The subject property has annual NOI of $105,000, and its building value is known to be $900,000. The land capitalization rate is 6% and the building capitalization rate is 8%. Using the land residual technique, what is the total property value?
Correct Answer
C) $1,450,000
Known income=900000×0.08=72000; residual value=(105000−72000)÷0.06=550000; total=900000+550000=1450000. Common errors: capitalizing the residual income at the known component rate gives $1,312,500; reporting only the residual component instead of the total value gives $550,000; allocating income to the known component at the other component rate gives $1,750,000.
Why This Is the Correct Answer
Option C is correct because income to the building is $900,000 × 0.08 = $72,000. The residual land income is $105,000 − $72,000 = $33,000, which capitalized at 6% gives $550,000. Total property value is $900,000 + $550,000 = $1,450,000.
Why the Other Options Are Wrong
Option A: $550,000
Option A, $550,000, is only the residual land value, ($105,000 − $72,000) ÷ 0.06. The question asks for total value, so the $900,000 building is added: $1,450,000.
Option B: $1,312,500
Option B, $1,312,500, capitalizes the residual land income at the building rate: ($105,000 − $72,000) ÷ 0.08 + $900,000. The land rate of 6% applies, giving $550,000 + $900,000 = $1,450,000.
Option D: $1,750,000
Option D, $1,750,000, charges building income at the land rate: ($105,000 − $900,000 × 0.06) ÷ 0.06 + $900,000. Building income should use the 8% building rate, giving $1,450,000.
Known part first, its own rate
Charge the known component income at its own rate, capitalize the rest at the other rate, and add the known value back if total value is asked.
How to use: Use this for residual problems that ask for either a component value or total value.
Exam Tip
Read whether the question wants the residual component or total property value. Distractors often give the residual component alone.
Common Mistakes to Avoid
- -Reporting the residual land value as total value
- -Charging building income at the land rate
- -Capitalizing residual land income at the building rate
Concept Deep Dive
Analysis
This question tests the land residual technique with a known building value and a request for total property value. Building income is charged at the building rate, the residual income is capitalized at the land rate, and the known building value is added back.
Background Knowledge
In the land residual technique, the building value is known, so the income attributable to the building (building value times building rate) is deducted from NOI. The remaining income is attributed to the land and capitalized at the land rate.
Real-World Application
An appraiser valuing a newly built property can estimate the building value reliably from cost. Using the land residual technique, the appraiser deducts building income from NOI and capitalizes the remainder to estimate land value, then adds the two for total value.
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