Current improvement cost new is $800,000. Separately supported, nonoverlapping physical 15% and functional 5% losses are each explicitly measured on that SAME original improvement base. Add site $200,000. What total results?
Correct Answer
B) $840,000
800000×(1−0.15−0.05)+200000=840000. Use the full stated cost buildup and the specified compatible loss base. Common errors: leaving out the site value gives $640,000; leaving out the 5% functional loss gives $880,000; applying the functional loss to the already-reduced base instead of the original base gives $846,000.
Why This Is the Correct Answer
Option B is correct because both losses are measured on the same $800,000 base, so total depreciation is 15% + 5% = 20%. The depreciated improvement is $800,000 x 0.80 = $640,000. Adding the $200,000 site gives $840,000.
Why the Other Options Are Wrong
Option A: $640,000
Option A, $640,000, is $800,000 x (1 - 0.15 - 0.05), which leaves out the $200,000 site value. The total indication is $640,000 + $200,000 = $840,000.
Option C: $846,000
Option C, $846,000, is $800,000 x 0.85 x 0.95 + $200,000, which applies the functional loss to the already-reduced base instead of the original base. The stem says both losses are measured on the same original base, giving $840,000.
Option D: $880,000
Option D, $880,000, is $800,000 x 0.85 + $200,000, which leaves out the 5% functional loss. Including both losses gives $840,000.
Same base, add percentages
When losses are measured on the same base, add the percentages first and apply them once. Only multiply them in sequence if each is measured on the reduced base.
How to use: Use this rule when a question gives more than one depreciation percentage.
Exam Tip
Read which base each percentage is measured on. Then check whether the question wants a total that includes site value.
Common Mistakes to Avoid
- -Applying the percentages in sequence when both use the original base
- -Leaving out site value from a total indication
- -Dropping one of the loss percentages
Concept Deep Dive
Analysis
This question tests applying two depreciation percentages that are both measured on the same original cost base. Because both are expressed against the same base and do not overlap, they are added (20%) and applied once. Then the site value is added for the total indication.
Background Knowledge
In the breakdown method, total depreciation is the sum of the individual estimates of physical, functional and external depreciation. When each is measured on the same cost base, the percentages can be added directly. If a later loss is measured on a base already reduced by an earlier one, the calculation is sequential instead, so the stated base matters.
Real-World Application
An appraiser estimates that a dated house has physical deterioration and a functional layout loss, each measured as a percentage of current cost new. The appraiser adds the two percentages, deducts the total from cost new, and adds site value for the cost approach indication.
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