Economics of Real Estate Development :Economics of Real Estate Development :

Appraisal can be described as a process of estimating marketing value, investment value, insurable value or other properly defined value of an identified interest or interests in a specific parcel or parcels of real estate as of a given date.

Baum and Mackmin (1989) give a better interpretation of the "process" :

• "...Valuation is a process which requires careful consideration of a number of variables before figures can be substituted in mathematically proven formula...Any assessment of present worth or market value can only be as good as the data input allows and that factor is dependent upon the education, skill and experience of the valuer. Ability to analyze and understand the market is of paramount importance..."

This process should be best described as appraisal or evaluation.

By appraisal, it means a process of information collection; selection; organization, analysis and eventually conclusion.

Analysis is an essential and vital part in this process before getting to this conclusion.

The divergence in the approaches in the treatment of the appraisal process comes from the fact that appraisal is always broken into different pieces of exercises or aspects depending on the objectives.

This makes appraisal only a practical way to solve problems within an established market system.

Whenever there is need to find value, it is a matter of appraisal. Appraisal ,therefore, should aim at getting the value' , not price. This is exactly what the term “valuation” implies. There is no estimation

of price, although there is estimation of possible price. This is because price can only be realized through actual market transaction.

Objectives of Appraisal : Appraisal is a discipline of philosophy. Like Law and Management, it has different branches of theories and

applications. Hence each of these methods can only explain part of the market to the

extent that the assumptions behind them can go. To examine the role and application of appraisal techniques under

different economic system, the rationale per se should be understood.

Appraisal literally means the finding of the value, not price. There is a basic difference as well as relationship between them.

Market is the place where value is transformed into a common indicator of trend - price - through a series of negotiation and legal proceedings.

Value should be taken as an element to help decision making and analysis process, while price is the decision made after this process. To use Marx's words , the measure of value exists before exchange.

Appraisal is not about the mathematical process through which a statistically precise figure can be created and proved.

It is about the explanation of the inter-relationship between the different variables in the real estate market from the micro level and in the economy from the macro level.

Market Comparison Market comparison approach is regarded as the most

reliable method of valuation. Only if the market is a normal one without an out of

proportion influence of speculation. When the asset value is unreasonably and speculatively

over-priced, market comparison can only provide a reference point for the market price in a very short time frame, without any indication of the market value of this asset, since there is a theoretical difference between price and value.

When the market is truly competitive, market price itself reflects truly the worth of the property. In this case, market comparison is acceptable.

The biggest advantage of market comparison approach is easy and quick.

Besides, in most other kinds of appraisal techniques, there is always an element of comparison.

Individual properties can be subjectively and even objectively distinguished from each other by a whole series of variables such as floor height, orientation, building age, and psychological impression to different individuals, or the factor of Feng Shui.

Hence, it is almost impossible to have an “apple-to-apple” comparison.

Adjusting intuitively becomes a normal practice. However, this can only be applicable if the valuer is very experienced and well-trained.

In the following, some of the more scientific comparison adjustment techniques are introduced as an alternative to pure intuition.

It should be emphasized that the degree of reliability depends very much on the skill of the valuer as much as the robustness of the technique.

Factor Adjustment Technique : Market Comparables : Property One Two Three Four Prices $4.3M $4.75M $5.85M $3.98M 1) Macro factors : Time adjustment +15% +5% --- +20% Location adjustment -5% +7% -10% +10% Size +10% +5% -3% +13% Stage 1 adjusted price level : $5.16M $5.558M $5.10M $5.69M

2) Micro Factors : Developer 1.05 1.01 1.1 1.0 Interior 1.05 0.95 1.2 1.01 Age 0.95 1.0 0.80 0.9 Floor 1.1 1.05 1.02 1.05 View/Orientation 1.0 1.1 1.15 0.95 Overall rating : 1.15 1.11 1.23 0.91 Adjusted value : $5.93M $6.17M $6.27M $5.2M

Weighted average by subjective judgment : Comparables Weight Value component 1 0.3 x $5.93M $1.779M 2 0.4 x $6.17M $2.468 3 0.2 x $6.27M $1.254 4 0.1 x $5.2M $0.52M value : $6.021M

Regression Analysis : Where more market transaction data is available, a more robust

version of the adjustment technique can be applied. This is the statistical model of multiple regression analysis.

One of the most effective ways of elaborating the importance of individual predictor variables on the determination of property prices is by way of statistical analysis in terms of a regression analysis. Achen (1982) remarks that

• “...the strength of ordinary regression is its great resilience. As the consistency theorem shows, if the researcher sets up the problem correctly, regression will tend to the right answer under any reasonable practical circumstances, even if a great many of the classical postulates are violated. ”

Regression analysis is a statistical approach of finding the extent to which a dependent variable such as property price is influenced by a set of other variables.

The common input procedures are stepwise and backward. The stepwise regression is one of the most popular and common regression procedures.

A stepwise model is a modification of the forward selection procedure and is a combination of backward and forward procedures.

In the stepwise model, the regression computer programme will first estimate the simple linear regression relationship using each of all the predictor variables specified.

If there are a total of 10 predictor variables, the computer programme will estimate 10 different simple linear regressions.

From these 10, the best one will be selected based on the coefficient of determination or commonly known as the R2 (which tells the extent to which variations in the dependent variable can be explained by the independent variables in the regression model).

In the next step, the computer will try each of the 9 remaining predictor variables together with the one chosen earlier one by one. Again, the best one will be selected. This process will be repeated automatically until the R2 cannot be improved anymore so that some of the original 10 predictor variables may not be included in the final result.

Using similar logic but working in reverse, a backward model for regression analysis includes all the predictor variables specified at the beginning.

The computer will then remove those predictor variables whose removal from the regression will improve the R2 , provided that the observed significance level is larger than the criterion for remaining in the model.

This procedure will keep on removing irrelevant predictor variables one by one until the R2 cannot be improved any further.

Usually, the backward model is a better procedure when the analyst wants to consider all the predictor variables from the outset so that no important variables will be missed out.

Regression Analysis - A test on HK markets number of samples put into statistical model is 310 for South

Horizon and 275 for Laguna City, in 1994.

The set of independent variables selected is categorized into three groups.

One of the groups is the physical character of the premises which includes :

i) age; ii) gross floor area of the unit; iii) the loss ratio, iv) number of storey of the building; v) vertical ratio and vii) the orientation.

The second group is the location variables, they include : i) the walking distance to the transport node or terminus and

ii) the walking distance to the nearest shopping arcade. Finally, it is the time variable on a monthly basis.

Physical factors : AGE is determined from the difference in time between the issue

date of occupation permits by the Building Department and the date of transaction.

GROSS is defined as the gross area claimed by the developer of the transacted unit.

LOSS means the loss factor. It is the ratio of non-usable floor area to the gross area (SIZE) of the unit. The non-usable area is defined as the gross area subtracted by the net area of the unit. The reason for this is because the higher the loss factor is, the less floor area of the unit the user can enjoy.

VERT is defined as the vertical ratio of the unit to the total number of floors in the corresponding building.

Locational factors : DISTT is the walking distance from the corresponding building

entrance to the nearest terminus with the most efficient transportation.

DISTS is the walking distance from the corresponding building entrance to the nearest or busiest shopping arcade.

Orientation (Dummy) factors : (ORIN), (ORIS), and (ORIW) are dummy variables describing

the effective orientation North, South, and West respectively of an unit. An entry of “1” to any of them represent the bearing of that direction. For instance, an entry of ORIN=1, ORIS=0, ORIW=0 represents the unit bear north in direction.

Time Series Factor TIME is defined as the transaction date of the unit. It is measured

in the unit of month. An entry of “11” means November, 1994, “12” means December, 1994 and so on.

Property Price Movement in 1994

222

224

226

228

230

232

234

236

238

1/94 2/94 3/94 4/94 1/95

Price Index

REGRESSION RESULTS (LAGUNA CITY)

Independent

Variable

Coefficient t-value Beta-

coefficient

AGE -14.4601 -9.928 *** -0.4493

GROSS 0.5370 -8.381 *** -0.3569

TIME -59.8742 -5.394 *** -0.2455

VERT 500.1769 4.508 *** 0.1914

(Constant) 5733.9179 48.740 ***

Functional Form: Linear

Dependent Variable: PRICE

Degree of Freedom: 270

Adjusted R2 : 0.51360

Excluded

Variables

t-value

DISTS 1.164

DISTT -1.270

LOSS 1.149

ORIN 0.027

ORIS 0.739

ORIW -0.560

* Coefficient is significantly different from zero at 90%

level of confidence.

** Coefficient is significantly different from zero at 95%

level of confidence.

*** Coefficient is significantly different from zero at 98%level of confidence.

Income Approach or Investment Method The logic of capitalising future rental values to obtain the property

value is well-recognised by the property professionals :

• "...The basic principles of property value suggest the existence of a predictable relationship between income and value. Knowing that real estate is only one of many investment opportunities, the behaviour of buyers and sellers in other investment markets should give us a clue about the income/value relationship...If a plausible relationship between income and value can be estimated when only the income is known..."

This provides a certain logic in arriving the value of the property. At least it gives a guarantee that the income to be generated from the property will be able to compensate for the cost of owning the property.

This gives a clearer picture of the relationship of the different elements in the appraisal process.

This logic has long been recognized by the well-established economic theory of capital value, as Fisher (1930) gives out his idea of what capital value is :

• "... 1) capital value is income capitalized or discounted, 2) if the rate of interest falls, the capital value rises and vise versa, 3)This rise or fall in capital value is relatively grate for durable goods like land, ...4) capital value is increased by savings, the income being decreased by the same amount that the capital is increased. 5) These savings thus diverted from income and turned back into capital will, except for mischance, be the basic for real income later..."

In the simplest form, income approach means the summation of all future rental income. The process of summation is called capitalization which takes the present value of these future income into consideration. In fact, income approach is the closest of property appraisal techniques to the investment and financial world. In the stock market, for example, the price/earning ratio (PER) has long been a common measurement for investment decision.

Basically, there are three major elements in this model, namely the rental income; capitalization yield and the holding period. The latter two will work out a multiplier - Years' Purchase in the U.K. appraisal terminology , or Income Multiplier in the U.S. system - which is then multiplied to the annual income to produce the capital value.

In Fisher's terms, it means :

• "... the price of income in terms of capital ... is called the ' rate of years' namely the number of years during which there would flow an amount of income equal to the capital ..."

Both the yield and rental income can be found from market data. Holding period is specific to the subject property.

As the capitalisation rate decides the magnitude of the income multiplier factor to a certain extent, the adjustment of yield (when valuing for the particular property) becomes very important. This adjustment depends on a set of assumptions each of which contribute to the final 'shape' of the figure.

These include the growth factor during the term and reversion, rent review pattern, and risk element. Among all these, growth factor is especially important for this is the element which defines the meaning of implied all risk yield for capitalization.

The basic logic of the investment method is the understanding that money has a time value. Money receivable in the future is worth less then money of the same amount receivable today.

Hence, the present value (PV) of one dollar receivable after n years at an interest rate (or discount rate) of i is worth :

The product of formula can be called a PV factor. This is a factor for this can be multiplied to any future value of a fixed sum (as opposed to a stream of future values in the case of years’ purchase factor, discussed later) of money to find the present value.

The PV factor is always less than 1 because future value is always less than present value in real terms. The reasons for this are mainly twofold. One is the opportunity cost in expecting future value. Opportunity cost is the return forgone in other investment opportunities when investing in a particular project.

PVi n

1

1( )

For instance, if an investor has HK$100 and he invests all of this sum into project A, the opportunity cost for this decision is the likely return he could have achieved from projects B,C or D had he chosen to do so. So long as project A compensates him enough or opportunity cost is less than return from project A, the investment is a sound one. In the present value situation, the utility of immediate consumption is always greater than deferred consumption. Hence future value is less than present value.

The second reason is the age of inflation. Future value is always readily eroded by inflation in terms of purchasing power.

In fact, the PV factor formula can be analyzed from reverse in an investment angle. For instance, if we have HK$100 today and invest this sum into a regular investment giving a 10% return per annum.

In one year’s time, we will have HK$110 (since HK$100 x (1+10%) = HK$110). In this case, 10% is our required rate of return.

Now, let’s look at this from the future. If we are given an opportunity to receive HK$110 in one year’s time, how much are we prepare to pay for such opportunity ? Since we can earn 10% from a regular investment, we will use 10% as the discount rate to find the present value. As a result, the present value of HK$110 in a year’s time is :HK$110 x 1/(1+10%) = HK$100. This illustrates the fact that the discount rate and rate of return for investment are closely related. To a certain extent, we can even assert that they are the same.

When the value of the stream of incomes (I) is fixed within the holding period, the capital value (V) of the interest in property (hence the summation of the future incomes) during the holding period then becomes :

It is also obvious that when the holding period approaches infinity, the re-sale value of the asset approaches zero, hence it becomes relatively insignificant. In infinity, PV of the reversionary capital value approaches 0 such that formula becomes :

VPV

iI

1*

VI

i

How different could Income Approach have made ?

Example 1:Mortgage Valuation using Investment Model :

( could negative asset have been avoided in 1997 ?)

Case 1 : Taikoo Shing Tower TH 20/F825 sqft. With seaview

Sold in Dec, 1996 - HK$6.5mMarket rental estimated to be :$19,000/mth

Simulation of Mortgage Valuation by Investment Model of appraisal :

HK$19,000 x 12 months /market yield

= HK$228,000/5.2% (RV data in 1996)=HK$4.38m

Similar units sold for HK$3.8m (Dec. 2001 value)

Case 2 : Kingswood Villa KW Court 20/F811 sq.ft.

Sold in Dec, 1996 - HK$2.5mMarket rental estimated to be :$6,500/mth

Simulation of Mortgage Valuation by Investment Model of appraisal :

HK$6,500 x 12 months /market yield

= HK$78,000/5.2% (RV data in 1996)=HK$1.5m

Similar units sold for HK$1.45m (Dec. 2001 value)

Example 1 :Advise your client on the investment value

for the following real estate :120-124, Charter Road is a 4-storey

building for commercial/residential use held under single ownership by Mr. Rich. Each floor has an area of 240 sq.m. Ground floor is a retail shop Me-2. The first floor is used as office. The second floor is residential floor with two units of equal size. Mr. Rich occupies the top floor.

The tenancies are as follows :

-Ground Floor : Retail shop held under long lease with 15 years

to go at HK$650,000 p.a. with 3-yearly rent review. Current market OMR for similar shops is about HK$850,000 p.a. The next rent review is two years from now. Expected growth rate of rent is about 8% p.a. All risk yield for retail shops in the neighbourhood is about 6%.

-First floor :Divided into two units. Unit A (120 sq.m.

in gross floor area) is occupied by a trading company with 7 years to go with no rent review at HK$350,000 p.a. Current OMR is about HK$450,000. Expected growth rate of rent is about 6% p.a. All risk yield for offices in the neighbourhood is about 8%. Unit B is currently empty (120 sq.m.) and expected to be rented out in 6 months’ time

-2nd floor Wong’s Family on Flat A (120 sq.m. in

gross floor area) just moved in two days ago paying HK$ 220,000 p.a. The tenancy agreement contains normal rent review pattern. Dum’s Family next door (120 sq.m. in gross floor area) is having a long lease with 7 years unexpired. The lease contains no rent review. Dum’s Family is now paying HK$ 135,000 p.a. Expected growth rate of rent is about 5% p.a. All risk yield for residential in the neighbourhood is about 9%.

-3rd floor.Occupied by Mr. Rich

In this example, we have both the properties with vacant possession ready (unit B on the first floor and the whole of third floor), and properties with sitting tenants paying less than open market rent. When we apply investment appraisal to value this real estate, we will separate the treatment for these two kinds of interests.

First of all, we can always be able to find the value of a property if we have the initial annual rental income and the all risk yield of this class of property.

For properties with sitting tenant paying less than market rent, under the British appraisal system, we have the Term and Reversion Method.

Under this method, we separate the rental income into term income and reversionary income.

Term income refers to the income receivable during the contract term with the sitting tenant before the expiry date of the tenancy or the next rent review date.

Reversionary income refers to the rental income achievable in the open market when either the occupation right reverts back to the landlord for another tenant or when the landlord is free to set a new open market rent at rent review date.

G/F : Term : HK$650,000 x YP @6% 2 yrs. = HK$650,000 x 1

1

1 6%

6%

2

= HK$650,000 x 1.83 = HK$1,189,500.

Reversion : HK$850,000 x YP 6% in perpetuity x PV6% 2 yrs.

= HK$850,000 x 1

6% x

1

1 6%2

= HK$850,000 x 16.67 x 0.89= HK$ 12,610,855

Value : = HK$1,189,500 + HK$ 12,610,855= HK$13,800,355

1st /F : Unit A

Term : HK$350,000 x YP 8% 7 yrs. = HK$350,000 x 1

1

1 8%

8%

7

= HK$350,000 x 5.21 = HK$1,823,500

Reversion : HK$450,000 x YP 8% in perpetuity x PV8% 7 yrs.

= HK$450,000 x 1

8% x

1

1 8%7

= HK$450,000 x 12.5 x 0.58= HK$ 3,262,500

Value : = HK$1,823,500 + HK$ 3,262,500= HK$5,086,000

1st /F : Unit BHK$450,000 x YP 8% in perpetuity x PV8% 0.5 yr

= HK$450,000 x 18% x

1

18%05 .

= HK$450,000 x 12.5 x 0.962Value : = HK$ 5,411,250

2nd /F : Unit AHK$220,000 x YP 9% in perpetuity

= HK$220,000 x 19%

= HK$220,000 x 11.11Value : = HK$ 2,444,200

2nd /F : Unit BTerm : HK$135,000 x YP 9% 7 yrs.

= HK$135,000 x 1

1

1 9%

9%

7

= HK$135,000 x 5.033 = HK$679,455

Reversion : HK$220,000 x YP 9% in perpetuity x PV9% 7 yrs.

= HK$220,000 x 1

9% x

1

1 9%7

= HK$220,000 x 11.11 x 0.55= HK$ 1,344,310

Value : = HK$1,344,310 + HK$ 679,455= HK$2,023,765

3rd /F : HK$440,000 x YP 9% in perpetuity

= HK$440,000 x 1

9%= HK$440,000 x 11.11

Value : = HK$ 4,888,400

Total investment value of 120-124, Charter Road is : = HK$ 33,653,970