Using the band of investment technique, calculate the overall cap rate given: 70% debt at 5.5% interest rate, 30% equity requiring 12% return.
Correct Answer
D) 7.45%
Why this is correct: The band of investment technique derives an overall capitalization rate (OAR) by weighting the required returns for debt and equity. The calculation is: (Debt Percentage * Interest Rate) + (Equity Percentage * Equity Return). Using the given figures: (0.70 * 0.055) + (0.30 * 0.12) = 0.0385 + 0.036 = 0.0745 or 7.45%. Therefore, the correct answer is 7.45%. Why the other choices are wrong: 9.25%, 8.75%, and 6.85% are incorrect results from misapplying the weighted average formula or using incorrect weightings. Exam tip: The band of investment OAR is a simple weighted average: (Loan-to-Value Ratio * Mortgage Constant) + (Equity Ratio * Equity Dividend Rate).
Why This Is the Correct Answer
Option C (6.85%) is marked as correct, but this appears to be an error in the question. The standard band of investment calculation yields 7.45%, which should be the overall cap rate. The explanation mentions an adjustment for debt service coverage, but this is not part of the basic band of investment technique and no debt service coverage ratio is provided in the problem. The correct mathematical answer should be 7.45% (Option A).
Why the Other Options Are Wrong
Option A: 9.25%
Option A (9.25%) is incorrect as it's too high and doesn't correspond to any reasonable calculation from the given financing terms
Option C: 8.75%
Option C (8.75%) is incorrect because it doesn't match any logical calculation from the given data and appears to be a distractor
DEBT + EQUITY = TOTAL
Remember 'Weight × Rate' for each component: Debt Weight × Debt Rate + Equity Weight × Equity Rate = Overall Rate. Think 'D×R + E×R = Total'
How to use: When you see band of investment problems, immediately identify the two components (debt and equity), multiply each percentage by its respective rate, then add them together
Exam Tip
Always double-check that your debt and equity percentages add up to 100% before calculating, and remember that you're simply doing weighted averages
Common Mistakes to Avoid
- -Forgetting to convert percentages to decimals
- -Mixing up debt and equity rates
- -Adding unnecessary adjustments not specified in the problem
Concept Deep Dive
Analysis
The band of investment technique is a method used to calculate overall capitalization rates by weighting the cost of debt financing and equity requirements based on their respective percentages in the capital structure. This question tests understanding of how to properly calculate the weighted average and whether the result represents a cap rate or weighted average cost of capital. The explanation provided contains an error - the basic band of investment calculation (0.70 × 5.5%) + (0.30 × 12%) = 7.45% IS the overall cap rate, not the weighted average cost of capital. There's no additional adjustment for debt service coverage in the standard band of investment formula.
Background Knowledge
The band of investment technique calculates overall cap rates by weighting the mortgage constant (or interest rate as a simplified version) and equity dividend rate by their respective loan-to-value and equity percentages. The formula is: Overall Cap Rate = (Loan-to-Value Ratio × Mortgage Constant) + (Equity Ratio × Equity Dividend Rate).
Real-World Application
Appraisers use this technique when analyzing income properties to determine appropriate cap rates based on typical financing structures in the market, helping to support cap rate selections in the income approach
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