The subject property has annual NOI of $96,000 and a known land value of $250,000. Capitalization rates are 6% for land and 9% for the building. Using the building residual technique, what is the total property value?
Correct Answer
C) $1,150,000
Known income=250000×0.06=15000; residual value=(96000−15000)÷0.09=900000; total=250000+900000=1150000. Common errors: capitalizing the residual income at the known component rate gives $1,600,000; reporting only the residual component instead of the total value gives $900,000; allocating income to the known component at the other component rate gives $1,066,667.
Why This Is the Correct Answer
Option C is correct because land income is $250,000 × 0.06 = $15,000, the building residual value is ($96,000 − $15,000) ÷ 0.09 = $900,000, and total value is $250,000 + $900,000 = $1,150,000. In the building residual technique the income imputable to the land is deducted first. Each component is capitalized at its own rate.
Why the Other Options Are Wrong
Option A: $900,000
Option A, $900,000, is only the building residual value, ($96,000 − $15,000) ÷ 0.09, without adding the land. The question asks for total value, $900,000 + $250,000 = $1,150,000.
Option B: $1,066,667
Option B, $1,066,667, allocates land income at the building rate: $250,000 × 0.09 = $22,500, then ($96,000 − $22,500) ÷ 0.09 + $250,000. Land income should use the 6% land rate, giving a total of $1,150,000.
Option D: $1,600,000
Option D, $1,600,000, capitalizes the residual income at the land rate: ($96,000 − $15,000) ÷ 0.06 + $250,000. The residual belongs to the building and is capitalized at 9%, giving $900,000 plus $250,000, or $1,150,000.
Known out, unknown capitalized
Take the known component's income out of NOI at its own rate, capitalize what remains at the unknown component's rate, then add both values.
How to use: Use this for any land or building residual problem.
Exam Tip
Match each rate to its own component, and read whether the question asks for one component or total value.
Common Mistakes to Avoid
- -Reporting only the residual component as total value
- -Capitalizing residual income at the known component's rate
- -Computing the known component's income at the wrong rate
Concept Deep Dive
Analysis
This question tests the building residual technique. Income needed to support the known land value is deducted from total NOI, and the residual income is capitalized at the building rate. The land and building values are then added for total property value.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). When one component's value is known, its income is deducted and the remainder is capitalized to value the other component.
Real-World Application
An appraiser with strong land sales but limited building cost data uses the building residual technique. Land income at the land rate is deducted from NOI, the remainder is capitalized at the building rate, and the two values are added.
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