Using the band of investment method, calculate the overall capitalization rate given: mortgage rate 5.5%, loan-to-value ratio 75%, and equity yield rate 12%.
Correct Answer
D) 9.125%
Overall cap rate = (Mortgage rate × LTV ratio) + (Equity yield rate × Equity ratio) = (5.5% × 0.75) + (12% × 0.25) = 4.125% + 3% = 7.125%. Wait, let me recalculate: 4.125% + 3% = 7.125%, but this doesn't match option d. The correct answer should be 7.125%.
Why This Is the Correct Answer
There appears to be an error in the provided correct answer designation. The calculation shows: (5.5% × 0.75) + (12% × 0.25) = 4.125% + 3% = 7.125%. Since both options A and C show 7.125%, and the mathematical calculation clearly results in 7.125%, the correct answer should be either A or C, not D (9.125%). The explanation provided confirms this calculation is accurate.
Why the Other Options Are Wrong
Option B: 8.75%
8.75% is incorrect because it appears to be calculated using an improper weighting or incorrect formula application, possibly mixing up the rates or ratios in the band of investment calculation.
MOLE Method
MOLE: Mortgage rate × LTV + Ownership equity rate × Equity ratio. Remember that LTV + Equity ratio must equal 100% (or 1.0), so if LTV is 75%, equity ratio is automatically 25%.
How to use: When you see a band of investment problem, immediately write 'MOLE' and set up: M×L + O×E, then substitute the given values and ensure your ratios add to 1.0 before calculating.
Exam Tip
Always double-check that your LTV ratio and equity ratio add up to 100% (or 1.0) before performing the calculation, and verify your arithmetic by adding the two weighted components.
Common Mistakes to Avoid
- -Forgetting that equity ratio = 1 - LTV ratio
- -Using the wrong rates (confusing mortgage rate with equity yield rate)
- -Failing to convert percentages to decimals in calculations
Concept Deep Dive
Analysis
The band of investment method is a technique used to calculate the overall capitalization rate by weighting the cost of debt financing and equity financing based on their respective proportions in the capital structure. This method recognizes that most real estate investments are financed through a combination of mortgage debt and equity capital, each with different required rates of return. The overall cap rate represents the weighted average of these two financing components, where the mortgage component is weighted by the loan-to-value ratio and the equity component is weighted by the equity ratio (1 - LTV ratio). This approach is fundamental in income capitalization analysis and helps appraisers derive market-supported capitalization rates.
Background Knowledge
The band of investment method requires understanding that real estate financing typically involves both debt (mortgage) and equity components, each demanding different returns. The loan-to-value ratio determines the debt portion, while the equity ratio (1 - LTV) determines the equity portion, and these must be weighted accordingly in the calculation.
Real-World Application
Appraisers use this method when comparable sales data is limited but financing terms and equity return expectations are known from market surveys, allowing them to derive supportable capitalization rates for income-producing properties.
More Math & Stats Questions
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