An appraiser identifies two comparable sales that are identical in all respects except that Sale #1 has a finished basement (1,200 sq ft) and sold for $432,000, while Sale #2 has an unfinished basement of the same size and sold for $408,000. Both sales occurred within three weeks of each other in a stable market. The appraiser intends to apply a per-square-foot adjustment for basement finish to the subject property, which has a 1,000 sq ft finished basement. What is the appropriate paired-sales-derived adjustment amount per square foot for a finished basement?
Correct Answer
B) $20 per sq ft
Why this is correct: Paired sales isolate a single difference between two otherwise similar transactions and let the market price it. The two sales differ only in basement finish and closed three weeks apart in a stable market, so no market-conditions adjustment intervenes: $432,000 - $408,000 = $24,000 attributable to finishing 1,200 square feet, and $24,000 / 1,200 = $20 per square foot. Applied to the subject's 1,000 finished square feet, that rate supports a $20,000 adjustment. Why the other choices are wrong: '$15 per sq ft' would require a price difference of $18,000 rather than the $24,000 the sales show. '$24 per sq ft' takes the $24,000 total difference and treats the thousands as dollars per square foot, dropping the division entirely. '$30 per sq ft' would require a $36,000 difference, or the same $24,000 spread over only 800 square feet. Exam tip: A paired sale is only as good as the word 'otherwise identical'. Confirm that the dates are close and the market stable before you attribute the whole price difference to the one feature named.
Why This Is the Correct Answer
Twenty-four thousand dollars of price difference divided by 1,200 square feet of finished area gives $20 per square foot. The rate is market derived rather than cost derived, which is what makes it a supportable adjustment; the cost to finish a basement would typically exceed what the market pays. Reverse multiplication confirms the arithmetic, since $20 times 1,200 returns the observed $24,000. Applying the rate to a differently sized subject feature should be checked against other pairs where possible.
Why the Other Options Are Wrong
Option A: $15 per sq ft
$15 per square foot implies a price gap of $18,000, which is $6,000 short of what the two sales actually show. The figure may come from a subtraction slip or from dividing by a larger area than the stem provides. Confirming the gap before dividing catches it.
Option C: $24 per sq ft
$24 per square foot implies a gap of $28,800 and appears to come from dividing the $24,000 gap by 1,000, the subject's finished area, rather than by 1,200, the area in the pair. That is a real and instructive error: the rate must be derived from the comparables' quantity and only then applied to the subject's. Deriving and applying are separate steps with separate denominators.
Option D: $30 per sq ft
$30 per square foot implies a gap of $36,000, half again the observed difference, and corresponds to dividing by 800 square feet. Nothing in the stem supplies that figure. Any answer that fails to reproduce $24,000 on reverse multiplication can be discarded.
Derive Here, Apply There
The denominator when deriving is the comparables' quantity. The multiplier when applying is the subject's quantity. Mixing the two is the single most common error in unit-rate problems.
How to use: Label two lines before computing: derivation uses the pair's square footage, application uses the subject's. Then verify the derived rate reproduces the observed price gap.
Exam Tip
Watch for a distractor built by dividing the gap by the subject's quantity instead of the comparables'. It is the most sophisticated wrong answer in these items.
Common Mistakes to Avoid
- -Dividing the price gap by the subject's quantity rather than the comparables'
- -Using cost to finish as a substitute for market-derived contribution
- -Assuming contribution per square foot holds constant across very different finished areas
Concept Deep Dive
Analysis
The isolated variable in this pair is not the basement itself but the finish of it, since both sales have basements of the same 1,200 square feet and differ only in whether that space is finished. That distinction matters because it means the derived rate measures the market's payment for finishing existing below-grade space, not for the space's existence. The computation is the familiar two steps: the price gap of $432,000 minus $408,000 is $24,000, and dividing by the 1,200 square feet of finish gives $20 per square foot. Applying that rate to the subject's 1,000 square feet of finished basement would indicate roughly $20,000 of contribution, though the appraiser should ask whether contribution scales linearly across that range before assuming it does. The stem's mention of three weeks in a stable market forecloses any market conditions adjustment, which is one of the two conditions that must hold before a gap can be attributed to a single feature.
Background Knowledge
You need paired sales analysis, the requirement that a pair differ in one characteristic, and the distinction between deriving a rate from comparables and applying it to the subject. You should also know that contributory value is market derived and typically differs from cost, and that below-grade finished area is reported separately from gross living area.
Real-World Application
An appraiser derives a $20 per square foot basement finish rate from a clean pair, applies it to the subject's 1,000 finished square feet for roughly $20,000, and notes in her workfile that the local cost to finish runs closer to $35 per square foot, illustrating that cost exceeds contribution here.
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