A building has a reproduction cost new of $800,000. Physical deterioration is estimated at $120,000, functional obsolescence at $50,000, and external obsolescence at $80,000. What is the depreciated cost of the improvements?
Correct Answer
A) $550,000
Depreciated cost equals reproduction cost new minus all forms of depreciation: $800,000 - $120,000 - $50,000 - $80,000 = $550,000. All three types of depreciation must be subtracted from the cost new.
Why This Is the Correct Answer
Option A ($550,000) correctly applies the depreciated cost formula by subtracting all three types of depreciation from the reproduction cost new. The calculation is: $800,000 - $120,000 (physical) - $50,000 (functional) - $80,000 (external) = $550,000. This represents the current contributory value of the improvements after accounting for all forms of value loss. All depreciation types are cumulative and must be subtracted to determine the depreciated cost.
Why the Other Options Are Wrong
Option B: $630,000
Option B ($630,000) incorrectly omits one form of depreciation from the calculation, likely external obsolescence ($800,000 - $120,000 - $50,000 = $630,000), which understates the total depreciation and overstates the current value of the improvements.
Option C: $680,000
Option C ($680,000) fails to account for functional obsolescence, only subtracting physical deterioration and external obsolescence ($800,000 - $120,000 - $80,000 = $600,000), or only subtracting physical deterioration ($800,000 - $120,000 = $680,000), resulting in an overvaluation.
Option D: $720,000
Option D ($720,000) only subtracts physical deterioration ($800,000 - $120,000 = $680,000) or makes an even larger calculation error, failing to account for functional and external obsolescence, significantly overstating the depreciated cost.
PFE Subtraction Rule
Remember 'PFE' - Physical, Functional, External - and 'Subtract ALL to get the CALL' (Current Actual Living value). All three depreciation types must be subtracted from cost new.
How to use: When you see a depreciated cost question, immediately identify the cost new, then look for all three PFE depreciation types and subtract each one systematically to avoid missing any component.
Exam Tip
Always double-check that you've identified and subtracted all three types of depreciation - many wrong answers result from omitting one type of depreciation in the calculation.
Common Mistakes to Avoid
- -Forgetting to subtract one or more types of depreciation
- -Adding depreciation instead of subtracting it
- -Confusing reproduction cost with depreciated cost
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation for determining depreciated cost of improvements. The cost approach requires appraisers to start with reproduction or replacement cost new and systematically subtract all forms of depreciation to arrive at the current contributory value of the improvements. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) are cumulative and must all be deducted from the cost new. This calculation is essential for the cost approach to value and represents the current worth of the building improvements after accounting for all value losses.
Background Knowledge
The cost approach requires understanding three types of depreciation: physical deterioration (wear and tear), functional obsolescence (design deficiencies or outdated features), and external obsolescence (negative influences from outside the property). Depreciated cost equals reproduction/replacement cost new minus the sum of all depreciation types.
Real-World Application
When appraising a property using the cost approach, appraisers must estimate each type of depreciation separately through market analysis, building inspection, and neighborhood study, then subtract all forms to determine the building's current contributory value to the overall property value.
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