A building cost $500,000 new and has depreciated $125,000. Using the extraction method, if the land is worth $150,000, what is the depreciated value of the improvements?
Correct Answer
B) $375,000
Why this is correct: The depreciated value of improvements is found by subtracting accrued depreciation from the reproduction or replacement cost new. Here, $500,000 (cost new) minus $125,000 (depreciation) equals $375,000. The land value ($150,000) is separate and not part of this calculation. Why the other choices are wrong: $500,000 is the cost new, ignoring depreciation. $125,000 is the amount of depreciation, not the depreciated value. $525,000 incorrectly adds land value to the cost new ($500,000 + $150,000 = $650,000) or makes another error. Exam tip: In the extraction method, depreciated improvement value = Cost New - Depreciation. Land value is handled separately.
Why This Is the Correct Answer
Option A ($375,000) correctly applies the fundamental depreciation formula: Depreciated Value = Original Cost - Total Depreciation. Starting with the reproduction/replacement cost of $500,000 and subtracting the accumulated depreciation of $125,000 yields $375,000. This represents the current contributory value of the building improvements to the overall property value.
Why the Other Options Are Wrong
Option A: $500,000
Option A ($500,000) incorrectly uses the original reproduction/replacement cost without accounting for any depreciation. This ignores the $125,000 in accumulated depreciation that has occurred.
Option C: $125,000
Option C ($125,000) incorrectly uses only the depreciation amount rather than the remaining value after depreciation. This represents what the building has lost in value, not what it's currently worth.
Option D: $525,000
Option D ($525,000) incorrectly adds the land value to the depreciated improvements value, but the question specifically asks only for the depreciated value of improvements, not the total property value.
The Subtraction Solution
Remember 'NEW minus OLD equals GOLD' - New construction cost minus accumulated depreciation equals the golden current value of improvements.
How to use: When you see depreciated value questions, immediately identify the 'NEW' (original/replacement cost) and 'OLD' (total depreciation), then subtract to find your 'GOLD' (current depreciated value).
Exam Tip
Always read carefully to determine what specific value is being requested - improvement value only, land value only, or total property value - and ignore irrelevant information provided in the question.
Common Mistakes to Avoid
- -Using the depreciation amount instead of subtracting it from original cost
- -Including land value when only improvement value is requested
- -Forgetting to subtract depreciation from the original cost
Concept Deep Dive
Analysis
This question tests understanding of the cost approach to valuation, specifically how to calculate depreciated value of improvements. The extraction method is mentioned as context, but the core calculation involves determining the current worth of building improvements after accounting for depreciation. The land value provided ($150,000) is actually irrelevant to this specific calculation, which may be intended to test whether students can identify which information is pertinent to the question being asked.
Background Knowledge
The cost approach involves three components: land value, reproduction/replacement cost of improvements, and depreciation. Depreciated value of improvements is calculated by subtracting all forms of depreciation (physical deterioration, functional obsolescence, and external obsolescence) from the reproduction or replacement cost new.
Real-World Application
Appraisers use this calculation when applying the cost approach for insurance purposes, tax assessments, or when comparable sales are limited. For example, when appraising a unique industrial building, the appraiser would estimate replacement cost new, then deduct depreciation to arrive at the building's contributory value.
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