A property produces net operating income of $240,000. The building is worth $1,500,000 and is capitalized at 9 percent, and the land capitalization rate is 7 percent. The income, building value and rates all reflect the market. What land value does the land residual technique indicate?
Correct Answer
B) $1,500,000
Building income = $1,500,000 × 0.09 = $135,000; land income = $240,000 − $135,000 = $105,000; land value = $105,000/0.07 = $1,500,000. The indicated value is $1,500,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: capitalizing all of the NOI as land income gives $3,428,571; capitalizing land income at the building rate gives $1,166,667; adding the building value to the land value gives $3,000,000.
Why This Is the Correct Answer
Option B is correct because building income is $1,500,000 × 0.09 = $135,000, leaving land income of $240,000 − $135,000 = $105,000. Capitalizing at the 7% land rate gives $105,000 ÷ 0.07 = $1,500,000.
Why the Other Options Are Wrong
Option A: $1,166,667
Option A, $1,166,667, capitalizes the land income at the building rate: ($240,000 − $135,000) ÷ 0.09 = $1,166,667. Land income must be capitalized at the land rate: $105,000 ÷ 0.07 = $1,500,000.
Option C: $3,000,000
Option C, $3,000,000, adds the $1,500,000 building value to the land value, reporting the whole property rather than the land. The land residual technique asks for land alone: ($240,000 − $135,000) ÷ 0.07 = $1,500,000.
Option D: $3,428,571
Option D, $3,428,571, capitalizes all of the NOI as land income: $240,000 ÷ 0.07 = $3,428,571. The building's $135,000 share must be deducted first.
Each part, its own rate
The building's income is figured at the building rate and the land's residual income is capitalized at the land rate; do not swap them.
How to use: Use this to avoid rate-swapping errors in residual technique problems.
Exam Tip
Write out the three steps (building income, residual income, capitalize at land rate) before looking at the options.
Common Mistakes to Avoid
- -Capitalizing total NOI at the land rate
- -Capitalizing land income at the building rate
- -Adding the building value to the land value
Concept Deep Dive
Analysis
This question tests the income land residual technique with stated component rates. You deduct the building's income requirement at the building rate, then capitalize the residual at the land rate. Swapping rates, skipping the building deduction or adding back the building value produces the distractors.
Background Knowledge
The land residual technique is used when building value can be estimated reliably, such as for a new building at its highest and best use. It relies on market-derived income and component capitalization rates that are consistent with each other.
Real-World Application
An appraiser values the land under a newly built retail building whose cost is known. Allocating income to the building at a market building rate and capitalizing the remainder at a land rate supports the land value indicated by scarce vacant land sales.
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