An appraiser is valuing a property with annual NOI of $152,000 and a known land value of $400,000. The land capitalization rate is 5% and the building capitalization rate is 11%. What total property value does the building residual technique indicate?
Correct Answer
C) $1,600,000
Known income=400000×0.05=20000; residual value=(152000−20000)÷0.11=1200000; total=400000+1200000=1600000. Common errors: capitalizing the residual income at the known component rate gives $3,040,000; reporting only the residual component instead of the total value gives $1,200,000; allocating income to the known component at the other component rate gives $1,381,818.
Why This Is the Correct Answer
Option C is correct because land income is $400,000 × 0.05 = $20,000, residual building income is $152,000 − $20,000 = $132,000, building value is $132,000 ÷ 0.11 = $1,200,000, and total value is $400,000 + $1,200,000 = $1,600,000.
Why the Other Options Are Wrong
Option A: $1,200,000
Option A, $1,200,000, is only the building value from the residual step ($132,000 ÷ 0.11). The question asks for total property value, so the $400,000 land value must be added to reach $1,600,000.
Option B: $1,381,818
Option B, $1,381,818, charges the land at the building rate: $400,000 × 0.11 = $44,000, then ($152,000 − $44,000) ÷ 0.11 = $981,818, plus $400,000. Land income should use the 5% land rate, giving $1,600,000.
Option D: $3,040,000
Option D, $3,040,000, capitalizes the residual $132,000 at the 5% land rate ($2,640,000) and adds $400,000. The residual building income belongs at the 11% building rate, giving $1,200,000 plus land for $1,600,000.
Known value, own rate
The known component earns at its own rate; the leftover income is capitalized at the unknown component's rate.
How to use: Use this pairing to assign the correct rate at each step of any residual problem.
Exam Tip
Read whether the question wants the residual component or the total property value before choosing.
Common Mistakes to Avoid
- -Capitalizing residual income at the known component's rate
- -Forgetting to add back the known component value
- -Charging land income at the building rate
Concept Deep Dive
Analysis
This question tests the building residual technique. The known land value earns income at the land rate; the remaining NOI is attributed to the building and capitalized at the building rate; then land and building values are added. Using the right rate for each component is the key.
Background Knowledge
Residual techniques split income between physical components such as land and building, or financial components such as debt and equity. In the building residual technique, income imputable to the land (land value times land rate) is deducted from NOI, and the remainder is capitalized at the building rate.
Real-World Application
An appraiser has strong land sales supporting a $400,000 site value for an older commercial building. Using the building residual technique, the appraiser isolates the income attributable to the improvements to estimate their contributory value.
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Previous Question
Annual effective gross income for the subject property is $320,000. Annual expenses are $112,000, and no other deductions apply. How much income remains after deducting those expenses?
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