# Specialised property valuation: Multiple criteria decision analysis

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## Abstract

The aim of valuation is to achieve the best estimate of the transaction price of property. The market of specialised properties is very diverse as property does not transact sufficiently often to allow the establishment of price by comparison with previously sold assets. This article describes a multiple criteria decision analysis method that can be used for specialised property valuation. This method is based on a market decision-making principle and is in line with the traditional comparative methods. To estimate the property price, information on as little as two comparable properties is required. The method takes into account a number of different criteria, such as qualitative, quantitative aspects and market conditions. In this article, I describe a theoretical model of the method and provide an example of the estimation of price for a specialised property.

### Keywords

multiple criteria decision analysis specialised property valuation## INTRODUCTION

The valuation of property is an important constituent for many businesses. Depending on the type and use, properties are divided into non-specialised and specialised (French, 2004; Maliene et al., 2010). For non-specialised property, there exists sufficient transaction activity, and thus the level of prices can be established without having to interpret the property's underlying essentials. The final price is determined by comparison. The market of specialised properties is significantly more diverse than the non-specialised one. The main reason for this is that specialised properties do not transact sufficiently often (or there is no established market of transactions) to allow establishing the price of property by comparison with previously sold assets (Pagourtzi et al., 2003). Under these circumstances, the process of valuation is based on a restricted number of methods, which assess the nature and underlying essentials of property in a way that its value can be established by referring to the cost of replacement, income- or profit-producing qualities of the property. This is the foundation of the valuation methods used for the valuation of specialised property (Sayce, 1995; Askham, 2003).

Traditional methods of property valuation cannot always be expressed mathematically to meet the needs of the interested parties – buyers, sellers, investors. Although valuation standards are available (IVSC, 2007), experts are increasingly confronting the shortcomings inherent in the traditional valuation methods when estimating the price of property. The valuer's task is impeded by the fact that the customer demands the analysis of real property, which is precise and easy to understand, and the valuation that is performed by using popular methods. In addition to that, the application of unconventional methods of property analysis and valuation has no legal framework. Therefore, the valuer is frequently forced to use such valuation methods, which have a superficial mathematical description. In such cases, the valuer cannot avoid subjective decisions being made, which make the property valuation methods unreliable. The fact is that a reliable and objective valuation method is key to the correct estimation of property price (McParland et al., 2002). Such a situation has brought the need for innovations in the price estimation methodology.

In addition to the mathematical model of the property valuation method and its application opportunities, a number of other criteria determining the price of property are important in the valuation process, that is, qualitative (local infrastructure, physical status of the property, site location, legal restrictions) and quantitative (area of the property, number of buildings on the land plot, volume, number of floors, year of construction) characteristics of the property, market conditions (real property supply and demand, investment opportunities, local economic and demographic situation), as well as other criteria. Comprehensive description of the criteria ensures the maximum precision in estimating price of property. Depending on the purpose for which it is used and the types of real property, the value is predetermined by economic, legal, social, political, public planning and psychological criteria, the assessment of which depends not only on the valuer's efficiency and skills, but also on the capacity of the valuation methods to analyse the above-mentioned criteria.

A number of problems in property valuation can be eliminated by the methods of multiple criteria decision analysis (MCDA) (Belton and Stewart, 2002). The article describes the method that is based on the market analysis and valuation principle. It facilitates the universal and more extensive multiple criteria analysis of the property (Urbanavičiene et al., 2009; Zavadskas et al., 2010), as the method takes into account a number of different criteria and can satisfy the demands of many interested parties.

## METHODOLOGY

To carry out the MCDA of the specialised property, the decision-making matrix must be prepared in the following stages: (1) all information about specialised property to be valued is collected; (2) the criteria defining the aims of the multiple criteria analysis are determined; (3) values, levels of significance and units of measurement of criteria of comparable alternatives are defined; (4) criteria, their value and levels of significance make up the grouped decision-making matrix (Zavadskas et al., 1997; Maliene, 2001).

One of the most important stages in multiple criteria analysis of property is the determination of the values and levels of significance of the criteria describing the properties. Levels of significance of the criteria defining the quality and quantity of the properties to be valued and values of the qualitative criteria for the alternatives are estimated through the application of expert, social, normative, calculation and analogue methods.

When the calculation is carried out in accordance with the expert method, the qualitative values of criteria can be expressed in a certain number of points. Criteria can be estimated according to the increasing or decreasing valuation scale.

*x*

_{ best }is selected; (2) the value of the best selected criterion is set equal to the magnitude of one point (

*x*

_{ best }

*=1*); (3) the ratio between the best criterion's value (

*x*

_{ best }

*=*1) and the remaining values (

*x*

_{ i }

*)*of the same criterion is estimated and expressed in percentage

*(p*

_{ i }

*)*; (4) the relative values are attributed to the remaining values of the criterion (

*x*

_{ i }=(1−

*p*

_{ i })÷100); (5) relative values of all the criteria are set equal to the magnitude of one point ( Table 1).

The grouped decision-making matrix of the MCDA of properties to be valued

Quantitative information on property | |||||||||
---|---|---|---|---|---|---|---|---|---|

Criteria | Significance | Measuring units | Property objects to be valued | ||||||

1 | 2 | … | j | … | n | ||||

Quantitative criteria | | | | | | … | | … | |

| | | | | … | | … | | |

… | … | … | … | … | … | … | … | … | |

| | | | | … | | … | | |

… | … | … | … | … | … | … | … | … | |

| | | | | … | | … | | |

Qualitative criteria | | | | | | … | | … | |

| | | | | … | | … | | |

… | … | … | … | … | … | … | … | … | |

| | | | | … | | … | | |

… | … | … | … | … | … | … | … | … | |

| | | | | … | | … | | |

Conceptual information on property (texts, drawings, graphics, tapes) | |||||||||

| | | | | | … | | … | |

Initial significance of the criteria is determined in a similar way. The market price of specialised property reflects quality and quantity, as well as supply and demand for the property; therefore, the significance of the market price criterion for the given specialised property is equal to the total sum of significance of all the remaining criteria, that is, to one point or 100 per cent. The levels of significance of other criteria are determined by the expert method.

The decision-making matrix must be prepared in order to carry out the multiple criteria analysis of specialised property. The matrix is prepared through the analysis of the quantitative and conceptual information of the specialised properties to be valued, as well as by estimation of the criteria values and levels of significance of the properties.

The value of the property under valuation is determined by means of reiteration through several repetitive cycles of refinement until the mean deviation *k*_{ x } of the degree of utility *N*_{ j } of the property *a*_{ x } under valuation satisfies the condition *k*_{ ax } < ±1%. The initial price of the property under valuation is estimated according to the purchase prices of the comparable properties and is equal to the mean of purchase prices of the comparable properties.

*d*

_{ ij }of each criterion

*x*

_{ i }always equals the significance

*q*

_{ i }of this criterion.

*S*

_{−j}and maximising indexes

*S*

_{ −j }characterising the

*j*variant are calculated. They are calculated according to the following formula:

In this case, the values of *S*_{ +j } and *S*_{ −j } express the degree to which the property being compared achieves its purposes.

*S*

_{ +j }and minuses

*S*

_{ −j }of the properties being compared are always equal to all the sums of significance of the maximising and minimising criteria:

*S*

_{ +j }and negative (minuses)

*S*

_{ −j }qualities that characterise these properties. The relative significance

*Q*

_{ j }of each alternative

*a*

_{ j }is determined according to the following formula:

The prioritisation of the properties is determined. The larger the *Q*_{ j }, the larger the effectiveness (prioritisation) of that alternative. The summarised criterion *Q*_{ j } directly and proportionately depends on the relative influence of the value and the initial significance of the criteria under comparison on the final result.

*N*

_{ j }of the property

*a*

_{ j }is determined according to the following formula:

*E*

_{ xj }of all the alternatives

*a*

_{ j }is determined. It shows by what percentage a property

*a*

_{ x }is better or worse in comparison with another property

*a*

_{ j }:

*k*

_{ x }of the degree of utility

*N*

_{ j }of the property

*a*

_{ x }is determined:

*k*

_{ x }of the degree of utility

*N*

_{ j }of the property

*a*

_{ x }under valuation does not satisfy the condition:

then proceed to formula 10.

*V*

_{ xp }of the property under valuation is refined according to the following formula:

*V*_{ xp } is the refined value of the property under valuation. *C*_{ x } is the refined value of the property under valuation after the *n*th iteration. *k*_{ x } is the mean deviation of the degree of utility *N*_{ j } of the property under valuation.

The price of the specialised property under valuation is refined by means of reiteration through several repetitive cycles of refinement until the mean deviation *k*_{ x } of the degree of utility of the property under valuation satisfies condition (9). After condition (9) is satisfied at stage 10 by the method of multiple criteria analysis in estimating the property price, proceed to stage 12.

*V*

_{ x }of the property being valued is determined according to the following formula:

*V*_{ x } is the value of the property under valuation, *C*_{ x } is the refined value of the property under valuation after nth iteration, *k*_{ x } is the mean deviation of the degree of utility *N*_{ j } of the property under valuation.

## EXAMPLE OF APPLICATION

Data on specialized properties for MCDA matrix

Criteria | Units of measurement | Weight, % | Property under valuation | Comparable property A | Comparable property B | |
---|---|---|---|---|---|---|

1.Selling price | − | £1000 | 100 | | 204.6 | 143.0 |

| ||||||

2.Construction design | + | Points | 3.50 | 0.85 | 0.80 | 1.00 |

3.Physical depreciation | − | Percent | 3.00 | 57.00 | 34.00 | 29.00 |

4.Functional depreciation | − | Percent | 2.50 | 37.00 | 42.00 | 42.00 |

5.Economic depreciation | − | Percent | 3.50 | 13.00 | 24.00 | 33.00 |

6.Number of Auxiliary buildings | + | Units | 4.00 | 0.00 | 1.00 | 0.00 |

Quantitative assessment of premises | ||||||

7.Total area | + | Square m | 5.50 | 490 | 334 | 308 |

8.Number of salerooms | + | Units | 1.50 | 2 | 1 | 2 |

9.Area of salerooms | + | Square m | 3.50 | 230 | 150 | 216 |

| ||||||

10.Interior | + | Points | 4.00 | 1.00 | 0.60 | 0.55 |

11.Exterior | + | Points | 2.50 | 0.75 | 0.80 | 1.00 |

12.The need for renovation | − | Points | 3.50 | 0.15 | 0.70 | 0.50 |

13.Trading equipment | + | Points | 4.50 | 1.00 | 0.75 | 0.00 |

14.Number of entrances | + | Units | 1.00 | 2.00 | 1.00 | 2.00 |

15.Entrances with respect to the street | + | Points | 5.50 | 1.00 | 0.95 | 0.60 |

16.Position of showcases | + | Points | 4.50 | 0.90 | 1.00 | 0.50 |

17.Advertising possibilities | + | Points | 4.00 | 0.90 | 1.00 | 1.00 |

18.Location with respect to parts of the world | + | Points | 0.50 | 0.60 | 0.80 | 1.00 |

| ||||||

19.Engineering communications | + | Points | 3.50 | 1.00 | 1.00 | 1.00 |

20.Number of telephone lines | + | Units | 1.50 | 1.00 | 1.00 | 2.00 |

21.Assessment of alarm systems | + | Points | 5.00 | 0.00 | 0.00 | 1.00 |

22.Assessment of air conditioning | + | Points | 2.00 | 0.75 | 1.00 | 0.25 |

| ||||||

23.Distance from city center | − | Km | 5.50 | 2.00 | 4.00 | 1.00 |

24.Public transport | + | Points | 5.00 | 0.80 | 1.00 | 0.75 |

25.Distance from bus stops | − | Km | 1.50 | 100 | 200 | 50 |

26.Car Park | + | Points | 5.00 | 0.70 | 0.50 | 1.00 |

| ||||||

27.Prestige of locality | + | Points | 7.50 | 0.90 | 0.80 | 1.00 |

28.Assessment of market conditions | + | Points | 6.50 | 0.95 | 0.95 | 1.00 |

*k*

_{ x }, of the degree of utility of the property under valuation, was calculated to satisfy the condition

*k*

_{ ax }<1%. Table 3 illustrates changes in the mean deviation of the degree of utility of the property and the refined price of the property throughout all six cycles of refinement. In the last (sixth) cycle of refinement, the required condition was satisfied and the market price of the specialised property was estimated to be £173 151.

Estimation of changes in the mean deviation of the utility degree, the refined price and the market value of the specialized property under valuation

Cycle of refinement | Refined price in £ of the property, | The mean deviation of the utility degree for property | Market value in £ of the property under valuation |
---|---|---|---|

1 | 171,600 | 8.83>1 | — |

2 | 189,145 | 3.96>1 | — |

3 | 181,841 | 2.11>1 | — |

4 | 178.002 | 1.14>1 | — |

5 | 175.978 | 1.03>1 | — |

6 | 174.163 | 0.58<1 | — |

173,151 |

## CONCLUSIONS

The method of MCDA for estimating the price of specialised property enables to estimate not only the property price, but other values as well. The application of this method facilitates the performance of a complex analysis of the property, the utility of the given properties and their prioritisation in terms of one another and the significance of criteria affecting the specialised property price and marketability of the given properties.

The method can be applied not only as a separate method for estimating price, but also as a composite method within the traditional valuation methods: in the comparative method – to evaluate specific criteria influencing the market value (for example, local infrastructure, location of a property under valuation and so on); in the method of cost of replacement approach – to evaluate the depreciation of a building under valuation.

The MCDA is based on the market and specialised property analysis and on the application and evaluation of the qualitative and quantitative criteria and market conditions influencing the price of property. Therefore, this method is instrumental in carrying out the complex analysis of property with not only qualitative and quantitative differences, but with different market conditions as well.

The method is useful for specialised property valuation, as it does not require large number of properties for comparison. The example demonstrates that two comparable properties are sufficient to perform analysis.

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