Annual potential rental income for the subject is $200,000. Vacancy and collection loss is 8% of that amount, and there is no other income. Annual operating expenses of $65,000 include property taxes and the same reserve allowance used to extract the 9% overall rate; they exclude debt service. What value is indicated by direct capitalization, rounded to the nearest dollar?
Correct Answer
A) $1,322,222
(200000×(1−0.08)−65000) ÷ 0.09 = 1322222.22. Common errors: not deducting the vacancy and collection loss gives $1,500,000; capitalizing EGI instead of NOI gives $2,044,444; applying the vacancy loss after deducting expenses gives $1,380,000.
Why This Is the Correct Answer
Option A is correct because EGI is $200,000 × 0.92 = $184,000. NOI is $184,000 − $65,000 = $119,000, and value is $119,000 ÷ 0.09 = $1,322,222. The expenses include taxes and reserves consistent with the rate, and debt service is properly excluded.
Why the Other Options Are Wrong
Option B: $1,380,000
Option B, $1,380,000, applies the vacancy loss after deducting expenses: ($200,000 − $65,000) × 0.92 ÷ 0.09. Vacancy comes off potential gross income first: ($184,000 − $65,000) ÷ 0.09 = $1,322,222.
Option C: $1,500,000
Option C, $1,500,000, does not deduct the 8% vacancy and collection loss: ($200,000 − $65,000) ÷ 0.09. Including it gives ($184,000 − $65,000) ÷ 0.09 = $1,322,222.
Option D: $2,044,444
Option D, $2,044,444, capitalizes EGI instead of NOI: $184,000 ÷ 0.09. Operating expenses must be deducted first, giving $119,000 ÷ 0.09 = $1,322,222.
Vacancy first, expenses second, rate last
Take vacancy off potential gross, take expenses off effective gross, then divide NOI by the rate.
How to use: Use this order on any multi-step direct capitalization problem.
Exam Tip
Vacancy is a percentage of potential gross income, not of income after expenses. Do not deduct debt service as an operating expense.
Common Mistakes to Avoid
- -Applying vacancy after operating expenses
- -Capitalizing effective gross income instead of NOI
- -Skipping the vacancy and collection allowance
Concept Deep Dive
Analysis
This question tests the full direct capitalization sequence. Vacancy and collection loss is deducted from potential gross income to get EGI, operating expenses are deducted to get NOI, and NOI is divided by the overall rate. Each step must be in the right order.
Background Knowledge
Potential gross income less vacancy and collection loss equals effective gross income, and effective gross income less operating expenses equals NOI. Direct capitalization divides NOI by an overall rate that was extracted using the same expense conventions.
Real-World Application
An appraiser valuing a small retail building applies a market vacancy allowance to scheduled rent, deducts operating expenses including taxes and reserves, and capitalizes the NOI at a rate extracted from sales analyzed the same way.
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