A cost of $500,000 is allocated in equal annual charges over 40 years with no salvage value. What is the annual charge?
Correct Answer
C) $12,500
500000÷40 = 12500. Common errors: reporting the total cost instead of the annual charge gives $500,000; reporting a monthly charge instead of the annual charge gives $1,042; counting 41 years (both end points) instead of 40 gives $12,195.
Why This Is the Correct Answer
Option C is correct because $500,000 / 40 years = $12,500 per year. With zero salvage and equal annual charges, each year carries the same share of the total. The answer is an annual figure, as the question asks.
Why the Other Options Are Wrong
Option A: $1,042
Option A is wrong because $1,042 is the monthly charge, $500,000 / 40 / 12 = $1,042, not the annual charge. The annual charge is $500,000 / 40 = $12,500.
Option B: $12,195
Option B is wrong because $12,195 comes from counting 41 years (both end points) instead of 40: $500,000 / 41 = $12,195. The schedule covers 40 years, so $500,000 / 40 = $12,500.
Option D: $500,000
Option D is wrong because $500,000 is the total cost being allocated, not the annual charge. Spreading it over 40 years gives $500,000 / 40 = $12,500 per year.
Total over years
Straight-line with no salvage is total over years. Check the units: per year, not per month and not the total.
How to use: Use this when a question asks for an equal annual charge over a stated life.
Exam Tip
Match the units the question asks for. Monthly and total figures often appear as distractors.
Common Mistakes to Avoid
- -Reporting the monthly charge instead of the annual charge
- -Counting an extra year in the life
- -Treating accounting depreciation as market value loss
Concept Deep Dive
Analysis
This question tests a simple straight-line allocation with no salvage value: the total amount is spread evenly over the stated number of years. The annual charge is $500,000 / 40 = $12,500. This is an accounting-style allocation, not a forecast of market value loss.
Background Knowledge
In accounting depreciation, the rate is set when the asset is new, based on a preselected life that fixes the periodic charge. Appraisal depreciation instead measures the market's loss in value, so an accounting schedule is not a substitute for supported appraisal depreciation.
Real-World Application
A client gives an appraiser a book depreciation schedule spreading a building's $500,000 cost evenly over 40 years. The appraiser notes the $12,500 annual charge is an accounting figure and develops market-based depreciation separately.
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