Installed direct costs of $385,000 and separate indirect costs of $65,000 make up the full cost of the improvements, which have an effective age of 12 years and a total economic life of 60 years. Using straight-line age-life depreciation on the full cost, with no salvage value, no site value and no other losses, what is the depreciated cost of the improvements?
Correct Answer
C) $360,000
(385000+65000)×(1−12÷60)=360000. Use the full cost buildup and apply the loss to that total. Common errors: leaving out the indirect costs gives $308,000; reporting the depreciation instead of the depreciated amount gives $90,000; not applying the 12/60 depreciation gives $450,000.
Why This Is the Correct Answer
Option C is correct because full cost is $385,000 + $65,000 = $450,000. The age-life ratio is 12 / 60 = 20%, so the remaining share is 80%. The depreciated amount is $450,000 x 0.80 = $360,000.
Why the Other Options Are Wrong
Option A: $90,000
Option A, $90,000, is ($385,000 + $65,000) x 12/60, which is the depreciation, not the depreciated amount. The question asks for $450,000 - $90,000 = $360,000.
Option B: $308,000
Option B, $308,000, is $385,000 x (1 - 12/60), which leaves out the $65,000 of indirect costs. Using the full cost gives $450,000 x 0.80 = $360,000.
Option D: $450,000
Option D, $450,000, is $385,000 + $65,000 with no depreciation applied. Applying the 12/60 ratio gives $450,000 x 0.80 = $360,000.
Build, ratio, subtract
Build the full cost first, compute effective age over total life, then subtract that share. Depreciated amount equals full cost times (1 minus the ratio).
How to use: Use this whenever an age-life question gives several cost pieces and asks for the depreciated amount.
Exam Tip
Read whether the question wants the depreciation or the depreciated amount; both figures usually appear among the options. Confirm that each stated cost piece is in the base before applying the ratio.
Common Mistakes to Avoid
- -Applying the age-life ratio to direct costs only
- -Reporting the depreciation figure as the answer
- -Forgetting to apply any depreciation
Concept Deep Dive
Analysis
This question tests building a full improvement cost and then applying the age-life method. Add direct and indirect costs to get the full cost base, find the depreciation ratio of effective age divided by total life, and subtract that share. The question asks for the depreciated amount, not the depreciation itself.
Background Knowledge
The age-life (straight-line) method estimates depreciation by dividing the effective age of an improvement by its total economic life. The ratio is applied to a cost new figure that includes all direct and indirect costs. Subtracting depreciation from cost new gives the depreciated cost of the improvement.
Real-World Application
An appraiser estimates the cost new of a single-family home using direct construction costs and separately listed indirect costs such as permits and financing. Judging the house to have an effective age of 12 years out of a 60-year economic life, the appraiser deducts 20% of full cost to estimate depreciated improvement cost.
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?
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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?
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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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A positive entrepreneurial incentive is independently supported and expressly excluded from all quoted base costs. What happens if the full-cost estimate omits it?
Next Question
An appraiser prices five installed components, with no overlap among them, at $48,000, $125,000, $58,000, $92,000 and $105,000. Indirect costs of $72,000 are additional. The effective age is 16 years and the total economic life is 64 years. Using straight-line age-life depreciation on the full cost, with no salvage value, other losses or site value, what is the depreciated cost of the improvements?