A property has annual NOI of $112,000 and annual debt service of $70,000. The mortgage interest is valued at $800,000. The equity dividend rate is 10%. What total property value does the equity residual technique indicate?
Correct Answer
C) $1,220,000
800000+(112000−70000)÷0.1 = 1220000. Common errors: leaving out the mortgage value gives $420,000; not deducting debt service before capitalizing equity income gives $1,920,000; adding the equity cash flow without capitalizing it gives $842,000.
Why This Is the Correct Answer
Option C is correct because the equity cash flow is $112,000 − $70,000 = $42,000, which capitalizes at 10% to an equity value of $420,000. Adding the $800,000 mortgage value gives $1,220,000.
Why the Other Options Are Wrong
Option A: $420,000
Option A, $420,000, is only the equity component ($42,000 ÷ 0.10); it leaves out the $800,000 mortgage value. Total value is $800,000 + $420,000 = $1,220,000.
Option B: $842,000
Option B, $842,000, comes from adding the uncapitalized equity cash flow to the mortgage ($800,000 + $112,000 − $70,000). The $42,000 annual cash flow must be divided by the 10% dividend rate to become a $420,000 equity value, giving $1,220,000.
Option D: $1,920,000
Option D, $1,920,000, results from capitalizing the full $112,000 NOI at the equity rate ($1,120,000) and then adding $800,000, without first deducting the $70,000 of debt service. Only the cash flow left after debt service belongs to equity, so the correct total is $1,220,000.
Lender first, then equity
The lender is paid first from NOI; whatever cash is left belongs to equity and is capitalized at the equity rate, then the two pieces are added together.
How to use: Use this payout order to set up any mortgage-and-equity residual problem.
Exam Tip
An equity dividend rate applies to cash flow after debt service, so subtract debt service before dividing by it.
Common Mistakes to Avoid
- -Reporting only the equity value as the total value
- -Capitalizing NOI at the equity rate without deducting debt service
- -Adding annual cash flow instead of its capitalized value
Concept Deep Dive
Analysis
This question tests an equity residual technique, which splits value into financial components. Subtract debt service from NOI to find the equity cash flow, capitalize it at the equity dividend rate to value the equity, then add the given mortgage value to reach total property value.
Background Knowledge
Residual techniques can be applied to physical components (land and building) or to financial components (mortgage and equity). In an equity residual, the mortgage claim on income (debt service) is deducted from NOI and the remaining pre-tax cash flow is capitalized at an equity dividend rate, then added to the mortgage amount.
Real-World Application
An appraiser analyzing a leveraged fourplex knows the loan amount and its annual payments. She deducts the debt service from NOI, capitalizes the remaining cash flow at a market-supported equity dividend rate, and adds the loan amount to estimate total value.
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Previous Question
The subject property has annual potential rental income of $240,000, vacancy and collection loss of 5% of that amount and no other income. Annual operating expenses of $48,000 include property taxes and the same reserve allowance used to extract the 8% overall rate; they exclude debt service. What value is indicated by direct capitalization, rounded to the nearest dollar?
Next Question
An appraiser finds a rented comparable that sold for a cash-equivalent price of $648,000 with monthly gross rent of $2,700. The subject has monthly gross rent of $2,450, measured on the same basis. Sales in the market area indicate the same price-to-rent ratio applies, and no other adjustments are required. What is the indicated value of the subject, rounded to the nearest dollar?