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?
Correct Answer
C) $375,000
(48000+125000+58000+92000+105000+72000)×(1−16÷64)=375000. Use the full cost buildup and apply the loss to that total. Common errors: leaving out the indirect costs gives $321,000; reporting the depreciation instead of the depreciated amount gives $125,000; not applying the 16/64 depreciation gives $500,000.
Why This Is the Correct Answer
Option C is correct because the components total $48,000 + $125,000 + $58,000 + $92,000 + $105,000 = $428,000, and adding $72,000 of indirect costs gives $500,000. The age-life ratio is 16 / 64 = 25%. The depreciated amount is $500,000 x 0.75 = $375,000.
Why the Other Options Are Wrong
Option A: $125,000
Option A, $125,000, is $500,000 x 16/64, which is the depreciation, not the depreciated improvement amount. The question asks for $500,000 - $125,000 = $375,000.
Option B: $321,000
Option B, $321,000, is $428,000 x (1 - 16/64), which leaves out the $72,000 of indirect costs. Using the full $500,000 cost gives $375,000.
Option D: $500,000
Option D, $500,000, is the full cost of $428,000 + $72,000 with no depreciation applied. Applying the 16/64 ratio gives $500,000 x 0.75 = $375,000.
Add it all, then age
Total all components and the indirect costs first, then apply the age-life ratio once to that full sum. Depreciating before adding everything leaves a piece out.
How to use: Use this when a question lists several component costs plus separate indirect costs and an age-life ratio.
Exam Tip
Add the list carefully and check your sum before applying the ratio, since arithmetic slips are common with five or more figures. Then confirm whether the question wants the depreciation or the remaining value.
Common Mistakes to Avoid
- -Leaving the indirect costs out of the depreciable base
- -Reporting the depreciation instead of the depreciated amount
- -Making an addition error when summing many components
Concept Deep Dive
Analysis
This question tests summing component costs, adding separate indirect costs, and applying an age-life ratio. The five components total $428,000, and the indirect costs bring full cost to $500,000. The 16/64 ratio is 25%, so 75% of full cost remains.
Background Knowledge
In a segregated or component cost buildup, the installed costs of individual building components are added together, and indirect costs not already embedded are added on top. Full economic cost includes all direct and indirect costs, plus a supported entrepreneurial profit where applicable. The age-life method then deducts depreciation equal to effective age divided by economic life.
Real-World Application
An appraiser uses a segregated cost method for a house, pricing foundation, framing, roofing, mechanical and finish components separately. After adding architect fees and other indirect costs, the appraiser applies an effective age to economic life ratio to estimate depreciated cost.
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Previous Question
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?
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