Recent market data for competing properties show vacancy rates of 8%, 12% and 6%. An appraiser uses the simple mean of these rates, with no further weighting, for a property with annual PGI of $240,000. There is no collection loss or other income. What is the annual EGI?
Correct Answer
C) $219,200
240000×(1−(0.08+0.12+0.06)/3) = 219200. Common errors: using the highest observed vacancy rate gives $211,200; using the lowest observed vacancy rate gives $225,600; deducting the sum of the three rates instead of their mean gives $177,600.
Why This Is the Correct Answer
Option C is correct because the mean vacancy is (8% + 12% + 6%) ÷ 3 = 26% ÷ 3 ≈ 8.67%, and $240,000 × (1 − 0.0867) ≈ $219,200. Exactly, the vacancy loss is $240,000 × 0.26 ÷ 3 = $20,800, so EGI is $240,000 − $20,800 = $219,200.
Why the Other Options Are Wrong
Option A: $177,600
Option A, $177,600, comes from deducting the sum of the three rates instead of their mean: $240,000 × (1 − 0.26). The rate to use is the average, 8.67%, giving $219,200.
Option B: $211,200
Option B, $211,200, uses only the highest observed rate: $240,000 × (1 − 0.12). The question requires the simple mean of all three rates, which gives $219,200.
Option D: $225,600
Option D, $225,600, uses only the lowest observed rate: $240,000 × (1 − 0.06). The simple mean of the three rates produces EGI of $219,200.
Add, divide, deduct
Add the observed rates, divide by how many there are, then deduct that average from potential income.
How to use: Use this three-step routine when a question asks for an average vacancy rate.
Exam Tip
Read exactly which statistic is requested; the highest, lowest and sum of the rates are common distractors.
Common Mistakes to Avoid
- -Subtracting the total of the rates instead of the average
- -Using only the highest or lowest observed rate
- -Applying the vacancy rate to an income figure other than PGI
Concept Deep Dive
Analysis
This question tests calculating a simple mean of vacancy rates and applying it to potential gross income. Add the three rates and divide by three, then reduce PGI by that average rate to get EGI.
Background Knowledge
Appraisers often estimate a vacancy and collection allowance from rates observed at competing properties. A simple mean is the sum of the observations divided by their number; once the allowance is chosen, it is deducted from potential gross income to reach effective gross income.
Real-World Application
An appraiser gathers vacancy data from three competing apartment complexes and, after considering whether any should be weighted more heavily, uses their average as the subject's stabilized vacancy allowance.
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