A building has a reproduction cost new of $850,000. Physical depreciation is estimated at 15%, functional obsolescence at 8%, and external obsolescence at 5%. What is the depreciated value of the improvements?
Correct Answer
D) $612,000
Why this is correct: The governing concept is calculating total depreciation as the sum of all types (physical, functional, external). Step 1: Sum the depreciation percentages: 15% + 8% + 5% = 28%. Step 2: Calculate the remaining value percentage: 100% - 28% = 72%. Step 3: Apply to cost new: $850,000 * 0.72 = $612,000. Why the other choices are wrong: "$238,000" is wrong; this is the total depreciation amount ($850,000 * 0.28). "$722,500" is wrong; this uses only 15% depreciation ($850,000 * 0.85). "$680,000" is wrong; this uses 20% depreciation ($850,000 * 0.80). Exam tip: Depreciated value = Cost New * (1 - (Physical% + Functional% + External%)).
Why This Is the Correct Answer
Option A ($612,000) correctly applies the depreciation calculation method. The total depreciation is calculated by adding all three types: 15% + 8% + 5% = 28%. The depreciated value is then found by multiplying the reproduction cost new by the remaining value percentage: $850,000 × (100% - 28%) = $850,000 × 72% = $612,000. This follows the standard cost approach formula used in real estate appraisal.
Why the Other Options Are Wrong
Option A: $238,000
Option A ($238,000) represents the total amount of depreciation ($850,000 × 28% = $238,000) rather than the remaining depreciated value. This is a fundamental error of providing the loss amount instead of the remaining value.
Option B: $722,500
Option B ($722,500) represents only 85% of the original cost, suggesting only physical depreciation (15%) was subtracted while ignoring functional and external obsolescence. This incomplete calculation fails to account for all forms of value loss.
Option C: $680,000
Option C ($680,000) represents 80% of the original cost, which would indicate only 20% total depreciation instead of the correct 28%. This suggests an error in adding the depreciation percentages or applying an incorrect calculation method.
PFE Addition Rule
Remember 'PFE' - Physical + Functional + External depreciation percentages ADD UP to total depreciation. Then use the formula: Cost New × (1 - Total Depreciation %) = Depreciated Value.
How to use: When you see a cost approach problem with multiple depreciation types, immediately write 'PFE' and add the percentages. Then subtract from 100% to get the remaining value percentage and multiply by cost new.
Exam Tip
Always double-check that you're calculating the remaining value (what's left) rather than the depreciation amount (what's lost). The question asks for 'depreciated value,' which means the current worth after depreciation.
Common Mistakes to Avoid
- -Calculating depreciation amounts instead of remaining depreciated value
- -Applying depreciation percentages sequentially rather than additively
- -Forgetting to include all three types of depreciation in the total calculation
Concept Deep Dive
Analysis
This question tests the cost approach to valuation, specifically the calculation of depreciated improvement value. The cost approach involves determining reproduction or replacement cost new, then subtracting all forms of depreciation to arrive at the current value of improvements. The three types of depreciation (physical, functional, and external) are additive when expressed as percentages, representing the total loss in value from the original cost new. This is a fundamental calculation in real estate appraisal that requires understanding how different depreciation factors compound to reduce 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). These depreciation percentages are additive when calculating total value loss from reproduction cost new.
Real-World Application
An appraiser evaluating a 20-year-old office building would assess physical wear (HVAC, roof condition), functional issues (outdated electrical systems, poor layout), and external factors (declining neighborhood, new competing properties) to determine how much value has been lost from the original construction cost.
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