A property produces annual NOI of $96,000, and its building value is known to be $800,000. Market data show a 6% land capitalization rate and a 9% building capitalization rate. Using the land residual technique, what is the land value?
Correct Answer
B) $400,000
Known income=800000×0.09=72000; residual value=(96000−72000)÷0.06=400000. Common errors: capitalizing the residual income at the known component rate gives $266,667; capitalizing all of the NOI without allocating income to the known component gives $1,600,000; allocating income to the known component at the other component rate gives $800,000.
Why This Is the Correct Answer
Option B is correct because building income is $800,000 × 0.09 = $72,000, leaving $96,000 − $72,000 = $24,000 for the land. Capitalizing that residual at the land rate gives $24,000 ÷ 0.06 = $400,000.
Why the Other Options Are Wrong
Option A: $266,667
Option A, $266,667, capitalizes the residual income at the known component's rate: ($96,000 − $72,000) ÷ 0.09 = $266,667. The residual belongs to the land, so it must be capitalized at the 6% land rate, giving $400,000.
Option C: $800,000
Option C, $800,000, allocates income to the building at the land rate: ($96,000 − $800,000 × 0.06) ÷ 0.06 = $48,000 ÷ 0.06 = $800,000. The building's income must use the 9% building rate, $72,000, leaving $24,000 ÷ 0.06 = $400,000.
Option D: $1,600,000
Option D, $1,600,000, capitalizes all of the NOI at the land rate without first deducting the building's share: $96,000 ÷ 0.06 = $1,600,000. The building's $72,000 must be removed first, leaving $24,000 ÷ 0.06 = $400,000.
Known Rate, Then Residual Rate
Use the known component's rate to take its income out, then use the unknown component's rate to capitalize what is left.
How to use: Use this two-rate sequence in any land or building residual problem.
Exam Tip
Label each rate with its component before calculating so the known value is paired with its own rate and the residual with the other.
Common Mistakes to Avoid
- -Capitalizing the residual at the known component's rate
- -Allocating income to the known component at the wrong rate
- -Capitalizing total NOI without removing the known component's income
Concept Deep Dive
Analysis
This question tests the land residual technique. Income attributable to the known building is found by multiplying building value by the building rate; the remaining income is attributed to the land and capitalized at the land rate. Using the wrong rate at either step produces the distractors.
Background Knowledge
Residual techniques split income between physical components (land and building) or financial components (debt and equity). In the land residual technique, the income needed to support the known building value is deducted from NOI and the remainder is capitalized at the land rate.
Real-World Application
An appraiser analyzing a site with a new building of known cost uses the land residual technique to test land value. The appraiser deducts the income needed to support the building and capitalizes the remaining income at a market land rate.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
Annual PGI is $250,000 and combined vacancy and collection loss is explicitly 12% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
Which statement correctly distinguishes the models?
Next Question
A comparable sold for a cash-equivalent price of $1,000,000 and has annual NOI of $80,000. The subject property has annual NOI of $88,000. Sales in the market area indicate the subject would sell at the same price-to-income ratio, with no other adjustments. What is the indicated value of the subject, to the nearest dollar?