A competitive improved property sold for $1,050,000, and the applicable land-to-total value ratio is 24%. Separately, a whole-property value indication is $1,100,000, with a depreciated improvement contribution of $820,000. What are the land indications by allocation and by extraction, respectively?
Correct Answer
D) Allocation $252,000; extraction $280,000
Allocation = $1,050,000 × 0.24 = $252,000. Decomposing the separate whole-property indication gives $1,100,000 − $820,000 = $280,000. The latter is $28,000 higher. This subtraction is not the income land residual technique, which allocates income to the building and capitalizes residual land income.
Why This Is the Correct Answer
Option D is correct because allocation gives $1,050,000 × 0.24 = $252,000, and decomposition gives $1,100,000 − $820,000 = $280,000. Each result uses its own inputs. The decomposition is not the income land residual technique, which works with income and capitalization rates.
Why the Other Options Are Wrong
Option A: Allocation $280,000; extraction $252,000
Option A, allocation $280,000 and extraction $252,000, swaps the two results. Allocation is $1,050,000 × 0.24 = $252,000 and decomposition is $1,100,000 − $820,000 = $280,000.
Option B: Allocation $252,000; extraction $230,000
Option B has the correct allocation of $252,000 but gives decomposition as $230,000, which comes from subtracting $820,000 from the $1,050,000 allocation sale instead of the separate $1,100,000 indication. The correct decomposition is $1,100,000 − $820,000 = $280,000.
Option C: Allocation $264,000; extraction $280,000
Option C gives allocation as $264,000 by applying the 24% ratio to the $1,100,000 indication: $1,100,000 × 0.24 = $264,000. The ratio was given for the $1,050,000 sale, so allocation is $252,000; its $280,000 decomposition figure is correct, but the pair as a whole is not.
Match each method to its inputs
The ratio goes with the sale it was given for, and the improvement contribution comes off the value it was given with.
How to use: Use this to avoid crossing inputs when a question pairs two land techniques.
Exam Tip
When a question asks for two results respectively, check both the figures and their order.
Common Mistakes to Avoid
- -Swapping the allocation and decomposition results
- -Subtracting the improvement contribution from the wrong total value
- -Applying the land-to-total ratio to the wrong total value
Concept Deep Dive
Analysis
This question tests two separate calculations and keeping their inputs straight. Allocation applies the 24% ratio to the $1,050,000 sale, while decomposition subtracts the $820,000 improvement contribution from the separate $1,100,000 whole-property indication. Mixing the inputs or swapping the results produces the distractors.
Background Knowledge
In the allocation method, a portion of total property value is allocated to the site using a supported land-to-total ratio. In extraction or value decomposition, site value is estimated by subtracting the improvement contribution from total property value. The two methods can produce different land indications and each depends on the quality of its inputs.
Real-World Application
An appraiser reviewing a land value tests an allocation ratio against an improved sale and also decomposes a separate whole-property value. When the two indications differ, the appraiser examines the support for the ratio and the improvement estimate before reconciling.
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An improved sale closed at $350,000. The improvements have a cost new of $280,000 and supported depreciation of 25%. What land value does extraction indicate?