A supported land indication WITH an access attribute is $1,200,000. Market evidence explicitly states this equals 115% of otherwise identical land WITHOUT that attribute. The subject lacks it. What without-attribute land indication follows, to the nearest dollar? No conclusion about improvement loss is requested.
Correct Answer
C) $1,043,478
1200000÷1.15 = 1043478.26. Common errors: deducting 15% of the with-attribute value instead of dividing by 1.15 gives $1,020,000; multiplying by 1.15 instead of dividing gives $1,380,000; reporting the attribute's premium instead of the land value gives $156,522.
Why This Is the Correct Answer
Option C is correct because the with-attribute value is 115% of the without-attribute value, so the without value equals $1,200,000 ÷ 1.15 = $1,043,478 to the nearest dollar. Checking: $1,043,478 × 1.15 is about $1,200,000.
Why the Other Options Are Wrong
Option A: $156,522
Option A, $156,522, is the attribute's premium rather than the land value: $1,200,000 − $1,200,000 ÷ 1.15 = $156,522. The question asks for the without-attribute land indication, $1,043,478.
Option B: $1,020,000
Option B, $1,020,000, deducts 15% of the with-attribute value: $1,200,000 × 0.85 = $1,020,000. The 15% premium is measured on the without-attribute base, so the correct step is $1,200,000 ÷ 1.15 = $1,043,478.
Option D: $1,380,000
Option D, $1,380,000, multiplies by 1.15 instead of dividing: $1,200,000 × 1.15 = $1,380,000. Since the subject lacks the attribute, its value is lower: $1,200,000 ÷ 1.15 = $1,043,478.
Find the 100% Base
If the known value is 115% of the unknown, divide by 1.15 to get back to 100%.
How to use: Use this whenever a premium or discount is stated relative to the other property.
Exam Tip
Identify which value equals 100% before applying a percentage; dividing and subtracting give different answers.
Common Mistakes to Avoid
- -Subtracting the percentage from the wrong base
- -Multiplying when the subject is inferior
- -Reporting the premium instead of the land value
Concept Deep Dive
Analysis
This question tests removing a percentage premium measured against the without-attribute base. If the with-attribute land equals 115% of the without-attribute land, the without value is found by dividing by 1.15, not by deducting 15% of the with value.
Background Knowledge
Percentage adjustments depend on which value serves as the base. A premium stated as a percent of the without-attribute value must be removed by dividing by (1 + rate). Deducting the same percentage from the with-attribute value gives a different and incorrect result.
Real-World Application
An appraiser finds that lots with direct highway access sell for 115% of similar lots without it. Her subject lacks access, so she divides the $1,200,000 access-lot indication by 1.15 to estimate $1,043,478.
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