A review appraiser is checking a depreciation extraction from a $625,000 improved sale with improvement cost new of $520,000. The appraisal used a site value of $175,000, but better land sales show that the site was worth $150,000 at the sale date. What effect did the site value error have on the extracted depreciation?
Correct Answer
A) Overstated by $25,000
As appraised, the improvement contribution is $625,000 − $175,000 = $450,000 and depreciation is $520,000 − $450,000 = $70,000. With the correct site value, the contribution is $475,000 and depreciation is $45,000, so the error overstated depreciation by $25,000. Reversing the direction gives an understatement, treating the whole $70,000 as error ignores the $45,000 that remains, and site value does affect the result because it determines the residual.
Why This Is the Correct Answer
Option A is correct because the $175,000 site value gave a $450,000 contribution and $70,000 of depreciation, while the $150,000 value gives $475,000 and $45,000. The difference is 70,000 − 45,000 = $25,000. An overstated site value understates the residual contribution and overstates depreciation by the same amount.
Why the Other Options Are Wrong
Option B: Understated by $25,000
Option B says depreciation was understated by $25,000. The size is right but the direction is reversed: correcting the site value lowers depreciation from $70,000 to $45,000.
Option C: Overstated by $70,000
Option C says depreciation was overstated by $70,000, treating the whole appraised figure as error. The corrected extraction still shows 520,000 − 475,000 = $45,000 of depreciation, so the overstatement is $25,000.
Option D: Not misstated
Option D says depreciation was not misstated. Site value is not part of cost new, but it determines the residual contribution compared with cost new, so the figure moves from $70,000 to $45,000.
Site up, depreciation up
Site value and extracted depreciation move in the same direction, dollar for dollar, when sale price and cost new hold still.
How to use: Use this when a question changes one input to a market extraction and asks about the effect on depreciation.
Exam Tip
Rework the two subtractions with the new input instead of relying on intuition. Then check that the direction of the change makes sense.
Common Mistakes to Avoid
- -Assuming a lower site value increases extracted depreciation
- -Treating extracted depreciation as unaffected by site value
- -Treating the whole extracted figure as the size of the error
Concept Deep Dive
Analysis
This tests how the inputs to market extraction connect. The improvement contribution is a residual, so any dollar taken off the site value goes onto the contribution. A larger contribution closer to cost new means less depreciation.
Background Knowledge
In market extraction, depreciation is the gap between cost new and the improvement contribution, and the contribution depends on an independent site value. The method's reliability therefore depends on sound land evidence as well as on sound cost estimates.
Real-World Application
A review appraiser finds that a report's site value relied on dated land sales. Replacing it with better evidence lowers the site value and raises the residual improvement contribution. The extracted depreciation from that sale falls, and the review notes the change in the cost approach.
More Cost Approach Questions
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