An appraiser is developing an overall rate for a 12-unit apartment building by the band of investment, based on 75% debt at a 6.5% mortgage constant and 25% equity at an 11% equity dividend rate. Before the report is issued, tighter credit raises the mortgage constant by 0.50 percentage point and the equity dividend rate by 1.00 percentage point. The loan-to-value ratio does not change. By how much does the indicated overall rate rise?
Correct Answer
B) 0.625 percentage point
Each change counts only at its band's weight: 0.75 × 0.50 + 0.25 × 1.00 = 0.625 percentage point, moving the overall rate from 7.625% to 8.25%. Counting only the equity change gives 0.250, averaging the two changes gives 0.750, and swapping the weights gives 0.875.
Why This Is the Correct Answer
Option B is correct because the debt change contributes 0.75 × 0.50 = 0.375 and the equity change contributes 0.25 × 1.00 = 0.25. Together they raise the overall rate by 0.625 percentage point, from 7.625% to 8.25%.
Why the Other Options Are Wrong
Option A: 0.250 percentage point
Option A, 0.250 percentage point, counts only the equity change: 0.25 × 1.00. The mortgage constant also rose, so the correct total is 0.375 + 0.25 = 0.625.
Option C: 0.750 percentage point
Option C, 0.750 percentage point, averages the two changes: (0.50 + 1.00) ÷ 2. The bands carry unequal weights, so the correct total is 0.75 × 0.50 + 0.25 × 1.00 = 0.625.
Option D: 0.875 percentage point
Option D, 0.875 percentage point, swaps the weights: 0.25 × 0.50 + 0.75 × 1.00. Debt holds the 75% share, so the correct total is 0.75 × 0.50 + 0.25 × 1.00 = 0.625.
Changes wear the same weights
A weighted average responds to changes with the same weights it uses for levels. Multiply each change by its band's share and add.
How to use: Use this shortcut whenever a band problem asks how much the overall rate moves.
Exam Tip
You can check a change question by computing the overall rate before and after. Here, 8.25% minus 7.625% confirms the weighted change.
Common Mistakes to Avoid
- -Adding the rate changes without weighting them
- -Averaging the changes as if the bands were equal
- -Assigning the debt weight to the equity change
Concept Deep Dive
Analysis
The problem tests the logic of a weighted average rather than a single computation of the overall rate. Each component's change reaches the overall rate only in proportion to that component's share of value. The starting rates are not needed, though they confirm the result.
Background Knowledge
An overall rate from the band of investment is a weighted average of the debt and equity rates. With high leverage, changes in the mortgage constant carry more weight than the same-sized change in the equity rate.
Real-World Application
As lenders tighten terms, an appraiser updates a band of investment for an apartment assignment. Because debt carries most of the weight, the rise in the mortgage constant accounts for more of the overall rate's increase than the larger rise in the equity rate.
More Income Approach Questions
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Previous Question
The subject property is a 12-unit apartment building with stabilized annual NOI of $108,000. An appraiser applies a 7.5% overall rate from sales of similar buildings. Those sales, and others in the market, also closed at $138,000 to $150,000 per unit. What should the appraiser do with the direct capitalization result?
Next Question
The subject property is a retail building leased to one tenant at base rent of $120,000 a year plus overage rent of 5% of annual sales above $1,000,000. Last year's sales were $1,160,000, and the appraiser projects stabilized sales of $1,240,000. Stabilized vacancy and credit loss is 5% of total rent, annual property expenses are $36,300, and the market overall rate is 8%. What is the indicated value of the leased fee interest by direct capitalization?