Using the band of investment method, calculate the overall capitalization rate given: mortgage rate 6.5%, loan-to-value ratio 75%, and equity yield rate 12%.
Correct Answer
A) 7.875%
Cap rate = (Loan ratio × Mortgage rate) + (Equity ratio × Equity yield rate) = (0.75 × 6.5%) + (0.25 × 12%) = 4.875% + 3% = 7.875%.
Why This Is the Correct Answer
Option A (7.875%) correctly applies the band of investment formula by multiplying each financing component by its respective proportion and rate. The debt component contributes 4.875% (75% × 6.5%) and the equity component contributes 3% (25% × 12%), totaling 7.875%. This weighted average properly reflects the blended cost of capital for the investment. The calculation follows the standard formula: Overall Cap Rate = (Loan-to-Value Ratio × Mortgage Rate) + (Equity Ratio × Equity Yield Rate).
Why the Other Options Are Wrong
Option B: 9.25%
Option B (9.25%) appears to be calculated incorrectly, possibly by using wrong weightings or rates in the formula, resulting in an overall cap rate that's too high for the given financing terms.
Option C: 8.375%
Option C (8.375%) is incorrect and may result from mathematical errors in applying the weights or rates, or possibly from incorrectly averaging the mortgage and equity rates without proper weighting.
Option D: 18.5%
Option D (18.5%) is clearly incorrect and likely results from adding the mortgage rate and equity yield rate together (6.5% + 12% = 18.5%) without applying the proper weightings, which completely ignores the band of investment methodology.
WELD Method
WELD: Weight × Each = Loan + Debt. Remember to Weight each component (debt and equity), multiply Each by its rate, then add Loan component plus Debt (equity) component together.
How to use: When you see a band of investment question, immediately think WELD: identify the weights (LTV ratio and equity ratio), multiply each weight by its respective rate, then add the loan component and equity component together for the final cap rate.
Exam Tip
Always verify that your debt and equity ratios add up to 100% (0.75 + 0.25 = 1.0) before calculating, and double-check your decimal conversions when working with percentages.
Common Mistakes to Avoid
- -Adding the rates together without weighting (6.5% + 12% = 18.5%)
- -Using incorrect equity ratio (forgetting that equity ratio = 1 - loan ratio)
- -Mixing up decimal and percentage forms in calculations (using 75 instead of 0.75)
Concept Deep Dive
Analysis
The band of investment method is a fundamental technique used to derive overall capitalization rates by analyzing the weighted cost of capital from both debt and equity financing sources. This method recognizes that real estate investments are typically financed through a combination of borrowed funds (mortgage) and investor equity, each requiring different rates of return. The overall cap rate represents the blended cost of capital, weighted by the proportion of debt and equity financing. This approach is particularly useful because it directly relates the cap rate to current market financing conditions and investor return expectations.
Background Knowledge
The band of investment method requires understanding that real estate investments use leveraged financing, where the total return requirement is a weighted average of debt and equity costs. Students must know that the loan-to-value ratio determines the debt portion, while the remaining percentage represents the equity portion (100% - LTV ratio).
Real-World Application
Appraisers use this method when analyzing income-producing properties to ensure the cap rate reflects current market financing conditions, helping determine if a property's asking price aligns with typical investor financing structures and return expectations.
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