A property's capital structure consists of $400,000 of debt and $200,000 of equity. The annual mortgage constant is 6%, and the current equity dividend rate is 12%. Using the band of investment, what is the indicated overall rate?
Correct Answer
B) 8.0%
(400000÷600000)×6+(200000÷600000)×12 = 8. Common errors: using a simple average instead of capital-weighted rates gives 9.0%; swapping the debt and equity weights gives 10.0%; leaving out the equity component gives 4.0%.
Why This Is the Correct Answer
Option B is correct because debt is two-thirds and equity one-third of the $600,000 total, so (400,000 ÷ 600,000) × 6% + (200,000 ÷ 600,000) × 12% = 4% + 4% = 8.0%. Each rate is weighted by its share of total capital.
Why the Other Options Are Wrong
Option A: 4.0%
Option A, 4.0%, is wrong because it leaves out the equity component: (400,000 ÷ 600,000) × 6% = 4.0%. Adding the equity part, (200,000 ÷ 600,000) × 12% = 4%, gives the correct 8.0%.
Option C: 9.0%
Option C, 9.0%, is wrong because it takes a simple average of the two rates instead of weighting them by capital: (6% + 12%) ÷ 2 = 9.0%. Weighting by the two-thirds debt and one-third equity shares gives 8.0%.
Option D: 10.0%
Option D, 10.0%, is wrong because it swaps the debt and equity weights: (200,000 ÷ 600,000) × 6% + (400,000 ÷ 600,000) × 12% = 10.0%. Debt is the larger share, so the correct result is 8.0%.
Dollars to Shares First
Turn debt and equity dollars into fractions of the total before weighting the rates.
How to use: Use this first step when a band-of-investment problem gives dollar amounts rather than ratios.
Exam Tip
Divide each dollar amount by the total capital to get the weights, and confirm the overall rate lies between the two component rates.
Common Mistakes to Avoid
- -Averaging the rates without capital weights
- -Applying the debt share to the equity rate
- -Using the loan coupon rate instead of the mortgage constant
Concept Deep Dive
Analysis
This question tests the band of investment using dollar amounts of debt and equity. Convert each to a share of total capital, $400,000 of $600,000 for debt and $200,000 of $600,000 for equity, then weight each cash-flow rate by its share. The mortgage constant and equity dividend rate are the right rates for this method.
Background Knowledge
An overall capitalization rate can be computed as a weighted average of the component investment claims on NOI. In the band of investment, Ro = M × Rm + (1 − M) × Re, where M is the loan share of value. The mortgage constant includes both interest and principal payments, so it differs from the loan coupon rate.
Real-World Application
An appraiser reviewing a proposed acquisition sees a $400,000 loan and $200,000 of investor cash. Using the lender's mortgage constant and the investor's required cash-on-cash return, the appraiser computes a band-of-investment overall rate to compare with market-extracted rates.
More Income Approach Questions
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Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
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The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
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