The subject property is an office building whose income is reported after management but with no deduction for replacement reserves. A comparable office building sold for $2,000,000 cash. Its reported NOI of $148,000 is after a $6,000 management fee and a $12,000 replacement reserve. What overall rate from this sale matches the subject's income?
Correct Answer
D) 8.0%
The rate must come from the same level of income to which it will be applied, so the $12,000 reserve is added back while management stays deducted. That gives ($148,000 + $12,000) ÷ $2,000,000 = 8.0%. The 7.4% figure leaves the mismatch in place, 7.7% adds back the management fee instead, and 6.8% deducts the reserve a second time.
Why This Is the Correct Answer
Option D is correct because the subject's income has no reserve deducted, so the comparable's income must also be stated before the reserve. Adding $12,000 to $148,000 gives $160,000, and dividing by $2,000,000 gives 8.0%. Management remains deducted because the subject's income is also after management.
Why the Other Options Are Wrong
Option A: 6.8%
Option A, 6.8%, is ($148,000 − $12,000) ÷ $2,000,000. The reported NOI already reflects the reserve, so this deducts it twice and moves away from the subject's convention. Adding it back gives 8.0%.
Option B: 7.4%
Option B, 7.4%, is $148,000 ÷ $2,000,000, the rate on an after-reserve basis. Applying it to before-reserve subject income would mix conventions and overstate value. The matching rate is 8.0%.
Option C: 7.7%
Option C, 7.7%, is ($148,000 + $6,000) ÷ $2,000,000. It adds back management, which the subject's income also deducts, and leaves the reserve in place. The correct add-back is the $12,000 reserve, which gives 8.0%.
Restate the sale to match
Compare the two income definitions line by line. Change the comparable's income only for the items that differ.
How to use: Use this when a comparable's NOI and the subject's NOI are defined differently.
Exam Tip
A rate calculated on higher income is higher. Before picking an answer, confirm that the rate's income basis and the subject's income basis are the same.
Common Mistakes to Avoid
- -Applying an after-reserve rate to before-reserve income
- -Adding back a cost that both incomes deduct
- -Deducting a reserve already reflected in NOI
Concept Deep Dive
Analysis
The arithmetic is short, but the judgment is which income level matches the subject. The comparable's income is after both management and a reserve, while the subject's is after management only. Adding back the reserve puts the sale on the subject's convention before the rate is calculated.
Background Knowledge
The type of rate derived depends on the level of income processed, and the rate must be applied to the same level from which it was derived. A replacement allowance is one common difference between income statements. Mixing a rate from after-reserve income with before-reserve income distorts value.
Real-World Application
An appraiser's subject operating statement shows no reserve, but sale data from a broker reports NOI after reserves. The appraiser restates the sale's income so that the extracted rate can be applied without distorting value.
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