A comparable improved sale closed at a cash-equivalent price of $750,000. At that time the site, valued independently, was worth $200,000, and the improvements would have cost $800,000 new. The sale included no other assets or interests. What total depreciation of the improvements does market extraction indicate?
Correct Answer
B) $250,000
800000−(750000−200000) = 250000. Common errors: taking the difference between cost new and sale price, ignoring the site value gives $50,000; reporting the extracted improvement contribution (sale price − site) instead of depreciation gives $550,000; deducting the site value from cost new instead of from the sale price gives $600,000.
Why This Is the Correct Answer
Option B is correct because the improvement contribution is $750,000 - $200,000 = $550,000, and cost new of $800,000 minus $550,000 equals $250,000 of total depreciation.
Why the Other Options Are Wrong
Option A: $50,000
Option A, $50,000, is $800,000 - $750,000, the difference between cost new and sale price, which ignores the $200,000 site value. The correct figure is $800,000 - ($750,000 - $200,000) = $250,000.
Option C: $550,000
Option C, $550,000, is $750,000 - $200,000, the extracted improvement contribution rather than depreciation. Depreciation is $800,000 - $550,000 = $250,000.
Option D: $600,000
Option D, $600,000, comes from deducting the $200,000 site value from the $800,000 cost new instead of from the sale price. The site belongs to the sale price, giving $250,000.
Price minus land, cost minus that
First strip the land from the price, then measure how far the building's contribution falls below cost new.
How to use: Use this two-step order for extraction questions.
Exam Tip
Site value is taken from the sale price, not from cost new; check which number you subtracted it from.
Common Mistakes to Avoid
- -Ignoring site value in the extraction
- -Reporting the improvement contribution as depreciation
- -Subtracting land value from cost new
Concept Deep Dive
Analysis
This question tests market extraction of depreciation. Subtract the site value from the sale price to find the improvements' contribution, then subtract that contribution from cost new to find total depreciation.
Background Knowledge
Market extraction isolates the contribution of improvements by removing land value from comparable sale prices. Comparing that contribution with current cost new gives total depreciation from all causes.
Real-World Application
An appraiser uses a sale of a similar house and supports the lot value with land sales. Subtracting the lot value from the sale and comparing the result with cost new gives total depreciation to apply to the subject.
More Cost Approach Questions
An undamaged but functionally inadequate system causes a supported $60,000 loss. Replacement costs $85,000 and restores only $60,000, with no other benefits. What loss classification and deduction fit?
The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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