Debt funds 70% of value at an annual mortgage constant of 5.5%, and the remaining equity requires an annual equity dividend rate of 12%. What overall rate does the band of investment indicate?
Correct Answer
B) 7.45%
Ro=0.7×0.055+0.3×0.12=0.0745; percent=7.45. Common errors: swapping the debt and equity weights gives 10.05%; averaging the two rates without weighting gives 8.75%; leaving out the equity component gives 3.85%.
Why This Is the Correct Answer
Option B is correct because Ro = 0.70 x 0.055 + 0.30 x 0.12 = 0.0385 + 0.036 = 0.0745, or 7.45%. Each component's rate is weighted by its share of value. The formula uses the mortgage constant and equity dividend rate, not loan interest or equity yield rates.
Why the Other Options Are Wrong
Option A: 3.85%
Option A is wrong because 3.85% leaves out the equity component: 0.70 x 5.5% = 3.85%. Adding the equity piece, 0.30 x 12% = 3.60%, gives 7.45%.
Option C: 8.75%
Option C is wrong because 8.75% averages the two rates without weighting: (5.5% + 12%) / 2 = 8.75%. The rates must be weighted by 70% and 30%, giving 7.45%.
Option D: 10.05%
Option D is wrong because 10.05% swaps the debt and equity weights: 0.30 x 5.5% + 0.70 x 12% = 10.05%. The correct weights give 0.70 x 5.5% + 0.30 x 12% = 7.45%.
Weight each band by share
Multiply each band's rate by its slice of value, then add the slices.
How to use: Use this whenever a question gives debt and equity shares with their rates.
Exam Tip
The overall rate must fall between the two component rates and closer to the larger-weighted one. Answers outside that range or at the simple average are traps.
Common Mistakes to Avoid
- -Swapping debt and equity weights
- -Taking a simple average of the rates
- -Using the loan interest rate instead of the mortgage constant
Concept Deep Dive
Analysis
This question tests the band of investment for an overall capitalization rate. Each financing component's rate is weighted by its share of value and the results are added. Debt is 70% at a 5.5% constant and equity is 30% at a 12% dividend rate.
Background Knowledge
The band of investment derives an overall rate as a weighted average of the claims of debt and equity on NOI. The mortgage component uses the mortgage constant, which includes principal and interest, and the equity component uses the equity dividend rate. Weights are the loan-to-value ratio and its complement.
Real-World Application
An appraiser surveys lenders offering 70% loans with a 5.5% annual constant and investors seeking 12% cash-on-cash. The band of investment produces a 7.45% overall rate, which the appraiser cross-checks against rates from comparable sales.
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