A property sold for a cash-equivalent price of $720,000. Site value, estimated independently, is $280,000, and the current cost new of the improvements is $560,000. All of the extracted depreciation is straight-line age-life loss with no salvage value and a total life of 70 years. What effective age is indicated?
Correct Answer
B) 15 years
((560000−(720000−280000))÷560000)×70 = 15. Common errors: dividing the depreciation by the sale price instead of cost new gives 12 years; dividing the depreciation by the improvement contribution instead of cost new gives 19 years; reporting the remaining life instead of the effective age gives 55 years.
Why This Is the Correct Answer
Option B is correct because the improvement contribution is $720,000 − $280,000 = $440,000, so depreciation is $560,000 − $440,000 = $120,000. That is $120,000 ÷ $560,000 = 21.43% of cost new, and 21.43% × 70 years = 15 years of effective age.
Why the Other Options Are Wrong
Option A: 12 years
Option A, 12 years, divides the depreciation by the sale price instead of cost new: $120,000 ÷ $720,000 × 70 = about 11.7, rounded to 12 years. The age-life fraction uses cost new, giving $120,000 ÷ $560,000 × 70 = 15 years.
Option C: 19 years
Option C, 19 years, divides the depreciation by the improvement contribution instead of cost new: $120,000 ÷ $440,000 × 70 = about 19.1, rounded to 19 years. The correct base is cost new, giving 15 years.
Option D: 55 years
Option D, 55 years, is the remaining economic life rather than the effective age: 70 − 15 = 55 years. The question asks for effective age, which is 15 years.
Sale Minus Site, Cost Minus Contribution
Contribution = Sale − Site; Depreciation = Cost new − Contribution; Effective age = (Depreciation ÷ Cost new) × Total life.
How to use: Use this chain for any market extraction problem that asks for effective age.
Exam Tip
In extraction problems, the depreciation percentage is computed on cost new; check the denominator before multiplying by life.
Common Mistakes to Avoid
- -Dividing depreciation by the sale price instead of cost new
- -Reporting remaining life instead of effective age
- -Forgetting to subtract site value from the sale price
Concept Deep Dive
Analysis
This question tests market extraction of depreciation and conversion of that loss to an effective age. The improvement contribution is the sale price minus site value; depreciation is cost new minus that contribution. Dividing depreciation by cost new gives the age-life fraction, which is multiplied by total life to find effective age.
Background Knowledge
In the market extraction method, site value is subtracted from a sale price to find the building's contribution, which is compared with current cost new; the difference is total depreciation. Dividing that depreciation by cost new gives a depreciation percentage. Under a straight-line model, that percentage times total economic life gives an implied effective age.
Real-World Application
An appraiser studies a $720,000 sale of a similar home with a $280,000 site and $560,000 cost new. She extracts $120,000 of depreciation and, with a 70-year life, infers a 15-year effective age to apply to the subject.
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Direct and indirect construction costs total $580,000 and exclude incentive. A separate supported entrepreneurial incentive is 8% of that base. Land and other additions are excluded. What full improvement cost results?
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An improvement has an effective age of 21 years and a total life of 70 years. Using straight-line age-life depreciation, what is the percentage of physical depreciation?