Annual NOI is $96,000 and annual debt service is $48,000. The mortgage interest is valued at $400,000, and the equity dividend rate is 12%. What total property value does the equity residual technique indicate?
Correct Answer
C) $800,000
(96000−48000)÷0.12+400000 = 800000. Common errors: leaving out the mortgage value gives $400,000; adding debt service to NOI instead of deducting it gives $1,600,000; deducting the debt service again after adding the mortgage value gives $752,000.
Why This Is the Correct Answer
Option C is correct because equity cash flow is $96,000 − $48,000 = $48,000, equity value is $48,000 ÷ 0.12 = $400,000, and adding the $400,000 mortgage gives $800,000. Debt service is deducted once, before capitalizing equity income.
Why the Other Options Are Wrong
Option A: $400,000
Option A, $400,000, is the equity value alone (($96,000 − $48,000) ÷ 0.12) without adding the mortgage value. Total value is $400,000 + $400,000 = $800,000.
Option B: $752,000
Option B, $752,000, deducts debt service a second time after adding the mortgage value ($400,000 + $400,000 − $48,000). Debt service is already reflected in the equity cash flow, so the total is $800,000.
Option D: $1,600,000
Option D, $1,600,000, adds debt service to NOI instead of deducting it: ($96,000 + $48,000) ÷ 0.12 + $400,000. Equity income is NOI minus debt service, giving $48,000 ÷ 0.12 + $400,000 = $800,000.
Lender paid first, equity gets rest
Debt service comes off NOI first; the remaining cash flow belongs to equity and is capitalized at the equity rate, then add back the loan.
How to use: Use this order to avoid double-counting or omitting debt service.
Exam Tip
Deduct debt service exactly once, before capitalizing equity cash flow, and remember to add the mortgage value.
Common Mistakes to Avoid
- -Adding debt service to NOI instead of deducting it
- -Forgetting to add the mortgage value
- -Deducting debt service twice
Concept Deep Dive
Analysis
This question tests the equity residual approach with financial components. Equity cash flow equals NOI minus debt service, which is capitalized at the equity dividend rate to value the equity. Adding the mortgage value gives total property value.
Background Knowledge
Residual techniques can be applied to physical components (land and building) or financial components (mortgage and equity). The equity dividend rate is annual pre-tax cash flow to equity divided by equity value. When the mortgage value is known, equity income after debt service is capitalized and added to it.
Real-World Application
An appraiser valuing a property with assumable financing knows the loan balance of $400,000 and its $48,000 annual payment. The appraiser capitalizes the $48,000 remaining cash flow at a 12% investor equity rate and adds the loan to estimate total value.
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