The subject property's annual NOI is $96,000, and its land value is known to be $400,000. Capitalization rates are 5% for land and 8% for the building. What total property value does the building residual technique indicate?
Correct Answer
C) $1,350,000
Known income=400000×0.05=20000; residual value=(96000−20000)÷0.08=950000; total=400000+950000=1350000. Common errors: capitalizing the residual income at the known component rate gives $1,920,000; reporting only the residual component instead of the total value gives $950,000; allocating income to the known component at the other component rate gives $1,200,000.
Why This Is the Correct Answer
Option C is correct because land income is $400,000 x 0.05 = $20,000, residual building income is $96,000 - $20,000 = $76,000, and $76,000 / 0.08 = $950,000. Adding the known land value gives $400,000 + $950,000 = $1,350,000. Each component's income is capitalized at its own rate.
Why the Other Options Are Wrong
Option A: $950,000
Option A is wrong because $950,000 is only the residual building value: ($96,000 - $400,000 x 0.05) / 0.08 = $950,000. The question asks for total property value, so the $400,000 land must be added for $1,350,000.
Option B: $1,200,000
Option B is wrong because $1,200,000 comes from allocating income to the land at the building rate: ($96,000 - $400,000 x 0.08) / 0.08 + $400,000 = $1,200,000. Land income uses the land rate: ($96,000 - $20,000) / 0.08 + $400,000 = $1,350,000.
Option D: $1,920,000
Option D is wrong because $1,920,000 comes from capitalizing the residual income at the land rate: ($96,000 - $20,000) / 0.05 + $400,000 = $1,920,000. The residual building income must be capitalized at the 8% building rate, giving $1,350,000.
Known first, residual second
Take the known component's income out first at its own rate, then capitalize what is left at the other rate and add the pieces.
How to use: Use this order for any land or building residual problem.
Exam Tip
Read whether the question asks for the residual component or total property value. Also match each rate to its own component.
Common Mistakes to Avoid
- -Stopping at the residual component value
- -Using the wrong component's rate for allocation
- -Capitalizing residual income at the known component's rate
Concept Deep Dive
Analysis
This question tests the building residual technique with a known land value. Income attributable to the land is land value times the land rate; the remaining income is attributed to the building and capitalized at the building rate. Total value is the land value plus the capitalized building value.
Background Knowledge
Residual techniques capitalize the income left over for a component of unknown value after the income needed by components of known value is satisfied. In the building residual technique, land value is known and the income imputable to land is deducted from NOI. Residual techniques can also split financial components such as debt and equity.
Real-World Application
An appraiser estimates land value from vacant land sales at $400,000 and needs to test the contribution of an older building. Using the building residual technique, the appraiser deducts land income and capitalizes the remainder to estimate the building's contribution.
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Annual potential gross rental income is $560,000. The corresponding vacancy loss is $42,000. What percentage of potential income does that loss represent?
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