A driveway and walk have a separate cost new of $18,000, an effective age of 8 years and their own total economic life of 20 years. Using straight-line age-life depreciation, with no salvage value and no other loss, what is the depreciated contribution of this site improvement?
Correct Answer
C) $10,800
18000×(1−8÷20)=10800. Use the component's own cost and life. Common errors: reporting the depreciation instead of the depreciated contribution gives $7,200; not depreciating the site improvement gives $18,000; dividing by the 12-year remaining life instead of the 20-year total life gives $6,000.
Why This Is the Correct Answer
Option C is correct because the depreciated contribution equals cost new times the remaining share of life. Depreciation is 8/20 = 40%, so 60% remains: $18,000 × (1 − 8 ÷ 20) = $10,800. This uses the driveway/walk's own 20-year life.
Why the Other Options Are Wrong
Option A: $6,000
Option A, $6,000, results from using 8/12 (effective age over the 12-year remaining life) as the depreciation fraction: $18,000 × (1 − 8/12) = $6,000. The age-life fraction uses the 20-year total life, giving $18,000 × (1 − 8/20) = $10,800.
Option B: $7,200
Option B, $7,200, is the depreciation, not the depreciated contribution: $18,000 × 8 ÷ 20 = $7,200. The question asks what contribution remains, which is $18,000 − $7,200 = $10,800.
Option D: $18,000
Option D, $18,000, is the cost new with no depreciation taken. With the 8/20 age-life ratio, the contribution is $18,000 × (1 − 8/20) = $10,800.
Own Life for Each Part
Each separately depreciated component uses its own effective age and its own life. Remaining value = Cost × (1 − Age ÷ Life).
How to use: Use this when a question separates site improvements from the dwelling.
Exam Tip
When a question says to depreciate a component separately, use only that component's age and life figures and check whether it asks for depreciation or remaining contribution.
Common Mistakes to Avoid
- -Applying the dwelling's economic life to a site improvement
- -Reporting the depreciation instead of the depreciated contribution
- -Using remaining life in the denominator of the age-life fraction
Concept Deep Dive
Analysis
This question applies the age-life method to a separate site improvement using its own effective age and life, not the dwelling's. The question asks for the depreciated contribution, so the remaining-value fraction (1 − effective age ÷ life) is applied to cost new.
Background Knowledge
Site improvements such as driveways, walks and fences often have shorter lives than the dwelling and may be depreciated separately. Each component's own effective age and economic life determine its age-life fraction. The depreciated contribution is cost new minus that component's accrued depreciation.
Real-World Application
An appraiser values a home whose concrete driveway and walks would cost $18,000 new. Because these items wear out faster than the house, she depreciates them on their own 20-year life and reports a $10,800 as-is contribution.
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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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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Previous Question
An appraiser is applying the straight-line age-life method to improvements with a current cost new of $360,000, an effective age of 15 years and a total economic life of 50 years. There are no other deductions and no salvage value. What is the age-life depreciation?
Next Question
The subject improvements contain 2,150 sf, and current cost new is $240 per square foot. Total depreciation of the improvements is $66,000, and site value is $100,000. No other costs or losses apply. What value does the cost approach indicate?