

13. H. C. Black, Black's Law Dictionary, 4th ed. (St. Paul, Minn.: West Publishing, 1951), 1276.

14. Often an inability to "cash" co-owners out causes severe hardship in this case.

15. Section 1 of the survey asked for a general profile of the respondents.

16. Hanford, "The Market Value of Partial Interests in Real Property"; Healy, "Valuation of Partial Interests"; Nelson, "Discounting Fractional Interests."

17. Hanford, "The Market Value of Partial Interests in Real Property"; Healy, "Valuation of Partial Interests."

18. Individual regression runs were also made of each independent variable against size of discount. Those results show that only the related party variable is significant with the expected sign. All of the equations had low |R.sup.2~s.

C. F. Sirmans, SRPA, PhD, is the director of the Center for Real Estate and Urban Economic Studies at the University of Connecticut. He received his PhD in real estate and urban development from the University of Georgia, and has written numerous books and articles on the subject of real estate.

John C. Doiron, MAI, has an appraisal practice in Baton Rouge, Louisiana. He received both a BA and an MBA from Louisiana State University and is a former adjunct professor of finance at Louisiana State University and Nicholls State University.

Krisandra A. Guidry, PhD, is assistant professor of finance at Nicholls State University in Thibodeaux, Louisiana. She received her doctorate from Louisiana State University.
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Title Annotation:includes appendix
Author:Sirmans, C.F.; Doiron, John C.; Guidry, Krisandra A.
Publication:Appraisal Journal
Date:Oct 1, 1993
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