An office building generates $500,000 in net operating income. The land value is $1,000,000 and the building cost new would be $4,000,000 with $800,000 in accrued depreciation. If the capitalization rate is 8%, what is the value indicated by the land residual technique?
Correct Answer
C) $3,050,000
Building value = $4,000,000 - $800,000 = $3,200,000. Building income = $3,200,000 × 8% = $256,000. Land income = $500,000 - $256,000 = $244,000. Land value = $244,000 ÷ 8% = $3,050,000.
Why This Is the Correct Answer
Option C correctly applies the land residual technique step-by-step. First, the current building value is calculated as $4,000,000 - $800,000 = $3,200,000. Next, the income required to support this building investment is $3,200,000 × 8% = $256,000. The residual income attributable to the land is $500,000 - $256,000 = $244,000. Finally, capitalizing this land income at 8% gives $244,000 ÷ 0.08 = $3,050,000.
Why the Other Options Are Wrong
Option A: $6,250,000
This answer of $6,250,000 appears to be the result of capitalizing the entire NOI ($500,000 ÷ 8% = $6,250,000) without separating the building and land components, which is not the land residual technique but rather a direct capitalization of total property value.
Option B: $2,950,000
This answer likely results from an error in calculating either the building value or incorrectly applying the capitalization rate, possibly by adding the calculated land value to some other component instead of isolating the land value alone.
Option D: $2,850,000
This answer suggests an error in the calculation process, possibly from incorrectly calculating the building's income requirement or making an arithmetic error in the final capitalization step.
BUILD-LAND-CAP Method
BUILD (calculate current building value), LAND (find residual land income), CAP (capitalize land income). Remember: 'Buildings eat first, land gets leftovers' - the building takes its required income first, then remaining income goes to land.
How to use: When you see land residual problems, follow BUILD-LAND-CAP: 1) BUILD - find building value (cost new minus depreciation), 2) LAND - calculate building income needed (building value × cap rate), subtract from total NOI to get land income, 3) CAP - divide land income by cap rate for land value.
Exam Tip
Always work systematically through residual problems: identify what's known, what's unknown, calculate the known component's income requirement first, then find the residual income for the unknown component.
Common Mistakes to Avoid
- -Using the given land value instead of calculating it
- -Forgetting to subtract depreciation from building cost new
- -Capitalizing the total NOI instead of just the residual land income
Concept Deep Dive
Analysis
The land residual technique is one of the three residual techniques used in income capitalization approach when the value of one component (building) is known and you need to determine the value of the other component (land). This method assumes the building is at its highest and best use and calculates what income is attributable to the land after deducting the income required to support the building investment. The technique works by first determining the building's current value (cost new minus depreciation), then calculating the income needed to support that building value using the cap rate, and finally attributing the remaining income to the land. The land value is then determined by capitalizing this residual income at the same cap rate.
Background Knowledge
The land residual technique is used when the building value is known or can be estimated, and the appraiser needs to determine the land value by attributing residual income to the land after satisfying the building's income requirements. This technique assumes that the building represents the highest and best use of the land and that the same capitalization rate applies to both land and building components.
Real-World Application
Appraisers use land residual technique when valuing development sites where proposed improvements are known, or when the building is relatively new and cost data is reliable, helping determine if land prices are justified by the income-producing potential.
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