The subject property is a 15-unit apartment building with potential gross income of $300,000, valued using an 8% overall rate. A competing complex has opened, and the appraiser raises stabilized vacancy and collection loss from 5% to 7% of PGI. The insurance premium rises $4,000 per year, and owner-paid utilities fall $1,500 per year at the lower occupancy. The overall rate does not change. What is the decrease in indicated value?
Correct Answer
C) $106,250
The extra loss is $300,000 × 0.02 = $6,000 and insurance adds $4,000, while the utility saving returns $1,500, so NOI falls by $8,500. At an unchanged 8% rate, value falls by $8,500 ÷ 0.08 = $106,250. The figure $125,000 ignores the utility saving, $75,000 counts the vacancy change alone, and $56,250 leaves out the insurance increase.
Why This Is the Correct Answer
Option C is correct because NOI falls by $6,000 from the added loss and $4,000 from insurance, and rises by $1,500 from lower utilities, for a net drop of $8,500. Capitalizing that change at 8% gives $8,500 ÷ 0.08 = $106,250. With an unchanged rate, the change in value follows directly from the change in NOI.
Why the Other Options Are Wrong
Option A: $56,250
Option A, $56,250, is ($6,000 − $1,500) ÷ 0.08. It leaves out the $4,000 insurance increase, which lowers NOI. Including it gives $8,500 ÷ 0.08 = $106,250.
Option B: $75,000
Option B, $75,000, is $6,000 ÷ 0.08. It considers only the vacancy change and ignores both expense changes. The net NOI change of $8,500 gives $106,250.
Option D: $125,000
Option D, $125,000, is ($6,000 + $4,000) ÷ 0.08. It ignores the $1,500 utility saving that partly offsets the losses. Netting it gives $8,500 ÷ 0.08 = $106,250.
Net it, then divide it
Add up each dollar change to NOI with its proper sign, then divide the net change by the rate. Do not capitalize each item until the signs are settled.
How to use: Use this whenever several income or expense lines change at once and the rate stays the same.
Exam Tip
A value change can be found without calculating value before and after. Find the net change in NOI first and divide it by the unchanged rate.
Common Mistakes to Avoid
- -Assuming all expenses stay level when occupancy falls
- -Capitalizing only the largest change and ignoring the others
- -Adding a cost saving to the loss instead of netting it
Concept Deep Dive
Analysis
You do not need the whole property value to answer this. With the rate unchanged, the change in value equals the change in NOI divided by the rate. The skill is netting three separate effects, including a variable expense that moves in the owner's favor when occupancy falls.
Background Knowledge
Fixed expenses such as property insurance do not vary with occupancy, while variable expenses such as utilities do. When occupancy falls, income drops but variable costs may also drop, so NOI falls by less than the lost income alone. Because capitalization divides by a small rate, modest NOI changes create large value changes.
Real-World Application
A new apartment complex opens nearby, so an appraiser raises the vacancy allowance on the subject and reflects a new insurance quote. Some tenant-related utility costs ease as occupancy drops, and the appraiser shows the owner how the net NOI change affects value.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
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