Improvements totaling 2,450 square feet have a current cost new of $210 per square foot, an effective age of 14 years and a total economic life of 70 years. There is no salvage value and no other depreciation. What is the depreciated cost of the improvements by the straight-line age-life method, excluding the site?
Correct Answer
C) $411,600
2450×210×(1−14÷70)=411600. Common errors: reporting the depreciation instead of the depreciated amount gives $102,900; stopping at cost new, before depreciation gives $514,500; dividing by the 56-year remaining life instead of the 70-year total life gives $385,875.
Why This Is the Correct Answer
Option C is correct because cost new is 2,450 sf × $210 = $514,500. Depreciation is 14/70 = 20%, so 80% remains: $514,500 × 0.8 = $411,600.
Why the Other Options Are Wrong
Option A: $102,900
Option A, $102,900, is the depreciation, not the depreciated amount: $514,500 × 14 ÷ 70 = $102,900. The question asks what remains, $514,500 − $102,900 = $411,600.
Option B: $385,875
Option B, $385,875, results from using 14/56 (effective age over the 56-year remaining life) as the depreciation fraction: $514,500 × (1 − 14/56) = $385,875. The age-life fraction uses the 70-year total life, giving $411,600.
Option D: $514,500
Option D, $514,500, is cost new (2,450 × $210) before any depreciation. Applying the 14/70 depreciation gives $411,600.
Area Times Rate, Then Percent Good
First find cost new from area × unit cost, then multiply by (1 − Age ÷ Life) for the depreciated amount.
How to use: Use this two-step order for square-foot cost questions with age-life depreciation.
Exam Tip
Finish the cost new calculation first, then decide whether the question asks for depreciation or depreciated cost.
Common Mistakes to Avoid
- -Reporting depreciation instead of the depreciated amount
- -Using remaining life in the age-life denominator
- -Stopping at cost new
Concept Deep Dive
Analysis
This question combines the square foot method with straight-line age-life depreciation. Cost new is area times unit cost, and the depreciated amount is cost new times the remaining share (1 − effective age ÷ total life).
Background Knowledge
The square foot method applies one all-in price per square foot to the subject's area to estimate cost new. The age-life method then estimates depreciation as effective age divided by total economic life. The depreciated improvement is cost new times the complement of that fraction.
Real-World Application
An appraiser applies a $210/sf cost from a cost manual to a 2,450 sf home with a 14-year effective age and a 70-year life. She reports a depreciated improvement cost of $411,600.
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?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Income Approach
8.2% of exam
Previous Question
A functional defect is economically incurable under a verified cost-benefit analysis. What supports its depreciation allowance?
Next Question
A supported land indication WITH an access attribute is $1,200,000. Market evidence explicitly states this equals 115% of otherwise identical land WITHOUT that attribute. The subject lacks it. What without-attribute land indication follows, to the nearest dollar? No conclusion about improvement loss is requested.