Annual PGI is $500,000. Vacancy loss is 5% of PGI and additional collection loss is 1.5% of that same PGI base. There is no other income. What annual effective gross income results?
Correct Answer
B) $467,500
500000−500000×0.05−500000×0.015 = 467500. Common errors: leaving out the 1.5% collection loss gives $475,000; leaving out the 5% vacancy loss gives $492,500; reporting the combined loss instead of EGI gives $32,500.
Why This Is the Correct Answer
Option B is correct because EGI = $500,000 - ($500,000 x 0.05) - ($500,000 x 0.015) = $500,000 - $25,000 - $7,500 = $467,500. Potential gross income minus vacancy and collection losses equals effective gross income, and there is no other income to add.
Why the Other Options Are Wrong
Option A: $32,500
Option A, $32,500, comes from $500,000 x 0.065 = $32,500, which reports the combined vacancy and collection loss instead of EGI. EGI is $500,000 - $32,500 = $467,500.
Option C: $475,000
Option C, $475,000, comes from $500,000 x 0.95 = $475,000, which leaves out the 1.5% collection loss. Deducting both losses gives $467,500.
Option D: $492,500
Option D, $492,500, comes from $500,000 x 0.985 = $492,500, which leaves out the 5% vacancy loss. Deducting both losses gives $467,500.
PGI minus V and C
PGI minus vacancy minus collection loss equals EGI. When both rates use the same PGI base, you can add them first: 5% + 1.5% = 6.5%.
How to use: Use the combined rate shortcut only when both losses are stated on the same base.
Exam Tip
Check whether each loss is stated on the same base; here both are on PGI, so 93.5% of PGI is EGI. Make sure the answer is EGI and not the loss amount.
Common Mistakes to Avoid
- -Deducting only vacancy and forgetting collection loss
- -Reporting the loss total as EGI
- -Applying the second loss to an already reduced base when the stem says the same base
Concept Deep Dive
Analysis
This calculation tests the step from potential gross income to effective gross income. Both the 5% vacancy loss and the 1.5% collection loss are taken from the same PGI base and subtracted. The distractors omit one of the losses or report the loss total instead of EGI.
Background Knowledge
Potential gross income is the total income a property could produce at full occupancy. Subtracting allowances for vacancy and collection loss, and adding any other income, gives effective gross income. Operating expenses are then deducted from EGI to reach net operating income.
Real-World Application
An appraiser estimates income for a fourplex using market rents for all units. Market surveys support a vacancy allowance, and the tenant history supports a separate collection-loss allowance. Both are deducted from PGI to reach the EGI used in the direct capitalization analysis.
More Income Approach Questions
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