A building has a reproduction cost of $500,000. It suffers from $75,000 in physical deterioration, $25,000 in functional obsolescence, and $40,000 in external obsolescence. What is the depreciated cost of the building?
Correct Answer
A) $360,000
Depreciated cost = Reproduction cost - Total depreciation. Total depreciation = $75,000 + $25,000 + $40,000 = $140,000. Depreciated cost = $500,000 - $140,000 = $360,000.
Why This Is the Correct Answer
Option A correctly applies the depreciated cost formula by subtracting total depreciation from reproduction cost. The calculation adds all three types of depreciation: $75,000 (physical) + $25,000 (functional) + $40,000 (external) = $140,000 total depreciation. Then subtracts this from the reproduction cost: $500,000 - $140,000 = $360,000. This represents the current value of the building after accounting for all forms of value loss.
Why the Other Options Are Wrong
Option B: $425,000
This answer ($425,000) incorrectly subtracts only the physical deterioration ($75,000) from the reproduction cost, ignoring both functional and external obsolescence, resulting in $500,000 - $75,000 = $425,000.
Option C: $460,000
This answer ($460,000) incorrectly subtracts only the external obsolescence ($40,000) from the reproduction cost, failing to account for physical deterioration and functional obsolescence, resulting in $500,000 - $40,000 = $460,000.
Option D: $640,000
This answer ($640,000) incorrectly adds the total depreciation to the reproduction cost instead of subtracting it, resulting in $500,000 + $140,000 = $640,000, which is mathematically backwards.
PFE Subtraction Rule
Remember 'PFE' (Physical, Functional, External) - 'Please Find Everything' to subtract. All depreciation types are subtracted from reproduction cost, never added.
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. Think 'Please Find Everything to subtract.'
Exam Tip
Always double-check that you're subtracting depreciation, not adding it - a common error that can lead to obviously inflated values that should immediately signal a mistake.
Common Mistakes to Avoid
- -Adding depreciation instead of subtracting it
- -Forgetting to include all three types of depreciation
- -Confusing reproduction cost with replacement cost
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation in real estate appraisal, specifically the depreciated cost method. The cost approach estimates property value by calculating what it would cost to reproduce or replace the building, then subtracting all forms of depreciation that have occurred over time. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) are cumulative and must all be subtracted from the reproduction cost. This method is particularly useful for newer properties, special-use properties, or when comparable sales data is limited.
Background Knowledge
The cost approach is one of three primary valuation methods in real estate appraisal, alongside the sales comparison and income approaches. Depreciation in appraisal context refers to any loss in value from the reproduction/replacement cost new, categorized into physical deterioration (wear and tear), functional obsolescence (outdated design/features), and external obsolescence (negative external factors).
Real-World Application
An appraiser evaluating a 10-year-old office building would assess physical wear (HVAC, roofing), functional issues (outdated technology infrastructure), and external factors (nearby highway construction), then subtract these cumulative losses from current construction costs to estimate building value.
More Valuation Principles Questions
Which of the following best describes the bundle of rights theory in real estate?
Market value is best defined as:
The principle of substitution states that:
A comparable sale occurred 8 months ago for $450,000. Market conditions analysis shows property values have increased 0.5% per month. What is the adjusted sale price?
What is the difference between reproduction cost and replacement cost?
People Also Study
Property Description & Analysis
20% of exam
Market Analysis & Highest/Best Use
15% of exam
Appraisal Math & Statistics
15% of exam
USPAP (Ethics & Standards)
15% of exam
Report Writing & Compliance
10% of exam
Related Tools
Previous Question
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?
Next Question
When using the gross rent multiplier (GRM), an appraiser should: