An overall cap rate extracted from a sale is 7.2%. The buyer financed 75% at a 6.9% constant. The equity dividend rate implied for the 25% equity share is about:
Correct Answer
A) 8.1%, the leverage-adjusted residual
Why this is correct: The overall cap rate (R) is a weighted average of the mortgage constant (M) and equity dividend rate (E). Given R = 7.2%, loan-to-value ratio = 75%, and M = 6.9%, solve: 0.072 = (0.75 × 0.069) + (0.25 × E). First, 0.75 × 0.069 = 0.05175. Then, 0.072 - 0.05175 = 0.02025. Finally, E = 0.02025 ÷ 0.25 = 0.081 or 8.1%. Why the other choices are wrong: "7.05%, splitting the difference" is an incorrect average. "6.9% exactly, matching the loan's constant" ignores that equity typically requires a higher return. "28.8%, the rate times leverage" misapplies the calculation. Exam tip: Use the band of investment formula: R = (LTV × M) + (Equity % × E). Solve for E when other variables are known.
Why This Is the Correct Answer
Why this is correct: The overall cap rate (R) is a weighted average of the mortgage constant (M) and equity dividend rate (E). Given R = 7.2%, loan-to-value ratio = 75%, and M = 6.9%, solve: 0.072 = (0.75 × 0.069) + (0.25 × E). First, 0.75 × 0.069 = 0.05175. Then, 0.072 - 0.05175 = 0.02025. Finally, E = 0.02025 ÷ 0.25 = 0.081 or 8.1%. Why the other choices are wrong: "7.05%, splitting the difference" is an incorrect average. "6.9% exactly, matching the loan's constant" ignores that equity typically requires a higher return. "28.8%, the rate times leverage" misapplies the calculation. Exam tip: Use the band of investment formula: R = (LTV × M) + (Equity % × E). Solve for E when other variables are known.
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