A 10-unit apartment building with identical units is listed for $1,083,000. Similar buildings sell at an effective gross income multiplier of 9.5, and stabilized vacancy/credit loss is 5% of PGI. There is no other income. What monthly rent per unit is needed to justify the list price?
Correct Answer
C) $1,000
The price implies EGI of $1,083,000 ÷ 9.5 = $114,000, and grossing up for loss gives potential rent of $114,000 ÷ 0.95 = $120,000. Over 10 units and 12 months that is $1,000 per unit. Treating EGI as potential rent gives $950, adding 5% instead of dividing by 0.95 gives $998, and spreading potential rent over 9.5 occupied units counts vacancy twice and gives $1,053.
Why This Is the Correct Answer
Option C is correct because $1,083,000 ÷ 9.5 = $114,000 of EGI, which requires $114,000 ÷ 0.95 = $120,000 of potential rent. Dividing by 10 units and 12 months gives $1,000 per unit per month.
Why the Other Options Are Wrong
Option A: $950
Option A, $950, treats EGI as potential rent: $114,000 ÷ 120. Potential rent comes before the 5% loss, so the correct figure is $120,000 ÷ 120 = $1,000.
Option B: $998
Option B, $998, grosses up by adding 5%: $114,000 × 1.05 ÷ 120 = $997.50. The loss is 5% of potential rent, so EGI is divided by 0.95, which gives $120,000 ÷ 120 = $1,000.
Option D: $1,053
Option D, $1,053, divides potential rent by 9.5 occupied units: $120,000 ÷ (9.5 × 12). Potential rent is already measured across all 10 units, so the correct figure is $120,000 ÷ (10 × 12) = $1,000.
Reverse the ladder, reverse the math
Going down the ladder you multiply by 0.95, so going up you divide by 0.95. Multiplying by 1.05 is not the same step.
How to use: Use this reminder whenever a question gives EGI and asks for potential rent.
Exam Tip
Test your answer by running it forward: $1,000 × 120 × 0.95 × 9.5 should return the asking price of $1,083,000.
Common Mistakes to Avoid
- -Grossing up by adding the loss percentage
- -Treating EGI as potential rent
- -Dividing potential rent by occupied units instead of total units
Concept Deep Dive
Analysis
The problem runs the multiplier in reverse to test an asking price. Dividing by the multiplier reaches EGI, and dividing by one minus the loss rate reaches potential rent. Only then is the result spread over all units and months.
Background Knowledge
Potential gross income assumes full occupancy, and effective gross income is what remains after vacancy and collection loss. Because the loss is a percentage of potential income, recovering potential income from EGI requires dividing by one minus the loss rate.
Real-World Application
A buyer wonders whether an asking price is supportable for a small apartment building. The appraiser translates the price into the rent per unit it requires, then compares that figure with rents at competing buildings.
More Income Approach Questions
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An appraiser is extracting an overall rate from the cash-equivalent sale of an apartment building at $2,000,000. The seller's statement shows income of $130,000 after deductions for on-site property management of $12,000, partnership accounting and investor reporting of $10,000, and the owner's personal vehicle costs of $4,000. All other deductions are property operating expenses. What overall rate does the sale indicate?