Download SIZE ADJUSTMENTS: GETTING WITH THE PROGRAM

SIZE ADJUSTMENTS: GETTING WITH THE PROGRAM
VERSION 7.04
11/94
Gene Dilmore
SIZE ADJUSTMENTS: GETTING WITH THE PROGRAM
Why Do We Need Size Adjustments?
When a purchaser buys a 40-acre tract of land, he usually pays a lower price per acre than does the
purchaser of a 20-acre tract, everything else being equal. Putting the principle in the more formal terms of
the land economist, size adjustments are an expression of the principle of marginal utility, defined in the
DICTIONARY OF REAL ESTATE APPRAISAL, 2n Ed., Chicago, American Institute of Real Estate
Appraisers, 1989, as follows: "The addition to total utility by the last unit of a good at any given point of
consumption. In general, the greater the number of items, the lower the marginal utility; i.e., a greater
supply of an item or product lowers the value of each item." The IAAO publication, PROPERTY
APPRAISAL AND ASSESSMENT ADMINISTRATION, Chicago, IAAO, 1990, pp 41-43, discusses
marginal utility theory as an explanation of the demand side of the market. It is this declining marginal
value assigned to each additional square foot of land that we seek to quantify with size adjustments.
Limiting Conditions
First off, let us acknowledge that size adjustments do not apply to every sample of
comparable sales. Some specific instances:
1. We are comparing two apartment sites; one has 20,000 square feet,
and the second has 19,800 square feet. In most markets, the primary
pricing unit for apartment sites is the number of units which can be
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built on the lot. In this case, the zoning allows one unit per 1,000
square feet of land and the apartments are typically 2-story, in order to
maximize parking area.
Thus 18 units would be feasible on the
19,800 square foot lot, and 20 on the 20,000 square foot site. The
19,800 square foot parcel would not sell for a higher price per square
foot. In fact, from the apartment developer's point of view, he is pricing
a site for 20 units as compared with one for 18 units. The additional
200 square feet, therefore, are worth the same amount as 2,000
square feet, since he can built two more apartment units on the second
site. So the 19,800 square foot lot would be worth only a little more
than a similar 18,000 square foot site.
2. 2. In the analysis of timberland values, we find that most markets will
not adjust a smaller size property upward on a per acre basis; often, in
fact, a premium might be paid (on a unit basis) for the larger tract,
since the operation of the timber enterprise can take advantage of
economies of scale.
3.
In analyzing land sales in the central business district of my home city, and
testing with both the Size Adjustment program and regression analysis using
"size" as one of the variables, I have never (so far) found a size adjustment to
be applied in the market. This may or may not be the case for your downtown
area; you can find out by running the size adjustment program, to see if the
adjustments reduce the dispersion of the data, as represented by the
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coefficient of variation (COV), the standard deviation as a percentage of the
mean of the adjusted sale prices.
There may well be other exceptions to the declining marginal price
concept in land sales. I have found that In some areas with a relatively
unsophisticated market, the concept does not apply, not for any arcane
technical reasons, but simply because buyers in the local market do not,
even subconsciously, analyze prospective purchases to this extent.
In any event, if size adjustments are not appropriate for the data set, the program will
tell you so.
Birth of the Size Adjustment Tables
It had always bothered me that I so often had to discard potential comparable sales
simply because I did not know how to account systematically and consistently for the price
differential generated by a size differential in land sales. In reviewing numerous appraisals
by others, I often encountered "plus 10% for size," or "minus 5% for size" obviously
reflecting completely arbitrary adjustments that could not pass the test of consistency.
Discussion with other appraisers indicated that this was a universally frustrating problem;
the appraisers were in some cases reluctantly applying arbitrary adjustments, and in many
cases even more reluctantly discarding land sales that they knew would have been usable
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had they only known what the pattern of differential was.
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One day in 1975, a pair of sales showed up, side by side on a major highway, with
the only major difference being that one was a 5-acre parcel, and the other a 10-acre
parcel, the 10-acre parcel selling for about 90% of the per-acre price of the 5-acre parcel.
(To the best of my recollection, excepting inside versus adjoining corner lot sales, this was
the first and last instance I've encountered of a set of real-world "paired sales," as opposed
to the sales with 12 variables identical, and only one variable different, as described in
many appraisal textbooks and articles.)
The teasing puzzle was too tempting to resist. I set to work over the weekend to find
an underlying relation between the two sales that could be generalized to other sales. That
is, what form of curve could make a consistent change when the size was doubled,
regardless of its absolute size? I tried a number of trial and error approaches--square
roots, various adaptations of the standard depth table formulas, logarithmic curves, and so
on.
The differential is obviously not directly proportionate to the size, since that would
result in every parcel selling for the same price: If a 40 acre tract sold for half the per acre
price of a 20 acre tract, then the total price would be exactly the same, and as every
doubling of size halved the unit price, the total sale would remain the same. Thus we are
obviously looking for a curve that constantly decreases in its steepness, and that begins
with an adjustment that is less than a 50% adjustment for a doubling of size.
There were obviously a number of curves that could be fitted to the sales; we could
even fit a different curve to each batch of sales, but the objective was the simplest, most
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elegant type of curve that would be totally consistent from one appraisal to the next.
The shape that made the most sense to me was an adaptation of the Airframe
Learning Curve. During WW2, Stanford Research Institute made a study of airframe
production efficiency. They found that, generally speaking, the 200th production item cost
approximately 80% as much as the 100th item; that is, a doubling of the number of
airframes (plane fuselages) produced resulted in a unit cost reduction of 20%. Since this
reduction in cost ratio was a result of learning from a repeated process, it was called a
learning curve, and it was soon discovered that many phenomena followed this pattern.
The formula for this curve, adapted to the land price problem is:
Y = [Ac.67808/.67808/Ac]/ [As.67808/.67808/As].
Where
Y = the size adjustment factor
Ac = area of the comparable
As = area of subject
This original formula can be simplified to:
Y = Ac1-.67808/As1-.67808
And simplifying one more step, we raise the area of the comparable to the 0.32192
power, and divide it by the area of the subject also raised to the 0.32192 power. This is the
formula for the "80%" curve, meaning that, if this curve fits the data, a parcel twice the size
of another parcel will, other things being equal, sell for about 80% of the unit price of the
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smaller parcel.
An example: Our subject is a 200-acre tract, and the first comparable is a 150-acre
tract. Applying the formula:
150.32192/200.32192 = .91.
Thus, if Comparable No. 1 sold for $10,000 per acre, the sale (assuming other
factors have been adjusted for) indicates a price for subject of $9,100 per acre.
The obvious next step was to adjust the formula to produce a set of curves of
varying steepness, covering the likely range of the curves. The adjustment factors for
steeper or less steep curves are calculated in the same way; all that changes is the value
of the power. Thus, a "90% curve," meaning that a parcel twice as large as another would
sell for about 90% of the unit price of the smaller parcel, follows the same calculations, but
with an exponent of 0.152 rather than the 0.32192 for the 80% curve; an 85% curve uses
an exponent of 0..23445, and so on.
The Size Adjustment Program
You don't need to memorize these numbers; the Size Adjustment program, which
was the next logical step, asks for the input data, consisting of (1) the size of subject, (2)
the number of sales, then (3) the size and unit price of each sale. The unit price is the
selling price adjusted for all factors except size. The program calculates the potential size
adjustment factors using fourteen curves, from 65% to 97.5%, in 2.5% steps.
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It then prints out, for each of the fourteen curves, a set of adjustment factors,
followed by the mean of the adjusted selling prices for each curve, the standard deviation,
and the coefficient of variation, which is the standard deviation as a percentage of the
mean. A coefficient of variation of 20%, for example, means that in a normally distributed
set of adjusted sale prices, about 68% of the adjusted sale prices would lie within about
20% plus or minus of the mean, or average of the adjusted prices.
Next the program selects the curve that results in the smallest coefficient of
variation, and applies the adjustment factors for that curve to the comparable sales. The
rationale here is that a major purpose of adjusting sales is to reduce the dispersion in the
raw data.
In other words, if all of your sellers and purchasers were perfectly
knowledgeable and rational, and all of your adjustments perfectly reflected every possible
difference in price, all of your adjusted sale prices would be identical.
So much for the appraiser's fantasy life; now back to the real world: In that world,
the real estate market itself is far from perfect, to say nothing of appraisers. We generally
assume, though, that a reduction in the dispersion of our data represents a closing in on
the indicated value of our subject property.
The reduction in the coefficient of variation by application of the final optimum curve
represents more reduction in dispersion than may appear at first glance. For example,
reducing the standard deviation from 45% of the mean to 35% of the mean is not a 10%
reduction, but a 22% reduction in the dispersion of your data.
The program next calculates a preliminary value indication based first on the mean
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of the adjusted prices, then a second indication based on the median of the adjusted
indications. When the remaining dispersion is still somewhat larger than you would like,
you may feel that the median has more appeal than the mean, since it could be considered
to represent a better measure of centrality.
The next step calculates a modal value indication. Clearly, with our comparable
sales constituting a quite small sample in most cases, and being in the form of continuous
values rather than discrete values, a directly observable mode will very rarely occur. We
therefore find an equivalent calculated mode, by simply taking the average of the two
observations that are closest to each other. The mode is obviously not a highly reliable
value indicator; the purpose of including it is to give a more complete representation of the
distribution of adjusted sales.
Along with the three measures of centrality, we also have measures of dispersion for
each. The coefficient of variation, which is the standard deviation as a percentage of the
mean, is used in the calculations rather than the raw standard deviation, since the
absolute amount of the standard deviation varies in accordance with the magnitude of the
mean. Thus, a standard deviation of 2.34 doesn't really tell us much, but if we know that
this deviation is 35% of the mean, we do know something, namely that we have a problem.
The coefficient of dispersion of the median is a simpler calculation: We subtract the
value of each observation from the median, sum the absolute differences, and divide by
the number of observations less one. The dispersion of the mode is calculated the same
way.
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The program also calculates two other characteristics of the distribution of adjusted
sales: the skewness and kurtosis. The skewness reflects a preponderance of values on
either side of the midpoint of the distribution.
Skewness may be calculated several ways; the method I am using is one that is
intuitively comprehensible: We measure the number of standard deviations that the mean
lies to the right of the median, or midpoint of the distribution. Thus, a skewness of 0.85
means that the mean is 85% of a standard deviation to the right of the mean. A negative
skewness, such as -0.85, says that the mean is 85% of a standard deviation to the left of
the median.
Kurtosis describes the peakedness or flatness of the distribution. An ideal perfectly
normal curve is given the value of three. A positive kurtosis figure means the distribution is
more peaked than normal. An acceptable range is 2.20 to +3.80. A kurtosis measure
higher than 3.80 reflects an extremely peaked distribution, and one
below 2.20 is
considered to be excessively flat.
The formula used in the program is
Alpha 4 = m4/(m2)2,
Alpha 4 is the name for the measure of kurtosis and m 2 and m4 represent the second
and fourth moments of the x's about their mean. Moments are the means of the powers of
the deviations of items in the distribution. The x's are values of the items (that is, adjusted
sales prices) minus their means. The formula for the calculation of kurtosis that I am using
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is therefore
Sum x4/N/(Sum x2/N)2
Geary's Ratio is an alternative kurtosis measure, consisting of: average
deviation/standard deviation. As N approaches infinity, this ratio approaches the square
root of 2/pi, or approximately 0.80.
The Quartile Deviation is defined as 1/2 of the mid-range, consisting of the difference
between the 75th quartile and the 25th quartile.
Its Coefficient of Variation is its
percentage of the Median.
The Standard Error gives us a measure which, when multiplied by the proper tvalue, gives us the number needed to calculate a confidence interval. In this program, a
90% confidence interval is automatically calculated. The standard error is also printed, in
case you want to apply some other confidence interval. To do this, find in the t-tables the tvalue for the number of degrees of freedom (N-1; in this case, 6), and multiply by the
standard error.
These measures help to give us a snapshot of the distribution of the
adjusted sales after the size adjustments are applied.
The amount of reduction in the dispersion of the prices that the size adjustments
account for is also shown.
One fruitful application of the program at this point, entirely aside from derivation of
size adjustment factors, is to spot sales whose adjusted prices are inconsistent with the
other adjusted prices.
Of course, we should not automatically discard an outlier just
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because it is an outlier. On the other hand, bearing in mind that one of the assumptions of
the size adjustment program is that we have already made adjustments for all other
relevant factors, we may want to see whether there were other property attributes or
variables in these sales that we had not previously adjusted for, or whether a sale may not
have been an arms-length transaction, or whether we may have made some arithmetic
error in analyzing the sale, or did not know all the conditions of the sale.
Remember, too, that the three preliminary value indications from the mean, median,
and mode implicitly assume that each sale carries equal weight. In a particular valuation
you may or may not feel that this assumption is appropriate.
In case you want to insert the final size adjustment factors into a spreadsheet
containing the other adjustments, the program automatically saves a temporary ASCII file
called <sizeadj.out>, for "size adjustment output," which contains nothing but the final
adjustment factors, and can be read into a "Size Adjustment" row in a spreadsheet.
Size7.04: Screens
The following are the three main screens for the Size Adjustment program:
Opening Screen:
**********************************************************************
Size Adjustment Program - Version 7.04 11/23/94
GENE DILMORE
Input consists of:
Size of Subject;
Number of sales (MUST be more than 3; MIN. OF 5 SUGGESTED)
Size & unit price of each comparable
Output consists of:
application of a set of 14 modified learning curves to the data,
with resulting mean, std dev, & coefficient of variation.
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The best fitting curve is selected and the program then applies the best set
of adjustment factors to the sales and prints out the indicated
adjusted mean, median, and mode. [Compressed print suggested.]
A file called SIZEADJ.OUT will also contain the final
adjustment factors for reading into a 1-2-3 file.
Best results are obtained if all other adjustments are applied first. Then use
the semi-adjusted unit sale prices as the input prices.
References: GD:Appraisal Journal 4/81, Right of Way 5/78, R E Appraiser 5-6/76.
W. N. Kinnard, Jr.: Journal of Property Tax Management, Winter 1991.
If problems, call: Gene Dilmore (205) 823-5479 or fax 822-7457
For a Glossary of terms, press F1
To continue, press any other key.
F1
Glossary Screen:
*******************************************************
Glossary:
MODE: The value occurring most often. The mode in this program is a calculated
equivalent mode, consisting of the
average of the two values in the data closest to
each other.
COEFFICIENT OF VARIATION: The standard deviation as a percentage of the mean.
COEFFICIENT OF DISPERSION: The measure of dispersion for the Median.
The absolute difference between the Median and each value is found. These differences
are summed, and the sum is divided by N-1.
The Coefficient of Dispersion for the Mode is derived by the same calculation except that
the differences are found between the Mode & each value.
Skewness: The measure used here is the number of std deviations that the mean is to
the right of the median. I.e., if the skewness measure is -.80, the distribution is skewed
.80 std dev's to the LEFT.
Kurtosis: The measure of 'peakedness' of the distribution. Perfect normality, at a value of
3.00, is mesokurtic (range >2.20 <+3.80). Positive is leptokurtic, or more peaked than
normal; (>3.80) and negative indicates a platykurtic, or flattened distribution (<2.20).
Press any key to continue.
Screen With Formulas:
If you have found the optimum curve for a property,
and want to use this subject as a composite comparable,
you can use a single adjustment for additional
subjects, with this formula, for example, for the 65% curve:
Comparable Area^.6214883/Subject Area^.6214883
Raise the comparable area to the .6214883 power, and divide by the subject area
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raised to the same power.
The powers for the 14 possible curves are:
65% = .6214883
82.5% = .277534
67.5% = .5670405
85% = .23445
70% = .51456
87.5% = .192645
72.5% = .463947
90% = .152
75% = .41503
92.5% = .1124747
77.5% = .36773
95% = .074
80% = .32192
97.5% = .03652585
Press any key to continue.
Let's go to the work screen, and key in the data for the appraisal of a 40,000 square
foot commercial lot on McFarland Boulevard, Tuscaloosa, Alabama.
Work Screen:
*********************************************
What is subject size (no commas!) ? 40000
How Many Sales? 7
Where would you like the output to go:
<1> Screen
<2> Printer
<3> Disk File
Your choice? 3
Output files are: 0.out Name of output file?
brand.out
Do you want to load a file of comparable sales? no
For Sale No. 1, enter size (no commas!), and unit price (example: 20000,7.75)?
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28674,7.30
For Sale No. 2, enter size (no commas), and unit price (example: 20000,7.75)?
21468,8.59
For Sale No. 3, enter size (no commas!), and unit price (example: 20000,7.75)?
39163,7.45
For Sale No. 4, enter size (no commas!), and unit price (example: 20000,7.75)?
24520,7.49
For Sale No. 5, enter size (no commas!), and unit price (example: 20000,7.75)?
479160,2.27
For Sale No. 6, enter size (no commas!), and unit price (example: 20000,7.75)?
25264,6.30
For Sale No. 7, enter size (no commas!), and unit price (example: 20000,7.75)?
306000,2.64
Do you want to save the data for later use (Y/N)? y
Input files in this directory: 0.siz Name for input file? brand.siz
The Output of the Program
At this point the program performs the calculations, sending the output to the file
<brand.out>, which looks like this:
Size Adjustment Factors for 14 Curves
ADJ FACTORS:
65% 67.5% 70% 72.5% 75% 77.5% 80%
# 1
0.81 0.83 0.84 0.86 0.87 0.88 0.90
# 2
0.68 0.71 0.73 0.75 0.77 0.80 0.82
# 3
0.99 0.99 0.99 0.99 0.99 0.99 0.99
# 4
0.74 0.76 0.78 0.80 0.82 0.84 0.85
# 5
4.68 4.09 3.59 3.16 2.80 2.49 2.22
# 6
0.75 0.78 0.79 0.81 0.83 0.84 0.86
# 7
3.54 3.18 2.85 2.57 2.33 2.11 1.93
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ADJ FACTORS: 82.5% 85% 87.5% 90% 92.5% 95% 97.5%
# 1
0.91 0.92 0.94 0.95 0.96 0.98 0.99
# 2
0.84 0.86 0.89 0.91 0.93 0.95 0.98
# 3
0.99 1.00 1.00 1.00 1.00 1.00 1.00
# 4
0.87 0.89 0.91 0.93 0.95 0.96 0.98
# 5
1.99 1.79 1.61 1.46 1.32 1.20 1.09
# 6
0.88 0.90 0.92 0.93 0.95 0.97 0.98
# 7
1.76 1.61 1.48 1.36 1.26 1.16 1.08
Analysis of 14 Size Adjustment Curves:
Mean of prices= 6.005714
Standard deviation of prices = 2.517042
Coefficient of variation = .4191079
Mean of prices adj'd w/65% curve = 7.052357
Std dev = 2.182436
Coeff of var = .3094619
Mean of prices adj'd w/67.5% curve = 6.831329
Std dev = 1.574014
Coeff of var = .230411
Mean of prices adj'd w/ 70% curve = 6.6101
Std dev = 1.109854
Coeff of var = .1679028
Mean of prices adj'd w/72.5% curve = 6.449857
Std dev = .7687079
Coeff of var = .1191822
Mean of prices adj'd w/ 75% curve = 6.316971
Std dev = .6394528
Coeff of var = .1012278
Mean of prices adj'd w/ 77.5% curve = 6.211114
Std dev = .754085
Coeff of var = .121409
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Mean of prices adj'd w/ 80% curve = 6.129771
Std dev = .9489481
Coeff of var = .1548097
Mean of prices adj'd w/ 82.5% curve = 6.065443
Std dev = 1.173194
Coeff of var = .1934226
Mean of prices adj'd w/ 85% curve = 6.029028
Std dev = 1.408227
Coeff of var = .2335745
Mean of prices adj'd w/ 87.5% curve = 6.0187
Std dev = 1.639968
Coeff of var = .2724788
Mean of prices adj'd w/ 90% curve = 5.990172
Std dev = 1.837085
Coeff of var = .3066832
Mean of prices adj'd w/92.5% curve= 5.981429
Std dev = 2.020123
Coeff of var = .3377325
Mean of prices adj'd w/95% curve = 5.9789
Std dev = 2.194307
Coeff of var = .3670085
Mean of prices adj'd w/97.5% curve = 5.9907
Std dev = 2.367384
Coeff of var = .3951766
RECAP OF SIZES & PRICES
SALE# SIZE
1
28,674.0000
2
21,468.0000
3
39,163.0000
4
24,520.0000
5
479,160.0000
6
25,264.0000
7
306,000.0000
PRICE
$7.30
$8.59
$7.45
$7.49
$2.27
$6.30
$2.64
FACTOR
0.87
0.77
0.99
0.82
2.80
0.83
2.33
ADJ PRICE
$6.35
$6.61
$7.38
$6.14
$6.36
$5.23
$6.15
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40,000.0000 @ mean adj'd price
$6.32 = $252,679
Coeff of Variation = 0.10
40,000.0000 @median adj'd price
$6.35 = $254,040
Coeff of Dispersion = 0.07
Skewness
= -0.05
Kurtosis
= 3.10
(Perfect mesokurtosis = 3.00)
Geary's Ratio
= 0.64
(Perfect normality = 0.80)
40,000.0000 @ modal adj'd price
$6.35 =
Coeff of Dispersion = 0.07
Quartile Deviation = $0.11
Coeff of Variation = 0.02
Standard Error
= $0.24
Reduction in Dispersion = 75.85%
90% Confidence Interval = $5.85--$6.79
$254,140
(These are preliminary indications only, and may or may not
represent the final value.)
The temporary ASCII file, called <sizeadj.out>, looks like this:
0.87 0.77 0.99 0.82 2.80 0.83 2.33
This little file can then be read into a "Size Adjustment" line in a spreadsheet.
Note: If the dispersion in the data is not reduced by application of size adjustments,
the program tells you so.
Caveats
Just as with any other valuation procedure, the preliminary value indications
resulting from application of size adjustment factors are just that, preliminary, and are not
necessarily final nor precisely exact. The market itself is not exact; we are not dealing in
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physical quantities, but in probabilities of mental reactions-- some logical, some emotional,
in sellers and purchasers.
The emotional element is inherent, even in transactions involving multi-million dollar
investment properties. While the appraiser is asked to postulate the perfectly rational and
perfectly informed seller and purchaser, these two gentlemen exist only in the same sense
that for the seasonal purposes of an editorial writer and his little Christmas-time
correspondent Virginia, there really is a Santa Claus.
Another factor coming into play at this point in the valuation process is the
phenomenon of anchoring. This is a natural occurrence related to the sequence in which
we perceive a series of magnitudes, and applies to all numeric estimates, only incidentally
including those made by appraisers. This means that value estimates will tend to cluster
toward the beginning point of the reasoning process from which they were derived.
Put another way, if you adjust a sale upward, you tend to end up a little below the
"true" value, and if you adjust it downward, you tend to end up a little above this desired
figure.
This factor does not pose any major dangers, except when most of your
adjustments are in the same direction.
In that case, you might want to take it into account in arriving at your final value
conclusion. A final caution: Just as with regression analyses or other similar statistical
analyses, if the magnitude of your subject is extremely remote from the range of the data in
your sample, the further its size is outside that range, the less reliable the conclusion is. Of
course, in an extreme case, it is possible that you are dealing with a different highest and
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best use category anyway, in which case the sale should not be included in the first place.
Remember that a crucial assumption in the program is that, despite the size
differential between a comparable and the subject, the general highest and best use for the
comparable and the subject are the same. Even so, the adjustment procedure of Size704
is quite robust, and can deal consistently with fairly large differentials.
For example, in the <brand.out> file, taken from the appraisal that we happened to
be working on when I started writing these notes, we see that, prior to applying the size
adjustments, Sale No. 1, with only 28,674 square feet, has a semi-adjusted price of $7.30
per square foot, while Sale No. 5, with 479,160 square feet, has a semi-adjusted price of
$2.27 per square foot. At first blush, we might be tempted to discard one or both sales,
since they appear to be so inconsistent. After the size adjustments are applied, however,
Sale No. 1 is now adjusted to $6.35 per square foot, and Sale No. 5 is adjusted to $6.36
per square foot. The Size Adjustment program won't always narrow the differences that
closely, but you will find that many collections of comparable sales contain much more
usable information than you thought.
Downloading the Program
The size adjustment program can be downloaded from Compuserve:
"Go
InvestForum"; Library 6; Real Estate; Download SIZE74.EXE. SIZE74.EXE is selfextracting, and contains SIZE704.EXE, which is Version 7.04 of the size adjustment
program, example input and output for two properties (the lot discussed here, and an
office site appraised on the basis of square footage of building), and a copy of this article in
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WordPerfect 6.0 (DOS).
It can also be found on the Appraisers BBS, established by SysOps Richard J.
Brandt, MAI and George S. Cochis, SRPA. Use default settings of No Parity, 8 Data Bits, 1
Stop Bit; dial 1-312-743-1769, and follow the prompts. The file name is the same,
SIZE74.EXE.
By the time you read this, it should also be on the American Society of Appraisers
BBS, Appraisal Profession Online, under the same file name: 1-703-478-5502
The program is "freeware," so feel free to pass along copies. Adjust in good health.
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