Within the sales comparison approach, three comparables adjust to $431,000, $420,000 and $412,000, with gross adjustments of 5%, 10% and 20% of sale price respectively. The appraiser weights each sale in proportion to the inverse of its gross adjustment percentage (1/5, 1/10 and 1/20), then scales the weights to total 100%. What is the indicated value, rounded to the nearest dollar?
Correct Answer
C) $425,143
The inverse factors 0.20, 0.10 and 0.05 total 0.35, giving weights of 4/7, 2/7 and 1/7, so the indication is (4 x $431,000 + 2 x $420,000 + 1 x $412,000) / 7 = $425,143. Inverse weighting puts the most weight on the least-adjusted, most comparable sale. $417,000 comes from weighting in proportion to the adjustments (the wrong direction), $421,000 is the simple average, and $427,333 leaves out the most heavily adjusted sale instead of giving it 1/7 of the weight.
Why This Is the Correct Answer
Option C is correct because the inverse factors 0.20, 0.10 and 0.05 total 0.35, which gives weights of 4/7, 2/7 and 1/7. Applying them gives (1,724,000 + 840,000 + 412,000) / 7 = $425,142.86, or $425,143. The result sits closest to the least-adjusted sale, as weighting by comparability should.
Why the Other Options Are Wrong
Option A: $417,000
Option A, $417,000, weights each sale in proportion to its gross adjustment rather than the inverse: (431,000 x 1 + 420,000 x 2 + 412,000 x 4) / 7 = $417,000. That gives the most weight to the 20% sale, the least comparable one, which reverses the logic. The correct weighting gives $425,143.
Option B: $421,000
Option B, $421,000, is the simple average (431,000 + 420,000 + 412,000) / 3. It ignores the weighting rule the appraiser chose and treats a 20%-adjusted sale the same as a 5%-adjusted one; the weighted result is $425,143.
Option D: $427,333
Option D, $427,333, drops the 20%-adjusted sale and spreads the weight over the other two in a 4:2 ratio: (1,724,000 + 840,000) / 6. The stem weights all three sales, so the $412,000 sale still carries 1/7 of the weight, which gives $425,143.
Less adjusted, more weight
The smaller a sale's total adjustments, the larger its share of the weight. Inverse factors must be scaled so they total 100% before use.
How to use: Use this when a stem gives gross adjustment percentages and asks for a weighted sales comparison indication.
Exam Tip
After computing weights, check that they add to 100% and that the biggest weight sits on the least-adjusted sale.
Common Mistakes to Avoid
- -Weighting in proportion to the adjustments instead of their inverse
- -Forgetting to scale the inverse factors to total 100%
- -Falling back on a simple average of the adjusted prices
Concept Deep Dive
Analysis
The question tests reconciliation within the sales comparison approach using an explicit weighting rule. The candidate must convert gross adjustment percentages into inverse factors, scale them to 100%, and then apply them to the right sales. The key check is direction: the sale with the smallest adjustment must get the largest weight.
Background Knowledge
Each comparable produces its own indication, and the appraiser resolves them within the approach by giving the most weight to the sales closest in comparability. Lower gross adjustments usually signal closer comparability, so an inverse-of-adjustment weighting is one way to quantify that judgment, provided it is explained.
Real-World Application
An appraiser has three sales of split-level homes with gross adjustments of 5%, 10% and 20%. To make the reconciliation transparent, the appraiser shows inverse-adjustment weights in an addendum and explains why the cleanest sale drives the indication.
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