32 Unit Appraisal for Pre-Market Sales

Scroll down to the last section which outlines the different pricing for the 32 units based up the 5 most important variables.

Please note: The figures (boxplots) throughout the report have been removed for privacy and simplicity.

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Executive Summary:

The valuation project is a 32-unit low-rise strata development, “University Gate” which is located in a mixed use suburban neighborhood in a growing market.  All municipal approvals and construction financing has been secured.  The target market is made up of professionals seeking to downsize, early retired empty nesters, and other higher net wealth individuals seeking a higher quality home and/ or investment opportunity in the area.  The project is located near community shopping and a park giving it a location quality of AVERAGE.  The project’s quality of construction and finish will be ABOVE AVERAGE relative to competing, existing, low-rise condos; furthermore, it is competitive with other new low-rise condo projects in the area.  Each strata unit includes one parking space in a secure underground lot. Pre-sales will begin as soon as this pricing information is complete.

The comparable sales used in this analysis contained 76 sales of condos that are sold in the similar market as the subject from December 31, 2007 until January 31, 2009. However, the focus was on the sales between June 2008 and February 2009. In the end 45 sales were used to estimate the sales price. In order to justify the premarket value of the units, it was based on a regression model which focused on five variables such as: orientation, size of living area, location quality, floor level and sales price per sq.ft.

After completing numerous statistical techniques, the regression model was used to estimate the Predicted Sales Price Per Square Foot and the Predicted Sales Price.  The estimated sales price per square foot for University Gate is $428 as of March 1, 2009.

Market Identification:

Purpose of Appraisal:  The purpose of this appraisal is to provide market analysis and support for determination of selling prices for strata (condominium) units in the University Gate residential Project.

Use of Appraisal:  The intended use of this appraisal is to guide the marketing specialists in pricing each strata unit in the University Gate residential project.

Market Value:  Is defined by The Appraisal of Real Estate (Canada 3^rd Edition) as

“The most probably price, as of a specified date, in cash, or in terms of equivalent to cash, or in other precisely revealed terms, for which the specified property rights should sell after reasonable exposure in a competitive market under all conditions requisite to a fair sale, with the buyer and selling each acting prudently, knowledgeably, and for self-interest, and assuming that neither is under undue duress.”

Property Characteristics:    University Gate is a brand new, 4-level, 32- unit condo which has 8- one bedroom and den units, 12 – two bedroom units and 12 – two bedroom and den units. All of the one bedroom units with a den have 1.5 bathrooms. The two bedrooms and two bedrooms with den all have 2 bathrooms. Lastly, every unit has one underground secured parking stall.

Scope of Work:  This report has researched and reviewed all the sales data, after which statistical methods were conducted to provide an estimate of market value as of March 1, 2009.

Data Decision:  University Gate is a 32 unit development which has received all of the necessary municipal approvals as well as financing.  The construction will begin immediately and therefore, the best comparable sales data is between 2008 and 2009.

Data Exploration

Basic Stats

 The condo sales database named “condosalesjul15” has 76 observations which include 23 variables.  45 of the comparable sales were built in 2008 while the remaining 31 were built between 1988 and 2006.  As you can see in Table 1, the sales prices between $141,750 and $611,100 which is a range of $469,350.  The mean, which is the average which can be affected by outliers, is $333,421.54 and the median, which is the middle sales price, is $332,947.50. The standard deviation is $99,041.76, which is over 1/3^rd the value of the mean which indicates the data is fairly dispersed or widely spread out.  This indicates that the mean becomes less representative when estimating the market value of the units when using all 76 comparable sales.  In order to delve deeper, exploratory data analysis is required.

Reduction

When reviewing the database of 76 comparables there were 8 comparables that were missing data.  Based on the information in the comparables database, the missing data was adjusted so that there is no missing data. The subject property, University Gate, is a 4 storey 32 unit strata building which is being constructed now and therefore grouping or breaking up the variable of new construction is required. This way we can look at the price and statistics on New Construction data.

Table 2

The data above in Table 2 indicates a few things.  Firstly, the mean and median price of new construction, as expected, is higher than non-new construction.  The standard deviation of non-new construction and new construction is about 1/3^rd of the mean which indicates that the data is fairly spread out.   A good tool to compare a continuous variable (sales price) and discrete variable (New Construction and Non –New Construction) is the Boxplot.

Figure 1

The left box in figure 1 shows the non new construction and the right box shows new construction.  Non new construction is less dispersed that new construction, and the sales price is between $220,000 and $315,000. It should be noted that non new construction has a circle outside of the box (17).  This indicates that the value of a sales price is outside of the norm and is an outlier. However, no further exploration was taken on this sale because the focus will be on new construction only.

Since University Gate is new construction, the only comparables that are relevant are new constructions and these will be used in predicting the market value for the strata units.  With this in mind, 29 non new construction comparables have been removed from the data set which leaves 47 sales that will be further explored. The next part will focus Revelation which is separating the signal from the noise.

Revelation

Even though the Boxplot didn’t uncover an outlier with regards to New Construction, extreme sales prices will impact the estimated value.  A great way to uncover this information is through the use of a Scatterplot (Figure 2) which will look at Sales Price and Sales Data.

Figure 2

The Scatterplot indicates that most of the sales have taken place between June 2008 and February 2009. Outside of these sales there is a large gap between sales for two of the data points.  These two sales have been removed from the dataset.  At this point we have gone from 76 comparable sales data to 45 and from this the data quality will be examined before the data can be reduced.

Table 3

Original Database

                                                                        Table 4

As you can see in Table 3 compared to Table 4, the Standard Deviation and Coefficient of Variation both decrease after some of the unrelated data was removed.    This is a positive sign as this indicated that the reduced data best resembles the subject property.

For clarification purposes, according to the Business 344 Statistical and Computer Applications in Valuation Workbook, the standard deviation is a measure of a distribution around its mean. It also states that the Coefficient of Variation is a measure designed to allow comparisons between two standard deviations of two data sets.  Lastly, it defines the correlation coefficient (r) as a statistic that characterizes two or more sets of numbers and when squared and multiplied by 100 gives the percentage strength of the linear relationship between two sets of numbers (2011).

Re-Expression of Data

We started with 76 comparables and after reduction we have arrived at 45 comparables as the best data to price the subject property.  We have used sales price, price per square foot, and sales price per bedroom as the three best dependent variables. To further uncover this relationship, we use two techniques to expose which one is a better fit which were the Coefficient of Variation (COV) and Coefficient of R or Correlation Coefficient. By scanning Table 4 it is apparent that Sales price per Square foot has the lowest COV at 16.8%.   To verify whether sales price per square foot is the best unit of comparison, a simple linear regression model was used to uncover the relationship between price with price per square foot and price per bedroom.  As you can see in Table 5, sales price per square foot has the highest match at .467 versus .254 for sale price/bedroom.

Data Residuals

The majority of the sales occurred between August 2008 and February 2009.  In order to see if a time adjustment is necessary a market condition analysis was conducted.

Figure 3

Figure 4

Both Figure 3 and 4 indicate that the sales prices are stable and that no adjustment was necessary.  This is verified by the R² measurements of .004 and 3.16 E-4 in both figures.  The R² or RSquare Linearis defined on page 2.22 in Business 344 Statistical and Computer Applications in Valuation Workbook as the coefficient of determination, which measures the degree to which the dependent variable (sales price or sales price per square foot) is explained by the independent variable (Sales Date).

Transformations:

There are a couple variables that need to be transformed which are Car_S (car sharing) and Orientation. All of the comparables have (Yes) in the Car_S column and therefore there is no transformation necessary.  However, with the variables Park_S and Orientation were further tested with a Boxplot to see if there was an impact on pricing.  In Figure 5 below, you can see that there is an impact on pricing when there is either secure parking or not.  Therefore, the Park_S variable has been transformed into a discrete variable with Y = 1 and N = 0 (secure parking).

Figure 5

Figure 6

As you can see above in Figure 6, the orientation of the units affects the sales price per square foot of the comparables. When analyzing the figures above, North is the most valuable direction followed by the South, East, and West.  We have set the North direction as the default and transformed the other variables into discrete variables with the names SView, EView and WView.

There are other variables that can impact the sales price and these have been explored using different statistical methods.  The variables that were explored are:  the Size Variable, Floor Level, Number of Bedrooms and Bathrooms, and lastly Competitive Set and Location Rank.

Size Variable

This variable is one of the largest influencers in real estate pricing, therefore it will be used in estimating the selling prices per units.

Floor Level

This variable has been included in the analysis of price because as you can see below in Table 6 and Figure 7, the higher the floor level, the more expensive it is per square ft.

Figure 7

Bedrooms and Bathrooms

As you can see below, the amount of bedrooms and bathrooms impacts the pricing of the units. It should be noted that as the number of bedrooms and bathrooms goes up, the lower the price per square foot is.

Figure 8

Figure 9

Competitive Set and Location Quality Rank Variable

As you can see below, the higher the quality of property and its location results in a higher sale price.    Properties that are located in an average to below average sell less per sq.ft than properties sold in an above average location.  All of this can be seen in (Tables 11, 12, 13, 14, and Figures 10 and 11)

Figure 10

Figure 11

List of Variables for Calibration

The variables below have been narrowed down to be Included in the Multiple Regression Model.

                                Table 16

All of the steps that were taken to this point has indicated that Sales Prices per Square Foot is the best measure in determining the value of the strata units. We started will a test of all the variables in Table and then different formations to see whether or not this would impact the outcome.

The first test was conducted which was a regression analysis of the variables in Table 16.  The R Square is relatively high at .84, and the Standard Error of the Estimate is relatively low at $32.14.  However, the Variance Inflation Factor (VIF) are high for some variables in this model.  According to Statistical and Computer Applications in Valuation, The Tolerance should be greater than 0.3 with a VIF less than 3.33.  A variable that has a tolerance value of less than the target of 0.3 is considered to show multicollinearity which can have a serious effect on the value of its coefficient (2011).  Therefore Competitive Set Rank, Park_Snew (Parking secured new), East View, Bathroom and Bedroom have been removed from the model.

After removing these variables, a new model was generated and this can be seen below in Table 17.   As you can see the Tolerance are all high and the VIF are below the 3.33 threshold.  The R value or correlation coefficient is high at .849 which means the variables that were used are highly correlated. The R Square which can be seen in Table 18 is .72 which means that 72% of the sales price per sq.ft can be explained by floor level, location quality rank, size (sq.ft), SView and WView.  The mean of $420.76 per square foot and the Standard Error of the Estimate is $39.70235, the result COV is 9.44% (rounded). This low percent indicates that the independent variables are a good indicator of the sales price for the subject property.   Lastly the F ratio of 20.084 indicates that the regression estimates fit the data well. As clarified by Statistical and Computer Applications in Valuations, a rough rule-of-thumb, modellers often use a critical level of F-statistic > 4 to indicate a statistically significant relationship (2011).

When looking at the data in Table 17 closer you can tell that for every floor that your rise in the building the price increases at $18.13  (rounded) per sq.ft; furthermore, there buyers would pay $8.86 (rounded) to have a view of the South while it would be discounted at $27.23 (rounded) to have a West View.  Lastly the location of the property has a heavy influence on the price because the constant is $114.84 (rounded) and the size influence is (-) negative at -.146.

Table 17

  Table 18

Valuation Analysis:

Residual Analysis

            Using the information obtained in Table 17 the regression model is represented by the following:

Estimated Selling Price/ Sq.FT = 171.997 – .146 x (size in sq.ft)   + 114.814 x (Location Quality Rank)   – 27.225 x (West View) +   8.861 x (South View)   + 18.127 x (Floor Level)

Table 19

Table 20

From Table 19 above, the residual statistics and Table 20 which is the descriptive statistics for the PRE_1 (Predicted Value), RES_1 (residuals), and Sales Price per Sq.ft the mean predicted value is $420.76, which is identical to the sales price per square foot. The model is skewed a bit because the median of $401.39 per Sq.ft is lower than the mean. In Table 20, there is a wider range in the Sale Price/ Sq.Ft which indicates there is the possibility of a few outliers.  However, in the end this regression model is a great fit in estimating the final sales price.

Applying the Model

As stated earlier in the project information, University Gate quality of construction and finished is above average; furthermore, it’s located near a shopping centre and park which results in the location quality ranking of average. This information has been used to predict the selling prices of each strata unit through the regression model.  The predicted sales price for University Gate can be seen in Table xx in Appendix C.

Table 21

The information in Table 21 above indicates the statistics for the Predicted Price per Sq.ft and the Predicted Price overall for the different units at University Gate.  As you can see the COV or Coefficient of Variation for the Predicted_Price_SQFT is 6.77% which is found by dividing the Standard Deviation by the Mean (28.9737/427.995 = .06769635).  The COV for Predicted_Price is 27786.28553/390467.0466 = .07116167 or 7.12%.  Both of the COV’s are below 10% which indicates that the regression model has produced a good result. Both the means and medians are almost identical for both predicted price per sq.ft and for predicted price.  However, they are both higher than the comparable data.  Lastly, the range of the prices for the price per square foot and estimated sales price is well within range of the comparable.  In the end the prices of the units for University Gate are reasonable.

Recommendations and Conclusion

Through the use of different statistical analysis techniques the market value for University Gate Complex was calculated.  Through the process of data reduction, data revelation, data re-expression, data residuals and data modelling the comparable data was adjusted to reflect the current market.  The original database started with 76 units and through the different techniques outlined above, 45 data points were used in the end.  The five variables that had the biggest impact on pricing were Location Quality Rank, SVIEW, WVIEW, Floor, and size (in sq.ft).

In the end, the estimated price per square foot on the valuation date of March 1, 2009 is $428 per sq.ft.

In order to improve the validity of the pricing, the comparable data set could be larger, or other more advanced calculations could be completed in order to verify the pricing.

Appendix A – Variable Calibration Stats Summary

Appendix C – Predicted Sales Price per Square Foot of UNIVERSITY GATE

                                                            Table