An appraiser previously capitalized a property's annual NOI of $80,000 at a 6.4% overall rate. NOI remains the same, but the overall rate is now 8.0%. What is the new indicated value?
Correct Answer
D) $1,000,000
Original value is $80,000 ÷ 0.064 = $1,250,000. New value is $80,000 ÷ 0.08 = $1,000,000. Thus value decreases $250,000, or 20%; a 1.6-percentage-point rate change is not itself a value percentage change.
Why This Is the Correct Answer
Option D is correct because the new value is $80,000 ÷ 0.08 = $1,000,000. With NOI unchanged, a higher overall rate produces a lower value; the original value at 6.4% was $1,250,000, so value falls by $250,000.
Why the Other Options Are Wrong
Option A: $1,250,000
Option A, $1,250,000, is the original value at the old rate ($80,000 ÷ 0.064). The question asks for the new value at 8.0%, which is $80,000 ÷ 0.08 = $1,000,000.
Option B: $80,000
Option B, $80,000, is simply the annual NOI. NOI must be divided by the overall rate to produce value: $80,000 ÷ 0.08 = $1,000,000.
Option C: $250,000
Option C, $250,000, is the decline in value ($1,250,000 − $1,000,000), not the new value. The new indicated value is $1,000,000.
Rate up, value down
With the same NOI, a higher cap rate divides into it fewer times, so value drops.
How to use: Use it to check that your new value moved in the right direction after a rate change.
Exam Tip
Read whether the question asks for the new value, the old value or the change; all three often appear as choices.
Common Mistakes to Avoid
- -Reporting the original value instead of the new value
- -Reporting the dollar change instead of the new value
- -Treating a 1.6-percentage-point rate change as a 1.6% value change
Concept Deep Dive
Analysis
This question tests the inverse relationship between capitalization rate and value when NOI is held constant. Divide the unchanged NOI by the new rate to get the new value. The distractors are the old value, the NOI itself and the size of the value change.
Background Knowledge
In direct capitalization, value equals NOI divided by the overall rate. With income fixed, value moves in the opposite direction of the cap rate, and the percentage change in value is not the same as the percentage-point change in the rate.
Real-World Application
Market cap rates for small industrial buildings rise as interest rates climb. An appraiser updating a valuation with the same NOI divides it by the higher market-supported rate and reports a lower value.
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