A property produces annual NOI of $120,000, and the land is known to be worth $400,000. Market data indicate a 6% land capitalization rate and a 10% building capitalization rate. What building value does the building residual technique indicate?
Correct Answer
B) $960,000
Known income=400000×0.06=24000; residual value=(120000−24000)÷0.1=960000. Common errors: capitalizing the residual income at the known component rate gives $1,600,000; capitalizing all of the NOI without allocating income to the known component gives $1,200,000; allocating income to the known component at the other component rate gives $800,000.
Why This Is the Correct Answer
Option B is correct because income to the land is $400,000 × 0.06 = $24,000. The residual income to the building is $120,000 − $24,000 = $96,000. Capitalizing at the 10% building rate gives $96,000 ÷ 0.10 = $960,000.
Why the Other Options Are Wrong
Option A: $800,000
Option A, $800,000, allocates land income at the building rate: ($120,000 − $400,000 × 0.10) ÷ 0.10. Land income should use the 6% land rate, giving ($120,000 − $24,000) ÷ 0.10 = $960,000.
Option C: $1,200,000
Option C, $1,200,000, capitalizes all NOI at the building rate without allocating income to the land: $120,000 ÷ 0.10. Deducting land income first gives $96,000 ÷ 0.10 = $960,000.
Option D: $1,600,000
Option D, $1,600,000, capitalizes the building's residual income at the land rate: ($120,000 − $24,000) ÷ 0.06. The building rate of 10% applies, giving $960,000.
Known part first, its own rate
Charge the known component income at its own rate, then capitalize what is left at the other component's rate.
How to use: Use this for both land and building residual problems.
Exam Tip
Match each rate to its component: land rate for land, building rate for building. Check whether the question wants the residual component or total property value.
Common Mistakes to Avoid
- -Using the building rate to compute land income
- -Capitalizing total NOI without allocating income to land
- -Capitalizing residual building income at the land rate
Concept Deep Dive
Analysis
This question tests the building residual technique. Income attributable to the known land is found at the land rate and subtracted from NOI. The residual income is then capitalized at the building rate to get building value.
Background Knowledge
In the building residual technique, the land value is known, so the income imputable to the land (land value times land rate) is deducted from NOI. The remaining income is attributed to the building and capitalized at the building rate, which typically includes recapture.
Real-World Application
An appraiser with strong land sales but limited improvement data uses the building residual technique. After charging income to the land at a market land rate, the remaining income is capitalized to estimate what the building contributes.
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