The subject property is a 12-unit apartment building with projected NOI of $92,000 after deducting a $4,000 annual replacement allowance. The appraiser's market-extracted overall rate of 8% comes from sales whose NOI was reported before any replacement allowance. What is the indicated value?
Correct Answer
D) $1,200,000
A rate must be applied to the same level of income from which it was derived. This rate is on a before-reserve basis, so the $4,000 allowance is added back: $92,000 + $4,000 = $96,000, and $96,000 ÷ 0.08 = $1,200,000. Capitalizing $92,000 mixes the two bases and gives $1,150,000. Deducting the allowance a second time gives $1,100,000, and adding $4,000 to the capitalized figure gives $1,154,000.
Why This Is the Correct Answer
Option D is correct because the rate was extracted before reserves, so the subject's income must also be before reserves. That gives $92,000 + $4,000 = $96,000. Dividing by 8% indicates $1,200,000.
Why the Other Options Are Wrong
Option A: $1,100,000
Option A, $1,100,000, moves the wrong way: ($92,000 − $4,000) ÷ 0.08. The $92,000 is already after the allowance, so this deducts it twice. The correct calculation is $96,000 ÷ 0.08 = $1,200,000.
Option B: $1,150,000
Option B, $1,150,000, is $92,000 ÷ 0.08. It applies a before-reserve rate to after-reserve income, which understates value. The correct calculation is $96,000 ÷ 0.08 = $1,200,000.
Option C: $1,154,000
Option C, $1,154,000, is $92,000 ÷ 0.08 + $4,000. The allowance is an annual income item, so adding it to value in dollars does not restore the matching basis. The correct calculation is $96,000 ÷ 0.08 = $1,200,000.
Match income to the rate
Whatever was or was not deducted when the rate was built should be treated the same way in the subject's income.
How to use: Use this when a reserve appears in either the rate data or the subject's NOI.
Exam Tip
Compare the basis of the rate and the basis of the income before dividing. Adjust income, not the final value, when they differ.
Common Mistakes to Avoid
- -Dividing after-reserve income by a before-reserve rate
- -Adding the annual allowance to the capitalized value
- -Deducting an allowance already reflected in the stated NOI
Concept Deep Dive
Analysis
The skill is noticing that income and rate are on different bases and knowing how to fix it. The sales are reported before any allowance, so the subject's income moves to the before-allowance level. The allowance is added to income before capitalizing, not to the value afterward.
Background Knowledge
A market-derived rate carries the income definition used to extract it. A rate extracted before reserves is lower than one extracted after reserves from the same sale, so mixing bases distorts value. Either convention can work if the rate and the income match.
Real-World Application
An appraiser's operating statement carries a replacement allowance, but brokers' sale data report NOI with no allowance. Unable to restate the sales, the appraiser adds the allowance back to the subject's income so that both figures rest on the same basis.
More Income Approach Questions
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Which two depreciation categories may each be classified as curable or incurable by comparing the cost to remedy a deficiency with the value gained?
Improvement cost new is $800,000. Separately supported improvement depreciation deductions of $120,000, $80,000, $40,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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Which highest-and-best-use criterion addresses whether a proposed use is allowed by zoning and applicable legal restrictions?
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When reconciling value indications from the three approaches to value, an appraiser should:
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