Annual NOI for the subject property is $180,000, and the building is known to be worth $1,500,000. The land capitalization rate is 6% and the building capitalization rate is 9%. What total property value does the land residual technique indicate?
Correct Answer
C) $2,250,000
Known income=1500000×0.09=135000; residual value=(180000−135000)÷0.06=750000; total=1500000+750000=2250000. Common errors: capitalizing the residual income at the known component rate gives $2,000,000; reporting only the residual component instead of the total value gives $750,000; allocating income to the known component at the other component rate gives $3,000,000.
Why This Is the Correct Answer
Option C is correct because building income = $1,500,000 × 0.09 = $135,000, residual land income = $180,000 − $135,000 = $45,000, land value = $45,000 ÷ 0.06 = $750,000, and total value = $1,500,000 + $750,000 = $2,250,000.
Why the Other Options Are Wrong
Option A: $750,000
Option A, $750,000, is wrong because it reports only the residual land value (($180,000 − $135,000) ÷ 0.06 = $750,000). The question asks for total property value, which adds the $1,500,000 building for $2,250,000.
Option B: $2,000,000
Option B, $2,000,000, is wrong because it capitalizes the residual income at the building rate instead of the land rate ($45,000 ÷ 0.09 = $500,000; $500,000 + $1,500,000 = $2,000,000). The residual is land income, so use 6%: $750,000 + $1,500,000 = $2,250,000.
Option D: $3,000,000
Option D, $3,000,000, is wrong because it allocates income to the building using the land rate ($1,500,000 × 0.06 = $90,000; ($180,000 − $90,000) ÷ 0.06 = $1,500,000; plus $1,500,000 = $3,000,000). Building income must use the 9% building rate, giving $2,250,000.
Known value, own rate
Charge the known component income at its own rate; capitalize the leftover at the other component's rate.
How to use: Use this when setting up any land or building residual problem.
Exam Tip
Check whether the question asks for the residual component or the total property value before choosing.
Common Mistakes to Avoid
- -Reporting only the residual component instead of the total
- -Capitalizing the residual income at the known component's rate
- -Using the land rate to compute building income
Concept Deep Dive
Analysis
This question tests the building-known residual technique (a land residual). Income needed to support the known building is its value times the building rate; the remaining income is attributed to the land and capitalized at the land rate. The two component values are then added.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). The known component's income is its value times its own rate, and the leftover income is capitalized at the unknown component's rate. The building rate typically exceeds the land rate because it includes recapture for a wasting asset.
Real-World Application
An appraiser values a parcel improved with a new building whose cost is well supported, but land sales are scarce. Using the land residual technique, the appraiser deducts the building's required return from NOI and capitalizes the remainder to estimate land value.
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An appraiser is verifying the sale of a 12-unit apartment building that sold for $1,150,000 cash at an 8% overall rate, based on NOI after replacement reserves. Potential gross income is $170,000, vacancy and collection loss is 5% of PGI, the replacement reserve is $4,000, and the buyer's annual debt service is $66,000. What are the implied annual operating expenses before reserves?
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A client planning a 24-unit apartment building asks what income the completed property must produce to be worth its $3,325,000 project cost. Overall capitalization rates for similar properties are 8%, operating expense ratios are 30% of EGI, and the vacancy/credit loss allowance is 5% of PGI. What PGI is required?