The subject property is a 20-unit apartment building with stabilized annual NOI of $172,800. The most similar comparable sold 18 months ago at an overall rate of 8.50%. Resales of similar buildings show that overall rates for this property type have declined 50 basis points since that sale. What is the indicated value by direct capitalization?
Correct Answer
D) $2,160,000
A 50-basis-point decline moves the 8.50% rate to 8.00%, so value is $172,800 ÷ 0.08 = $2,160,000. Moving the rate up instead of down gives 9.00% and $1,920,000. Using the unadjusted rate gives $2,032,941, and splitting the difference at 8.25% gives $2,094,545.
Why This Is the Correct Answer
Option D is correct because 50 basis points equals 0.50 percentage point, and rates have fallen, so 8.50% − 0.50% = 8.00%. Value is then $172,800 ÷ 0.08 = $2,160,000. The adjusted rate reflects market conditions on the valuation date rather than on the older sale date.
Why the Other Options Are Wrong
Option A: $1,920,000
Option A, $1,920,000, moves the rate up: 8.50% + 0.50% = 9.00%, and $172,800 ÷ 0.09 = $1,920,000. Rates have fallen, so the correct calculation is $172,800 ÷ 0.08 = $2,160,000.
Option B: $2,032,941
Option B, $2,032,941, uses the rate from the sale date: $172,800 ÷ 0.085 = $2,032,941. That ignores the supported market change since the sale. The correct calculation is $172,800 ÷ 0.08 = $2,160,000.
Option C: $2,094,545
Option C, $2,094,545, averages the old and current rates: $172,800 ÷ 0.0825 = $2,094,545. The current rate is the one that fits the valuation date, so the correct calculation is $172,800 ÷ 0.08 = $2,160,000.
Hundred points, one percent
One hundred basis points equal one percentage point, so 50 basis points equal 0.50%. Rates and values move like the two ends of a seesaw.
How to use: Use this conversion whenever a problem states a rate change in basis points.
Exam Tip
Note the date of each sale and any stated market trend before using an extracted rate. Then check that your value moved the way the rate change implies: lower rate, higher value.
Common Mistakes to Avoid
- -Reading 50 basis points as 5 percentage points
- -Adjusting the rate in the wrong direction
- -Using an older sale's rate with no check on market conditions
Concept Deep Dive
Analysis
The problem adds a judgment step before the division. A rate from an older sale reflects the market on its sale date, so the appraiser must bring it to the valuation date. You need to read basis points correctly, apply the change in the stated direction, and then capitalize.
Background Knowledge
Market conditions can change between a comparable's sale date and the valuation date, and comparable data may need adjustment to reflect the conditions on the valuation date. One hundred basis points equal one percentage point. Value moves opposite to the capitalization rate, so a lower rate on the same income means a higher value.
Real-World Application
An appraiser's closest comparable closed well before the effective date, and recent resales show buyers now accept lower rates. The appraiser documents the shift with paired data and adjusts the extracted rate before capitalizing. The report explains why the applied rate differs from the rate on the sale date.
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