A building has a replacement cost new of $400,000. It suffers from $30,000 in physical deterioration, $20,000 in functional obsolescence, and $15,000 in external obsolescence. What is the depreciated cost of the building?
Correct Answer
D) $335,000
Depreciated cost = Replacement cost new minus all forms of depreciation: $400,000 - $30,000 - $20,000 - $15,000 = $335,000.
Why This Is the Correct Answer
Option D correctly applies the depreciated cost formula by subtracting all three types of depreciation from the replacement cost new. The calculation is: $400,000 (replacement cost new) - $30,000 (physical deterioration) - $20,000 (functional obsolescence) - $15,000 (external obsolescence) = $335,000. This represents the building's current contributory value after accounting for all forms of value loss.
Why the Other Options Are Wrong
Option A: $400,000
Option A represents the replacement cost new without any depreciation deducted, which ignores the building's actual condition and obsolescence factors that reduce its current value.
Option B: $370,000
Option B only deducts physical deterioration ($30,000) from the replacement cost new, failing to account for functional and external obsolescence totaling $35,000.
Option C: $350,000
Option C deducts physical deterioration and functional obsolescence ($50,000 total) but fails to subtract the external obsolescence of $15,000.
PFE Subtraction Method
Remember 'PFE' - Physical, Functional, External depreciation must ALL be subtracted. Think 'PFE = Problems For Everyone' - all three problems reduce building value.
How to use: When you see a depreciated cost question, immediately identify the replacement cost new, then look for all three PFE depreciation types and subtract each one systematically.
Exam Tip
Always double-check that you've subtracted ALL forms of depreciation listed in the problem - partial deductions are common wrong answer choices designed to catch incomplete calculations.
Common Mistakes to Avoid
- -Only subtracting one or two types of depreciation instead of all three
- -Adding depreciation to replacement cost instead of subtracting
- -Confusing replacement cost new with the final depreciated value
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 replacement cost new and systematically deduct all forms of depreciation to arrive at the current contributory value of the building. Understanding the three types of depreciation - physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (location/market factors) - is crucial for accurate valuation. All forms of depreciation must be subtracted from the replacement cost new to determine the building's current depreciated value.
Background Knowledge
The cost approach involves estimating replacement cost new of improvements and deducting accrued depreciation to determine current value. Depreciation includes physical deterioration (curable and incurable), functional obsolescence (superadequacy and deficiency), and external obsolescence (locational and economic factors).
Real-World Application
When appraising an older commercial building, an appraiser might find $50,000 in needed repairs (physical), $25,000 for outdated HVAC system (functional), and $40,000 loss due to declining neighborhood (external) - all must be deducted from replacement cost for accurate valuation.
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