A property has stabilized NOI of $217,000. The building value is $1,850,000 and the building capitalization rate is 8.0%. The land capitalization rate is 6.0%. Using the land residual technique, what is the indicated land value?
Correct Answer
A) $1,150,000
Income attributable to the building is $1,850,000 × 8% = $148,000. Residual land income is $69,000. At the land capitalization rate of 6%, indicated land value is $1,150,000. This is an income allocation and capitalization method, not simply whole-property sale price minus depreciated cost.
Why This Is the Correct Answer
Option A is correct because building income is $1,850,000 × 8% = $148,000, residual land income is $217,000 − $148,000 = $69,000, and $69,000 ÷ 0.06 = $1,150,000.
Why the Other Options Are Wrong
Option B: $3,616,666.67
Option B ($3,616,666.67) capitalizes all NOI at the land rate, $217,000 ÷ 0.06, with no deduction for building income. The building's $148,000 must come out first, leaving $69,000 ÷ 0.06 = $1,150,000.
Option C: $1,850,000
Option C ($1,850,000) is the building value given in the facts, not a land value. The land indication is ($217,000 − $148,000) ÷ 0.06 = $1,150,000.
Option D: $1,325,000
Option D ($1,325,000) swaps the two rates: building income at 6% is $1,850,000 × 0.06 = $111,000, and the residual $106,000 ÷ 0.08 = $1,325,000. The building rate belongs to the building and the land rate to the land: ($217,000 − $148,000) ÷ 0.06 = $1,150,000.
Building eats first, land gets rest
The building takes its income at its rate first; the land is valued from what remains at the land rate.
How to use: Use this to order the steps in any land residual calculation.
Exam Tip
Check that the building rate is applied to the building value and the land rate to the residual income, not the other way round.
Common Mistakes to Avoid
- -Capitalizing total NOI as if it were land income
- -Swapping the building and land rates
- -Confusing the land residual technique with extraction
Concept Deep Dive
Analysis
This question tests the land residual technique with a known building value. Building income equals building value times the building rate; it is deducted from NOI, and the residual land income is capitalized at the land rate. Each rate must be applied to its own component.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). The land residual technique assumes the building value is known and the land value is unknown. It is an income allocation method, distinct from extraction, which subtracts value from a sale price.
Real-World Application
An appraiser values the land under a new office building whose cost is well documented. Using market-derived building and land rates, the appraiser deducts the building's required income from stabilized NOI and capitalizes the residual.
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