Cost ApproachMEDIUM13.6% of exam

A building cost $2,500,000 to construct 8 years ago. Using straight-line depreciation over a 40-year life, what is the current depreciated value?

Correct Answer

A) $2,000,000

Why this is correct: Straight-line depreciation spreads the cost evenly over the economic life. Annual depreciation is $2,500,000 ÷ 40 = $62,500. After 8 years, accumulated depreciation is $62,500 × 8 = $500,000. The current depreciated value is original cost minus accumulated depreciation: $2,500,000 - $500,000 = $2,000,000. Therefore A is correct. Why the other choices are wrong: B, $500,000, is the accumulated depreciation, not the remaining value. C, $312,500, is the result of dividing the original cost by 8 years, which confuses elapsed time with the total life. D, $2,300,000, would require subtracting only $200,000, which is not supported by the straight-line calculation. The correct method is to subtract total accumulated depreciation from the original cost. Exam tip: Remember that 'depreciated value' means cost minus accumulated depreciation. Compute the annual depreciation first, then multiply by the number of years.

Answer Options

$2,000,000

$500,000

$312,500

$2,300,000

Why This Is the Correct Answer

Option A is correct because it follows the proper straight-line depreciation formula. First, calculate annual depreciation: $2,500,000 ÷ 40 years = $62,500 per year. Then multiply by the elapsed time: $62,500 × 8 years = $500,000 total depreciation. Finally, subtract total depreciation from original cost: $2,500,000 - $500,000 = $2,000,000. This represents the current depreciated value of the building after 8 years of use.

Why the Other Options Are Wrong

Option B: $500,000

Option B ($500,000) represents only the total accumulated depreciation over 8 years, not the current depreciated value of the building. This is a common error where test-takers stop at calculating the depreciation amount rather than subtracting it from the original cost to find the remaining value.

Option C: $312,500

Option C ($312,500) represents 2.5 years of depreciation ($62,500 × 5 = $312,500), suggesting a calculation error in the time period or a misunderstanding of what value is being requested. This amount is neither the correct depreciated value nor the proper accumulated depreciation for 8 years.

Option D: $2,300,000

Option D ($2,300,000) appears to use an incorrect depreciation calculation, possibly assuming a shorter useful life or different depreciation rate. This value would result from subtracting only $200,000 in depreciation, which doesn't align with the straight-line method over 40 years.

The COST-D Formula

COST-D: Cost ÷ Useful life = Annual depreciation; Annual × Time = Total depreciation; Cost - Total depreciation = Depreciated value. Remember 'Cost Divided, Annual Times, Cost Take-away' to get your final answer.

How to use: When you see a straight-line depreciation problem, immediately write 'COST-D' and follow the three steps: divide original cost by useful life, multiply annual depreciation by elapsed years, then subtract total depreciation from original cost.

Exam Tip

Always double-check that you're providing the depreciated VALUE (original cost minus depreciation), not just the depreciation amount itself, as this is a frequent source of incorrect answers on the exam.

Common Mistakes to Avoid

-Providing the depreciation amount instead of the depreciated value
-Using the wrong time period in calculations
-Forgetting to subtract total depreciation from the original cost

Concept Deep Dive

Analysis

This question tests the fundamental concept of straight-line depreciation in real estate appraisal, specifically within the cost approach to valuation. Straight-line depreciation assumes that a building loses value at a constant rate over its useful life, making it the simplest and most commonly used depreciation method in appraisal practice. The calculation requires determining the annual depreciation amount by dividing the original cost by the useful life, then multiplying by the number of years that have passed. The depreciated value represents the current worth of the improvement after accounting for physical deterioration, functional obsolescence, and external obsolescence over time.

Background Knowledge

Straight-line depreciation is a key component of the cost approach to value, where appraisers estimate property value by calculating replacement cost new less depreciation plus land value. Understanding depreciation calculations is essential because most buildings lose value over time due to physical wear, functional obsolescence, and external factors affecting desirability.

Real-World Application

Appraisers use straight-line depreciation when applying the cost approach for insurance appraisals, tax assessments, and litigation support, particularly for newer commercial and industrial properties where comparable sales are limited and the cost approach provides the most reliable value indication.

straight-line depreciationcost approachuseful lifedepreciated valueannual depreciation

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