A property has annual NOI of $96,000 and a known land value of $200,000. The land capitalization rate is 7% and the building capitalization rate is 10%. Using the building residual technique, what is the building value?
Correct Answer
B) $820,000
Known income=200000×0.07=14000; residual value=(96000−14000)÷0.1=820000. Common errors: capitalizing the residual income at the known component rate gives $1,171,429; capitalizing all of the NOI without allocating income to the known component gives $960,000; allocating income to the known component at the other component rate gives $760,000.
Why This Is the Correct Answer
Option B is correct because the land needs $200,000 × 0.07 = $14,000 of income. The residual income to the building is $96,000 − $14,000 = $82,000, and capitalizing at the 10% building rate gives $82,000 ÷ 0.10 = $820,000.
Why the Other Options Are Wrong
Option A: $760,000
Option A, $760,000, comes from allocating income to the land at the building rate: $200,000 × 0.10 = $20,000, then ($96,000 − $20,000) ÷ 0.10 = $760,000. The land income must use the 7% land rate, giving $820,000.
Option C: $960,000
Option C, $960,000, comes from capitalizing all of the NOI at the building rate without allocating income to the land: $96,000 ÷ 0.10. Deducting the land's $14,000 first gives $820,000.
Option D: $1,171,429
Option D, $1,171,429, comes from capitalizing the residual income at the land rate: $82,000 ÷ 0.07 = $1,171,429. The building's residual income must be capitalized at the 10% building rate, giving $820,000.
Feed the land, cap the rest
Give the land its income at the land rate; capitalize whatever is left at the building rate to get building value.
How to use: Use this to keep the two rates matched to their components in building residual problems.
Exam Tip
Check whether the question asks for building value only or total value; this one wants the residual component alone.
Common Mistakes to Avoid
- -Capitalizing all NOI without allocating income to the land
- -Using the building rate to calculate the land's income
- -Adding land value when only building value is requested
Concept Deep Dive
Analysis
This question tests the building residual technique when land value is known. You allocate income to the land at the land rate, then capitalize the remaining income at the building rate. Because only the building value is requested, you do not add back the land.
Background Knowledge
In the building residual technique, land value is known, the income imputable to land is deducted from NOI, and the remainder is capitalized at a building rate. The method is useful when land value is well supported by sales. The building rate generally reflects both a return on and recapture of the improvement investment.
Real-World Application
An appraiser analyzing an older commercial building has strong land sales but uncertain building depreciation. Using the building residual technique, the appraiser deducts the land's required income from NOI. The remaining income capitalized at a building rate indicates the contributory value of the improvements.
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An appraiser finds a comparable that sold for a cash-equivalent price of $990,000 with annual EGI of $110,000. The subject has annual EGI of $108,000, measured on the same basis. Sales in the market area indicate the subject would sell at the same price-to-income ratio, with no other adjustments. What is the indicated value of the subject, rounded to the nearest dollar?