A house's cost approach: site value $120,000, cost new $380,000, total depreciation $95,000. The indicated value is:
Correct Answer
A) $405,000 by summation
Why this is correct: The governing concept is the cost approach formula: Value = Land Value + (Cost New - Total Depreciation). Step 1: Calculate depreciated improvement value: $380,000 - $95,000 = $285,000. Step 2: Add land value: $285,000 + $120,000 = $405,000. Why the other choices are wrong: "$500,000 ignoring depreciation" is wrong because it adds land and cost new without subtracting depreciation ($120,000 + $380,000 = $500,000). "$285,000 for improvements only" is wrong because it omits the land value. "$357,000 with land depreciated too" is wrong because land is not depreciated in the cost approach. Exam tip: In the cost approach, land value is added last and is never depreciated.
Why This Is the Correct Answer
Subtracting depreciation from cost new gives the depreciated contribution of the improvements: $380,000 minus $95,000 is $285,000. Adding site value of $120,000 produces an indicated value of $405,000. The site enters at full value because land is not depreciated, and the depreciation figure supplied is already the total across all three categories, so no further deduction applies. The arithmetic is trivial once the structure is right, which is exactly what the question is testing.
Why the Other Options Are Wrong
Option B: $500,000 ignoring depreciation
This adds site value to cost new and stops, which values the house as though it were brand new. Ignoring $95,000 of accrued depreciation overstates the indication by 23 percent and defeats the purpose of the approach, since a cost figure without depreciation is a construction budget rather than a value opinion. The number is tempting because it is the easiest arithmetic on the page.
Option C: $285,000 for improvements only
This is the depreciated contribution of the improvements alone and forgets that the buyer is also purchasing the land under them. A cost approach that stops at the improvements would value an identical house on a $30,000 lot and a $400,000 lot at the same figure. Completing step one and mistaking it for the answer is the classic half-finished calculation.
Option D: $357,000 with land depreciated too
Land is not depreciated in the cost approach, because a site does not physically deteriorate and does not become functionally obsolete the way a structure does. Where external forces have damaged the market, that shows up directly in the site value drawn from comparable land sales, not in a depreciation deduction taken against the land. Extending the depreciation math to the site double counts a loss the market has already priced.
Depreciate the House, Not the Dirt
Houses rot, dirt does not. Take depreciation out of the building, then set the building back down on land you added at full price. The land line never gets a haircut.
How to use: Work it in two written steps every time. Depreciated improvements first, then add site value, and check your answer against the distractor patterns of no depreciation, no land, and depreciated land.
Exam Tip
Before choosing, ask which term each wrong number dropped. Cost approach distractors are built by omitting the depreciation, omitting the land, or depreciating the land, and spotting the pattern is faster than recomputing.
Common Mistakes to Avoid
- -Forgetting to add site value after depreciating the improvements
- -Subtracting depreciation from the total rather than only from the improvements
- -Adding land value before depreciating and then depreciating the combined figure
Concept Deep Dive
Analysis
The cost approach is a summation: the depreciated contribution of the improvements plus the value of the site as though vacant and available for its highest and best use. The order of operations matters because depreciation attaches only to the improvements, which wear out, become functionally dated, and suffer from external forces, while the site is valued directly from market evidence and is never run through a depreciation deduction. Written out, value equals site value plus cost new minus total depreciation, and total depreciation here is the combined figure for physical deterioration, functional obsolescence, and external obsolescence. Each distractor in a question like this corresponds to dropping one term or misapplying it, so working the formula in two clean steps, depreciated improvements first and then the land addition, protects you from all of them.
Background Knowledge
You need the cost approach formula, site value plus cost new less accrued depreciation, and the three categories of depreciation: physical deterioration, functional obsolescence, and external obsolescence. You also need to know that site value is developed separately as though the site were vacant and available for its highest and best use, and that it is added at full value.
Real-World Application
An appraiser valuing a new custom home in an area with few comparable sales estimates site value from four land sales, prices the structure from a cost service with local multipliers, deducts modest physical depreciation, and reconciles the cost indication against a thin sales comparison analysis.
More Cost Approach Questions
In a cost approach for a proposed building, the appropriate cost basis is generally:
A warehouse cost $210,000 to build when the cost index stood at 105. The index is now 210. Its indicated current cost is:
The age-life method expresses depreciation as:
Market extraction of depreciation is limited by the fact that it:
Functional obsolescence caused by a deficiency is measured as curable when:
Curable physical deterioration is measured at cost to cure because:
A 2,050 sq ft dwelling is priced at $178 per square foot with a $34,000 detached garage and $21,500 of site improvements. Cost new is:
A house has three bedrooms sharing one bathroom, and adding a second bath is economically justified. This is:
Direct costs in a construction budget include:
An appraiser writes that a 40-year-old house has an effective age of 10 but describes original wiring, original kitchen and a 25-year-old roof. The report's problem is:
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