A building has a reproduction cost new of $500,000. It has 20% physical deterioration, 10% functional obsolescence, and 5% external obsolescence. What is the depreciated value of the improvements?
Correct Answer
A) $325,000
Why this is correct: The three separately estimated depreciation components total 35% of cost new: 20% + 10% + 5%. Depreciated value = $500,000 × 65% = $325,000. Why the other choices are wrong: The other choices result from omitting a depreciation component or applying percentages to inconsistent bases. Exam tip: If each rate is stated as a percentage of cost new, add the rates and deduct the total once.
Why This Is the Correct Answer
Option B correctly applies the sequential depreciation method. Starting with $500,000, physical deterioration of 20% reduces the value to $400,000. Then functional obsolescence of 10% is applied to the remaining $400,000 (not the original $500,000), reducing it by $40,000 to $360,000. Finally, external obsolescence of 5% is applied to $360,000, reducing it by $18,000 to arrive at the final depreciated value of $342,000. The slight discrepancy with $342,500 in the answer choice likely accounts for rounding.
Why the Other Options Are Wrong
PFE Sequential Stack
Remember 'PFE' (Physical, Functional, External) and visualize stacking blocks where each depreciation 'eats away' at what's left, not the original. Think: 'Each bite is smaller because there's less cake left.'
How to use: When you see multiple depreciation types, immediately think 'PFE Sequential Stack' and calculate each depreciation on the remaining value from the previous step, never on the original reproduction cost new.
Exam Tip
Always write out each step clearly: show the remaining value after each depreciation calculation rather than trying to do it all in your head, as this prevents calculation errors.
Common Mistakes to Avoid
- -Adding all depreciation percentages together and applying as one lump sum
- -Applying all depreciation factors to the original reproduction cost new instead of sequentially
- -Applying depreciation factors in the wrong order (external before physical, etc.)
Concept Deep Dive
Analysis
This question tests the cost approach to valuation, specifically the sequential application of depreciation factors to determine the depreciated value of improvements. The three types of depreciation (physical deterioration, functional obsolescence, and external obsolescence) must be applied in order, with each subsequent depreciation calculated on the remaining value after the previous depreciation has been deducted. This sequential method reflects how depreciation factors compound in real-world scenarios, where each type of obsolescence affects the already-diminished value of the property. Understanding this compounding effect is crucial for accurate cost approach valuations.
Background Knowledge
The cost approach requires understanding that depreciation factors are applied sequentially, not additively, because each type of depreciation affects the remaining value after previous depreciation has been accounted for. Physical deterioration is typically applied first, followed by functional obsolescence, then external obsolescence, with each calculation based on the value remaining after the previous depreciation.
Real-World Application
In practice, appraisers encounter buildings with multiple forms of depreciation - an older office building might have physical wear (deterioration), outdated HVAC systems (functional), and declining neighborhood conditions (external), requiring sequential analysis for accurate valuation.
More Cost Approach Questions
A property generates $85,000 in Net Operating Income and sells for $1,062,500. What is the overall capitalization rate?
A property has potential gross income of $180,000, vacancy and collection loss of $15,000, and operating expenses of $65,000. What is the Net Operating Income?
A comparable sale occurred 8 months ago for $425,000. Market conditions indicate property values have increased 0.5% per month since that time. What is the adjusted sale price?
A property generates $150,000 in potential gross income. Market data indicates a 7% vacancy rate and operating expenses of 35% of effective gross income. If the cap rate is 9.5%, what is the indicated value?
A property sold for $320,000 one year ago. If market conditions have improved by 6% since that sale, what is the time-adjusted sale price for comparison purposes?
A commercial building cost $2,500,000 to construct. The land value is $600,000. If the building has suffered 15% physical deterioration and 8% functional obsolescence, what is the depreciated cost of the improvements?
A building's gross rent multiplier (GRM) is 120. If the monthly rent is $2,500, what is the indicated value?
In the cost approach, economic obsolescence is characterized as:
The concept of regression in property values means that:
A commercial property has potential gross income of $120,000, vacancy and collection loss of 8%, and operating expenses of $35,000. Using a cap rate of 9.5%, what is the indicated value?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Income Approach
8.2% of exam