A building has a replacement cost of $850,000 and suffers from $45,000 in physical deterioration, $25,000 in functional obsolescence, and $30,000 in external obsolescence. What is the depreciated value of the improvements?
Correct Answer
D) $750,000
Why this is correct: In the cost approach, the depreciated value of improvements is found by subtracting all forms of depreciation (physical, functional, external) from the replacement cost. Calculation: $850,000 (Replacement Cost) - $45,000 (Physical) - $25,000 (Functional) - $30,000 (External) = $750,000. Why the other choices are wrong: '$825,000' results from subtracting only one or two of the depreciation amounts. '$880,000' incorrectly adds some depreciation back to the cost. '$820,000' is close to the result if only physical and functional depreciation were subtracted, omitting external obsolescence. Exam tip: In cost approach problems, always check that you have subtracted all three types of depreciation (physical, functional, external) from the cost new to find the depreciated value.
Why This Is the Correct Answer
Option A ($750,000) correctly applies the depreciated value formula by subtracting all three types of depreciation from the replacement cost. The calculation is: $850,000 (replacement cost) - $45,000 (physical deterioration) - $25,000 (functional obsolescence) - $30,000 (external obsolescence) = $750,000. This represents the current value of the improvements after accounting for all forms of value loss. All depreciation types are additive losses that reduce the original replacement cost.
Why the Other Options Are Wrong
Option A: $825,000
Option A ($825,000) incorrectly subtracts only the physical deterioration ($850,000 - $25,000 = $825,000), failing to account for functional and external obsolescence, which significantly underestimates the total depreciation.
Option B: $880,000
Option B ($880,000) is impossible since it exceeds the replacement cost of $850,000, indicating a fundamental misunderstanding that depreciation should be added rather than subtracted, which violates basic appraisal principles.
Option C: $820,000
Option C ($820,000) appears to subtract only physical deterioration and functional obsolescence ($850,000 - $45,000 - $25,000 = $780,000), but the math doesn't align, suggesting a calculation error or partial consideration of depreciation factors.
PFE Subtraction Rule
Remember 'PFE' - Physical, Functional, External depreciation all get subtracted. Think 'PFE = Problems From Everything' that reduce value from replacement cost.
How to use: When you see a cost approach problem, immediately identify the replacement cost, then look for all PFE depreciation types and subtract each one systematically to get the final depreciated value.
Exam Tip
Always double-check that your final answer is less than the replacement cost - if it's higher, you've made a calculation error since depreciation always reduces value.
Common Mistakes to Avoid
- -Adding depreciation to replacement cost instead of subtracting it
- -Forgetting to include all three types of depreciation in the calculation
- -Confusing replacement cost with reproduction cost in the initial calculation
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation for determining depreciated value of improvements. The cost approach requires appraisers to start with replacement cost new and systematically subtract all forms of depreciation to arrive at the current market value of the improvements. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) are cumulative and must all be deducted from the replacement cost. This calculation is essential in the cost approach to value, particularly for newer properties or special-use properties where comparable sales are limited.
Background Knowledge
The cost approach determines property value by calculating replacement cost new and subtracting accrued depreciation from all sources. The three types of depreciation are: physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (location or economic factors).
Real-World Application
An appraiser evaluating a 10-year-old office building would measure physical wear (HVAC, roofing), functional issues (outdated layout, inadequate parking), and external factors (neighborhood decline, new competing developments) to determine current improvement value for lending or tax purposes.
More Cost Approach Questions
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