An appraiser is valuing a property with annual NOI of $162,000. Land value is known to be $450,000. The land capitalization rate is 6% and the building capitalization rate is 9%. What total property value does the building residual technique indicate?
Correct Answer
C) $1,950,000
Known income=450000×0.06=27000; residual value=(162000−27000)÷0.09=1500000; total=450000+1500000=1950000. Common errors: capitalizing the residual income at the known component rate gives $2,700,000; reporting only the residual component instead of the total value gives $1,500,000; allocating income to the known component at the other component rate gives $1,800,000.
Why This Is the Correct Answer
Option C is correct because land income is $450,000 × 0.06 = $27,000, leaving $162,000 − $27,000 = $135,000 for the building. Capitalized at 9%, that is $135,000 ÷ 0.09 = $1,500,000, and adding the $450,000 land gives $1,950,000.
Why the Other Options Are Wrong
Option A: $1,500,000
Option A, $1,500,000, is ($162,000 − $27,000) ÷ 0.09, the building value alone. The question asks for total value, so the $450,000 land must be added for $1,950,000.
Option B: $1,800,000
Option B, $1,800,000, comes from ($162,000 − $450,000 × 0.09) ÷ 0.09 + $450,000, allocating land income at the 9% building rate. Land income should use the 6% land rate, giving $1,950,000.
Option D: $2,700,000
Option D, $2,700,000, comes from ($162,000 − $27,000) ÷ 0.06 + $450,000, capitalizing the building's residual income at the 6% land rate. The residual should use the 9% building rate, giving $1,500,000 + $450,000 = $1,950,000.
Known first, residual last
Take income for the known part at its own rate, capitalize what remains at the other part's rate, then add both values.
How to use: Use this for land residual and building residual problems alike.
Exam Tip
Pair each rate with its own component and remember to add the components when the question asks for total value.
Common Mistakes to Avoid
- -Capitalizing residual income at the known component's rate
- -Reporting only the residual component value
- -Allocating income to the known component at the wrong rate
Concept Deep Dive
Analysis
This question tests a building residual calculation. Income is first allocated to the known land value at the land rate, the remaining income is capitalized at the building rate, and the two component values are added. Using the wrong rate at either step, or stopping before adding, gives the distractors.
Background Knowledge
Residual techniques split income between physical components, land and building, or financial components, debt and equity. In the building residual technique, income attributable to the known land value is deducted from NOI, and the remaining income is capitalized at the building rate. Adding the component values gives total property value.
Real-World Application
An appraiser values an older commercial building where land value is well supported by vacant land sales. She deducts the land's share of NOI at a land rate and capitalizes the residual income at a building rate to estimate the improvements' contribution and total value.
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Previous Question
The subject property is a two-story mixed-use building. The owner operates a bakery on the 6,000-sf ground floor and pays no rent; last year the bakery earned a net profit of $88,000. The upper floor is leased as offices at market rent totaling $84,000 a year. Similar ground-floor retail space rents for $12 per square foot annually on the same expense terms as the offices. Stabilized vacancy and credit loss is 5% of PGI, real property operating expenses are $52,200, excluding the bakery's own costs, and the market overall rate is 8%. What is the indicated value of the fee simple interest?
Next Question
A lender's terms for a property are an 80% loan-to-value ratio, a 10% annual mortgage constant, and a 1.25 debt coverage ratio. Annual NOI is $85,000. What value is indicated by capitalizing NOI at the overall rate from the debt coverage formula?