Annual PGI for the subject is $150,000, with combined vacancy and collection loss of 7% of PGI and no other income. Operating expenses, excluding debt service, are 35% of EGI. Using a 9.5% overall rate, what is the indicated value, rounded to the nearest dollar?
Correct Answer
B) $954,474
150000×0.93×0.65÷0.095 = 954473.68. Common errors: not deducting the 7% loss gives $1,026,316; capitalizing EGI instead of NOI gives $1,468,421; applying the 35% expense ratio to PGI instead of EGI gives $915,789.
Why This Is the Correct Answer
Option B is correct because EGI = $150,000 × 0.93 = $139,500, NOI = $139,500 × 0.65 = $90,675, and $90,675 ÷ 0.095 = $954,473.68, or $954,474. The 35% expense ratio is applied to EGI as the problem states.
Why the Other Options Are Wrong
Option A: $915,789
Option A, $915,789, applies the 35% expense ratio to PGI instead of EGI: $150,000 × (1 − 0.07 − 0.35) ÷ 0.095 = $87,000 ÷ 0.095 = $915,789. Expenses are 35% of EGI, giving $139,500 × 0.65 ÷ 0.095 = $954,474.
Option C: $1,026,316
Option C, $1,026,316, skips the 7% loss: $150,000 × 0.65 ÷ 0.095 = $1,026,316. Deducting the loss first gives $150,000 × 0.93 × 0.65 ÷ 0.095 = $954,474.
Option D: $1,468,421
Option D, $1,468,421, capitalizes EGI instead of NOI: $150,000 × 0.93 ÷ 0.095 = $1,468,421. Deducting expenses at 35% of EGI gives NOI of $90,675 and value of $954,474.
Check the ratio's base
A percentage means nothing until you know what it is a percentage of. Expenses of 35% of EGI must be taken from EGI, not PGI.
How to use: Use this to apply each percentage in a problem to its stated base.
Exam Tip
When a problem chains several percentages, write out each intermediate figure so each percentage is applied to the correct base.
Common Mistakes to Avoid
- -Applying an EGI-based expense ratio to PGI
- -Capitalizing EGI instead of NOI
- -Skipping the vacancy and collection loss
Concept Deep Dive
Analysis
This question tests a multi-step capitalization where expenses are a percentage of EGI, not PGI. First apply the 7% loss to PGI to get EGI, then keep 65% of EGI as NOI, then divide by 9.5%. Applying the expense ratio to the wrong base or skipping a step produces the distractors.
Background Knowledge
Vacancy and collection loss reduces potential gross income to effective gross income. An operating expense ratio is usually stated as a share of EGI, so NOI equals EGI times one minus the ratio. Direct capitalization then divides NOI by the overall rate.
Real-World Application
An appraiser valuing a garden apartment complex applies a market vacancy rate to potential rent, then applies an expense ratio derived from comparable properties' EGI, and capitalizes the resulting NOI at a market-extracted overall rate.
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