A lender underwrites a loan at a 1.25 debt coverage ratio, a 7.5% annual mortgage constant, and a 70% loan-to-value ratio. What overall capitalization rate does the debt coverage formula indicate, rounded to one decimal place?
Correct Answer
C) 6.6%
1.25×0.075×0.70×100 = 6.5625. Common errors: dividing by the coverage ratio instead of multiplying gives 4.2%; leaving out the loan-to-value ratio gives 9.4%; using the equity ratio instead of the loan-to-value ratio gives 2.8%.
Why This Is the Correct Answer
Option C is correct because Ro = 1.25 × 0.075 × 0.70 = 0.065625, or 6.5625%. Rounded to one decimal place, that is 6.6%.
Why the Other Options Are Wrong
Option A: 2.8%
Option A, 2.8%, comes from using the equity ratio instead of the loan-to-value ratio: 1.25 × 0.075 × 0.30 = 0.028125, or 2.8%. The formula uses the 70% loan ratio, giving 1.25 × 0.075 × 0.70 = 6.6%.
Option B: 4.2%
Option B, 4.2%, comes from dividing by the coverage ratio instead of multiplying: 0.075 × 0.70 ÷ 1.25 = 0.042, or 4.2%. The formula multiplies by 1.25, giving 6.5625%, which rounds to 6.6%.
Option D: 9.4%
Option D, 9.4%, comes from leaving out the loan-to-value ratio: 1.25 × 0.075 = 0.09375, or 9.4%. Including the 0.70 loan ratio gives 6.5625%, which rounds to 6.6%.
Multiply all three: DCR, Rm, M
The debt coverage formula is a straight product of the coverage ratio, the mortgage constant and the loan ratio. No division is involved.
How to use: Use this when a question gives a DCR, a mortgage constant and a loan-to-value ratio and asks for Ro.
Exam Tip
Use the loan-to-value ratio, not the equity ratio, in the debt coverage formula, and watch the rounding instruction.
Common Mistakes to Avoid
- -Dividing by the debt coverage ratio
- -Using the equity ratio in place of the loan-to-value ratio
- -Treating the formula result as proof of a market capitalization rate
Concept Deep Dive
Analysis
This question tests the debt coverage formula for an overall rate: Ro equals the debt coverage ratio times the mortgage constant times the loan-to-value ratio. It is a straightforward multiplication of three inputs with rounding. The distractors come from dividing by the DCR, dropping the loan ratio, or using the equity ratio.
Background Knowledge
The debt coverage formula, Ro = DCR × Rm × M, derives an overall rate from lender underwriting criteria. The debt coverage ratio is NOI divided by annual debt service, and the mortgage constant is annual debt service divided by loan amount. The result reflects financing terms and is a check rather than proof of a market capitalization rate.
Real-World Application
A lender requires a 1.25 debt coverage ratio on a 70% loan with a 7.5% annual constant. An appraiser computes the implied 6.6% overall rate as a reasonableness check against rates extracted from comparable sales.
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