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Ratiostudies

Sr Ezwan Bustamin
Sr Ezwan Bustamin

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.

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TO REAPPRAISE OR NOT? PERFORMANCE ANALYSIS USING RATIO STUDIES Sr EZWAN BUSTAMIN PUSAT PENGAJIAN KERAJAAN TEMPATAN I-KPKT | BERJAYA HILLS | PAHANG
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 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 DETERMINE REAPPRAISAL PRIORITIES DEVELOP MARKET ADJUSTMENT (TREND) FACTORS ADJUSTMENT OF APPRAISED VALUES BETWEEN APPRAISAL 0.90 1.00 1.10
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 歎 $99,000 = 0.94 Appraised Value = $6,120 Annual rent = $6,000 Rental ratio = $6,120 歎 $6,000 = 1.02
6 Median Midpoint or middle ratio when ratios are arrayed If an even number of observations, it is the average of the two middle numbers Preferred measure of central tendency in ratio sales Advantages Easy to compute Not affected by extreme outliers Sample median provides an unbiased estimate of population median Disadvantes Gives no added weight to legitimate outliers Does not lend itself to certain statistical calculation
7 Mean Average ratio Obtained by summing the ratios and then dividing by the number of ratios Accurately reflects the magnitude of every ratio, which is desirable only if outliers are based on valid data Weighted Mean Computed by: Summing the appraisal Summing the sales/rentals Dividing the appraisal by sales/rentals Weighted each ratio based on its sales/rental price Also known as the aggregate ratio
8 SALE NUMBER APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 89,100 90,000 0.99 2 84,150 85,000 0.99 3 91,200 95,000 0.96 4 86,700 85,000 1.02 5 102,900 98,000 1.05 6 109,200 104,000 1.05 7 95,000 100,000 0.95 8 111,550 115,000 0.97 RATIO = APPRAISED VALUE 歎 SALE PRICE
9 SALE NUMBER (arrayed) APPRAISED VALUE ($) SALE PRICE ($) RATIO 7 95,000 100,000 0.95 3 91,200 95,000 0.96 8 111,550 115,000 0.97 1 89,100 90,000 0.99 2 84,150 85,000 0.99 4 86,700 85,000 1.02 5 102,900 98,000 1.05 6 109,200 104,000 1.05 median
10 SALE NUMBER (arrayed) APPRAISED VALUE ($) 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 歎 8 = 1.00 MEDIAN RATIO = (0.99 + 0.99) 歎 2 = 0.99 WEIGHTED MEAN RATIO = $769,800 歎 $772,000 = 1.00 median
11 EXERCISE
12 SALE NUMBER APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 108,000 120,000 2 85,000 100,000 3 154,000 140,000 4 123,500 130,000 5 120,000 150,000 6 105,000 105,000 7 126,500 110,000 Calculate the mean, median and weighted mean ratio. Round the mean and weighted mean to two decimals.
13 Minimum, maximum and range Useful for identifying extremes Coefficient of Dispersion (COD) Most common measure of appraisal uniformity 100 X | (Ai / Si) - (A/ S) | 歎 (A/ S) n ~ ~ A = APPRAISED VALUE S = SALE/RENTAL PRICE (A / S) = MEDIAN RATIO~
14 Minimum, maximum and range Useful for identifying extremes Coefficient of Dispersion (COD) Most common measure of appraisal uniformity 100 X | (Ai / Si) - (A/ S) | 歎 (A/ S) n ~ ~ A = APPRAISED VALUE S = SALE/RENTAL PRICE (A / S) = MEDIAN RATIO~ AVERAGE ABSOLUTE DEVIATION
15 SALE NUMBER (arrayed) RATIO (Ai / Si) MEDIAN RATIO (A / S) ABSOLUTE DEVIATION 1 0.75 0.95 0.20 2 0.85 0.95 0.10 3 0.90 0.95 0.05 4 0.95 0.95 0.00 5 1.05 0.95 0.10 6 1.15 0.95 0.20 7 1.20 0.95 0.25 Accumulated = Absolute Deviation 0.90 ~
16 Average Absolute Deviation = Accumulated Absolute Deviation 歎 n = 0.90 歎 7 = 0.129 Coefficient of Dispersion = 100 X Average Absolute Deviation 歎 Median Ratio = 100 X 0.129 歎 0.95 = 13.6%
17 EXERCISE
18 SALE NUMBER (arrayed) APPRAISED VALUE ($) 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 歎 7 = 0.96 MEDIAN RATIO = 0.95 WEIGHTED MEAN RATIO = $822,000 歎 $855,000 = 0.96
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 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 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 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 ($000) PRD 0.85 Favours Low Higher value properties are over appraised relative to lower properties PROGRESSIVE
23 SALE NUMBER APPRAISED VALUE ($) 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 歎 6 = 0.864 WEIGHTED MEAN RATIO = $546,000 歎 $540,000 = 1.011 PRD = Mean Ratio Weighted Mean Ratio = 0.864 = 0.85 (PROGRESSIVE) 1.011
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 ($000) PRD 1.13 Favours High Lower value properties are over appraised relative to higher properties REGRESSIVE
25 SALE NUMBER APPRAISED VALUE ($) 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 歎 6 = 1.045 WEIGHTED MEAN RATIO = $546,000 歎 $540,000 = 0.926 PRD = Mean Ratio Weighted Mean Ratio = 1.045 = 1.13 (PROGRESSIVE) 0.926
26 EXERCISE
27 SALE NUMBER (arrayed) APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 193,000 215,000 2 180,000 150,000 3 216,000 200,000 4 213,750 225,000 5 270,000 200,000 6 70,000 100,000 7 97,000 114,000 Calculate the price-related differential (PRD). Round the PRD to two decimals.
28 SALES RATIO TRENDING Ratio studies can be used to adjust appraisal levels to acceptable standards. However, this is only effective if the values in given area (a neighborhood for example) are fairly uniform. This can determined by reviewing the coefficient of dispersion (COD) for the area under consideration. A low COD indicates acceptable uniformity.
29 SALES RATIO TRENDING A trend factor can be obtained by first determining a target level of assessment for the chosen area. The target level is then divided by the current level (as indicated by the median sales ratio) providing a trend factor. By applying the trend factor to all the holdings in the selected area the level of assessment will move from the calculated level to the selected target level.
30 A sale ratio analysis conducted for Area A in XYZ jurisdiction reveals a 76% percent level of appraisal. The target level for Area A is 95%. The sales ratio analysis also indicated that values are fairly uniform in this area. A sales ratio trend factor could be developed by dividing the target level by the current level. 0.95 歎 0.76 = 1.25 A factor of 1.25 could be applied to all of the parcels in the Area A. By applying this factor, the level of appraisal would change from 76% to 95%
31 EXERCISE
32 AREA A CURRENT LEVEL TARGET LEVEL SALE RATIO TRENDING Residential single-family 0.78 .95 Condominiums 0.80 .98 Commercial office 0.75 .90 Commercial - retail 0.72 .90 Calculate the trend factor for each class of property in Area A & B. Round the PRD to three decimals. AREA B CURRENT LEVEL TARGET LEVEL SALE RATIO TRENDING Vacant land 0.80 0.90 Residential single-family 0.81 0.95 Commercial office 0.79 0.90 Commercial - retail 0.83 0.90
33 END OF SESSION
34 SALE NUMBER APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 193,000 215,000 2 180,000 150,000 3 216,000 200,000 4 213,750 225,000 5 270,000 200,000 6 70,000 100,000 7 97,000 114,000 Calculate the mean, median and weighted mean, coefficient of dispersion (based on the median) and price-related differential. Round the mean and weighted mean to two decimals. Use at least four decimal places in calculating the coefficient of dispersion
35 SALE NUMBER APPRAISED VALUE ($) 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

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Ratiostudies

  • 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 歎 $99,000 = 0.94 Appraised Value = $6,120 Annual rent = $6,000 Rental ratio = $6,120 歎 $6,000 = 1.02
  • 6. 6 Median Midpoint or middle ratio when ratios are arrayed If an even number of observations, it is the average of the two middle numbers Preferred measure of central tendency in ratio sales Advantages Easy to compute Not affected by extreme outliers Sample median provides an unbiased estimate of population median Disadvantes Gives no added weight to legitimate outliers Does not lend itself to certain statistical calculation
  • 7. 7 Mean Average ratio Obtained by summing the ratios and then dividing by the number of ratios Accurately reflects the magnitude of every ratio, which is desirable only if outliers are based on valid data Weighted Mean Computed by: Summing the appraisal Summing the sales/rentals Dividing the appraisal by sales/rentals Weighted each ratio based on its sales/rental price Also known as the aggregate ratio
  • 8. 8 SALE NUMBER APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 89,100 90,000 0.99 2 84,150 85,000 0.99 3 91,200 95,000 0.96 4 86,700 85,000 1.02 5 102,900 98,000 1.05 6 109,200 104,000 1.05 7 95,000 100,000 0.95 8 111,550 115,000 0.97 RATIO = APPRAISED VALUE 歎 SALE PRICE
  • 9. 9 SALE NUMBER (arrayed) APPRAISED VALUE ($) 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 歎 8 = 1.00 MEDIAN RATIO = (0.99 + 0.99) 歎 2 = 0.99 WEIGHTED MEAN RATIO = $769,800 歎 $772,000 = 1.00 median
  • 12. 12 SALE NUMBER APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 108,000 120,000 2 85,000 100,000 3 154,000 140,000 4 123,500 130,000 5 120,000 150,000 6 105,000 105,000 7 126,500 110,000 Calculate the mean, median and weighted mean ratio. Round the mean and weighted mean to two decimals.
  • 13. 13 Minimum, maximum and range Useful for identifying extremes Coefficient of Dispersion (COD) Most common measure of appraisal uniformity 100 X | (Ai / Si) - (A/ S) | 歎 (A/ S) n ~ ~ A = APPRAISED VALUE S = SALE/RENTAL PRICE (A / S) = MEDIAN RATIO~
  • 14. 14 Minimum, maximum and range Useful for identifying extremes Coefficient of Dispersion (COD) Most common measure of appraisal uniformity 100 X | (Ai / Si) - (A/ S) | 歎 (A/ S) n ~ ~ A = APPRAISED VALUE S = SALE/RENTAL PRICE (A / S) = MEDIAN RATIO~ AVERAGE ABSOLUTE DEVIATION
  • 15. 15 SALE NUMBER (arrayed) RATIO (Ai / Si) MEDIAN RATIO (A / S) ABSOLUTE DEVIATION 1 0.75 0.95 0.20 2 0.85 0.95 0.10 3 0.90 0.95 0.05 4 0.95 0.95 0.00 5 1.05 0.95 0.10 6 1.15 0.95 0.20 7 1.20 0.95 0.25 Accumulated = Absolute Deviation 0.90 ~
  • 16. 16 Average Absolute Deviation = Accumulated Absolute Deviation 歎 n = 0.90 歎 7 = 0.129 Coefficient of Dispersion = 100 X Average Absolute Deviation 歎 Median Ratio = 100 X 0.129 歎 0.95 = 13.6%
  • 18. 18 SALE NUMBER (arrayed) APPRAISED VALUE ($) 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 歎 7 = 0.96 MEDIAN RATIO = 0.95 WEIGHTED MEAN RATIO = $822,000 歎 $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 歎 6 = 0.864 WEIGHTED MEAN RATIO = $546,000 歎 $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 歎 6 = 1.045 WEIGHTED MEAN RATIO = $546,000 歎 $540,000 = 0.926 PRD = Mean Ratio Weighted Mean Ratio = 1.045 = 1.13 (PROGRESSIVE) 0.926
  • 27. 27 SALE NUMBER (arrayed) APPRAISED VALUE ($) SALE PRICE ($) RATIO 1 193,000 215,000 2 180,000 150,000 3 216,000 200,000 4 213,750 225,000 5 270,000 200,000 6 70,000 100,000 7 97,000 114,000 Calculate the price-related differential (PRD). Round the PRD to two decimals.
  • 28. 28 SALES RATIO TRENDING Ratio studies can be used to adjust appraisal levels to acceptable standards. However, this is only effective if the values in given area (a neighborhood for example) are fairly uniform. This can determined by reviewing the coefficient of dispersion (COD) for the area under consideration. A low COD indicates acceptable uniformity.
  • 29. 29 SALES RATIO TRENDING A trend factor can be obtained by first determining a target level of assessment for the chosen area. The target level is then divided by the current level (as indicated by the median sales ratio) providing a trend factor. By applying the trend factor to all the holdings in the selected area the level of assessment will move from the calculated level to the selected target level.
  • 30. 30 A sale ratio analysis conducted for Area A in XYZ jurisdiction reveals a 76% percent level of appraisal. The target level for Area A is 95%. The sales ratio analysis also indicated that values are fairly uniform in this area. A sales ratio trend factor could be developed by dividing the target level by the current level. 0.95 歎 0.76 = 1.25 A factor of 1.25 could be applied to all of the parcels in the Area A. By applying this factor, the level of appraisal would change from 76% to 95%
  • 32. 32 AREA A CURRENT LEVEL TARGET LEVEL SALE RATIO TRENDING Residential single-family 0.78 .95 Condominiums 0.80 .98 Commercial office 0.75 .90 Commercial - retail 0.72 .90 Calculate the trend factor for each class of property in Area A & B. Round the PRD to three decimals. AREA B CURRENT LEVEL TARGET LEVEL SALE RATIO TRENDING Vacant land 0.80 0.90 Residential single-family 0.81 0.95 Commercial office 0.79 0.90 Commercial - retail 0.83 0.90
  • 34. 34 SALE NUMBER APPRAISED VALUE ($) 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