Annual NOI is known, and operating expenses are 35% of EGI, with no other deductions. Which expression recovers EGI from NOI?
Correct Answer
A) EGI=NOI÷0.65.
If expenses are 35% of EGI and there are no other deductions, NOI = EGI − 0.35×EGI = 0.65×EGI, so EGI = NOI ÷ 0.65. Dividing by 1.35 adds the expense ratio to 1 instead of subtracting it from 1 and produces a figure smaller than NOI; multiplying NOI by 0.35 gives neither EGI nor expenses; setting EGI equal to NOI ignores the expenses. The 35% ratio is on EGI, so it does not by itself recover PGI before vacancy and collection loss.
Why This Is the Correct Answer
Option A is correct because NOI = EGI − 0.35 × EGI = 0.65 × EGI, so EGI = NOI ÷ 0.65. The expense ratio is a share of EGI, which is why the complement 0.65 is the divisor.
Why the Other Options Are Wrong
Option B: EGI=NOI÷1.35.
Option B, EGI = NOI ÷ 1.35, is wrong because dividing by a number greater than 1 gives a figure smaller than NOI, yet EGI must be larger than NOI when expenses are deducted from it. Because expenses are 35% of EGI, NOI is 65% of EGI, so the correct divisor is 1 − 0.35 = 0.65.
Option C: EGI=NOI×0.35.
Option C, EGI = NOI × 0.35, is wrong because multiplying NOI by 0.35 gives neither EGI nor the expense amount. Expenses are 35% of EGI, not of NOI, and EGI must be larger than NOI.
Option D: EGI=NOI, without any allowance for expenses.
Option D, EGI = NOI without any allowance for expenses, is wrong because it ignores the 35% expense ratio. With expenses deducted from EGI to reach NOI, EGI must be greater than NOI.
Divide by What Remains
If 35% of EGI goes to expenses, 65% remains as NOI, so divide NOI by what remains to get back to EGI.
How to use: Use this when working backward from NOI to EGI with an expense ratio.
Exam Tip
Working backward, EGI must be larger than NOI; any formula that produces a smaller number is wrong.
Common Mistakes to Avoid
- -Dividing by 1 plus the expense ratio instead of 1 minus the expense ratio
- -Applying the expense ratio to NOI instead of EGI
- -Assuming the result is PGI rather than EGI
Concept Deep Dive
Analysis
This question tests algebra with the operating expense ratio. If expenses are 35% of EGI and nothing else is deducted, NOI is 65% of EGI. Solving NOI = 0.65 × EGI for EGI gives EGI = NOI ÷ 0.65.
Background Knowledge
The operating expense ratio is total operating expenses divided by effective gross income. The net income ratio is its complement, so NOI divided by EGI equals one minus the expense ratio. A ratio stated on EGI does not by itself recover PGI before vacancy and collection loss.
Real-World Application
An appraiser has an NOI reported in a sale verification but no income detail. Using a market-supported operating expense ratio for similar properties, the appraiser divides NOI by the net income ratio to estimate the comparable's EGI for an effective gross income multiplier analysis.
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An appraiser finds a sale of a retail building at 12.0 times annual NOI, with a 15-year lease to a national tenant. The subject property is a similar retail building with the same NOI, leased on short terms to local tenants with higher turnover. Compared with the sale, how should the subject's NOI multiplier and overall rate differ?
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