Using the straight-line method, what is the annual depreciation for a building with a cost new of $500,000 and an economic life of 40 years?
Correct Answer
B) $12,500
Why this is correct: Straight-line depreciation allocates the total cost evenly over the economic life. The governing formula is Annual Depreciation = Cost New / Economic Life. Applying the facts: $500,000 / 40 years = $12,500 per year. Why the other choices are wrong: "$25,000" incorrectly divides $500,000 by 20 years. "$10,000" incorrectly divides $500,000 by 50 years. "$20,000" incorrectly divides $500,000 by 25 years. Exam tip: For straight-line, remember the simple division: Cost / Life.
Why This Is the Correct Answer
Option A ($12,500) is correct because straight-line depreciation uses the simple formula: Annual Depreciation = Cost New ÷ Economic Life. Applying this formula: $500,000 ÷ 40 years = $12,500 per year. This represents the amount of value the building loses each year due to aging, assuming a constant rate of depreciation. The calculation is straightforward division with no additional factors or adjustments needed for the basic straight-line method.
Why the Other Options Are Wrong
Option A: $25,000
Option A ($25,000) is incorrect because it represents what the annual depreciation would be if the economic life were only 20 years ($500,000 ÷ 20 = $25,000). This error typically occurs when students misread the economic life or confuse it with a different time period from the problem.
Option C: $10,000
Option C ($10,000) is incorrect because it represents what the annual depreciation would be if the economic life were 50 years ($500,000 ÷ 50 = $10,000). This error suggests using too long of an economic life period in the calculation.
Option D: $20,000
Option D ($20,000) is incorrect because it represents what the annual depreciation would be if the economic life were 25 years ($500,000 ÷ 25 = $20,000). This is a common calculation error that occurs when students use an incorrect denominator in their division.
The Straight Division Rule
Remember 'STRAIGHT = SIMPLE DIVISION': Cost ÷ Years = Annual Loss. Think of a straight line going down - it drops the same amount each step.
How to use: When you see 'straight-line depreciation,' immediately think 'simple division' and look for Cost New and Economic Life. Divide the first by the second - no other calculations needed.
Exam Tip
Always double-check that you're using the economic life (not physical life or other time periods) as your denominator, and ensure your calculator work is accurate since these are straightforward division problems.
Common Mistakes to Avoid
- -Using the wrong time period (physical life instead of economic life)
- -Making basic division calculation errors
- -Overthinking the problem and trying to apply additional factors when only straight-line depreciation is requested
Concept Deep Dive
Analysis
This question tests understanding of straight-line depreciation, one of the fundamental methods used in the cost approach to real estate valuation. Straight-line depreciation assumes that a building loses value at a constant rate over its economic life, making it the simplest and most commonly used depreciation method in appraisal. The concept is essential for calculating accrued depreciation when estimating the current value of improvements using the cost approach. Understanding this method is crucial because it forms the foundation for more complex depreciation calculations and is frequently used in both residential and commercial property appraisals.
Background Knowledge
Straight-line depreciation is based on the assumption that a building depreciates at a uniform rate throughout its economic life, losing equal dollar amounts each year. Economic life refers to the period over which improvements contribute to property value, which may differ from physical life or accounting life.
Real-World Application
Appraisers use straight-line depreciation when applying the cost approach to value older buildings, helping determine how much value has been lost due to age and allowing calculation of the depreciated value of improvements for the final property valuation.
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