A property produces net operating income of $180,000. The building is worth $1,200,000 and the building capitalization rate is 10 percent. If the land capitalization rate is 8 percent, what is the indicated land value?
Correct Answer
B) $750,000
Building income = $1,200,000 × 0.10 = $120,000; land income = $180,000 − $120,000 = $60,000; land value = $60,000/0.08 = $750,000. The indicated value is $750,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: capitalizing all of the NOI as land income gives $2,250,000; allocating building income at the land rate gives $1,050,000; capitalizing land income at the building rate gives $600,000.
Why This Is the Correct Answer
Option B is correct because building income is $1,200,000 × 0.10 = $120,000, land income is $180,000 − $120,000 = $60,000, and land value is $60,000 ÷ 0.08 = $750,000. The building's share of income is removed first, using the building rate. The residual income is then capitalized at the land rate.
Why the Other Options Are Wrong
Option A: $600,000
Option A, $600,000, capitalizes the land income at the building rate: ($180,000 − $120,000) ÷ 0.10 = $600,000. Land income should be capitalized at the 8% land rate: $60,000 ÷ 0.08 = $750,000.
Option C: $1,050,000
Option C, $1,050,000, allocates building income at the land rate: $1,200,000 × 0.08 = $96,000, then ($180,000 − $96,000) ÷ 0.08 = $1,050,000. Building income should use the 10% building rate, giving $120,000 and a land value of $750,000.
Option D: $2,250,000
Option D, $2,250,000, capitalizes all of the NOI as land income: $180,000 ÷ 0.08 = $2,250,000. The building's $120,000 share must be deducted first, leaving $60,000 ÷ 0.08 = $750,000.
Each part gets its own rate
Building value times building rate gives building income; land income divided by land rate gives land value.
How to use: Use this pairing to avoid mixing rates in residual technique problems.
Exam Tip
Write the three steps (building income, residual land income, land value) and confirm each uses the correct rate before choosing an answer.
Common Mistakes to Avoid
- -Capitalizing total NOI as if it were all land income
- -Using the land rate to compute building income
- -Capitalizing residual land income at the building rate
Concept Deep Dive
Analysis
This question tests the income land residual technique. The income needed to support the building at its capitalization rate is deducted from total net operating income, and the remaining land income is capitalized at the land rate. Using each rate with its own component is the key.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). In the land residual technique, the building value is known, its income requirement is deducted from NOI, and the remainder is capitalized as land value. The building residual technique reverses the roles.
Real-World Application
An appraiser values the land under an income-producing building whose improvements are new and reliably estimated at $1,200,000. After deducting the building's required return from the $180,000 NOI, the remaining $60,000 is capitalized at the land rate to indicate $750,000.
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