A building has a replacement cost of $800,000, and the land value is $200,000. If the building suffers from 15% physical deterioration and 5% functional obsolescence, what is the indicated value by the cost approach?
Correct Answer
B) $840,000
Why this is correct: The cost approach formula is: Indicated Value = (Replacement Cost New - Depreciation) + Land Value. Here, total depreciation is 15% physical + 5% functional = 20%. Depreciated building cost = $800,000 × (1 - 0.20) = $800,000 × 0.80 = $640,000. Adding the $200,000 land value yields $840,000. Why the other choices are wrong: "$800,000" incorrectly uses only the building's replacement cost without depreciation or land. "$720,000" mistakenly applies the 20% depreciation to the total property value ($1,000,000 × 0.80). "$760,000" results from an arithmetic error, perhaps subtracting only 15% from the building cost. Exam tip: In the cost approach, always apply depreciation percentages to the building's replacement cost new, not the total property value.
Why This Is the Correct Answer
Option A is correct because it properly applies the cost approach formula. The building's replacement cost of $800,000 is reduced by both the 15% physical deterioration and 5% functional obsolescence (total 20% depreciation), resulting in $800,000 × 0.80 = $640,000. This depreciated building value is then added to the land value of $200,000, yielding a total indicated value of $840,000. The calculation correctly treats land as not depreciating and only applies depreciation to the building improvements.
Why the Other Options Are Wrong
Option A: $800,000
$800,000 represents only the replacement cost of the building without accounting for any depreciation or adding the land value, making it an incomplete application of the cost approach.
Option C: $720,000
$720,000 results from incorrectly subtracting the land value instead of adding it, or from applying depreciation incorrectly to arrive at a value that's too low for the given parameters.
Option D: $760,000
$760,000 incorrectly applies the 20% total depreciation to the entire property value ($1,000,000 × 0.80 = $800,000, then subtracting $40,000), rather than applying depreciation only to the building improvements.
LAND Never Dies
Remember 'LAND Never Dies' - Land Always Needs Depreciation = NEVER. Only buildings depreciate, land maintains its value in the cost approach calculation.
How to use: When you see a cost approach problem, immediately identify what's land and what's building. Apply the depreciation formula only to the building: Building Value = Replacement Cost × (1 - total depreciation %), then add the unchanged land value.
Exam Tip
Always double-check that you're adding the land value at the end, not subtracting it, and ensure depreciation percentages are applied only to the building improvements, not the total property value.
Common Mistakes to Avoid
- -Applying depreciation to the total property value instead of just the building
- -Forgetting to add the land value to the final calculation
- -Subtracting land value instead of adding it
Concept Deep Dive
Analysis
This question tests the fundamental application of the cost approach to valuation, which is one of the three primary approaches used in real estate appraisal. The cost approach involves calculating the replacement cost of improvements, subtracting all forms of depreciation, and adding the land value to arrive at the total property value. The key concept being tested is the proper calculation and application of depreciation factors, specifically physical deterioration and functional obsolescence, which are subtracted from the replacement cost before adding land value.
Background Knowledge
The cost approach is based on the principle of substitution, which states that a rational buyer will not pay more for a property than the cost to acquire a similar site and construct improvements of equivalent utility. Depreciation in appraisal includes physical deterioration, functional obsolescence, and external obsolescence, and only applies to improvements, never to land.
Real-World Application
Appraisers commonly use the cost approach for newer properties, special-use properties, or when comparable sales are limited. They must carefully estimate all forms of depreciation by inspecting the property for physical wear, functional deficiencies, and external factors that might affect value.
More Cost Approach Questions
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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?
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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?
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