An appraiser is developing an overall rate for a small warehouse from its physical components. Land sales indicate that the land represents 30% of total property value. Ground lease data indicate a land capitalization rate of 6%, and the building capitalization rate, including recapture, is 10%. Lenders on similar warehouses quote a 7.5% annual mortgage constant at a 70% loan-to-value ratio. What overall rate does the band of investment indicate?
Correct Answer
C) 8.80%
The physical band weights each component rate by its share of value: 0.30 × 6% + 0.70 × 10% = 1.8% + 7.0% = 8.80%. Swapping the weights gives 7.20%, and a simple average gives 8.00%. Using the building rate alone gives 10.00%. The lenders' terms belong to a financial band, not this one.
Why This Is the Correct Answer
Option C is correct because each physical component's rate is weighted by its share of total value: 0.30 × 6% = 1.8% for land and 0.70 × 10% = 7.0% for the building. These sum to 8.80%.
Why the Other Options Are Wrong
Option A: 7.20%
Option A, 7.20%, swaps the weights: 0.70 × 6% + 0.30 × 10%. Land is the 30% share, so the correct total is 0.30 × 6% + 0.70 × 10% = 8.80%.
Option B: 8.00%
Option B, 8.00%, averages the rates: (6% + 10%) ÷ 2. That would be right only if land and building were equal shares; at 30% and 70% the result is 8.80%.
Option D: 10.00%
Option D, 10.00%, is the building rate alone. The rate must reflect the whole property, including the 30% land share at 6%, which brings it down to 8.80%.
Share Times Rate, Then Add
Whether the bands are debt and equity or land and building, the method is the same: share times rate for each, then add.
How to use: Use this routine after confirming which pair of components the facts call for.
Exam Tip
Decide first whether the facts describe a financial or a physical band. A figure from the other kind of band does not belong in the weighting.
Common Mistakes to Avoid
- -Applying the land share to the building rate
- -Averaging the two rates without weighting them
- -Mixing financing terms into a land-and-building band
Concept Deep Dive
Analysis
The band of investment can weight physical components as well as financial ones. Here the bands are land and building, each with its own rate and share of value. The candidate must find the building share as the remainder and recognize that the lender's terms have no place in this calculation.
Background Knowledge
A band of investment combines the rates attributable to components of an investment into a weighted average. The components can be financial, such as debt and equity, or physical, such as land and improvements. The building rate typically exceeds the land rate because the building's rate also provides for recapture.
Real-World Application
An appraiser has reliable land and building rate evidence for a small industrial property. The appraiser weights the two rates by value shares and compares the result with rates extracted from sales before relying on it.
More Income Approach Questions
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