An appraiser estimates the current cost new of a 2,400-sf building at $205 per square foot. The effective age is 16 years and the total economic life is 64 years. Using straight-line age-life depreciation with no salvage value, and with no other losses, what is the depreciated cost of the improvements, excluding any site value?
Correct Answer
C) $369,000
2400×205×(1−16÷64)=369000. Common errors: reporting the depreciation instead of the depreciated amount gives $123,000; stopping at cost new, before depreciation gives $492,000; dividing by the 48-year remaining life instead of the 64-year total life gives $328,000.
Why This Is the Correct Answer
Option C is correct because cost new is 2,400 x $205 = $492,000, and $492,000 x (1 - 16/64) = $492,000 x 0.75 = $369,000. The ratio uses total life of 64 years.
Why the Other Options Are Wrong
Option A: $123,000
Option A, $123,000, is $492,000 x 16/64, the depreciation rather than the depreciated amount. Subtracting it from cost new gives $492,000 - $123,000 = $369,000.
Option B: $328,000
Option B, $328,000, comes from $492,000 x (1 - 16/48), dividing by the 48-year remaining life instead of the 64-year total life. The age-life ratio uses total life, giving $369,000.
Option D: $492,000
Option D, $492,000, is the cost new before depreciation. Applying the 0.75 remaining factor gives $369,000.
Age over total life
The age-life ratio is effective age over total life; remaining life does not go in the denominator.
How to use: Use this to avoid dividing by remaining life on age-life questions.
Exam Tip
When a remaining-life figure appears in the choices, check that you divided by total life, not remaining life.
Common Mistakes to Avoid
- -Dividing effective age by remaining life
- -Reporting depreciation instead of depreciated cost
- -Stopping at cost new
Concept Deep Dive
Analysis
This question tests age-life depreciation on a single-area cost. You compute cost new from area and rate, then multiply by the remaining-value factor 1 - 16/64 = 0.75.
Background Knowledge
In the age-life method, depreciation equals effective age divided by total economic life, applied to cost new. Remaining economic life is total life minus effective age and is not the denominator of the ratio.
Real-World Application
An appraiser estimates a building's effective age at 16 years with a 64-year economic life. One quarter of cost new is deducted as depreciation, leaving three quarters as the depreciated 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?
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
The subject dwelling contains 2,400 square feet, and its current cost new is $185 per square foot. Total depreciation of the improvements is estimated at 25%, and the site value is $210,000. What is the indicated value by the cost approach?
Next Question
A sound building has supported market loss from insufficient ceiling clearance, but no cure analysis. What follows?