A property has a replacement cost new of $400,000, physical depreciation of $50,000, functional obsolescence of $25,000, and external obsolescence of $30,000. What is the depreciated cost of the improvements?
Correct Answer
A) $295,000
Depreciated cost = Replacement cost new - Total depreciation. $400,000 - ($50,000 + $25,000 + $30,000) = $400,000 - $105,000 = $295,000.
Why This Is the Correct Answer
Option A is correct because it properly applies the depreciated cost formula: Replacement Cost New minus Total Depreciation. The calculation adds all three types of depreciation ($50,000 + $25,000 + $30,000 = $105,000) and subtracts this total from the replacement cost new ($400,000 - $105,000 = $295,000). This follows the standard cost approach methodology where all forms of depreciation are cumulative losses that reduce the value of improvements.
Why the Other Options Are Wrong
Option B: $320,000
Option B ($320,000) incorrectly calculates the depreciation by only subtracting $80,000 from the replacement cost new, suggesting the candidate either missed one category of depreciation or made an arithmetic error in adding the depreciation amounts.
Option C: $350,000
Option C ($350,000) represents subtracting only $50,000 from the replacement cost new, indicating the candidate likely only considered physical depreciation and ignored both functional and external obsolescence entirely.
Option D: $375,000
Option D ($375,000) shows a deduction of only $25,000, suggesting the candidate either only considered functional obsolescence or made a significant calculation error in determining total depreciation.
PFE Depreciation Stack
Remember 'PFE' - Physical, Functional, External depreciation all STACK UP against your replacement cost. Visualize these as three weights stacked on top of each other, all pressing down on your original cost.
How to use: When you see a depreciated cost question, immediately identify and list all PFE depreciation amounts, stack them together (add them up), then subtract this total stack from the replacement cost new.
Exam Tip
Always double-check that you've identified and included ALL types of depreciation mentioned in the problem - physical, functional, and external - before performing your final calculation.
Common Mistakes to Avoid
- -Only considering one or two types of depreciation instead of all three
- -Forgetting to add all depreciation amounts together before subtracting from replacement cost
- -Confusing replacement cost new with reproduction cost new in the calculation
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation for determining depreciated cost of improvements. The cost approach requires understanding that all forms of depreciation must be subtracted from the replacement cost new to arrive at the current value of improvements. Physical depreciation represents wear and tear, functional obsolescence represents design deficiencies or outdated features, and external obsolescence represents loss in value due to factors outside the property. These three types of depreciation are additive and must all be deducted from the replacement cost new.
Background Knowledge
The cost approach is one of three primary valuation methods in real estate appraisal, used to estimate property value by calculating the cost to replace or reproduce improvements minus depreciation, plus land value. Depreciation in appraisal includes physical deterioration, functional obsolescence, and external obsolescence, all of which reduce the value of improvements from their replacement cost new.
Real-World Application
An appraiser evaluating a 20-year-old office building would assess physical wear (HVAC, roofing), functional issues (outdated electrical systems, poor layout), and external factors (declining neighborhood, new competing developments) to determine the building's current contributory value to the overall property.
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