A building has a replacement cost of $500,000. It suffers from $75,000 in physical deterioration, $25,000 in functional obsolescence, and $50,000 in external obsolescence. What is the depreciated cost of the building?
Correct Answer
A) $350,000
Depreciated cost equals replacement cost minus all forms of depreciation: $500,000 - $75,000 - $25,000 - $50,000 = $350,000.
Why This Is the Correct Answer
Option A correctly applies the depreciated cost formula by subtracting all forms of depreciation from the replacement cost new. The calculation follows the standard cost approach methodology: $500,000 (replacement cost) - $75,000 (physical deterioration) - $25,000 (functional obsolescence) - $50,000 (external obsolescence) = $350,000. This represents the current value of the building after accounting for all value losses due to wear and tear, design deficiencies, and external market factors.
Why the Other Options Are Wrong
Option B: $425,000
This answer of $425,000 results from only subtracting physical deterioration ($500,000 - $75,000 = $425,000) while ignoring functional and external obsolescence, which is an incomplete application of the cost approach.
Option C: $450,000
This answer of $450,000 results from only subtracting external obsolescence ($500,000 - $50,000 = $450,000) while failing to account for physical deterioration and functional obsolescence.
Option D: $475,000
This answer of $475,000 results from only subtracting functional obsolescence ($500,000 - $25,000 = $475,000) while neglecting to subtract physical deterioration and external obsolescence.
PFE Subtraction Rule
Remember 'PFE' - Physical, Functional, External - and 'Subtract ALL to get the CALL (current actual value)'. All three types of depreciation must be subtracted from replacement cost.
How to use: When you see a cost approach question, immediately identify the replacement cost, then look for all three PFE depreciation types and subtract each one systematically to avoid missing any component.
Exam Tip
Always double-check that you've subtracted ALL forms of depreciation mentioned in the problem - partial calculations are common wrong answer choices designed to catch incomplete work.
Common Mistakes to Avoid
- -Only subtracting one or two types of depreciation instead of all three
- -Adding depreciation instead of subtracting it from replacement cost
- -Confusing replacement cost with reproduction cost in the initial calculation
Concept Deep Dive
Analysis
This question tests the fundamental cost approach calculation for determining depreciated cost (also known as depreciated replacement cost new). The cost approach is one of the three primary valuation methods in real estate appraisal, requiring appraisers to understand how various forms of depreciation reduce a property's value from its replacement cost new. All three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) must be subtracted from the replacement cost to arrive at the current depreciated value. This calculation is essential for insurance purposes, tax assessments, and situations where comparable sales data is limited.
Background Knowledge
The cost approach determines property value by calculating what it would cost to replace the structure new, then subtracting all forms of depreciation that have occurred since construction. The three types of depreciation are: physical deterioration (wear and tear), functional obsolescence (design deficiencies), and external obsolescence (negative external influences).
Real-World Application
Insurance adjusters use this calculation when determining settlement amounts for property damage claims, ensuring they account for pre-existing depreciation before the loss occurred, not just the replacement cost of damaged components.
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
When using paired sales analysis, the appraiser is attempting to:
Next Question
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?