A building has a reproduction cost new of $800,000. Physical deterioration is estimated at $120,000, functional obsolescence at $50,000, and external obsolescence at $80,000. What is the depreciated cost of the building?
Correct Answer
A) $550,000
Depreciated cost = Reproduction cost new - Total depreciation. Total depreciation = $120,000 + $50,000 + $80,000 = $250,000. Therefore: $800,000 - $250,000 = $550,000.
Why This Is the Correct Answer
Option A ($550,000) correctly applies the depreciated cost formula by subtracting total depreciation from reproduction cost new. The calculation properly adds all three types of depreciation: $120,000 (physical) + $50,000 (functional) + $80,000 (external) = $250,000 total depreciation. Then subtracts this total from the reproduction cost: $800,000 - $250,000 = $550,000. This represents the current value of the building after accounting for all forms of value loss.
Why the Other Options Are Wrong
Option B: $630,000
Option B ($630,000) appears to have subtracted only some forms of depreciation, possibly omitting external obsolescence ($800,000 - $120,000 - $50,000 = $630,000), which would be an incomplete calculation that fails to account for all value-reducing factors.
Option C: $680,000
Option C ($680,000) likely subtracted only physical deterioration ($800,000 - $120,000 = $680,000), ignoring both functional and external obsolescence, which significantly understates the total depreciation affecting the property.
Option D: $720,000
Option D ($720,000) appears to have subtracted only external obsolescence ($800,000 - $80,000 = $720,000), failing to account for the substantial physical deterioration and functional obsolescence that reduce the building's value.
PFE Depreciation Stack
Remember 'PFE' - Physical, Functional, External depreciation all STACK UP and must be subtracted together. Think of depreciation as a stack of bills you must pay - you can't ignore any of them when calculating what you have left.
How to use: When you see a cost approach problem, immediately identify the reproduction cost new, then look for all PFE depreciation types, add them together in your 'stack,' and subtract the total stack from the reproduction cost.
Exam Tip
Always double-check that you've identified and included ALL types of depreciation mentioned in the problem - partial depreciation calculations are a common trap in multiple choice answers.
Common Mistakes to Avoid
- -Forgetting to add all three types of depreciation together before subtracting
- -Subtracting each depreciation type separately instead of calculating total depreciation first
- -Confusing reproduction cost with replacement cost in the initial calculation
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 additive and must all be subtracted from the reproduction cost new. 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 reproduction cost new, categorized into physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (outside economic factors).
Real-World Application
An appraiser evaluating a 10-year-old office building would assess physical wear (HVAC, roofing), functional issues (outdated electrical systems, poor layout), and external factors (economic decline in the area) to determine how much value the building has lost since construction.
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