A client plans to build a 10-unit apartment building and needs a completed value of $1,800,000. The overall rate for similar properties is 7.5%. Forecast operating expenses are $81,000, laundry income net of losses is $4,500, and vacancy and collection loss is 10% of potential rental income. The client paid $350,000 for the land. What annual potential rental income is required?
Correct Answer
C) $235,000
Required NOI is $1,800,000 × 0.075 = $135,000, so required EGI is $135,000 + $81,000 = $216,000. Laundry income covers $4,500, leaving $211,500 to come from effective rent, and potential rent must be $211,500 ÷ 0.90 = $235,000. The figure $232,650 adds 10% instead of dividing by 0.90, $211,500 skips the vacancy gross-up, and $240,000 applies the gross-up without removing laundry income. The land cost does not enter the income calculation.
Why This Is the Correct Answer
Option C is correct because the value and rate require NOI of $135,000, and adding $81,000 of expenses requires EGI of $216,000. With $4,500 from laundry, effective rent must be $211,500. Since effective rent is 90% of potential rent, potential rent is $211,500 ÷ 0.90 = $235,000.
Why the Other Options Are Wrong
Option A: $211,500
Option A, $211,500, is the required effective rent, $216,000 − $4,500. It stops before allowing for the 10% loss. Potential rent must be higher, at $211,500 ÷ 0.90 = $235,000.
Option B: $232,650
Option B, $232,650, is $211,500 × 1.10. The 10% loss is measured on potential rent, not effective rent, so adding 10% falls short. Dividing by 0.90 gives $235,000.
Option D: $240,000
Option D, $240,000, is $216,000 ÷ 0.90. It grosses up all of EGI, including $4,500 of laundry income that is already effective and is not rent. Removing it first gives $235,000.
Reverse each step in order
Going down the statement you multiply by 0.90, so going up you divide by 0.90. Each backward step undoes its matching forward step.
How to use: Use this whenever a problem starts from a value and asks for rent or potential income.
Exam Tip
Percent-of-a-larger-base problems reverse by division. Check your answer by running it forward to confirm it reproduces the stated value.
Common Mistakes to Avoid
- -Adding the vacancy percentage rather than dividing by the collection factor
- -Grossing up income that is already effective
- -Forgetting to add expenses back to NOI
Concept Deep Dive
Analysis
The calculation runs the whole income statement upward from a value target. Each step reverses a forward step: multiply value by rate, add expenses, subtract other income, and divide by the collection factor. A 10% loss on potential rent means dividing by 0.90, not adding 10%, and the land cost plays no part.
Background Knowledge
Effective gross income is what remains after vacancy and collection loss, and it can also include other income from the real property. Working from a target value is common in feasibility analysis, because it shows what rents a project must achieve. Income already stated at an effective amount receives no further loss adjustment.
Real-World Application
A developer needs a planned building to reach a target value before a lender will commit. An appraiser works back to the rent required and compares it with market rents to judge whether the project is feasible.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
Annual PGI is $250,000 and combined vacancy and collection loss is explicitly 12% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
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Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
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The subject property is a fourplex with annual NOI of $42,000. A similar fourplex recently sold for $650,000 with below-market seller financing. The appraiser estimates its cash-equivalent price at $600,000, and its annual NOI is $48,000. What is the indicated value of the subject by direct capitalization?