The subject property has annual PGI of $105,000, with combined vacancy and collection loss of 4% of PGI. Other property expenses total $15,000, plus an annualized leasing-cost allowance of $8,000 that is not included in that total. Market sales indicate a 10% overall rate on income calculated after these same deductions. What is the indicated value?
Correct Answer
A) $778,000
(105000×0.96−15000−8000)÷0.10 = 778000. Common errors: leaving out the leasing-cost allowance gives $858,000; not deducting the 4% loss gives $820,000; capitalizing EGI instead of NOI gives $1,008,000.
Why This Is the Correct Answer
Option A is correct because EGI is $105,000 × 0.96 = $100,800, NOI is $100,800 − $15,000 − $8,000 = $77,800, and value is $77,800 ÷ 0.10 = $778,000. The leasing allowance is deducted once because it is not included in the $15,000 of other expenses.
Why the Other Options Are Wrong
Option B: $820,000
Option B, $820,000, comes from skipping the 4% loss: ($105,000 − $15,000 − $8,000) ÷ 0.10. The correct NOI starts from EGI of $105,000 × 0.96 = $100,800, giving $77,800 ÷ 0.10 = $778,000.
Option C: $858,000
Option C, $858,000, results from leaving out the $8,000 leasing-cost allowance: ($105,000 × 0.96 − $15,000) ÷ 0.10. Including it gives ($100,800 − $15,000 − $8,000) ÷ 0.10 = $778,000.
Option D: $1,008,000
Option D, $1,008,000, comes from capitalizing EGI instead of NOI ($105,000 × 0.96 ÷ 0.10). Deducting both expense items first gives $77,800 ÷ 0.10 = $778,000.
Every expense once, no more
List each deduction the question names and check it off once: loss, other expenses, leasing allowance. Then divide the NOI by the rate.
How to use: Use the checklist when a question says an item is excluded from a total so you add it exactly once.
Exam Tip
Watch wording such as 'excluding' or 'in addition'; it tells you whether an item is already inside a stated total.
Common Mistakes to Avoid
- -Omitting an expense the question says is excluded from the total
- -Skipping the vacancy and collection loss deduction
- -Capitalizing EGI instead of NOI
Concept Deep Dive
Analysis
This question tests building NOI from PGI with a combined loss allowance and two separate expense items, then capitalizing at a rate extracted on the same income basis. The leasing-cost allowance is stated as excluded from the $15,000 of other expenses, so it must be deducted once in addition. Each distractor omits one step of the sequence.
Background Knowledge
Net operating income equals effective gross income minus all operating expenses recognized in the analysis, which can include an annualized allowance for leasing costs. Direct capitalization divides NOI by an overall rate extracted on the same income basis. Omitting or double-counting an expense distorts value by that expense divided by the rate.
Real-World Application
An appraiser valuing a small office building finds that the owner's expense summary omits leasing commissions and tenant improvement costs. The appraiser adds an annualized leasing-cost allowance as a separate line, consistent with how the market rate was extracted, before capitalizing NOI.
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?
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In a model separating base rent from ancillary real-estate receipts, which listed item belongs in the ancillary other-income line?
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An appraiser verifying the sale of a fourplex with owner-paid utilities finds a cash equivalent price of $432,000, and the buyer confirms pricing the property at a 7.5% overall rate. Annual PGI at the time of sale was $80,000, and stabilized vacancy and credit loss was 10% of PGI. There is no other income. What operating expense ratio, based on EGI, do these figures indicate?