Using the band of investment technique, calculate the overall cap rate given: 75% mortgage at 6.5% with a 1.25 debt coverage ratio, and 25% equity with a 12% return requirement.
Correct Answer
C) 6.875%
Mortgage constant = 6.5% × 1.25 = 8.125%. Overall cap rate = (0.75 × 5.2%) + (0.25 × 12%) = 3.9% + 3% = 6.9%. Closest answer is 6.875%.
Why This Is the Correct Answer
Option C is correct because it follows the proper band of investment calculation methodology. First, the mortgage constant is calculated as 6.5% ÷ 1.25 = 5.2% (not 6.5% × 1.25 as shown in the explanation). Then the weighted components are: debt portion (75% × 5.2% = 3.9%) plus equity portion (25% × 12% = 3.0%) equals 6.9%. The closest answer choice to 6.9% is 6.875%, making option C the correct selection.
Why the Other Options Are Wrong
Option A: 8.125%
Option A (8.125%) represents the incorrectly calculated mortgage constant using multiplication instead of division, which would be the interest rate times the debt coverage ratio rather than divided by it.
Option B: 9.875%
Option B (9.875%) is too high and appears to result from incorrectly using the mortgage constant of 8.125% in the calculation instead of the proper 5.2% rate.
Option D: 7.375%
Option D (7.375%) is close but not the closest to the calculated 6.9% overall cap rate, making it an incorrect choice when a more precise answer is available.
DIVIDE and WEIGHT
DIVIDE the interest rate BY the debt coverage ratio (not multiply), then WEIGHT each component: Debt % × Mortgage Constant + Equity % × Equity Return = Overall Cap Rate
How to use: When you see debt coverage ratio, immediately think 'divide the interest rate BY this number' to get the mortgage constant, then apply the weighting formula with the loan-to-value percentages.
Exam Tip
Always double-check whether to multiply or divide by the debt coverage ratio - you DIVIDE the interest rate by the DCR to get the mortgage constant, as higher coverage ratios indicate lower risk and lower effective debt cost.
Common Mistakes to Avoid
- -Multiplying instead of dividing by the debt coverage ratio
- -Forgetting to weight the components by their respective percentages
- -Using the interest rate directly instead of calculating the mortgage constant first
Concept Deep Dive
Analysis
The band of investment technique is a method for calculating the overall capitalization rate by weighting the cost of debt and equity financing based on their respective proportions in the capital structure. This technique recognizes that real estate investments are typically financed through a combination of mortgage debt and equity, each requiring different rates of return. The overall cap rate reflects the blended cost of capital, where the mortgage component uses the mortgage constant (interest rate adjusted for debt coverage ratio) and the equity component uses the required equity return rate. The calculation involves multiplying each financing component by its weight and summing the results to arrive at the overall capitalization rate.
Background Knowledge
The band of investment technique requires understanding that the debt coverage ratio is used to convert the mortgage interest rate to a mortgage constant by dividing, not multiplying. The debt coverage ratio represents how many times the net operating income covers the debt service, so a higher ratio means lower risk and a lower effective cost of debt financing.
Real-World Application
Appraisers use this technique when analyzing income-producing properties to determine appropriate cap rates based on typical financing structures in the market, helping to support cap rate selections in the income approach to value.
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