In paired sales analysis, two similar properties sold within one month of each other. Property A (2,000 sq ft) sold for $400,000, and Property B (2,200 sq ft) sold for $440,000. What is the indicated adjustment per square foot?
Correct Answer
A) $200 per sq ft
Paired sales analysis: ($440,000 - $400,000) ÷ (2,200 - 2,000) = $40,000 ÷ 200 sq ft = $200 per square foot.
Why This Is the Correct Answer
Option A is correct because it properly applies the paired sales analysis formula. The calculation takes the price difference ($440,000 - $400,000 = $40,000) and divides it by the size difference (2,200 - 2,000 = 200 sq ft). This yields $40,000 ÷ 200 sq ft = $200 per square foot, which represents the market-indicated value per square foot of additional living space. This adjustment factor can then be used to make size adjustments when comparing properties of different square footages.
Why the Other Options Are Wrong
Option B: $20 per sq ft
Option B ($20 per sq ft) represents an error in calculation, likely from dividing the price difference by the wrong denominator or making an arithmetic mistake. This would significantly undervalue the per-square-foot adjustment and lead to inaccurate property valuations.
Option C: $40 per sq ft
Option C ($40 per sq ft) appears to result from dividing the total price difference ($40,000) by an incorrect divisor, possibly confusing the price difference with the per-unit calculation. This error would understate the true market-indicated adjustment.
Option D: $180 per sq ft
Option D ($180 per sq ft) likely results from a calculation error or misunderstanding of the formula application. This figure doesn't mathematically derive from the given data using proper paired sales analysis methodology.
PAID Formula
PAID: Price difference ÷ Attribute difference = Indicated adjustment per unit. Remember 'you get PAID for doing the math correctly' - always subtract the smaller from the larger for both price and attribute differences.
How to use: When you see a paired sales question, immediately identify the PAID components: find the Price difference between sales, find the Attribute difference (sq ft, bedrooms, etc.), then Divide to get the Indicated per-unit adjustment.
Exam Tip
Always double-check your arithmetic and ensure you're dividing price difference by the correct attribute difference. Write out the formula before calculating to avoid simple errors.
Common Mistakes to Avoid
- -Dividing by the wrong number (using total square footage instead of the difference)
- -Reversing the calculation (dividing attribute difference by price difference)
- -Failing to ensure the properties are truly comparable except for the analyzed feature
Concept Deep Dive
Analysis
Paired sales analysis is a fundamental technique in real estate appraisal used to isolate and quantify the value impact of specific property characteristics. This method compares two similar properties that differ primarily in one feature, allowing appraisers to determine the market's perception of that feature's value. The analysis requires properties that are truly comparable except for the characteristic being measured, and ideally sold close in time to minimize market condition variations. The mathematical calculation involves finding the difference in sale prices and dividing by the difference in the measured characteristic to derive a per-unit adjustment factor.
Background Knowledge
Paired sales analysis requires understanding that market value adjustments should be based on actual market evidence rather than cost or subjective estimates. The technique assumes that the difference in sale prices between two comparable properties can be attributed to the specific characteristic being analyzed, provided all other factors are reasonably similar.
Real-World Application
Appraisers use paired sales analysis daily to develop adjustment grids for the sales comparison approach. For example, when appraising a 1,800 sq ft home, an appraiser might use this $200/sq ft adjustment to modify comparable sales of different sizes, ensuring accurate value conclusions.
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