The subject property has annual NOI of $102,000 and a known land value of $300,000. Market data indicate a land capitalization rate of 6% and a building capitalization rate of 8%. Using the building residual technique, what is the building value?
Correct Answer
B) $1,050,000
Known income=300000×0.06=18000; residual value=(102000−18000)÷0.08=1050000. Common errors: capitalizing the residual income at the known component rate gives $1,400,000; capitalizing all of the NOI without allocating income to the known component gives $1,275,000; allocating income to the known component at the other component rate gives $975,000.
Why This Is the Correct Answer
Option B is correct because land income is $300,000 × 0.06 = $18,000, leaving $102,000 − $18,000 = $84,000 for the building. Capitalizing that residual at the 8% building rate gives $84,000 ÷ 0.08 = $1,050,000.
Why the Other Options Are Wrong
Option A: $975,000
Option A, $975,000, allocates income to the land at the building rate: ($102,000 − $300,000 × 0.08) ÷ 0.08 = $78,000 ÷ 0.08 = $975,000. Land income uses the 6% land rate, giving $84,000 ÷ 0.08 = $1,050,000.
Option C: $1,275,000
Option C, $1,275,000, capitalizes all of the NOI at the building rate without first deducting land income: $102,000 ÷ 0.08 = $1,275,000. Removing the $18,000 of land income first gives $84,000 ÷ 0.08 = $1,050,000.
Option D: $1,400,000
Option D, $1,400,000, capitalizes the building's residual income at the land rate: $84,000 ÷ 0.06 = $1,400,000. The residual belongs to the building and should be capitalized at 8%, giving $1,050,000.
Known first, residual second
Use the known component's own rate to take its income off the top, then capitalize what is left at the unknown component's rate.
How to use: Use this two-step order on any land, building, mortgage or equity residual problem.
Exam Tip
Match each rate to its own component; most wrong answers swap the land and building rates in one of the two steps.
Common Mistakes to Avoid
- -Capitalizing the residual income at the land rate
- -Skipping the land income deduction
- -Computing land income with the building 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 remaining income is capitalized at the building rate. Land income is $300,000 × 0.06 = $18,000, the residual is $84,000, and $84,000 ÷ 0.08 = $1,050,000.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). In the building residual technique, land value is known, so the income imputable to land is deducted and the remainder is capitalized at the building rate. Each component's income is matched with that component's own rate.
Real-World Application
An appraiser has a reliable land value of $300,000 from vacant land sales but no good data on the building's value. Using the building residual technique, the appraiser deducts the land's required return from NOI and capitalizes the remainder to estimate the building's contribution.
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