A review appraiser is testing a report that values a 10-unit apartment building at $1,500,000 using a 7.8% overall rate. Operating expenses other than management total $54,000, and management is 5% of effective gross income. What effective gross income does the reported value reflect?
Correct Answer
D) $180,000
Implied NOI is $1,500,000 × 0.078 = $117,000, so $117,000 + $54,000 = $171,000 must equal 95% of EGI once the 5% management fee is taken. EGI is therefore $171,000 ÷ 0.95 = $180,000. The $171,000 answer omits management, $176,850 bases the fee on NOI, and $179,550 adds 5% rather than dividing by 0.95.
Why This Is the Correct Answer
Option D is correct because NOI of $117,000 and the other operating expenses of $54,000 together equal 95% of EGI once the 5% fee is taken. Dividing $171,000 by 0.95 gives $180,000. As a check, $180,000 less $9,000 of management and $54,000 of other expenses equals $117,000.
Why the Other Options Are Wrong
Option A: $171,000
Option A, $171,000, is $117,000 + $54,000, which leaves out the management fee altogether. EGI must also pay 5% management, so it is $171,000 ÷ 0.95 = $180,000.
Option B: $176,850
Option B, $176,850, adds 5% of NOI to $171,000: $117,000 × 0.05 = $5,850. The fee is based on EGI rather than NOI, so the fee is $9,000 and EGI is $180,000.
Option C: $179,550
Option C, $179,550, is $171,000 × 1.05. This calculates the fee on $171,000 rather than on EGI, so the fee is too small. Dividing by 0.95 gives $180,000.
Percent of the unknown means divide
When an expense is a percentage of the figure being solved for, divide by one minus that percentage. Then run the numbers forward to check.
How to use: Use this when a management fee or expense ratio is tied to the EGI you need to find.
Exam Tip
Answers on this type of problem can be very close together, so test your choice forward. The correct EGI reproduces the stated NOI exactly.
Common Mistakes to Avoid
- -Adding the management percentage instead of dividing by the remaining share
- -Calculating the fee on NOI rather than EGI
- -Omitting a percentage expense when reversing the income statement
Concept Deep Dive
Analysis
A percentage expense creates a small algebra problem, because the fee depends on the very EGI you are solving for. After NOI and the fixed-dollar expenses are combined, the remaining share of EGI is 95%. Dividing by that share resolves the circular relationship.
Background Knowledge
Net operating income is what remains after expenses are subtracted from effective gross income. Some expenses are stated in dollars and others, such as management, as a percentage of EGI. When reversing the calculation, a percentage-of-EGI expense is handled by dividing by the share of EGI that remains.
Real-World Application
A reviewer wants to know what collections an owner's value claim assumes. Because the management contract charges a percentage of collections, the reviewer solves for EGI algebraically and compares it with the rent roll.
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Previous Question
The subject property is a four-unit apartment building with potential rent of $60,000 a year and stabilized vacancy and credit loss of 5% of rent. The owner's records also show $2,400 of collected fees for the on-site parking spaces, $3,000 of net receipts from renting furniture to tenants, and $1,600 of net profit from a vending business the owner runs. Operating expenses of the real property are $19,400 a year, and the market overall rate is 8%. What is the indicated value of the real property?
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