A property produces net operating income of $180,000. The building is worth $1,200,000 and the building capitalization rate is 10 percent. If the land capitalization rate is 8 percent, what is the indicated land value?
Correct Answer
B) $750,000
Why this is correct: Using the land residual technique: 1) Calculate income attributable to the building: $1,200,000 × 10% = $120,000. 2) Residual income to land: $180,000 - $120,000 = $60,000. 3) Capitalize land income at its rate: $60,000 ÷ 0.08 = $750,000. Why the other choices are wrong: "$600,000" is wrong; it uses a 10% land cap rate ($60,000 ÷ 0.10). "$900,000" is wrong; it miscalculates building income or uses a 6.67% land cap rate. "$1,500,000" is wrong; it capitalizes total NOI at the land rate ($180,000 ÷ 0.08). Exam tip: In land residual, subtract building income requirement (Value × Rate) from total NOI before capitalizing the residual at the land rate.
Why This Is the Correct Answer
Option B is correct and follows the three-step sequence exactly. Building income is $1,200,000 times 10 percent, or $120,000; residual income to land is $180,000 minus $120,000, or $60,000; land value is $60,000 divided by 0.08, which equals $750,000. Each step uses its own rate on its own component, which is the discipline the technique demands. As a check, capitalizing the land income back at 8 percent reproduces $60,000, and the two component incomes sum to the stated $180,000.
Why the Other Options Are Wrong
Option A: $600,000
$600,000 results from computing the $60,000 residual correctly and then capitalizing it at the building rate of 10 percent instead of the land rate of 8 percent. Mixing the rates defeats the purpose of separating them, since the whole technique depends on land and improvements being capitalized differently. Remember the land rate is the lower of the two because land requires no recapture.
Option C: $900,000
$900,000 does not follow from these figures under a correct application. Reaching it requires either an incorrect building income deduction or an invented land rate near 6.7 percent, neither of which the stem supplies. It functions as a plausible-looking middle value for a candidate estimating instead of computing.
Option D: $1,500,000
$1,500,000 comes from capitalizing the entire $180,000 net operating income at the 8 percent land rate, which skips the deduction for building income altogether. That treats the whole property's income as though the land produced all of it, which would also make the land worth more than the total property. The building's $120,000 income requirement must be satisfied before anything is attributed to land.
Pay the building first
The building is a creditor that must be paid before the land collects anything. Building value times building rate is its bill; subtract it from net operating income and the leftover belongs to the land, capitalized at the land's own lower rate.
How to use: Write three lines every time: building income, residual income, land value. Label which rate belongs on which line before you divide, since swapping the rates is the error the distractors are built from.
Exam Tip
Total your components before selecting. Building value plus land value should be consistent with the property value that total net operating income would support, and land income plus building income must equal the stated net operating income.
Common Mistakes to Avoid
- -Capitalizing the residual land income at the building rate
- -Forgetting to deduct building income and capitalizing total NOI at the land rate
- -Using the same rate for land and improvements
- -Applying the technique where the existing improvements are not the highest and best use of the site
Concept Deep Dive
Analysis
This tests the land residual technique, which isolates land value by charging the building for the income it must earn and treating whatever income is left over as attributable to the land. The technique rests on the principle of surplus productivity: land is the residual claimant, receiving what remains after the agent of production representing the improvements is satisfied. It requires three inputs, a reliable net operating income for the whole property, a known or well-supported building value, and separate capitalization rates for building and land. The building rate is higher than the land rate because it must provide both a return on the investment and a return of the wasting asset through recapture, while land does not depreciate and needs only a return on. Sequence matters: compute building income first, subtract, then capitalize the residual at the land rate.
Background Knowledge
You need the land residual technique and its sibling, the building residual technique, which reverses the roles when land value is the known input. You also need to understand why the building rate exceeds the land rate, since it includes a recapture component for a depreciating asset, and to know that the method presumes the improvements represent the highest and best use of the site.
Real-World Application
For a proposed retail building you have solid cost data for the improvements but almost no vacant land sales to work from. You capitalize the projected net operating income, deduct the building's income requirement at a rate that includes recapture, and capitalize the residual to support a site value, disclosing the technique and its assumptions because the result is sensitive to both rates.
More Land/Site Questions
Under which condition is the land residual technique most applicable?
Why can the same physical parcel carry different values in two assignments?
In a built-up area where no vacant land has sold for years, which approach to site value is the usual fallback?
How is entrepreneurial profit treated in the subdivision development method?
A land comparable sold 18 months ago in a market rising about 4 percent a year. What adjustment direction applies?
Why does a developer's required profit rise for a longer subdivision project?
How does holding cost enter the valuation of land bought for future development?
Excess land is best described as land that has which characteristic?
Plottage value arises in which of the following situations?
Which of the following is an off-site improvement rather than a site improvement?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Income Approach
8.2% of exam