Annual PGI is $720,000. Vacancy loss is 4% of PGI and additional collection loss is 3% of that same PGI base. No other income applies. What EGI results?
Correct Answer
B) $669,600
720000×(1−0.04−0.03) = 669600. Common errors: leaving out the 3% collection loss gives $691,200; leaving out the 4% vacancy loss gives $698,400; reporting the combined loss instead of EGI gives $50,400.
Why This Is the Correct Answer
Option B is correct because EGI equals PGI minus vacancy and collection losses: $720,000 × (1 − 0.04 − 0.03) = $720,000 × 0.93 = $669,600. Both losses apply to the same PGI base, and no other income is added. This follows the standard sequence of potential gross income minus vacancy and collection losses equals effective gross income.
Why the Other Options Are Wrong
Option A: $50,400
Option A, $50,400, reports the combined loss instead of EGI: $720,000 × 0.07 = $50,400. EGI is what remains after that loss, $720,000 − $50,400 = $669,600.
Option C: $691,200
Option C, $691,200, leaves out the 3% collection loss: $720,000 × 0.96 = $691,200. Deducting both losses gives $720,000 × 0.93 = $669,600.
Option D: $698,400
Option D, $698,400, leaves out the 4% vacancy loss: $720,000 × 0.97 = $698,400. Deducting both losses gives $720,000 × 0.93 = $669,600.
PGI, EGI, NOI ladder
Start at potential, subtract losses to reach effective, subtract expenses to reach net.
How to use: Use this ladder to know which deductions belong at each step.
Exam Tip
Note whether each loss percentage is applied to the same base or to a reduced base, since that changes the arithmetic.
Common Mistakes to Avoid
- -Deducting only one of the two loss allowances
- -Reporting the loss amount as EGI
- -Applying the second loss to an already reduced base when the question specifies the same PGI base
Concept Deep Dive
Analysis
This question tests the step from potential gross income to effective gross income. Both the 4% vacancy loss and the 3% collection loss are computed on the same PGI base, so together they remove 7% of PGI. EGI is $720,000 × (1 − 0.04 − 0.03) = $669,600.
Background Knowledge
Potential gross income is the income at full occupancy before losses. Effective gross income subtracts vacancy and collection losses and adds any other income. Net operating income then subtracts operating expenses from EGI.
Real-World Application
An appraiser analyzing a fourplex estimates market vacancy and a separate allowance for tenants who fall behind on rent. She applies both to potential gross income to reach effective gross income. She then deducts operating expenses to estimate NOI.
More Income Approach Questions
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Previous Question
A property produces annual NOI of $160,000. The equity interest has a known value of $500,000 and a 12% current dividend rate, and the annual mortgage constant is 8%. Using the mortgage residual technique, what is the total property value?
Next Question
The subject property is a four-unit apartment building with potential rent of $60,000 a year and stabilized vacancy and credit loss of 5% of rent. The owner's records also show $2,400 of collected fees for the on-site parking spaces, $3,000 of net receipts from renting furniture to tenants, and $1,600 of net profit from a vending business the owner runs. Operating expenses of the real property are $19,400 a year, and the market overall rate is 8%. What is the indicated value of the real property?