The building on the subject site is known to be worth $1,800,000, and total annual NOI is $216,000. Market data indicate a 6% land capitalization rate and a 9% building capitalization rate. Using the land residual technique, what is the land value?
Correct Answer
B) $900,000
Known income=1800000×0.09=162000; residual value=(216000−162000)÷0.06=900000. Common errors: capitalizing the residual income at the known component rate gives $600,000; capitalizing all of the NOI without allocating income to the known component gives $3,600,000; allocating income to the known component at the other component rate gives $1,800,000.
Why This Is the Correct Answer
Option B is correct because the building's income is $1,800,000 × 0.09 = $162,000, leaving $216,000 − $162,000 = $54,000 for the land. Capitalizing that at the 6% land rate gives $54,000 ÷ 0.06 = $900,000.
Why the Other Options Are Wrong
Option A: $600,000
Option A, $600,000, comes from capitalizing the $54,000 of residual land income at the 9% building rate instead of the 6% land rate ($54,000 ÷ 0.09). The residual income is the land's, so it is capitalized at the land rate to give $900,000.
Option C: $1,800,000
Option C, $1,800,000, results from allocating income to the building at the 6% land rate ($1,800,000 × 0.06 = $108,000) and capitalizing the remaining $108,000 at 6%. The building's income must use the building rate, giving $162,000 to the building and a land value of $900,000.
Option D: $3,600,000
Option D, $3,600,000, comes from capitalizing the entire $216,000 NOI at the land rate ($216,000 ÷ 0.06) without first deducting the income attributable to the building. Only the residual $54,000 belongs to the land, giving $900,000.
Known times its rate
Multiply the known component by its own rate to take its income, then divide what is left by the unknown component's rate.
How to use: Use this pattern for both land residual and building residual problems.
Exam Tip
Match each rate to its own component: the known component's rate is used to allocate income, and the unknown component's rate is used to capitalize the residual.
Common Mistakes to Avoid
- -Capitalizing the residual income at the known component's rate
- -Capitalizing total NOI without removing the known component's income
- -Using the wrong rate when allocating income to the known component
Concept Deep Dive
Analysis
This question tests the land residual technique. The building value is known, so first allocate income to the building at the building rate, then capitalize the leftover (residual) income at the land rate to find land value.
Background Knowledge
Physical residual techniques split NOI between land and building. In the land residual technique, income attributable to the known building value (building value × building rate) is deducted from NOI, and the remaining income is capitalized at the land rate to estimate land value.
Real-World Application
An appraiser evaluating whether a site is worth redeveloping estimates the cost of a new building that represents its highest and best use, allocates income to that building at a building rate, and capitalizes the remaining income at a land rate to estimate land value.
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Previous Question
Two DCFs have identical positive projected operating cash flows and a positive terminal NOI, with no offsetting terminal costs. Model A uses a 6.0% discount rate and 5.5% terminal rate; B uses 7.2% and 6.8%. Which indicates more value?
Next Question
An appraiser is verifying the sale of a 24-unit apartment building that was listed at $2,187,500 and sold for $2,050,000 cash. Several units were vacant at the time of sale while the seller finished a renovation at the seller's expense, and NOI over the prior 12 months was $150,000. The buyer confirms the purchase was underwritten on anticipated NOI of $164,000 for the coming year. What is the market-extracted overall rate?