A property’s stabilized NOI is $90,000. The building is worth $600,000 and the building capitalization rate is 10%. The land capitalization rate is 7.5%. What land value does the land residual technique indicate?
Correct Answer
D) $400,000
Income to the building is $600,000 × 10% = $60,000. Residual income to land is $90,000 − $60,000 = $30,000, capitalized at 7.5%: $30,000 ÷ 0.075 = $400,000.
Why This Is the Correct Answer
Option D is correct because the residual land income is $90,000 − ($600,000 × 0.10) = $30,000, and capitalizing it at the land rate gives $30,000 ÷ 0.075 = $400,000. Each income stream is capitalized at its own rate.
Why the Other Options Are Wrong
Option A: $300,000
Option A, $300,000, capitalizes the land's residual income at the building rate: $30,000 ÷ 0.10 = $300,000. Land income should use the 7.5% land rate: $30,000 ÷ 0.075 = $400,000.
Option B: $1,200,000
Option B, $1,200,000, capitalizes all NOI at the land rate with no building deduction: $90,000 ÷ 0.075 = $1,200,000. The building's $60,000 must be removed first, leaving $30,000 ÷ 0.075 = $400,000.
Option C: $800,000
Option C, $800,000, capitalizes the building income at the land rate: $60,000 ÷ 0.075 = $800,000. The land residual is $30,000, so land is $30,000 ÷ 0.075 = $400,000.
Building first, land gets leftovers
Pay the building its share of income first; whatever is left belongs to the land and is capitalized at the land rate.
How to use: Use this order of steps in any land residual problem.
Exam Tip
Match each income stream to its own rate: building income with the building rate, residual land income with the land rate.
Common Mistakes to Avoid
- -Capitalizing the land residual at the building rate
- -Capitalizing total NOI without deducting building income
- -Capitalizing the building's income share instead of the residual
Concept Deep Dive
Analysis
This question tests the land residual technique. The building's income requirement is deducted from total NOI, and the residual income is capitalized at the land rate. Building income is $600,000 × 10% = $60,000, residual is $30,000, and $30,000 ÷ 0.075 gives land value.
Background Knowledge
The land residual technique is used when building value is known or can be estimated and land value is sought. Income attributable to the building is deducted from total NOI, and the remaining income is capitalized using the land capitalization rate. It is often applied in highest and best use studies of proposed improvements.
Real-World Application
A developer proposes a new office building with a known cost. The appraiser estimates its stabilized NOI, deducts the return needed on and of the building, and capitalizes the leftover income at a land rate to test what the site can support under that use.
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