An existing building has a replacement cost new of $900,000 and 10% accrued depreciation. The property’s stabilized NOI is $120,000, the building capitalization rate is 11% and the land capitalization rate is 8%. What land value does the land residual technique indicate?
Correct Answer
D) $386,250
Building value is $900,000 × 0.90 = $810,000, and income to the building is $810,000 × 11% = $89,100. Residual income to land is $120,000 − $89,100 = $30,900, and $30,900 ÷ 0.08 = $386,250. Ignoring depreciation gives $262,500; applying the land rate to the building gives $690,000.
Why This Is the Correct Answer
Option D is correct because the building is worth $900,000 × 0.90 = $810,000, it requires $810,000 × 11% = $89,100 of income, and the residual land income of $120,000 − $89,100 = $30,900 capitalized at 8% gives $30,900 ÷ 0.08 = $386,250.
Why the Other Options Are Wrong
Option A: $690,000
Option A ($690,000) applies the land rate to the building: ($120,000 − $810,000 × 0.08) ÷ 0.08 = $55,200 ÷ 0.08. Building income must use the 11% building rate, giving ($120,000 − $89,100) ÷ 0.08 = $386,250.
Option B: $1,500,000
Option B ($1,500,000) capitalizes all NOI as land income, $120,000 ÷ 0.08, with no deduction for the building. The building's $89,100 share must come out first, leaving $30,900 ÷ 0.08 = $386,250.
Option C: $262,500
Option C ($262,500) uses cost new without depreciation: $900,000 × 11% = $99,000, and ($120,000 − $99,000) ÷ 0.08 = $262,500. The building value is $810,000 after 10% depreciation, which gives $386,250.
Build, deduct, divide
Build the building value (cost less depreciation), deduct its income at the building rate, then divide what is left by the land rate.
How to use: Use this sequence for any land residual problem that gives cost, depreciation and two capitalization rates.
Exam Tip
Keep each rate paired with its own component: the building rate goes with the building value and the land rate with the residual land income.
Common Mistakes to Avoid
- -Using replacement cost new instead of depreciated building value
- -Applying the land rate to the building
- -Capitalizing total NOI without deducting building income
Concept Deep Dive
Analysis
This question tests the land residual technique when the building value must first be derived from cost less depreciation. You estimate the building value, multiply it by the building capitalization rate to find the income the building needs, subtract that from total NOI, and capitalize the remaining land income at the land rate.
Background Knowledge
The land residual technique assumes the building value is known or can be estimated reliably, such as for a new or nearly new building or from cost less depreciation. Income attributable to the building is building value times the building rate; the remainder is attributed to land and capitalized at the land rate. The building rate typically exceeds the land rate because it includes recapture of the wasting improvement.
Real-World Application
An appraiser values the land under an older retail building with a reliable cost estimate and known depreciation. Using market-derived building and land rates, the appraiser subtracts the building's required income from stabilized NOI and capitalizes the residual to estimate land value.
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