A building's reproduction cost is $800,000. Physical deterioration is estimated at $120,000, functional obsolescence at $80,000, and external obsolescence at $40,000. What is the depreciated value of the improvements?
Correct Answer
D) $560,000
Why this is correct: In the cost approach, depreciated value equals reproduction cost minus total depreciation. Sum all forms of depreciation: Physical ($120,000) + Functional ($80,000) + External ($40,000) = $240,000. Then subtract from cost: $800,000 - $240,000 = $560,000. Why the other choices are wrong: "$680,000" results from subtracting only physical deterioration. "$720,000" subtracts only physical and functional obsolescence. "$1,040,000" incorrectly adds the depreciation amounts to the cost. Exam tip: Total all depreciation types before subtracting from cost. The formula is: Value = Cost - (Physical + Functional + External Depreciation).
Why This Is the Correct Answer
Option A correctly applies the depreciated value formula by subtracting total depreciation from reproduction cost. The calculation adds all three types of depreciation ($120,000 + $80,000 + $40,000 = $240,000) and subtracts this total from the reproduction cost ($800,000 - $240,000 = $560,000). This follows the standard cost approach methodology where all forms of depreciation reduce the value of the improvements from their reproduction cost.
Why the Other Options Are Wrong
Option A: $680,000
This answer ($680,000) incorrectly subtracts only $120,000 from the reproduction cost, suggesting the candidate only accounted for physical deterioration and ignored functional and external obsolescence.
Option B: $720,000
This answer ($720,000) results from subtracting only $80,000 from reproduction cost, indicating the candidate may have confused which depreciation types to include or made an arithmetic error.
Option C: $1,040,000
This answer ($1,040,000) is greater than the reproduction cost, which is impossible since depreciation always reduces value. This suggests the candidate added depreciation instead of subtracting it.
PFE Subtraction Rule
Remember 'PFE' (Physical, Functional, External) - all three depreciation types are 'Subtracted From Everything' (reproduction cost). Think: 'Please Find Everyone's Subtractions For Exact' value.
How to use: When you see a cost approach problem, immediately identify PFE depreciation amounts, add them together, then subtract the total from reproduction/replacement cost. Never add depreciation to cost.
Exam Tip
Always double-check that your final answer is less than the reproduction cost - if it's higher, you likely added instead of subtracted depreciation.
Common Mistakes to Avoid
- -Adding depreciation to reproduction cost instead of subtracting it
- -Forgetting to include all three types of depreciation in the calculation
- -Subtracting each depreciation type separately instead of adding them first then subtracting the total
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation for determining depreciated value of improvements. The cost approach involves starting with reproduction or replacement cost and then subtracting all forms of depreciation to arrive at the current value. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) are additive and must all be subtracted from the reproduction cost. This is a core valuation principle that appraisers use regularly when applying the cost approach to estimate property value.
Background Knowledge
The cost approach requires understanding three types of depreciation: physical deterioration (wear and tear), functional obsolescence (outdated design or features), and external obsolescence (negative external factors). All depreciation types are cumulative and must be subtracted from reproduction or replacement cost to determine current value.
Real-World Application
An appraiser valuing a 20-year-old office building would estimate physical wear (HVAC, roof condition), functional issues (outdated electrical systems), and external factors (declining neighborhood) to determine how much value has been lost since construction.
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