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?
Correct Answer
A) 30.0%
21÷70×100 = 30. Common errors: reporting the remaining share (1 − 21/70) instead of depreciation gives 70.0%; dividing by the 49-year remaining life instead of the 70-year total life gives 42.9%; inverting the ratio (70 ÷ 21) gives 333.3%.
Why This Is the Correct Answer
Option A is correct because the age-life depreciation percentage is effective age divided by total life: 21 ÷ 70 = 0.30, or 30.0%. That share of cost new is the physical depreciation.
Why the Other Options Are Wrong
Option B: 42.9%
Option B, 42.9%, divides by the 49-year remaining life instead of the 70-year total life: 21 ÷ 49 = 42.9%. The age-life fraction uses total life, giving 21 ÷ 70 = 30.0%.
Option C: 70.0%
Option C, 70.0%, is the remaining share rather than the depreciation: (1 − 21/70) = 70.0%. Depreciation is 21 ÷ 70 = 30.0%.
Option D: 333.3%
Option D, 333.3%, inverts the ratio: 70 ÷ 21 = 333.3%. The depreciation percentage is 21 ÷ 70 = 30.0%.
Small Over Big
Effective age is smaller than total life, so the age-life fraction is less than 100%. Age on top, total life on the bottom.
How to use: Use this as a quick sanity check on any age-life percentage.
Exam Tip
An age-life depreciation percentage above 100% signals that the ratio was inverted.
Common Mistakes to Avoid
- -Reporting percent good instead of depreciation
- -Using remaining life as the denominator
- -Inverting the ratio
Concept Deep Dive
Analysis
This question tests the basic age-life depreciation percentage. Effective age goes in the numerator and total life in the denominator, and the result is expressed as a percentage.
Background Knowledge
In the age-life method, depreciation is estimated by dividing an improvement's effective age by its total economic life. The complement of that percentage is percent good, the share of cost new that remains. Depreciation over 100% is not meaningful under this model.
Real-World Application
An appraiser judges a house's effective age at 21 years within a 70-year economic life. She applies 30% physical depreciation to the cost new in her cost approach.
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Previous Question
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?
Next Question
The cost new of the subject dwelling is $480,000, and total depreciation of the building is estimated at 25%. Site improvements, valued separately on an as-is basis, contribute $35,000, and the land, excluding those improvements, is valued at $150,000. None of these amounts overlap. What is the indicated value by the cost approach?