A property has a reproduction cost new of $280,000. Physical depreciation is $35,000, functional obsolescence is $15,000, and external obsolescence is $20,000. What is the depreciated cost of the improvements?
Correct Answer
A) $210,000
Why this is correct: The depreciated cost is calculated by subtracting all forms of depreciation from reproduction cost new: $280,000 - $35,000 (physical) - $15,000 (functional) - $20,000 (external) = $210,000. Why the other choices are wrong: $350,000 incorrectly adds depreciation. $260,000 omits one depreciation type. $245,000 only subtracts physical depreciation. Exam tip: In cost approach problems, sum all depreciation amounts first, then subtract from cost new.
Why This Is the Correct Answer
Option A ($210,000) correctly applies the depreciated cost formula by subtracting all three forms of depreciation from the reproduction cost new. The calculation follows the proper sequence: $280,000 (reproduction cost new) minus $35,000 (physical depreciation) minus $15,000 (functional obsolescence) minus $20,000 (external obsolescence) equals $210,000. This represents the current contributory value of the improvements after accounting for all value losses.
Why the Other Options Are Wrong
Option B: $350,000
Option B ($350,000) incorrectly adds all depreciation amounts to the reproduction cost new instead of subtracting them, demonstrating a fundamental misunderstanding of the depreciated cost calculation.
Option C: $260,000
Option C ($260,000) only accounts for external obsolescence ($20,000), failing to subtract the much larger physical depreciation ($35,000) and functional obsolescence ($15,000) components.
Option D: $245,000
Option D ($245,000) incorrectly omits external obsolescence from the calculation, only subtracting physical depreciation ($35,000) and functional obsolescence ($15,000) for a total deduction of $50,000 instead of $70,000.
PFE Subtraction Rule
Remember 'PFE' (Physical, Functional, External) - all three must be subtracted from reproduction cost new. Think 'PFE = Problems For Everyone' - all depreciation problems reduce value.
How to use: When you see a depreciated cost question, immediately identify the reproduction cost new, then look for all three PFE depreciation types and subtract each one systematically.
Exam Tip
Always double-check that you're subtracting (not adding) depreciation amounts, and verify you've included all three types of depreciation in your calculation.
Common Mistakes to Avoid
- -Adding depreciation instead of subtracting it
- -Omitting one or more types of depreciation from the calculation
- -Confusing reproduction cost with replacement cost in the initial calculation
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 cost new and systematically subtract all forms of depreciation to arrive at the current contributory value of the improvements. Understanding the three types of depreciation (physical, functional, and external) and how they cumulatively reduce value is essential for accurate cost approach valuations. This calculation forms the foundation for determining the total property value when combined with land value in the cost approach.
Background Knowledge
The cost approach requires understanding three types of depreciation: physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (location/market factors). All depreciation types must be subtracted from reproduction cost new to determine the current value contribution of improvements.
Real-World Application
When appraising a 15-year-old custom home, an appraiser calculates reproduction cost new at $400,000, then deducts $45,000 for physical wear, $25,000 for an outdated floor plan (functional), and $30,000 for nearby commercial development (external) to arrive at $300,000 depreciated cost.
More Cost Approach Questions
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A commercial building cost $2,500,000 to construct. The land value is $600,000. If the building has suffered 15% physical deterioration and 8% functional obsolescence, what is the depreciated cost of the improvements?
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