The current cost new of a 2,200-sf dwelling is $195 per square foot. Its effective age is 12 years and its total economic life is 60 years. Using the straight-line age-life method with no salvage value, and with no other depreciation, what is the depreciated cost of the improvements, excluding the site?
Correct Answer
C) $343,200
2200×195×(1−12÷60)=343200. Common errors: reporting the depreciation instead of the depreciated amount gives $85,800; stopping at cost new, before depreciation gives $429,000; dividing by the 48-year remaining life instead of the 60-year total life gives $321,750.
Why This Is the Correct Answer
Option C is correct because 2,200 x $195 = $429,000 cost new, and 12/60 = 20% depreciation leaves 80% good. $429,000 x 0.80 = $343,200. The question asks for the depreciated amount, not the depreciation itself.
Why the Other Options Are Wrong
Option A: $85,800
Option A is wrong because $85,800 is the depreciation, $429,000 x 12/60 = $85,800, not the depreciated amount. Subtracting it from cost new gives $429,000 - $85,800 = $343,200.
Option B: $321,750
Option B is wrong because $321,750 comes from dividing by the 48-year remaining life instead of the 60-year total life: $429,000 x (1 - 12/48) = $321,750. The correct figure is $429,000 x (1 - 12/60) = $343,200.
Option D: $429,000
Option D is wrong because $429,000 is cost new before depreciation (2,200 x $195). After 20% age-life depreciation, the amount is $343,200.
Area, rate, then percent good
Multiply area by rate for cost new, then by percent good (1 minus age over life). Two steps, in that order.
How to use: Use this for any question that pairs a cost per square foot with age-life depreciation.
Exam Tip
Decide whether the question asks for depreciation or the depreciated amount. Both figures usually appear among the choices.
Common Mistakes to Avoid
- -Reporting the depreciation instead of the depreciated value
- -Using remaining life in place of total economic life
- -Forgetting to apply depreciation to cost new
Concept Deep Dive
Analysis
This question combines a square-foot cost estimate with age-life depreciation. First compute cost new: 2,200 sf x $195 = $429,000. Then apply the percent good, 1 - 12/60 = 0.80, to get $343,200.
Background Knowledge
The square foot method combines all construction costs into one price per square foot applied to the subject's area. Age-life depreciation divides effective age by total economic life, and its complement is percent good.
Real-World Application
An appraiser estimates a 2,200-square-foot ranch home at $195 per square foot from a cost service. With an effective age of 12 years and a 60-year life, the appraiser carries $343,200 as the depreciated improvement value.
More Cost Approach Questions
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