A property has a replacement cost new of $1,800,000. Physical deterioration is $200,000, functional obsolescence is $75,000, and external obsolescence is $125,000. What is the depreciated value of the improvements?
Correct Answer
A) $1,400,000
Depreciated value = Replacement cost new - Total depreciation = $1,800,000 - ($200,000 + $75,000 + $125,000) = $1,800,000 - $400,000 = $1,400,000.
Why This Is the Correct Answer
Option A correctly applies the depreciated value formula by subtracting total depreciation from replacement cost new. The calculation adds all three types of depreciation: $200,000 (physical) + $75,000 (functional) + $125,000 (external) = $400,000 total depreciation. Subtracting this from the $1,800,000 replacement cost new yields $1,400,000. This represents the current contributory value of the improvements after accounting for all forms of value loss.
Why the Other Options Are Wrong
Option B: $1,600,000
Option B ($1,600,000) incorrectly subtracts only the physical deterioration ($200,000) from the replacement cost new, ignoring both functional and external obsolescence. This fundamental error would significantly overstate the value of the improvements by $200,000.
Option C: $1,525,000
Option C ($1,525,000) appears to subtract only physical deterioration and functional obsolescence ($275,000 total) while omitting external obsolescence. This partial calculation understates the total depreciation by $125,000, resulting in an overvalued improvement estimate.
Option D: $1,725,000
Option D ($1,725,000) only deducts functional obsolescence ($75,000) from the replacement cost new, completely ignoring both physical deterioration and external obsolescence. This represents a major calculation error that would drastically overstate the improvement value by $325,000.
PFE Subtraction Rule
Remember 'PFE' - Physical, Functional, External depreciation all get subtracted. Think 'Pretty Fierce Enemy' - depreciation is the enemy of value that must be completely defeated (subtracted) to find true worth.
How to use: When you see a cost approach depreciation problem, immediately identify and add up all PFE components, then subtract the total from replacement cost new. Never subtract depreciation types individually or skip any category.
Exam Tip
Always double-check that you've identified and included all three types of depreciation before performing the final subtraction. Write out the addition of depreciation components separately to avoid arithmetic errors.
Common Mistakes to Avoid
- -Forgetting to add all three types of depreciation together before subtracting
- -Subtracting each depreciation type individually instead of subtracting the total
- -Confusing depreciated value with total property value (forgetting that land value still needs to be added)
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 deduct all forms of depreciation to arrive at the current contributory value of the improvements. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) are additive and must all be subtracted from the replacement cost new. This calculation is essential in the cost approach to value and represents the current worth of the building improvements after accounting for all value losses.
Background Knowledge
The cost approach requires understanding that depreciation comes in three forms: physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (location/market factors). All forms of depreciation are cumulative and must be subtracted from replacement cost new to determine current improvement value.
Real-World Application
In practice, appraisers must carefully estimate each type of depreciation through property inspection, market analysis, and comparable sales. The depreciated improvement value is then added to land value to determine total property value using the cost approach.
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