An overall capitalization rate of 7.2% was extracted from a sale. The buyer financed 75% of the price at a 6.9% annual mortgage constant and paid the remaining 25% in equity. Using the band of investment, what equity dividend rate is indicated?
Correct Answer
D) 8.1%
(0.072−0.75×0.069)÷0.25×100 = 8.1. Common errors: not dividing by the 25% equity fraction gives 2.0%; subtracting the unweighted mortgage constant gives 1.2%; swapping the debt and equity fractions gives 7.3%.
Why This Is the Correct Answer
Option D is correct because the weighted mortgage component is 0.75 × 0.069 = 0.05175. Subtracting from Ro leaves 0.072 − 0.05175 = 0.02025 for equity, and dividing by the 25% equity share gives 0.02025 ÷ 0.25 = 0.081, or 8.1%.
Why the Other Options Are Wrong
Option A: 1.2%
Option A, 1.2%, comes from subtracting the unweighted mortgage constant: (0.072 − 0.069) ÷ 0.25 = 0.012. The mortgage constant must first be weighted by 75%, giving (0.072 − 0.05175) ÷ 0.25 = 8.1%.
Option B: 2.0%
Option B, 2.0%, comes from not dividing by the 25% equity fraction: 0.072 − 0.75 × 0.069 = 0.02025, about 2.0%. That is only the weighted equity component; dividing by 0.25 gives 8.1%.
Option C: 7.3%
Option C, 7.3%, comes from swapping the debt and equity fractions: (0.072 − 0.25 × 0.069) ÷ 0.75 = 0.073. Using the correct weights gives (0.072 − 0.75 × 0.069) ÷ 0.25 = 8.1%.
Subtract debt, divide by equity
Take Ro, remove the weighted debt piece, and what remains belongs to equity; divide it by the equity share to get the equity rate.
How to use: Use this two-step order whenever a question asks you to back into the equity dividend rate.
Exam Tip
After solving, plug your answer back into the formula; 0.75 × 6.9% + 0.25 × 8.1% should return the 7.2% overall rate.
Common Mistakes to Avoid
- -Stopping after subtracting the weighted mortgage component without dividing by the equity share
- -Subtracting the full mortgage constant rather than its weighted amount
- -Pairing the loan ratio with the equity rate
Concept Deep Dive
Analysis
This question tests solving the band of investment formula for an unknown equity dividend rate. You subtract the weighted mortgage component from the overall rate, which leaves the weighted equity component, and then divide by the equity share. The algebra must keep each rate paired with its correct weight.
Background Knowledge
The band of investment formula is Ro = M × Rm + (1 − M) × Re, where M is the loan ratio, Rm the mortgage constant and Re the equity dividend rate. Any one unknown can be solved if the others are given. Solving for Re isolates the equity share of NOI and divides it by the equity share of value.
Real-World Application
An appraiser has a market-extracted overall rate and current loan terms for a type of property. To judge whether the implied equity return is reasonable, the appraiser solves the band formula for the equity dividend rate. The result is compared with return expectations reported by investors.
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