An improved property sold for a cash-equivalent price of $1,100,000. Site value at the date of sale, estimated independently, was $300,000, and the cost new of the improvements at that date was $1,200,000. No other assets or interests were part of the sale. Using market extraction, what is the total depreciation of the improvements?
Correct Answer
B) $400,000
1200000−(1100000−300000) = 400000. Common errors: subtracting the whole sale price from cost new without first removing the site value gives $100,000; reporting the extracted improvement contribution (sale price − site) instead of depreciation gives $800,000; deducting the site value from cost new instead of from the sale price gives $900,000.
Why This Is the Correct Answer
Option B is correct because the improvement contribution is $1,100,000 − $300,000 = $800,000. Total depreciation is cost new minus that contribution: $1,200,000 − $800,000 = $400,000.
Why the Other Options Are Wrong
Option A: $100,000
Option A, $100,000, subtracts the whole sale price from cost new ($1,200,000 − $1,100,000) without first removing the $300,000 site value. The correct calculation is $1,200,000 − ($1,100,000 − $300,000) = $400,000.
Option C: $800,000
Option C, $800,000, is the extracted improvement contribution ($1,100,000 − $300,000), not depreciation. Subtracting it from cost new gives $1,200,000 − $800,000 = $400,000.
Option D: $900,000
Option D, $900,000, deducts site value from cost new ($1,200,000 − $300,000) instead of from the sale price. Site belongs with the sale price, which leads to $1,200,000 − $800,000 = $400,000.
Land comes off the price
Take land off the sale price, not off cost new. Cost new minus what is left equals depreciation.
How to use: Use this to place the site deduction correctly in any extraction problem.
Exam Tip
Cost new already excludes land, so the site value must be subtracted from the sale price. Check whether the question wants the contribution or the depreciation.
Common Mistakes to Avoid
- -Subtracting the site value from cost new instead of from the sale price
- -Reporting the improvement contribution as depreciation
- -Comparing the full sale price directly with cost new
Concept Deep Dive
Analysis
This question tests the market extraction method. Subtract site value from the sale price to find the improvements' contribution, then subtract that contribution from cost new. The difference is total improvement depreciation.
Background Knowledge
In market extraction, the site value is subtracted from a cash-equivalent sale price to find the building's contribution. That contribution is compared with current cost new, and the difference is total depreciation. Depreciation estimates should be supported by market data using methods like breakdown or market extraction.
Real-World Application
An appraiser finds a comparable that sold for $1,100,000 with a supported site value of $300,000. Comparing the $800,000 improvement contribution with $1,200,000 current cost new gives $400,000 of depreciation to apply as evidence for 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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