The subject property has annual potential rental income of $240,000, vacancy and collection loss of 5% of that amount and no other income. Annual operating expenses of $48,000 include property taxes and the same reserve allowance used to extract the 8% overall rate; they exclude debt service. What value is indicated by direct capitalization, rounded to the nearest dollar?
Correct Answer
A) $2,250,000
(240000×(1−0.05)−48000) ÷ 0.08 = 2250000. Common errors: not deducting the vacancy and collection loss gives $2,400,000; capitalizing EGI instead of NOI gives $2,850,000; applying the vacancy loss after deducting expenses gives $2,280,000.
Why This Is the Correct Answer
Option A is correct because EGI is $240,000 × 0.95 = $228,000, NOI is $228,000 − $48,000 = $180,000, and $180,000 ÷ 0.08 = $2,250,000. The expense treatment matches the way the 8% rate was extracted, so the rate and income are compatible.
Why the Other Options Are Wrong
Option B: $2,280,000
Option B, $2,280,000, comes from deducting expenses first and then applying the vacancy loss to the remainder: ($240,000 − $48,000) × 0.95 ÷ 0.08. Vacancy is a deduction from gross income, so the correct order gives ($228,000 − $48,000) ÷ 0.08 = $2,250,000.
Option C: $2,400,000
Option C, $2,400,000, results from ignoring the vacancy and collection loss: ($240,000 − $48,000) ÷ 0.08. The correct NOI after the 5% loss is $180,000, which capitalizes to $2,250,000.
Option D: $2,850,000
Option D, $2,850,000, comes from capitalizing EGI of $228,000 at 8% without deducting the $48,000 of expenses. The overall rate applies to NOI, so the value is $180,000 ÷ 0.08 = $2,250,000.
IRV: Income over Rate
Value equals Income divided by Rate (V = I ÷ R), where the income is NOI built on the same basis as the rate.
How to use: Use IRV to set up any one-year direct capitalization problem once NOI is calculated.
Exam Tip
Watch for wording about how the cap rate was extracted; it tells you which expenses belong in NOI so that income and rate match.
Common Mistakes to Avoid
- -Capitalizing EGI rather than NOI
- -Applying vacancy after expenses instead of to gross income
- -Using a rate extracted on a different expense basis than the subject NOI
Concept Deep Dive
Analysis
This question combines building NOI from potential income with direct capitalization. Apply the 5% loss to potential rent to get EGI, deduct the $48,000 of expenses (which include the reserve used to extract the rate), and divide the NOI by the 8% overall rate.
Background Knowledge
Direct capitalization divides a single year's NOI by an overall rate. The income and the rate must be compatible: if the rate was extracted from sales whose NOI included a reserve deduction, the subject NOI should also include that reserve.
Real-World Application
An appraiser extracts overall rates from apartment sales whose NOI deducted a replacement reserve. To stay consistent, she includes the same type of reserve in the subject's expenses before dividing NOI by the extracted rate.
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?
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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?
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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?
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Previous Question
The subject property is an eight-unit apartment building appraised at $1,400,000 using an 8.5% overall rate. Operating expenses are $61,000 and annual debt service is $75,000. Potential rental income is $200,000, and parking income of $6,000 is collected separately with no loss. What vacancy and collection loss, as a percentage of potential rental income, does the appraisal reflect?
Next Question
A property has annual NOI of $112,000 and annual debt service of $70,000. The mortgage interest is valued at $800,000. The equity dividend rate is 10%. What total property value does the equity residual technique indicate?