The document discusses performance analysis of property appraisals using ratio studies. It outlines standards for acceptable levels of appraisal and uniformity according to the International Association of Assessing Officers. Ratios are calculated by dividing appraised values by sale prices. Key statistics discussed include the median, mean, weighted mean ratios, and the coefficient of dispersion, which measures appraisal uniformity. Vertical equity is also examined using the price-related differential. Sales ratio trending can be used to adjust appraised values to meet target levels.

1. TO REAPPRAISE
OR NOT?
PERFORMANCE ANALYSIS USING
RATIO STUDIES
Sr EZWAN BUSTAMIN
PUSAT PENGAJIAN KERAJAAN TEMPATAN
I-KPKT | BERJAYA HILLS | PAHANG

2. 2
MONITOR PERFORMANCE
1. Level of Appraisal
– Overall ratio of appraised value
to market/annual value
– Provides information about the
degree to which goals or legal
requirement are met
2. Uniformity (equity) of appraisal
– Between groups – based on
comparisons of measures of
central tendency
– Within groups – based on
measures of dispersion

3. 3
IAAO PERFORMANCE STANDARD
• Level of appraisal as measured by the median ratio is between
0.90 and 1.10
• Uniformity of appraisal as measured by the coefficient of
dispersion (COD)
– Residential
• Single family residential : 5.0 to 10.0 (new market); 5.0 to 15.0 (older market)
• Heterogeneous/rural/recreational/seasonal : 5.0 to 20.0
– Income Producing
• Large urban market : 5.0 to 15.0
• Smaller urban market : 5.0 to 20.00
– Vacant Land
• Large to mid size jurisdiction : 5.0 to 15.0
• Rural or small jurisdiction : 5.0 to 30.0
• Uniformity of appraisal as measured by the Price-Related
Differential

4. 4
• DETERMINE REAPPRAISAL
PRIORITIES
• DEVELOP MARKET
ADJUSTMENT (TREND)
FACTORS
• ADJUSTMENT OF
APPRAISED VALUES
BETWEEN APPRAISAL
0.90 1.00 1.10

5. 5
• Sale/Rental ratio
– A ratio represents the variance between the appraisal and the
sale/rental
– It is computed by dividing appraisal with the sale/rental
Appraised Value = $93,200
Sale price = $99,000
Sale ratio = $93,200 ÷ $99,000
= 0.94
Appraised Value = $6,120
Annual rent = $6,000
Rental ratio = $6,120 ÷ $6,000
= 1.02

6. 6
• Median
– Midpoint or middle ratio when ratios are arrayed
– If an even number of observations, it is the average of the two
middle numbers
– Preferred measure of central tendency in ratio sales
– Advantages
• Easy to compute
• Not affected by extreme outliers
• Sample median provides an unbiased estimate of population median
– Disadvantes
• Gives no added weight to legitimate outliers
• Does not lend itself to certain statistical calculation

7. 7
• Mean
– Average ratio
– Obtained by summing the ratios and then dividing by the number of
ratios
– Accurately reflects the magnitude of every ratio, which is desirable
only if outliers are based on valid data
• Weighted Mean
– Computed by:
• Summing the appraisal
• Summing the sales/rentals
• Dividing the appraisal by sales/rentals
– Weighted each ratio based on its sales/rental price
– Also known as the ‘aggregate ratio’

8. 8
SALE NUMBER APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 89,100 90,000 0.99
2 84,150 85,000 0.99
3 91,200 95,000 0.96
4 86,700 85,000 1.02
5 102,900 98,000 1.05
6 109,200 104,000 1.05
7 95,000 100,000 0.95
8 111,550 115,000 0.97
RATIO = APPRAISED VALUE ÷ SALE PRICE

9. 9
SALE NUMBER
(arrayed)
APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
7 95,000 100,000 0.95
3 91,200 95,000 0.96
8 111,550 115,000 0.97
1 89,100 90,000 0.99
2 84,150 85,000 0.99
4 86,700 85,000 1.02
5 102,900 98,000 1.05
6 109,200 104,000 1.05
median

10. 10
SALE NUMBER
(arrayed)
APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
7 95,000 100,000 0.95
3 91,200 95,000 0.96
8 111,550 115,000 0.97
1 89,100 90,000 0.99
2 84,150 85,000 0.99
4 86,700 85,000 1.02
5 102,900 98,000 1.05
6 109,200 104,000 1.05
$769,800 $772,000 7.98
MEAN RATIO = 7.98 ÷ 8 = 1.00
MEDIAN RATIO = (0.99 + 0.99) ÷ 2 = 0.99
WEIGHTED MEAN RATIO = $769,800 ÷ $772,000 = 1.00
median

11. 11
EXERCISE

12. 12
SALE NUMBER APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 108,000 120,000
2 85,000 100,000
3 154,000 140,000
4 123,500 130,000
5 120,000 150,000
6 105,000 105,000
7 126,500 110,000
Calculate the mean, median and weighted mean ratio.
Round the mean and weighted mean to two decimals.

13. 13
• Minimum, maximum and range
– Useful for identifying extremes
• Coefficient of Dispersion (COD)
– Most common measure of appraisal uniformity
100 X ∑ | (Ai / Si) - (A/ S) | ÷ (A/ S)
n
~ ~
A = APPRAISED VALUE
S = SALE/RENTAL PRICE
(A / S) = MEDIAN RATIO~

14. 14
• Minimum, maximum and range
– Useful for identifying extremes
• Coefficient of Dispersion (COD)
– Most common measure of appraisal uniformity
100 X ∑ | (Ai / Si) - (A/ S) | ÷ (A/ S)
n
~ ~
A = APPRAISED VALUE
S = SALE/RENTAL PRICE
(A / S) = MEDIAN RATIO~
AVERAGE ABSOLUTE
DEVIATION

15. 15
SALE NUMBER
(arrayed)
RATIO
(Ai / Si)
MEDIAN RATIO
(A / S)
ABSOLUTE
DEVIATION
1 0.75 0.95 0.20
2 0.85 0.95 0.10
3 0.90 0.95 0.05
4 0.95 0.95 0.00
5 1.05 0.95 0.10
6 1.15 0.95 0.20
7 1.20 0.95 0.25
Accumulated =
Absolute Deviation
0.90
~

16. 16
Average Absolute Deviation = Accumulated Absolute Deviation ÷ n
= 0.90 ÷ 7
= 0.129
Coefficient of Dispersion = 100 X Average Absolute Deviation ÷ Median Ratio
= 100 X 0.129 ÷ 0.95
= 13.6%

17. 17
EXERCISE

18. 18
SALE NUMBER
(arrayed)
APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
5 120,000 150,000 0.800
2 85,000 100,000 0.850
1 108,000 120,000 0.900
4 123,500 130,000 0.950
6 105,000 105,000 1.00
3 154,000 140,000 1.10
7 126,500 110,000 1.15
$822,000 $855,000 6.75
MEAN RATIO = 6.75 ÷ 7 = 0.96
MEDIAN RATIO = 0.95
WEIGHTED MEAN RATIO = $822,000 ÷ $855,000 = 0.96

19. 19
SALE NUMBER
(arrayed)
RATIO
(Ai / Si)
MEDIAN RATIO
(A / S)
ABSOLUTE
DEVIATION
5 0.80
2 0.85
1 0.90
4 0.95
6 1.00
3 1.10
7 1.15
Accumulated =
Absolute Deviation
~

20. 20
VERTICAL EQUITY
1. Equity in the appraisal of low-
value and high-value parcels
2. Price-related Differential (PFD)
– a rough measure of vertical
equity
– Acceptable range : 0.98 – 1.03
3. Can also be evaluated by
comparing measures of central
tendency by value range
4. Statistical test are also available
< 0.98
UNDER APPRAISED
> 1.10
OVER APPRAISED

21. 21
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80 100
Assessment /
Sale Price
Ratios (1.0 =
Market Value)
Sale prices ($’000)
PRD 1.00
No Bias

22. 22
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80 100
Assessment /
Sale Price
Ratios (1.0 =
Market Value)
Sale prices ($’000)
PRD 0.85
Favours Low
Higher value properties are
over appraised relative to
lower properties
PROGRESSIVE

23. 23
SALE NUMBER APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 12,000 40,000 0.300
2 24,000 60,000 0.400
3 60,000 80,000 0.750
4 120,000 100,000 1.200
5 150,000 120,000 1.250
6 180,000 140,000 1.286
$546,000 $540,000 6.75
MEAN RATIO = 5.186 ÷ 6 = 0.864
WEIGHTED MEAN RATIO = $546,000 ÷ $540,000 = 1.011
PRD = Mean Ratio
Weighted Mean Ratio
= 0.864 = 0.85 (PROGRESSIVE)
1.011

24. 24
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80 100
Assessment /
Sale Price
Ratios (1.0 =
Market Value)
Sale prices ($’000)
PRD 1.13
Favours High
Lower value properties are
over appraised relative to
higher properties
REGRESSIVE

25. 25
SALE NUMBER APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 60,000 40,000 1.500
2 80,000 60,000 1.333
3 90,000 80,000 1.125
4 100,000 100,000 1.000
5 80,000 120,000 0.667
6 90,000 140,000 0.643
$500,000 $540,000 6.268
MEAN RATIO = 6.268 ÷ 6 = 1.045
WEIGHTED MEAN RATIO = $546,000 ÷ $540,000 = 0.926
PRD = Mean Ratio
Weighted Mean Ratio
= 1.045 = 1.13 (PROGRESSIVE)
0.926

26. 26
EXERCISE

27. 27
SALE NUMBER
(arrayed)
APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 193,000 215,000
2 180,000 150,000
3 216,000 200,000
4 213,750 225,000
5 270,000 200,000
6 70,000 100,000
7 97,000 114,000
Calculate the price-related differential (PRD). Round the PRD
to two decimals.

28. 28
SALES RATIO TRENDING
• Ratio studies can be used to adjust
appraisal levels to acceptable
standards.
• However, this is only effective if
the values in given area (a
neighborhood for example) are
fairly uniform.
• This can determined by reviewing
the coefficient of dispersion (COD)
for the area under consideration.
• A low COD indicates acceptable
uniformity.

29. 29
SALES RATIO TRENDING
• A trend factor can be obtained by
first determining a target level of
assessment for the chosen area.
• The target level is then divided by
the current level (as indicated by
the median sales ratio) providing
a trend factor.
• By applying the trend factor to all
the holdings in the selected area
the level of assessment will move
from the calculated level to the
selected target level.

30. 30
A sale ratio analysis conducted for Area A in XYZ jurisdiction reveals a 76%
percent level of appraisal. The target level for Area A is 95%. The sales ratio
analysis also indicated that values are fairly uniform in this area. A sales ratio
trend factor could be developed by dividing the target level by the current
level.
0.95 ÷ 0.76 = 1.25
A factor of 1.25 could be applied to all of the parcels in the Area A. By
applying this factor, the level of appraisal would change from 76% to 95%

31. 31
EXERCISE

32. 32
AREA A CURRENT
LEVEL
TARGET
LEVEL
SALE RATIO
TRENDING
Residential single-family 0.78 .95
Condominiums 0.80 .98
Commercial – office 0.75 .90
Commercial - retail 0.72 .90
Calculate the trend factor for each class of property in Area
A & B. Round the PRD to three decimals.
AREA B CURRENT
LEVEL
TARGET
LEVEL
SALE RATIO
TRENDING
Vacant land 0.80 0.90
Residential single-family 0.81 0.95
Commercial – office 0.79 0.90
Commercial - retail 0.83 0.90

33. 33
END OF
SESSION

34. 34
SALE NUMBER APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 193,000 215,000
2 180,000 150,000
3 216,000 200,000
4 213,750 225,000
5 270,000 200,000
6 70,000 100,000
7 97,000 114,000
Calculate the mean, median and weighted mean, coefficient of
dispersion (based on the median) and price-related differential. Round
the mean and weighted mean to two decimals. Use at least four decimal
places in calculating the coefficient of dispersion

35. 35
SALE NUMBER APPRAISED VALUE
($)
SALE PRICE
($)
RATIO
1 120,000 160,000
2 105,000 103,000
3 145,000 165,000
4 98,000 85,000
5 110,000 105,000
6 134,000 130,000
7 145,000 156,000
Calculate the mean, median and weighted mean, coefficient of
dispersion (based on the median) and price-related differential. Round
the mean and weighted mean to two decimals. Use at least four decimal
places in calculating the coefficient of dispersion