An appraiser is verifying the sale of a 12-unit apartment building that sold for $1,150,000 cash at an 8% overall rate, based on NOI after replacement reserves. Potential gross income is $170,000, vacancy and collection loss is 5% of PGI, the replacement reserve is $4,000, and the buyer's annual debt service is $66,000. What are the implied annual operating expenses before reserves?
Correct Answer
A) $65,500
NOI implied by the sale is $1,150,000 × 0.08 = $92,000, and EGI is $170,000 × 0.95 = $161,500. Total deductions are therefore $161,500 − $92,000 = $69,500, and removing the $4,000 reserve leaves operating expenses of $65,500. The figure $69,500 forgets to take out the reserve, $74,000 starts from potential income instead of EGI, and $78,000 makes both errors. The buyer's debt service is financing and is not an operating expense.
Why This Is the Correct Answer
Option A is correct because the sale implies NOI of $1,150,000 × 0.08 = $92,000 and EGI of $170,000 × 0.95 = $161,500. The gap of $69,500 covers operating expenses plus the reserve. Subtracting the $4,000 reserve leaves $65,500 of operating expenses.
Why the Other Options Are Wrong
Option B: $69,500
Option B, $69,500, is the total of all deductions: $161,500 − $92,000. It still contains the $4,000 reserve, while the amount sought excludes it, so the correct figure is $69,500 − $4,000 = $65,500.
Option C: $74,000
Option C, $74,000, subtracts NOI and the reserve from potential income: $170,000 − $92,000 − $4,000. Potential income overstates what is collected, so the $8,500 vacancy and collection loss is wrongly counted as expense. The correct start is EGI of $161,500, which gives $65,500.
Option D: $78,000
Option D, $78,000, is $170,000 − $92,000. It ignores the 5% loss and also leaves the reserve in the result. Starting from EGI of $161,500 and removing the $4,000 reserve gives $65,500.
Top minus bottom equals middle
EGI is the top line and NOI is the bottom line, so the difference is everything deducted between them. Then peel off any item that is not part of the figure you need.
How to use: Use this whenever value and rate are known and an expense figure is missing.
Exam Tip
When both a price and a rate are given, turn them into NOI first. Then check whether the expense figure you need includes or excludes a reserve.
Common Mistakes to Avoid
- -Subtracting NOI from potential gross income instead of effective gross income
- -Treating total deductions as operating expenses when a reserve is stated separately
- -Multiplying the price by the rate and stopping at NOI
Concept Deep Dive
Analysis
This tests whether you can run the income statement in reverse. The price and rate give NOI, the potential income and loss give EGI, and the gap between them is the total deducted above the NOI line. The last step is to separate the stated reserve from the operating expenses being asked for.
Background Knowledge
Direct capitalization links value, income and rate through V = I/R, so any two of them reveal the third. Above NOI, the income statement moves from potential gross income to effective gross income and then deducts expenses. A market rate must be read with its income convention, including whether a reserve was deducted.
Real-World Application
An appraiser verifying a sale knows the price, the reported overall rate and the rent roll, but the seller will not release the expense statement. Backing into the implied expenses lets the appraiser test whether the reported rate is believable against comparable operating costs.
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?
An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
The subject property is a duplex with both units rented at $1,000 per month, while market rent is $1,250 per month per unit. Stabilized vacancy and credit loss is 5% of PGI at either rent level. The owner pays $11,400 a year for property taxes, insurance and maintenance contracts. These costs are at market levels and would not change if rents moved to market. What operating expense ratio, based on EGI, should the appraiser expect at market rent?
Next Question
Annual NOI for the subject property is $180,000, and the building is known to be worth $1,500,000. The land capitalization rate is 6% and the building capitalization rate is 9%. What total property value does the land residual technique indicate?