A comparable’s $420,000 price expressly equals 105% of its supported price in the subject’s location, with all else unchanged. What subject-location-equivalent price removes that premium? Do not deduct 5% of the already higher amount.
Correct Answer
B) $400,000
420000÷1.05=400000. Common errors: deducting 5% of the already higher price gives $399,000; multiplying by 1.05 instead of dividing gives $441,000; not removing the location premium gives $420,000.
Why This Is the Correct Answer
Option B is correct because if $420,000 is 105% of the subject-location price, then that price is 420,000 ÷ 1.05 = $400,000. Dividing removes a premium that was measured on the lower base. Checking: $400,000 × 1.05 = $420,000.
Why the Other Options Are Wrong
Option A: $399,000
Option A, $399,000, is wrong because it deducts 5% of the already higher price: 420,000 × 0.95 = 399,000. The premium was 5% of the lower base, so the correct calculation is 420,000 ÷ 1.05 = $400,000.
Option C: $420,000
Option C, $420,000, is wrong because it leaves the location premium in place. Removing it gives 420,000 ÷ 1.05 = $400,000.
Option D: $441,000
Option D, $441,000, is wrong because it multiplies by 1.05 instead of dividing: 420,000 × 1.05 = 441,000. That adds a second premium rather than removing the first; the correct result is $400,000.
Undo a markup by dividing
If a price is 105% of the base, divide by 1.05 to get back to the base.
How to use: Use this whenever a premium is defined as a percentage of the lower price.
Exam Tip
Check your answer by reapplying the percentage to see whether you get back to the starting figure.
Common Mistakes to Avoid
- -Subtracting 5% of the higher price instead of dividing by 1.05
- -Multiplying by the factor when the premium needs to be removed
- -Ignoring which price the percentage was measured against
Concept Deep Dive
Analysis
This question tests removing a percentage premium defined relative to a lower base. The $420,000 price equals 105% of the subject-location price, so the subject-location price is found by dividing by 1.05. Deducting 5% of $420,000 uses the wrong base.
Background Knowledge
A percentage relationship depends on its base. When a price is a stated percentage above another price, reversing it requires dividing by the factor, not subtracting the same percentage of the larger number. Location adjustments bring the comparable's price to what it would be in the subject's location.
Real-World Application
Market analysis shows homes in a comparable's school zone sell about 5% above similar homes in the subject's zone. The appraiser divides the comparable's price by 1.05 to estimate its price in the subject's location. The report notes the derivation of the location relationship.
More Sales Comparison Questions
Supported adjustments are: non-market financing $10,000, GLA $36/sf, garage $3,500 per car, pool/spa $12,500. A comparable identical to the 2,800 sf subject sold for $267,000 with non-market financing. What is its adjusted price?
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