MRA vs AVM
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Transcript of MRA vs AVM
Multiple Multiple RegressionRegression
AnalysisAnalysisTCADTCAD
2011 Reappraisal2011 Reappraisal
Part 1Part 1Common Themes:Common Themes:
TCAD TCAD TARB TARB
Texas ConstitutionTexas ConstitutionProperty Value Property Value
StudyStudy
Fair Market Fair Market ValueValue&&
Equality/Equality/UniformityUniformity
TCAD TCAD Mission StatementMission Statement
To provide market value appraisals of all To provide market value appraisals of all taxable property in Travis County in a taxable property in Travis County in a fair fair and equitableand equitable, and cost effective manner, , and cost effective manner, and to provide services and assistance to and to provide services and assistance to the public and taxing jurisdictions.the public and taxing jurisdictions. Fair (Market Value) Fair (Market Value) Equitable (Consistent Value Application) Equitable (Consistent Value Application)
TARB TARB MissionMission
Mission - To provide taxpayers with Mission - To provide taxpayers with opportunity to resolve their conflicts opportunity to resolve their conflicts with the appraisal district, according to with the appraisal district, according to the Texas Property Tax Code.the Texas Property Tax Code.
GoalsGoals To To LISTENLISTEN to taxpayer protests to taxpayer protests WITHOUTWITHOUT prejudice. prejudice. Render a Render a fair and equitablefair and equitable decision, decision,
based on testimony presented.based on testimony presented.
The Texas ConstitutionThe Texas ConstitutionArticle 8, Section 1Article 8, Section 1
Tax in Proportion Tax in Proportion to Valueto Value Ad Valorem (Fair Ad Valorem (Fair
Market Value) Market Value) Equality and Equality and
UniformityUniformity Consistent Value Consistent Value
ApplicationsApplications
Property Value Study Property Value Study (PVS)(PVS)
Section 5.10 of the Texas Property Tax
Code Comptroller must conduct a study every
other year to determine: Median level of appraisal (Market) Uniformity of appraisal (Equity)
The PVS uses The PVS uses ratio statisticsratio statistics to evaluate to evaluate TCAD appraisal performance.TCAD appraisal performance.
Only one ratio is considered....Only one ratio is considered....
““The Appraisal Ratio”The Appraisal Ratio”
Model ValueModel Value Sale PriceSale Price
Ratio StatisticsRatio Statistics Other Other
ConsiderationsConsiderations Price Related Price Related
Differential Differential RangeRange Standard DeviationStandard Deviation Coefficient of Coefficient of
VariationVariation
The most The most important important statistics used to statistics used to evaluate TCAD evaluate TCAD appraisal appraisal performance:performance:
1.1. Median Level of Median Level of ValueValue
1.1. Market ValueMarket Value2.2. Coefficient of Coefficient of
DispersionDispersion 1.1. Uniformity of Uniformity of
Appraisal Appraisal
Ratio StatisticsRatio Statistics MediMedi
an an Level Level of of ValueValue 98%98%
C.O.DC.O.D.. 6.96.9
%%
The ChallengeThe Challenge Can TCAD improve its appraisal Can TCAD improve its appraisal
performance with the help of performance with the help of Multiple Regression Analysis?Multiple Regression Analysis? Produce a Fair Market Level of ValueProduce a Fair Market Level of Value Tighten the C.O.D.Tighten the C.O.D.
Reduce the Standard Error Reduce the Standard Error Reduce the Standard DeviationReduce the Standard Deviation
COMMON GOALS:COMMON GOALS:Fair Market Value & Fair Market Value &
Uniformity/EqualityUniformity/Equality
Part 2Part 2From Here to There:From Here to There:
AdjustedAdjustedCostCost
ModelModel(ACM)(ACM)
Vs.Vs.MultipleMultiple
RegressionRegressionAnalysisAnalysis(MRA)(MRA)
Adjusted Cost Model Adjusted Cost Model (ACM)(ACM)
ACM Prediction EquationACM Prediction Equation Model Value = (Land * %Adj) + Model Value = (Land * %Adj) +
((Variable * Unit Value * Depreciation) + ((Variable * Unit Value * Depreciation) + (V(V22 * U * U22 * D * D22) + (V) + (V33 * U * U33 * D * D33) ... ) * NAF)) ... ) * NAF)
4 Categories of attributes4 Categories of attributes1.1. LandLand2.2. ImprovementsImprovements3.3. DepreciationDepreciation4.4. Neighborhood Adjustment Factor (NAF)Neighborhood Adjustment Factor (NAF)
ACM – Land ACM – Land
Bluff (B - 1)Bluff (B - 1) Golf Course (GC - Golf Course (GC -
5)5) Lake View (LV - 33)Lake View (LV - 33) Size and Shape (N -Size and Shape (N -
393)393) Terrain (P - 3)Terrain (P - 3) View (Q - 49)View (Q - 49)
Size (SZ - 1)Size (SZ - 1) Drainage (W - 3)Drainage (W - 3) Greenbelt (Y - Greenbelt (Y -
85)85)
54 others... (0)54 others... (0)
9 of 63 Land adjustments present (n = 9 of 63 Land adjustments present (n = 1390)1390)
2 methods (Lot, FF)2 methods (Lot, FF)
ACM – Land AdjustmentsACM – Land Adjustments
ACM – Improvements ACM – Improvements
Baths (1390)*Baths (1390)* Porch (1385)*Porch (1385)* Garage (1380)*Garage (1380)* Fireplace Fireplace
(1355)*(1355)* Terrace (436)*Terrace (436)* Deck (288)*Deck (288)* Pool (168)*Pool (168)* HVAC (1388)HVAC (1388) Carports (110)Carports (110)
Marshall and Swift Cost Index = Unit Marshall and Swift Cost Index = Unit Values*Values*
15 of 26 Improvement Attributes in the 15 of 26 Improvement Attributes in the sales filesales file Spa (71)Spa (71)
Hot Tub (8 = Hot Tub (8 = Spa)Spa)
Sport Court Sport Court (7)(7)
Fountain (3)Fountain (3) Courtyard (2)Courtyard (2) Outside Stair Outside Stair
(2)(2) SolariumSolarium LoftLoft BoathouseBoathouse
Boat DockBoat Dock SaunaSauna GreenhouseGreenhouse PenthousePenthouse StableStable Tennis CourtsTennis Courts BathhouseBathhouse
*MRA Sample *MRA Sample Size (n = Size (n = 1390)1390)
ACM – Depreciation ACM – Depreciation
Straight-line (age-life)Straight-line (age-life) Grade/Condition floors:Grade/Condition floors:
Excellent (90%); Good (85%); Average Excellent (90%); Good (85%); Average (75%)...(75%)...
Physical, Functional, Economic Physical, Functional, Economic 1 case each in Sales file (n = 1390)1 case each in Sales file (n = 1390) Each case was a 10% discountEach case was a 10% discount
ACM Straight-Line ACM Straight-Line DepreciationDepreciation
Excellent 90%Good 85%
Average 75%Dep % Fair 65%
Poor 40%
Salvage 20%
10 20 30 40 50 60 70Age
ACM – Neighborhood ACM – Neighborhood Adjustment Factor (NAF)Adjustment Factor (NAF)
Calibrated to a target median ratio Calibrated to a target median ratio (.98) during valuation season for all (.98) during valuation season for all NBHDs with sufficient sales to value.NBHDs with sufficient sales to value.
ACM – Neighborhood ACM – Neighborhood Adjustment Factor Adjustment Factor
MRA ModelMRA ModelListen to the market....Listen to the market....
...To Find Unit Values!...To Find Unit Values!
Time Adjustments Time Adjustments (TASP3)(TASP3)
Time Adjusted Sales Price (TASP3)Time Adjusted Sales Price (TASP3) Section 23.01.a of the Texas Property Tax Section 23.01.a of the Texas Property Tax
CodeCode requires requires Appraisal Districts to Appraisal Districts to appraise market value as of appraise market value as of January 1stJanuary 1st. . Furthermore, section 23.013.c of the Texas Furthermore, section 23.013.c of the Texas Property Tax Code Property Tax Code requiresrequires the appraisal the appraisal district to district to adjust all sales for any adjust all sales for any change in the market value from the change in the market value from the date of sale to the date as of which the date of sale to the date as of which the market value is to be determinedmarket value is to be determined. .
Steiner RanchMonthly Median Sales Ratio
0.8
0.9
1
1.1
1.2
Month - Year
Med
ian
(Sal
e Pr
ice/
2010
Val
)
January 1st, 2011
Monthly Median Sales Monthly Median Sales RatioRatio
Steiner Ranch 5 Year Time Trend
0.8
0.9
1
1.1
1.2
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month - Year
Med
ian
(Sal
e Pr
ice/
2010
Val
)
January 1st, 2011
Linear Regression
Linear Regression (Time Linear Regression (Time Trend)Trend)
Visual Test (Zero Slope)Visual Test (Zero Slope)Zero Slope Visual Test (Linear)
0.8
0.9
1
1.1
1.2
Month-Year
Adju
sted
Sal
es R
atio
January 1st, 2011
66thth Order Polynomial Order Polynomial5-Year Time Trend
0.80
0.90
1.00
1.10
1.20
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month-Year
Med
ian
(Sal
e Pr
ice/
2010
Val
)
January 1, 2011
4th, 5th, 6th polynomial trendlines
Zero Slope Achieved!Zero Slope Achieved!TASP3TASP3
Zero Slope Visual Test (6th order)
0.95
1
1.05
1.1
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Month-Year
Adju
sted
Sal
es R
atio
TASP3 EquationTASP3 Equation The 6th order polynomial equation adequately The 6th order polynomial equation adequately
addresses changes in market value over time. addresses changes in market value over time. The following equation was be used to adjust The following equation was be used to adjust sale prices to the January 1, 2011 appraisal sale prices to the January 1, 2011 appraisal date.date.
TASP3 = SPRICE*(1.0183 /TASP3R).TASP3 = SPRICE*(1.0183 /TASP3R). TASP3R = 0.0000000000471*MONTH^6 - TASP3R = 0.0000000000471*MONTH^6 -
0.0000000199942*MONTH^5 + 0.0000000199942*MONTH^5 + 0.0000021807069*MONTH^4 - 0.0000021807069*MONTH^4 - 0.00008852402*MONTH^3 + 0.00008852402*MONTH^3 +
0.0010720575848*MONTH^2 + 0.0010720575848*MONTH^2 + 0.0057238812883*MONTH + 1.021465983192. 0.0057238812883*MONTH + 1.021465983192.
MRA Prediction EquationMRA Prediction Equation Identify TASP3 (Jan 1, 2011)Identify TASP3 (Jan 1, 2011)
Achieved with Time Trend EquationAchieved with Time Trend Equation Predict TASP3Predict TASP3
Solve for Prediction EquationSolve for Prediction Equation
Linear EquationLinear Equation Linear Regression - Single VariableLinear Regression - Single Variable Example: “Volume of Sales over time...”Example: “Volume of Sales over time...” Y = mX + bY = mX + b
Y = Dependant Variable - Number of SalesY = Dependant Variable - Number of Sales X = Independent Variable - Time (in years)X = Independent Variable - Time (in years) b = Constant - (y-intercept or # of sales at b = Constant - (y-intercept or # of sales at
time zero)time zero) m = Coefficient - Calculated rate of change m = Coefficient - Calculated rate of change
in the # of sales over timein the # of sales over time
Linear RegressionLinear Regression“Least Squares Analysis” “Least Squares Analysis”
“The Line of Best Fit”“The Line of Best Fit”
Multiple RegressionMultiple Regression Multiple Regression (More than one Multiple Regression (More than one
variable)variable) ““Advanced Paired Sales” Advanced Paired Sales” Ceteris Paribus - “All else the same”Ceteris Paribus - “All else the same” Value = (Constant + (Variable * Unit Value) + Value = (Constant + (Variable * Unit Value) +
(V(V22 * U * U22) + (V) + (V33 * U * U33)) * NAF)) * NAF Remember ACM equation???Remember ACM equation???
Value = (Land * %Adj) + ((Variable * Unit Value = (Land * %Adj) + ((Variable * Unit Value * Depreciation) + (VValue * Depreciation) + (V22 * U * U22 * D * D22) + (V) + (V33 * * UU33 * D * D33) ... ) * NAF)) ... ) * NAF)
Multiple Regression Multiple Regression (Visual)(Visual)
MRA Model MRA Model (10 Variables)(10 Variables)
Landcode/SizeLandcode/Size Square Square
Foot/QualityFoot/Quality Age (sqrt)Age (sqrt) BathsBaths Deck sfDeck sf
Terrace sfTerrace sf FireplaceFireplace Garage SpaceGarage Space Porch sfPorch sf PoolPool
MRA Model (Thrown MRA Model (Thrown Out)Out)
Percentage of sales with insignificant Percentage of sales with insignificant attributesattributes Land Adjustments – 100%Land Adjustments – 100%
Replaced by LandcodingReplaced by Landcoding Carports – 8%Carports – 8% Spa – 5%Spa – 5% Others (<2%)Others (<2%)
CourtyardCourtyard Outside StairOutside Stair
ACM – Land AdjustmentsACM – Land Adjustments
MRA – Land CodesMRA – Land Codes
The ResultsThe ResultsModel Summary
.976a .952 .951 39698.34800Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
Predictors: (Constant), TERRASFZ, B301100,L303200, L303101, B301450, L302150, QUALLOW,L301425, L302250, B301300, B302300, L301210,L301400, L301800, B302200, B301350, L301600,SQFT6M, L301750, DECKSFZ, SQFT5M, L302800,L301455, SQFT5P, EFFSQRT, SQFT6P, QUALLOWP,POOLZ, SQFT7M, PORCHZ, SQFT6, FIRPLZ, GARSPZ,LSQFT, QUALHP, SQFT5, BATHSZ
a.
PREDICTION EQUATIONPREDICTION EQUATIONCONSTANT 93,030$
+ 21,785$ * B301100 + 1$ * L302250+ 85,537$ * B301300 + 2$ * L302800+ 254,354$ * B301350 + 22$ * L303101+ 98,006$ * B301450 + 20$ * L303200+ 42,460$ * B302200 + 1$ * LSQFT+ 76,286$ * B302300 + 29,107$ * POOLZ+ 3,776$ * BATHSZ + 38$ * PORCHZ+ 32$ * DECKSFZ + 468,124$ * QUALHP+ (10,637)$ * EFFSQRT + 61,818$ * QUALLOW+ 7,847$ * FIRPLZ + 99,676$ * QUALLOWP+ 9,330$ * GARSPZ + 62$ * SQFT5+ 8$ * L301210 + 60$ * SQFT5M+ 3$ * L301400 + 66$ * SQFT5P+ 2$ * L301425 + 76$ * SQFT6+ 1$ * L301455 + 78$ * SQFT6M+ 7$ * L301600 + 79$ * SQFT6P+ 8$ * L301750 + 64$ * SQFT7M+ 3$ * L301800 + 15$ * TERRASFZ.+ 2$ * L302150
ACM vs MRAACM vs MRA
Ratio Study StandardsRatio Study Standards IAAOIAAO
All Single Family ResidenceAll Single Family Residence C.O.D. < 15%C.O.D. < 15%
‘‘Fairly’ Homogeneous Areas (SFR)Fairly’ Homogeneous Areas (SFR) C.O.D. < 10%C.O.D. < 10%
PVSPVS 5 – 10% (Homogeneous) 5 – 10% (Homogeneous)
Appraisal UniformityAppraisal Uniformity MRA – 20% improvement over ACMMRA – 20% improvement over ACM
Standard Deviation and Standard Deviation and ProbabilityProbability
Standard Standard Deviation Deviation = .09 rd.= .09 rd.
Mean = .98Mean = .98 68% 68%
from .89 to from .89 to 1.071.07
SE = 39KSE = 39K Avg Val = Avg Val =
438K438K 68% from 68% from
399K to 399K to 477K477K
68.2%68.2%
95.5%95.5%99.7%99.7%
Freq
uenc
yFr
eque
ncy
-3s-3s -2s-2s -1s-1s MeanMean +1s+1s +2s+2s +3s+3s
X
Ratio StatisticsRatio Statistics MediMedi
an an Level Level of of ValueValue
98%98%
C.O.DC.O.D..
6.9%6.9%
ACM vs MRAACM vs MRA
Defense GridsDefense Grids EquityEquity
41.43.b.3 - An 41.43.b.3 - An ‘appropriately adjusted’ ‘appropriately adjusted’ equity grid should use the equity grid should use the same values for adjustment same values for adjustment as used in the mass model.as used in the mass model.
Its a ‘Non-Model Test’. The Its a ‘Non-Model Test’. The adjusted value is the same adjusted value is the same as notice valueas notice value if everyone if everyone was treated fairly.was treated fairly.
MarketMarket Adjustments come solely Adjustments come solely
from the market.from the market. Proven quantifiable Proven quantifiable
evidence evidence
QualityLiving Area (sf)Size x Quality
LandcodeLand Difference
ClassAge
Age FactorLand Size (sf)
BathDeck (sf)
Terrace (sf)Fireplace
Garage SpacePorch (sf)
PoolBoat DocksSport Court
Additional DetailMkt Level Adjustment
ConclusionConclusion The two models are similar but The two models are similar but
different... different... Value = (Variable * Unit Price)Value = (Variable * Unit Price) ACM – Marshall and SwiftACM – Marshall and Swift MRA – Immediate MarketMRA – Immediate Market
The quality of any model will mirror The quality of any model will mirror the quality of the data.the quality of the data.
Improve and Expand – MRA valuation Improve and Expand – MRA valuation in 2012.in 2012.
Thank You!!Thank You!!