An appraiser is estimating external obsolescence for a residential property near a closed landfill using paired sales analysis. Pair 1: affected home sold for $340,000; unaffected comparable sold for $400,000. Pair 2: affected home sold for $380,000; unaffected comparable sold for $440,000. The subject property has a replacement cost new of $280,000 and a land value of $180,000. Using the percentage loss method, what is the dollar amount of external obsolescence attributable to the improvements only?
Correct Answer
C) $40,000
Step 1 — Calculate the percentage loss from each pair by dividing the value difference by the unaffected sale price: Pair 1: ($400,000 − $340,000) / $400,000 = 15.00%. Pair 2: ($440,000 − $380,000) / $440,000 = 13.64%. Step 2 — Average the two rates: (15.00% + 13.64%) / 2 = 14.32%. Step 3 — Apply the average rate to the subject's replacement cost new (improvements only): $280,000 × 14.32% = $40,096, which rounds to $40,000. The percentage is applied to improvements only because external obsolescence is allocated between land and improvements in proportion to their respective values; the question specifically asks for the improvements' share, which is derived by applying the market-extracted rate directly to RCN. This method is consistent with Appraisal Institute guidance on extracting and allocating external obsolescence.
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