The cost new of the improvements is $310,000, and they have depreciated 20% of that cost. The site value of $88,000 already reflects any site influences. What is the indicated value by the cost approach?
Correct Answer
C) $336,000
310000×(1−0.2)+88000 = 336000. Common errors: leaving out the site value gives $248,000; not deducting the 20% depreciation gives $398,000; applying the 20% depreciation as the remaining share gives $150,000.
Why This Is the Correct Answer
Option C is correct because the improvements retain 80% of cost new: $310,000 × 0.80 = $248,000. Adding the $88,000 site value gives $336,000.
Why the Other Options Are Wrong
Option A: $150,000
Option A, $150,000, uses the 20% depreciation as if it were the remaining share ($310,000 × 0.20 + $88,000 = $62,000 + $88,000). The improvement keeps 80%, so the result is $310,000 × 0.80 + $88,000 = $336,000.
Option B: $248,000
Option B, $248,000, is only the depreciated improvement value ($310,000 × 0.80). It omits the $88,000 site value; adding it gives $336,000.
Option D: $398,000
Option D, $398,000, adds site value to undepreciated cost ($310,000 + $88,000). The 20% depreciation of $62,000 must be deducted first, giving $336,000.
Depreciation plus percent good equals 100
Depreciation and percent good add up to 100%. Multiply cost new by percent good to get what remains.
How to use: Use this to convert a depreciation percentage into the remaining value share before multiplying.
Exam Tip
Decide whether the question wants the depreciation amount or the depreciated value, and whether site is included. Each choice matches a different distractor.
Common Mistakes to Avoid
- -Multiplying cost new by the depreciation percentage and treating that as remaining value
- -Omitting the site value
- -Adding site value without deducting depreciation
Concept Deep Dive
Analysis
This question tests percentage depreciation and the percent good concept. Deducting 20% leaves 80% of cost new as the depreciated improvement value. Add the site value to get the total indicated value.
Background Knowledge
Percent good is the complement of depreciation measured as a percentage. If depreciation is 20%, percent good is 80%, and the depreciated cost equals cost new times percent good. Site value is added separately in the cost approach.
Real-World Application
An appraiser estimates that a home's improvements have lost about 20% of their cost new. The appraiser multiplies cost new by 80% and adds a site value from land sales to produce the cost approach indication.
More Cost Approach Questions
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Previous Question
Market data show that an external influence causes an annual net income loss of $14,400 and indicate a 9% capitalization rate for the loss. Risk and growth do not change. What is the indicated loss to the whole property, before allocation between site and improvements?
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