The improvements consist of two component groups that do not overlap, with costs new of $40,000 and $610,000. The first group is fully depreciated; the second has total depreciation of 20%. No other loss applies, and the site is valued at $170,000. What value does the cost approach indicate?
Correct Answer
B) $658,000
40000−40000+610000×0.80+170000 = 658000. Common errors: not removing the fully depreciated first group gives $698,000; leaving out the site value gives $488,000; not applying any loss gives $820,000.
Why This Is the Correct Answer
Option B is correct because the fully depreciated $40,000 group contributes $40,000 - $40,000 = $0, and the $610,000 group contributes $610,000 x 0.80 = $488,000. Adding the $170,000 site gives $0 + $488,000 + $170,000 = $658,000.
Why the Other Options Are Wrong
Option A: $488,000
Option A, $488,000, is wrong because it is only the depreciated value of the second group ($610,000 x 0.80) and leaves out the $170,000 site value. The correct total is $488,000 + $170,000 = $658,000.
Option C: $698,000
Option C, $698,000, is wrong because it keeps the fully depreciated $40,000 group at full cost ($40,000 + $488,000 + $170,000). A fully depreciated group contributes nothing, so the total is $658,000.
Option D: $820,000
Option D, $820,000, is wrong because it applies no depreciation at all ($40,000 + $610,000 + $170,000). Removing the first group's full loss and the second group's 20% loss gives $658,000.
Depreciate each, then add dirt
Work out what each component has left (cost x percent good), add the pieces together, then add the land last.
How to use: Use this sequence whenever a cost problem gives several components with different losses plus a site value.
Exam Tip
A fully depreciated component contributes zero, so do not carry its cost into the total. Check that the site value is added at the end.
Common Mistakes to Avoid
- -Leaving a fully depreciated component in the total at its full cost
- -Forgetting to add site value after depreciating the improvements
- -Applying the 20% loss rate to all components instead of the one it was stated for
Concept Deep Dive
Analysis
This question tests depreciating component groups separately and then adding site value. The first group ($40,000) is fully depreciated, so it contributes nothing; the second ($610,000) keeps 80% after a 20% loss, or $488,000. Adding the $170,000 site gives $658,000.
Background Knowledge
In the cost approach, depreciation may be estimated separately for different components and then summed. Percent good is the complement of the depreciation percentage, so a 20% loss leaves 80% of cost new. Site value is added after the improvements are depreciated.
Real-World Application
An appraiser values an older property with a worn-out detached shed and a main building with moderate wear. The shed's remaining contribution is nil, the building is depreciated by its supported percentage, and the supported land value is added to reach the cost indication.
More Cost Approach Questions
Why can equivalent-utility replacement cost be useful for an obsolete improvement?
An appraiser estimates the current replacement cost new of the improvements at $890,000, accrued depreciation from all causes at $170,000, and land value at $325,000. All necessary cost components and depreciation are included in those amounts. What is the indicated property value?
Improvement cost new is $595,000. Separately supported improvement depreciation deductions of $48,000, $27,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $155,000, already reflecting any site losses. What total indicated value results?
What best supports a claimed loss from a bathroom-layout deficiency?
Improvement cost new is $1,850,000. Separately supported improvement depreciation deductions of $310,000, $620,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
Which scenario most strongly supports giving the cost approach substantial weight?
A cost total $650,000 explicitly includes $40,000 of non-realty FF&E outside the appraised real-property interest. Exclude it. Supported realty-only total depreciation is $55,000. Add site $200,000, with no overlap. What real-property cost indication results?
A 2,200-sf dwelling costs $200 per square foot, and a separate 400-sf garage costs $75 per square foot. These costs are complete and do not overlap. Both have an effective age of 15 years and a total life of 50 years, with straight-line depreciation and no salvage value. No site value or other loss is involved. What is the combined depreciated cost of the dwelling and garage?
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An external influence causes an annual net income loss of $9,600. The capitalization rate for the loss is 8%, and no other economic factors change. What is the indicated loss in value of the whole property, before allocation between site and improvements?
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