An appraiser estimates the physical deterioration of a building component by the age-life method, using an effective physical age of 15 years, a total physical life of 50 years and a replacement cost of $40,000. A $620,000 value indication does not yet reflect this loss. What is the indicated value after deducting it?
Correct Answer
D) $608,000
By the age-life method, physical loss = 15 ÷ 50 × $40,000 = $12,000. Deducting it once gives $620,000 − $12,000 = $608,000. This does not mean that economic life alone isolates physical loss or that an already depreciated value needs another deduction.
Why This Is the Correct Answer
Option D is correct because the physical loss by the age-life method is 15 ÷ 50 × $40,000 = $12,000. The $620,000 value indication does not yet reflect this loss, so deducting it once gives $620,000 − $12,000 = $608,000.
Why the Other Options Are Wrong
Option A: $620,000
Option A, $620,000, is the baseline before any deduction. It ignores the $12,000 physical loss (15 ÷ 50 × $40,000), which the baseline expressly excludes; the correct result is $620,000 − $12,000 = $608,000.
Option B: $592,000
Option B, $592,000, uses the 35 years of remaining life (50 − 15) in place of effective age: 35 ÷ 50 × $40,000 = $28,000, and $620,000 − $28,000 = $592,000. The model uses effective age, so the loss is 15 ÷ 50 × $40,000 = $12,000 and the result is $608,000.
Option C: $40,000
Option C, $40,000, is the component's replacement cost, an input rather than an indication of value. The correct calculation uses it to find the loss, 15 ÷ 50 × $40,000 = $12,000, then $620,000 − $12,000 = $608,000.
Ratio, cost, then subtract
First divide effective age by total life to get the share used up, then multiply by cost to get dollars of loss. Finally subtract that loss once from the baseline that excludes it.
How to use: Use this three-step order on any age-life deduction problem.
Exam Tip
Check whether the baseline already includes or excludes the loss before deducting, and put effective age, not remaining life, on top of the ratio.
Common Mistakes to Avoid
- -Using remaining life instead of effective age in the age-life ratio
- -Reporting the baseline without making the deduction
- -Reporting the component's replacement cost as the answer
Concept Deep Dive
Analysis
This question tests applying a stated age-life model for physical deterioration and deducting the result once from a baseline that excludes it. Compute the loss as effective physical age divided by total physical life times replacement cost, then subtract it from the baseline. Watch for answers that skip the deduction, use remaining life in place of effective age, or report an input as the result.
Background Knowledge
The age-life method estimates depreciation as the ratio of effective age to total life applied to cost. In this question the model is limited to physical deterioration of one component. A value that already reflects a loss should not have the same loss deducted again.
Real-World Application
An appraiser using the cost approach estimates that a roof system with a $40,000 replacement cost has an effective age of 15 years and a total physical life of 50 years. The appraiser calculates $12,000 of physical deterioration for that component. That amount is deducted once from an indication that did not yet account for it.
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