Under the land residual technique, stabilized NOI is $210,000. The building is worth $1,800,000 and is capitalized at 8%. The land capitalization rate is 6%. What is the indicated land value?
Correct Answer
B) $1,100,000
Building income = $1,800,000 × 0.08 = $144,000; land income = $210,000 − $144,000 = $66,000; land value = $66,000/0.06 = $1,100,000. The indicated value is $1,100,000. 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 $3,500,000; allocating building income at the land rate gives $1,700,000; capitalizing land income at the building rate gives $825,000.
Why This Is the Correct Answer
Option B is correct because building income is $1,800,000 × 0.08 = $144,000, leaving land income of $210,000 − $144,000 = $66,000. Capitalizing that at the land rate gives $66,000 / 0.06 = $1,100,000. Each income stream is matched to its own capitalization rate.
Why the Other Options Are Wrong
Option A: $825,000
Option A, $825,000, capitalizes the land income at the building rate: ($210,000 − $144,000) / 0.08 = $66,000 / 0.08. Land income must be capitalized at the 6% land rate, giving $1,100,000.
Option C: $1,700,000
Option C, $1,700,000, allocates building income at the land rate: ($210,000 − $1,800,000 × 0.06) / 0.06 = $102,000 / 0.06. Building income must use the 8% building rate ($144,000), leaving $66,000 for land and a value of $1,100,000.
Option D: $3,500,000
Option D, $3,500,000, capitalizes the entire NOI as land income: $210,000 / 0.06. Part of the NOI is required by the building ($144,000), so only $66,000 is land income, giving $1,100,000.
Known part first, residual last
Take the component whose value you know, figure its income with its own rate, and subtract. Whatever income is left belongs to the unknown component and uses that component's rate.
How to use: Use this for land residual and building residual problems alike.
Exam Tip
Write each rate next to its component before calculating so you do not swap the building and land rates.
Common Mistakes to Avoid
- -Capitalizing all NOI at the land rate
- -Using the land rate to compute building income
- -Capitalizing the residual land income at the building rate
Concept Deep Dive
Analysis
This question tests the land residual technique. The building's value is known, so its income requirement is the building value times the building rate. The remaining NOI is attributed to the land and capitalized at the land 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 income attributable to the building is deducted from total net income, and the residual is capitalized into land value. The technique works best when building value can be estimated reliably, such as for new improvements.
Real-World Application
An appraiser values the site under a newly built office building where construction cost is well documented. Deducting the income needed to support the building from the stabilized NOI leaves the income the land produces, which is capitalized at a market land rate.
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