An appraiser reviewing a trainee's cost approach for a dwelling finds that an 18% depreciation rate, developed for the improvements, was applied to the combined total of $1,170,000 improvement cost new and $365,000 land. By how much does this mistake understate the indicated value?
Correct Answer
A) $65,700
Land is not generally subject to depreciation, so the correct indication is $1,170,000 × 0.82 + $365,000 = $1,324,400. The trainee's figure is $1,535,000 × 0.82 = $1,258,700, which is $65,700 too low, the same as 18% of the land. The improvement depreciation of $210,600, the trainee's whole deduction of $276,300, and 82% of the land at $299,300 are not the size of the error.
Why This Is the Correct Answer
Option A is correct because the correct indication is $959,400 + $365,000 = $1,324,400, while the trainee's is $1,535,000 × 0.82 = $1,258,700. The gap is $65,700. It equals 18% of the $365,000 land, the depreciation that was wrongly taken on land.
Why the Other Options Are Wrong
Option B: $210,600
Option B shows $210,600, from 0.18 × 1,170,000. That is the proper depreciation on the improvements, not the error; the error is 0.18 × 365,000 = $65,700.
Option C: $276,300
Option C shows $276,300, from 0.18 × 1,535,000, which is everything the trainee deducted. Part of that was properly taken on the improvements, so the error is 276,300 − 210,600 = $65,700.
Option D: $299,300
Option D shows $299,300, from 0.82 × 365,000, which is the land value left after the rate. The amount wrongly removed from the land is 0.18 × 365,000 = $65,700.
Buildings wear, land does not
Depreciate the improvements first, then add the land at full value. If land is included in the rate's base, the error equals the rate times the land.
How to use: Use this when checking a cost-approach calculation to see whether land was included in the depreciation base.
Exam Tip
Separate the correct calculation from the mistaken one before you compare. The question asks for the size of the error, not the amount of depreciation.
Common Mistakes to Avoid
- -Applying a depreciation rate to land and improvements together
- -Reporting total depreciation as the size of the error
- -Confusing the rate applied to the land with the percent-good share of the land
Concept Deep Dive
Analysis
This tests the structure of the cost approach by measuring a common error. Depreciation belongs to the improvements, and land value is added afterward. Compare the correct and mistaken results, or see directly that the error is the rate applied to the land.
Background Knowledge
The cost approach estimates the cost of the land, plus construction costs, less depreciation, with the depreciation attached to the improvements. Land is valued separately, commonly by direct comparison with sold properties, and is not generally subject to depreciation.
Real-World Application
A supervising appraiser reviewing a trainee's cost approach sees a single percentage applied to the combined cost and land total. Recalculating shows the indication is too low by the rate times the land value. The trainee revises the worksheet so that land is added after depreciation.
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?
A new feature in the improvements has a current cost of $45,000 and a market contribution of $18,000. The entire difference is due to superadequacy, with no physical or external loss and no overlap. What is the loss from the superadequacy?
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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Previous Question
The subject improvements have a cost new of $490,000, a remaining economic life of 33 years and a total economic life of 55 years. The site is valued at $171,000. Using straight-line age-life depreciation with no salvage value and no additional loss, what value does the cost approach indicate?
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