Annual potential gross rent for the subject property is $120,000, and combined vacancy and collection loss is 5% of rent. There is no other income. All annual property expenses, including real estate taxes and reserves but excluding debt service, total $38,000. Using an overall rate of 9%, what is the indicated value, rounded to the nearest dollar?
Correct Answer
B) $844,444
120000×(1−0.05)−38000 = 76000; 76000÷0.09 = 844444.44. Common errors: capitalizing EGI instead of NOI gives $1,266,667; not deducting the 5% vacancy and collection loss gives $911,111; misplacing the decimal in the 9% rate gives $84,444.
Why This Is the Correct Answer
Option B is correct because EGI is $120,000 × 0.95 = $114,000, NOI is $114,000 − $38,000 = $76,000, and $76,000 ÷ 0.09 = $844,444 rounded. Expenses include taxes and reserves but exclude debt service.
Why the Other Options Are Wrong
Option A: $84,444
Option A, $84,444, comes from misplacing the decimal in the rate (($120,000 × 0.95 − $38,000) ÷ 0.9). Using 0.09 gives $76,000 ÷ 0.09 = $844,444.
Option C: $911,111
Option C, $911,111, results from skipping the 5% vacancy and collection loss (($120,000 − $38,000) ÷ 0.09). Deducting the loss first gives $76,000 ÷ 0.09 = $844,444.
Option D: $1,266,667
Option D, $1,266,667, capitalizes EGI instead of NOI ($120,000 × 0.95 ÷ 0.09). Deducting the $38,000 of expenses gives $76,000 ÷ 0.09 = $844,444.
PGI, EGI, NOI, then divide
Take off losses, take off expenses, then divide by the rate as a decimal.
How to use: Use the ladder and a decimal check before selecting an answer.
Exam Tip
Check the magnitude: at a 9% rate, value should be roughly eleven times NOI.
Common Mistakes to Avoid
- -Capitalizing EGI instead of NOI
- -Skipping the vacancy and collection loss
- -Entering 9% as 0.9
Concept Deep Dive
Analysis
This question tests processing PGI to NOI and capitalizing at 9%. EGI is PGI after the 5% loss, NOI is EGI minus $38,000 of expenses, and value is NOI divided by 0.09. Distractors skip a step or misplace the decimal.
Background Knowledge
Potential gross income minus vacancy and collection loss equals effective gross income; EGI minus operating expenses equals NOI. Direct capitalization divides NOI by an overall rate extracted on the same expense convention. Real estate taxes and reserves are included in expenses when the rate is derived that way.
Real-World Application
An appraiser values a duplex portfolio with $120,000 of scheduled rent, a 5% loss allowance and $38,000 of expenses including taxes and reserves. Capitalizing the $76,000 NOI at 9% indicates about $844,444.
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