A building has a reproduction cost of $400,000. Physical deterioration is estimated at $50,000, functional obsolescence at $30,000, and external obsolescence at $20,000. What is the depreciated cost of the building?
Correct Answer
A) $300,000
Depreciated cost = Reproduction cost - Total depreciation. $400,000 - ($50,000 + $30,000 + $20,000) = $300,000.
Why This Is the Correct Answer
Option A is correct because it properly applies the depreciated cost formula: Reproduction Cost minus Total Depreciation. The calculation is $400,000 - ($50,000 + $30,000 + $20,000) = $400,000 - $100,000 = $300,000. All three types of depreciation must be added together and subtracted from the reproduction cost as they represent cumulative value losses. This straightforward subtraction gives us the current depreciated value of the building improvements.
Why the Other Options Are Wrong
Option B: $320,000
Option B ($320,000) is incorrect because it fails to account for all depreciation types, likely omitting external obsolescence ($20,000) from the total depreciation calculation, resulting in $400,000 - $80,000 = $320,000.
Option C: $350,000
Option C ($350,000) is incorrect because it only subtracts physical deterioration ($50,000) from the reproduction cost, ignoring both functional and external obsolescence, resulting in $400,000 - $50,000 = $350,000.
Option D: $370,000
Option D ($370,000) is incorrect because it only accounts for functional and external obsolescence ($50,000 total) while omitting physical deterioration, resulting in $400,000 - $30,000 = $370,000.
PFE Subtraction Rule
Remember 'PFE' - Physical deterioration, Functional obsolescence, External obsolescence - all must be subtracted. Think 'PFE = Problems From Everything' that reduce building value.
How to use: When you see a depreciated cost question, immediately identify the reproduction/replacement cost, then look for all PFE components to subtract. Add all depreciation types together first, then subtract the total from the cost.
Exam Tip
Always double-check that you've identified and included ALL types of depreciation mentioned in the problem - partial depreciation calculations are common wrong answer choices designed to trap test-takers.
Common Mistakes to Avoid
- -Forgetting to include all three types of depreciation in the calculation
- -Subtracting depreciation types individually instead of adding them together first
- -Confusing reproduction cost with replacement cost in the initial 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 estimates property value by calculating what it would cost to reproduce or replace the building, then subtracting all forms of depreciation that have occurred over time. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) must all be deducted from the reproduction cost to arrive at the current depreciated value. This calculation forms the basis for determining the contributory value of improvements to the total property value.
Background Knowledge
The cost approach is one of three primary valuation methods in real estate appraisal, alongside sales comparison and income approaches. Depreciation in appraisal context refers to any loss in value from the reproduction/replacement cost new, categorized into physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (location or economic factors).
Real-World Application
Appraisers use this calculation when valuing properties where comparable sales are limited, such as special-purpose buildings, new construction, or insurance appraisals where the cost to rebuild must be determined after accounting for all value losses.
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