A building has a reproduction cost new of $800,000. Physical deterioration is estimated at $150,000, functional obsolescence at $75,000, and external obsolescence at $50,000. What is the depreciated cost of the building?
Correct Answer
B) $525,000
Why this is correct: The depreciated cost in the cost approach is calculated as Reproduction Cost New minus total depreciation. The calculation is: $800,000 (cost new) - $150,000 (physical) - $75,000 (functional) - $50,000 (external) = $525,000. Why the other choices are wrong: $650,000 results from subtracting only physical deterioration ($800,000 - $150,000). $575,000 results from subtracting only physical and functional depreciation ($800,000 - $150,000 - $75,000). $725,000 results from subtracting only external obsolescence ($800,000 - $50,000). Exam tip: When calculating depreciated cost, sum all forms of depreciation (physical, functional, external) first, then subtract the total from cost new.
Why This Is the Correct Answer
Option A ($525,000) correctly applies the depreciated cost formula by subtracting all three forms of depreciation from the reproduction cost new. The calculation follows the standard approach: $800,000 (reproduction cost new) minus $150,000 (physical deterioration) minus $75,000 (functional obsolescence) minus $50,000 (external obsolescence) equals $525,000. This represents the current value of the building improvements after accounting for all depreciation factors that have diminished its worth from the original reproduction cost.
Why the Other Options Are Wrong
Option A: $650,000
Option A ($650,000) incorrectly subtracts only physical deterioration ($150,000) from the reproduction cost new, calculating $800,000 - $150,000 = $650,000, while ignoring both functional and external obsolescence entirely.
Option C: $575,000
Option C ($575,000) incorrectly omits one form of depreciation from the calculation, likely external obsolescence ($50,000), resulting in $800,000 - $150,000 - $75,000 = $575,000, which fails to account for all depreciation factors.
Option D: $725,000
Option D ($725,000) incorrectly subtracts only functional obsolescence ($75,000) from the reproduction cost new, calculating $800,000 - $75,000 = $725,000, while failing to account for physical deterioration and external obsolescence.
PFE Subtraction Method
Remember 'PFE' - Physical, Functional, External - and think 'Subtract PFE from RCN' (Reproduction Cost New). Visualize peeling away layers: first Physical damage, then Functional problems, finally External issues.
How to use: When you see a depreciated cost question, immediately identify the RCN and look for all three PFE depreciation types. Write the formula: RCN - P - F - E = Depreciated Cost, then plug in the numbers systematically.
Exam Tip
Always double-check that you've subtracted ALL forms of depreciation listed in the problem - it's easy to miss one type and select a wrong answer that represents a partial calculation.
Common Mistakes to Avoid
- -Forgetting to subtract one or more types of depreciation
- -Adding depreciation instead of subtracting it
- -Confusing reproduction cost with replacement cost in the calculation
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation in real estate appraisal, specifically the depreciated cost method. The cost approach determines property value by calculating what it would cost to reproduce or replace a building, then subtracting all forms of depreciation that have occurred over time. Understanding the three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) and how they collectively reduce the reproduction cost new is essential for accurate property valuation. This calculation represents the current worth of the improvements after accounting for all value losses.
Background Knowledge
The cost approach is one of three primary valuation methods in real estate appraisal, alongside the sales comparison and income approaches. Depreciation in appraisal context refers to any loss in value from the reproduction cost new, categorized into physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (outside economic factors).
Real-World Application
Appraisers use this calculation when valuing unique properties with limited comparable sales, such as special-purpose buildings, new construction, or properties in markets with insufficient sales data. Insurance companies also rely on depreciated cost calculations for coverage determinations and claim settlements.
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