An appraiser is applying the land residual technique to a property with stabilized NOI of $198,000. The building value is known to be $1,600,000, the building capitalization rate is 9%, and the land capitalization rate is 6%. What is the indicated land value?
Correct Answer
D) $900,000
Income attributable to the building is $1,600,000 × 9% = $144,000. Residual land income is $54,000. At the land capitalization rate of 6%, indicated land value is $900,000. This is an income allocation and capitalization method, not simply whole-property sale price minus depreciated cost.
Why This Is the Correct Answer
Option D is correct because building income is $1,600,000 × 9% = $144,000, leaving $198,000 − $144,000 = $54,000 of residual land income. Capitalizing that income at the 6% land rate gives $54,000 ÷ 0.06 = $900,000.
Why the Other Options Are Wrong
Option A: $3,300,000
Option A, $3,300,000, capitalizes all of the NOI at the land rate: $198,000 ÷ 0.06 = $3,300,000. The building's $144,000 share must be deducted first, leaving $54,000 ÷ 0.06 = $900,000.
Option B: $1,600,000
Option B, $1,600,000, is the known building value, not the land value. The land indication comes from the residual income: ($198,000 − $144,000) ÷ 0.06 = $900,000.
Option C: $600,000
Option C, $600,000, finds the correct $54,000 of land income but capitalizes it at the 9% building rate: $54,000 ÷ 0.09 = $600,000. Land income belongs with the land rate, so $54,000 ÷ 0.06 = $900,000.
Known out, unknown capped
Take out the income the known building needs at its own rate, then capitalize what is left at the land's rate.
How to use: Use this to set up any land or building residual problem in the right order.
Exam Tip
Match each rate to its own component: building rate times building value, then residual income divided by the land rate.
Common Mistakes to Avoid
- -Capitalizing total NOI at the land rate
- -Capitalizing land income at the building rate
- -Reporting the building value as the answer
Concept Deep Dive
Analysis
This question tests the income land residual technique. When the building value is known, you allocate income to the building using the building capitalization rate, subtract it from NOI, and capitalize the remaining land income at the land rate. Each income component must be paired with its own rate.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). In the land residual technique, the known component's income requirement is deducted from NOI and the remainder is capitalized at the rate for the unknown component.
Real-World Application
An appraiser values the land under a recently built small office building whose cost is well supported. Because few vacant land sales exist nearby, the appraiser allocates income to the new building at a market building rate and capitalizes the leftover income at a land rate to estimate land value.
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