Using the extraction method, if land value is $200,000, total property value is $750,000, and the building is 10 years old with a 50-year life, what is the reproduction cost new of the building?
Correct Answer
A) $687,500
Why this is correct: First, find the depreciated building value: Property Value - Land Value = 750000 - 200000 = 550000. The building is 10 years old with a 50-year life, so it has depreciated 10/50 = 20%. Therefore, the Reproduction Cost New (RCN) equals the depreciated value divided by the remaining life ratio: 550000 / (1 - 0.20) = 550000 / 0.80 = 687500. Why the other choices are wrong: 440000 is the land value plus incorrect depreciation. 950000 is an incorrect sum. 550000 is the depreciated building value, not the RCN. Exam tip: Extraction method: RCN = (Property Value - Land Value) / (1 - (Effective Age / Total Economic Life)).
Why This Is the Correct Answer
Option B correctly applies the extraction method formula. First, the current building value is calculated by subtracting land value from total property value ($750,000 - $200,000 = $550,000). Next, the depreciation percentage is determined as 20% (10 years ÷ 50 years = 0.20 or 20%). Since the building has depreciated 20%, it retains 80% of its original value. Therefore, the reproduction cost new equals the current building value divided by the remaining percentage: $550,000 ÷ 0.80 = $687,500.
Why the Other Options Are Wrong
Option B: $440,000
Option B ($440,000) appears to incorrectly apply depreciation by multiplying the current building value by the remaining life percentage (80%), which would give an even more depreciated value rather than the reproduction cost new. This represents a fundamental misunderstanding of the extraction method formula.
Option C: $950,000
Option C ($950,000) is too high and doesn't follow any logical calculation path from the given data. This might result from incorrectly adding values together or applying an erroneous formula that inflates the reproduction cost new beyond reasonable parameters.
Option D: $550,000
Option D ($550,000) represents only the current depreciated building value, not the reproduction cost new. This is the intermediate step where land value is subtracted from total property value, but it fails to account for the fact that this current value represents a depreciated amount that needs to be grossed up to find the original cost.
EXTRACT the Truth Formula
EXTRACT: Extract land value, eXamine age ratio, Then Reverse Accumulated Cost Total. Remember the formula: Current Value ÷ (1 - Depreciation Rate) = Reproduction Cost New. Think 'reverse the depreciation damage' to get back to original cost.
How to use: When you see extraction method questions, immediately EXTRACT the land value from total value, calculate the age-to-life ratio for depreciation, then reverse the process by dividing the current building value by the remaining value percentage to find reproduction cost new.
Exam Tip
Always work in steps: (1) Find current building value by subtracting land from total, (2) Calculate depreciation percentage using age/life ratio, (3) Determine remaining value percentage (100% - depreciation%), (4) Divide current value by remaining percentage to get reproduction cost new.
Common Mistakes to Avoid
- -Stopping at the current building value without adjusting for depreciation
- -Multiplying by the depreciation rate instead of dividing by the remaining value percentage
- -Confusing effective age with chronological age in the depreciation calculation
Concept Deep Dive
Analysis
The extraction method is a cost approach technique used to determine the reproduction cost new of a building by working backwards from the current depreciated value. This method requires understanding that the current building value represents the reproduction cost new minus all forms of depreciation that have occurred over time. The key insight is that depreciation is typically calculated as a percentage based on the building's effective age relative to its total economic life. Once you determine the current depreciated value and the depreciation percentage, you can solve for the original reproduction cost new by dividing the current value by the remaining value percentage.
Background Knowledge
The extraction method is part of the cost approach to valuation and requires understanding depreciation calculations based on effective age and economic life. Students must know that current building value equals reproduction cost new minus accumulated depreciation, and this relationship can be algebraically rearranged to solve for any unknown variable.
Real-World Application
Appraisers use the extraction method when they have reliable sales data for total property values and land values, but need to determine building reproduction costs for cost approach analysis. This is particularly useful in markets where construction cost data is limited but comparable sales and land values are readily available.
More Cost Approach Questions
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