An appraiser is developing an overall rate for a subject 12-unit apartment building, for which typical financing is a 70% loan-to-value ratio. A comparable 12-unit building sold for $800,000 with a $600,000 market-rate loan. Its net operating income was $62,000 and its annual debt service was $42,000. Based on the mortgage constant and equity dividend rate from this sale, what overall rate does the band of investment indicate for the subject?
Correct Answer
B) 7.90%
The mortgage constant is $42,000 ÷ $600,000 = 7%. Cash flow to equity is $62,000 − $42,000 = $20,000 on $200,000 of equity, a 10% dividend rate. At the subject's typical 70% loan-to-value ratio, 0.70 × 7% + 0.30 × 10% = 7.90%. Keeping the sale's 75% loan-to-value ratio gives 7.75%, an unweighted average gives 8.50%, and swapped weights give 9.10%.
Why This Is the Correct Answer
Option B is correct because the sale supports a 7% mortgage constant and a 10% equity dividend rate, and the subject's typical financing is 70% debt. The weighted result is 0.70 × 7% + 0.30 × 10% = 7.90%.
Why the Other Options Are Wrong
Option A: 7.75%
Option A, 7.75%, keeps the sale's own 75% loan-to-value ratio: 0.75 × 7% + 0.25 × 10%. The weights should reflect typical financing for the subject, so the correct result is 0.70 × 7% + 0.30 × 10% = 7.90%.
Option C: 8.50%
Option C, 8.50%, is the unweighted average: (7% + 10%) ÷ 2. Debt and equity do not hold equal shares of value here, so the correct result is 7.90%.
Option D: 9.10%
Option D, 9.10%, swaps the weights: 0.30 × 7% + 0.70 × 10%. Debt holds the 70% share, so the correct result is 0.70 × 7% + 0.30 × 10% = 7.90%.
Rates from sale, weights from subject
The comparable can supply market rates, but the weights describe how a property like the subject is typically financed.
How to use: Use this phrase whenever a band problem gives two different loan-to-value ratios.
Exam Tip
When a sale's financing differs from typical financing, weight by the typical ratio for the subject. Finding the equity dividend rate requires debt service to come off NOI first.
Common Mistakes to Avoid
- -Weighting by the comparable's loan-to-value ratio instead of the typical one
- -Dividing NOI rather than cash flow after debt service by equity
- -Averaging the two rates without weights
Concept Deep Dive
Analysis
The problem has two stages. First, each rate is extracted from the sale's cash flows, with equity income measured after debt service. Second, the appraiser chooses the weights, which come from typical financing for the subject and not from the comparable's particular loan.
Background Knowledge
The equity capitalization rate is pre-tax cash flow to equity divided by the equity investment, and cash flow to equity is net income less annual debt service. The band's weights rest on the typical debt and equity proportions for the property being appraised.
Real-World Application
An appraiser verifies that a sale closed with a higher loan-to-value ratio than is typical for similar buildings. The sale still supplies useful evidence of the mortgage constant and equity return, but the appraiser weights those rates using the leverage typical for the subject.
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