Four construction components, with no overlap among them, cost $55,000, $142,000, $88,000 and $126,000. Soft costs of $79,000 are additional. The improvements have an effective age of 15 years and a total economic life of 75 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?
Correct Answer
C) $392,000
(55000+142000+88000+126000+79000)×(1−15÷75)=392000. Use the full cost buildup and apply the loss to that total. Common errors: leaving out the soft costs gives $328,800; reporting the depreciation instead of the depreciated amount gives $98,000; not applying the 15/75 depreciation gives $490,000.
Why This Is the Correct Answer
Option C is correct because the components total $55,000 + $142,000 + $88,000 + $126,000 = $411,000, and adding $79,000 of soft costs gives $490,000. The age-life ratio is 15 / 75 = 20%. The depreciated amount is $490,000 x 0.80 = $392,000.
Why the Other Options Are Wrong
Option A: $98,000
Option A, $98,000, is $490,000 x 15/75, which is the depreciation, not the depreciated amount. The question asks for $490,000 - $98,000 = $392,000.
Option B: $328,800
Option B, $328,800, is $411,000 x (1 - 15/75), which leaves out the $79,000 of soft costs. Using the full $490,000 cost gives $392,000.
Option D: $490,000
Option D, $490,000, is the full cost of $411,000 + $79,000 with no depreciation applied. Applying the 15/75 ratio gives $490,000 x 0.80 = $392,000.
Hard plus soft, then age
Add hard components and soft costs into one full cost, then take off effective age over life.
How to use: Use this order for any question combining component costs, soft costs and an age-life ratio.
Exam Tip
Simplify the ratio first (15/75 is 1/5) to make the arithmetic easier. Then check whether the question asks for depreciation or the remaining value.
Common Mistakes to Avoid
- -Leaving soft costs out of the depreciable base
- -Reporting the depreciation figure as the answer
- -Skipping the depreciation step
Concept Deep Dive
Analysis
This question tests a component cost buildup followed by age-life depreciation. The four components total $411,000, and the soft costs bring full cost to $490,000. The 15/75 ratio is 20%, so 80% of full cost remains.
Background Knowledge
Soft costs are indirect costs such as fees, financing and insurance that are part of full economic cost. The age-life method divides effective age by economic life to find the percentage of depreciation. That percentage is applied to the full cost new to reach the depreciated improvement cost.
Real-World Application
An appraiser estimating cost for a house prices the foundation, framing, roof and mechanical systems separately and adds plans, permits and financing costs as soft costs. With an effective age of 15 years on a 75-year life, the appraiser deducts 20% from full cost.
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Previous Question
Installed direct construction costs of the improvements total $400,000. Indirect costs of $60,000 are not included in that figure, and together the two amounts cover all required cost components. Land is excluded. What is the full cost new of the improvements?
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