Annual NOI is $165,000, and the building value is known to be $1,100,000. Capitalization rates are 5% for land and 11% for the building. Using the land residual technique, what is the total property value?
Correct Answer
C) $1,980,000
Known income=1100000×0.11=121000; residual value=(165000−121000)÷0.05=880000; total=1100000+880000=1980000. Common errors: capitalizing the residual income at the known component rate gives $1,500,000; reporting only the residual component instead of the total value gives $880,000; allocating income to the known component at the other component rate gives $3,300,000.
Why This Is the Correct Answer
Option C is correct because the income needed by the building is $1,100,000 × 0.11 = $121,000. The residual income to land is $165,000 − $121,000 = $44,000, and $44,000 ÷ 0.05 = $880,000. Adding the known building value gives $1,100,000 + $880,000 = $1,980,000.
Why the Other Options Are Wrong
Option A: $880,000
Option A, $880,000, is only the residual land value: ($165,000 − $121,000) ÷ 0.05. The question asks for total property value, so the $1,100,000 building must be added, giving $1,980,000.
Option B: $1,500,000
Option B, $1,500,000, comes from capitalizing the residual income at the known component's rate: $44,000 ÷ 0.11 = $400,000, plus $1,100,000. The residual land income must be capitalized at the 5% land rate, giving $880,000 and a total of $1,980,000.
Option D: $3,300,000
Option D, $3,300,000, comes from allocating income to the building at the land rate: $1,100,000 × 0.05 = $55,000, then ($165,000 − $55,000) ÷ 0.05 = $2,200,000, plus $1,100,000. The building income must use the 11% building rate, giving $1,980,000.
Known first, residual second
Feed the known component its income at its own rate; what is left over is capitalized at the unknown component's rate.
How to use: Use this order in any land, building, mortgage or equity residual problem.
Exam Tip
Read the last sentence carefully to see whether the question wants the residual component alone or the total property value.
Common Mistakes to Avoid
- -Reporting only the residual component when total value is asked
- -Capitalizing the residual income at the known component's rate
- -Using the land rate to calculate the building's share of income
Concept Deep Dive
Analysis
This question tests the land residual technique when the building value is known. You allocate income to the known building at the building rate, capitalize the leftover income at the land rate, and add the two component values for total value. Each step must use the rate that matches its component.
Background Knowledge
Residual techniques split income between physical components, land and building, or financial components, debt and equity. In the land residual technique, the building value is known, its required income is deducted, and the remaining income is capitalized into land value. Building rates are often higher than land rates because they include recapture for a wasting asset.
Real-World Application
An appraiser values a site with a new building whose cost is well supported but where few land sales exist. Using the building value and a building capitalization rate, the appraiser deducts the building's income from NOI. The remaining income is capitalized at a land rate to estimate land value, which is added to the building value.
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An overall capitalization rate of 7.2% was extracted from a sale. The buyer financed 75% of the price at a 6.9% annual mortgage constant and paid the remaining 25% in equity. Using the band of investment, what equity dividend rate is indicated?
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The mortgage interest in a property is valued at $1,050,000, and annual debt service is $96,000. Annual NOI is $142,000. The equity dividend rate is 10%. Using the equity residual technique, what is the total property value?