Improvement cost new is $360,000 and its supported as-is contribution is $270,000. What percentage loss relative to cost new results?
Correct Answer
B) 25%
(360000−270000)÷360000×100 = 25. Common errors: dividing by the as-is contribution instead of cost new gives 33%; reporting percent good instead of the loss gives 75%; reporting the unscaled decimal ratio 0.25 as a percent (omitting the ×100) gives 0.25%.
Why This Is the Correct Answer
Option B is correct because the loss is $360,000 - $270,000 = $90,000, and $90,000 / $360,000 x 100 = 25%. The building's contribution compared with current cost new gives the total depreciation, and expressing it relative to cost new gives the percentage loss.
Why the Other Options Are Wrong
Option A: 0.25%
Option A, 0.25%, comes from stopping at the decimal ratio $90,000 / $360,000 = 0.25 and attaching a percent sign without multiplying by 100. The ratio 0.25 equals 25%, which is the correct loss.
Option C: 33%
Option C is wrong because 33% comes from $90,000 / $270,000 x 100, dividing by the as-is contribution instead of cost new. The question asks for loss relative to cost new: $90,000 / $360,000 = 25%.
Option D: 75%
Option D is wrong because 75% is $270,000 / $360,000 x 100, which is percent good, not the loss. The loss is 100% - 75% = 25%.
Loss over new
Depreciation percent equals the dollar loss divided by cost new, times 100. What remains is percent good, the complement.
How to use: Use this to pick the correct denominator when converting a dollar loss into a depreciation percentage.
Exam Tip
Confirm which base the question names for the percentage; here it is cost new, not the as-is contribution. Then convert the decimal to a percent by multiplying by 100.
Common Mistakes to Avoid
- -Dividing the loss by the as-is contribution instead of cost new
- -Reporting percent good as the depreciation percentage
- -Writing the decimal ratio as a percent without multiplying by 100
Concept Deep Dive
Analysis
This question tests extracting total depreciation as a percentage of cost new. The loss is the difference between cost new and the improvement's as-is contribution, and the percentage is that loss divided by cost new, multiplied by 100. Dividing by the wrong base, reporting the remaining percentage, or skipping the conversion to a percent are the typical traps.
Background Knowledge
In the sales comparison or market extraction method, the building's contribution is compared with its current cost new, and the difference is total depreciation. Dividing that depreciation by cost new gives a depreciation percentage. The complement of the depreciation percentage is called percent good.
Real-World Application
An appraiser extracts depreciation from a comparable sale by subtracting land value from its price, leaving a $270,000 building contribution. With a current cost new of $360,000, the appraiser reports 25% total depreciation for use in analyzing the subject.
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Previous Question
Direct improvement costs are $430,000. Additional soft costs are 12% of direct, and separate entrepreneurial incentive is $38,400. None overlap. Supported total improvement depreciation $110,000 applies to the complete cost. Add site $200,000. What total indication results?
Next Question
A 2,200-sf dwelling has a cost of $195 per square foot, and a separate 400-sf garage costs $65 per square foot. These figures include all relevant cost components with no overlap. Excluding land, what is the total cost new of the improvements?