A lender's terms for a property are an 80% loan-to-value ratio, a 10% annual mortgage constant, and a 1.25 debt coverage ratio. Annual NOI is $85,000. What value is indicated by capitalizing NOI at the overall rate from the debt coverage formula?
Correct Answer
C) $850,000
Ro=0.80×0.10×1.25=0.10; value=85000÷0.10=850000. Common errors: leaving out the debt-coverage ratio gives $1,062,500; leaving out the loan-to-value ratio gives $680,000; multiplying NOI by the mortgage constant instead of dividing by Ro gives $8,500.
Why This Is the Correct Answer
Option C is correct because Ro = 0.80 × 0.10 × 1.25 = 0.10, and $85,000 ÷ 0.10 = $850,000. The debt coverage formula combines lender underwriting factors into an overall rate, which is then used for direct capitalization.
Why the Other Options Are Wrong
Option A: $8,500
Option A, $8,500, comes from $85,000 × 0.10, multiplying NOI by the mortgage constant instead of dividing by Ro. The value is $85,000 ÷ (0.80 × 0.10 × 1.25) = $850,000.
Option B: $680,000
Option B, $680,000, comes from $85,000 ÷ (0.10 × 1.25), leaving out the 80% loan-to-value ratio. Including it gives Ro of 0.10 and value of $850,000.
Option D: $1,062,500
Option D, $1,062,500, comes from $85,000 ÷ (0.80 × 0.10), leaving out the 1.25 debt coverage ratio. Including it gives Ro of 0.10 and value of $850,000.
D times C times M
Ro = DCR × mortgage constant × loan-to-value ratio; all three factors are multiplied.
How to use: Use this to build Ro from lender terms before dividing NOI.
Exam Tip
Make sure all three factors appear in Ro; each wrong answer here drops or misuses one of them.
Common Mistakes to Avoid
- -Leaving out the debt coverage ratio
- -Leaving out the loan-to-value ratio
- -Treating the mortgage constant alone as the overall rate
Concept Deep Dive
Analysis
This question tests the debt coverage formula for an overall capitalization rate. Multiply the loan-to-value ratio, the annual mortgage constant and the debt coverage ratio to get Ro, then divide NOI by Ro. Leaving out any factor produces a distractor.
Background Knowledge
The debt coverage formula expresses the overall rate as the debt coverage ratio times the mortgage constant times the loan-to-value ratio. It reflects lender underwriting criteria rather than equity investor requirements alone. Its result should be tested against market-derived rates because the identity does not independently establish market value.
Real-World Application
An appraiser valuing a small apartment property checks her market-extracted cap rate against typical lender terms. Using an 80% loan-to-value ratio, a 10% annual mortgage constant and a 1.25 debt coverage ratio, she computes a 10% Ro as a cross-check.
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