A property's annual NOI is $120,000 and does not change. If the capitalization rate used in direct capitalization decreases from 8.0% to 7.5%, how does the indicated value change?
Correct Answer
C) It rises by about 6.7 percent
Holding annual NOI at $120,000 and applying direct capitalization V=NOI/R, initial value=120000/0.08=$1,500,000 and new value=120000/0.075=$1,600,000. Change=100000/1500000×100=6.6667%, about 6.7%. The cap-rate decrease is 0.5 percentage points, not a 0.5% value change. The comparison holds all other inputs fixed.
Why This Is the Correct Answer
Option C is correct because $120,000 / 0.08 = $1,500,000 and $120,000 / 0.075 = $1,600,000. The $100,000 increase divided by the starting value of $1,500,000 equals about 6.67%, which rounds to about 6.7%. The rate fell, so the indicated value rose.
Why the Other Options Are Wrong
Option A: It falls by about 6.7 percent
Option A says value falls by about 6.7 percent, which reverses the direction. Lowering the cap rate from 8.0% to 7.5% raises value from $1,500,000 to $1,600,000, an increase of about 6.7%, not a decrease.
Option B: It rises by exactly 0.5 percent
Option B says value rises by exactly 0.5 percent, which confuses the 0.5 percentage-point drop in the cap rate with the change in value. The value change is $100,000 / $1,500,000, or about 6.7%.
Option D: It remains unchanged at $1,500,000
Option D says value remains unchanged at $1,500,000, but $1,500,000 is only the value at 8.0%. At 7.5% the same $120,000 NOI capitalizes to $120,000 / 0.075 = $1,600,000.
Rate down, value up
In V = I / R, the rate sits underneath like a seesaw: push the rate down and value goes up. Measure the percent change against the starting value.
How to use: Use this whenever a question changes only the cap rate and asks how value moves.
Exam Tip
Separate percentage points of rate change from percentage change in value; compute both values and divide the difference by the original value.
Common Mistakes to Avoid
- -Treating a 0.5 percentage-point rate change as a 0.5% value change
- -Assuming a lower cap rate lowers value
- -Dividing the value change by the new value instead of the original value
Concept Deep Dive
Analysis
This question tests the inverse relationship between the capitalization rate and value in direct capitalization. With NOI held at $120,000, compute the value at each rate and then measure the percentage change from the starting value. A lower cap rate means each dollar of income is worth more, so value must rise.
Background Knowledge
Direct capitalization converts a single year's NOI to value by dividing by an overall capitalization rate (V = I / R). Because the rate is in the denominator, value moves opposite to the rate, and small rate changes can produce large value changes.
Real-World Application
An appraiser valuing a small retail center finds that recent sales support a 7.5% cap rate rather than the 8.0% used in last year's report. With NOI unchanged, the indicated value rises by roughly 6.7%, and the appraiser explains the rate support in the report.
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Previous Question
An appraiser reviewing a trainee's work finds that the trainee extracted an 8% overall rate from sales of older fourplexes similar to the subject. The trainee then added 2.5 percentage points as a recapture allowance for the building's remaining economic life before capitalizing NOI. What is the main problem with this step?
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