An appraiser is valuing a property with annual NOI of $120,000. The mortgage interest has a known value of $800,000 and a 7.5% annual mortgage constant, and the current dividend rate on equity is 12%. Using the equity residual technique, what is the total property value?
Correct Answer
B) $1,300,000
Debt service=800000×0.075=60000; equity=(120000−60000)÷0.12=500000; total=1300000. Common errors: leaving out the mortgage value gives $500,000; not deducting debt service before capitalizing equity income gives $1,800,000; capitalizing equity income at the mortgage constant gives $1,600,000.
Why This Is the Correct Answer
Option B is correct because debt service is $800,000 x 0.075 = $60,000, equity cash flow is $120,000 - $60,000 = $60,000, and equity value is $60,000 / 0.12 = $500,000. Adding the $800,000 mortgage gives $1,300,000.
Why the Other Options Are Wrong
Option A: $500,000
Option A, $500,000, is the equity value alone: ($120,000 - $60,000) / 0.12. The question asks for the total, so the $800,000 mortgage value must be added for $1,300,000.
Option C: $1,600,000
Option C, $1,600,000, capitalizes equity cash flow at the mortgage constant: ($120,000 - $60,000) / 0.075 + $800,000. Equity income must be capitalized at the 12% equity dividend rate, giving $500,000 + $800,000 = $1,300,000.
Option D: $1,800,000
Option D, $1,800,000, capitalizes the full NOI as equity income without deducting debt service: $120,000 / 0.12 + $800,000. Deducting the $60,000 debt service first gives $1,300,000.
Pay the bank first
The lender is paid first from NOI; what is left belongs to equity and is capitalized at the equity rate.
How to use: Use this order to set up any equity residual calculation.
Exam Tip
Match each income stream to its own rate: debt service goes with the mortgage constant, and equity cash flow goes with the equity dividend rate.
Common Mistakes to Avoid
- -Forgetting to add the mortgage value back
- -Capitalizing the full NOI at the equity rate
- -Using the mortgage constant to capitalize equity income
Concept Deep Dive
Analysis
This question tests a financial-component residual technique. Known mortgage value times the mortgage constant gives debt service; NOI less debt service is the equity cash flow, which is capitalized at the equity dividend rate; then mortgage and equity values are added.
Background Knowledge
Residual techniques can be applied to physical components (land and building) or financial components (mortgage and equity). The annual loan constant is the ratio of annual loan payment to loan principal, and the equity dividend rate relates annual pre-tax cash flow to equity value.
Real-World Application
An investor is assuming an existing $800,000 loan on an apartment property. The appraiser deducts the loan's annual payment from NOI, capitalizes the remaining cash flow at a market equity dividend rate, and adds back the loan amount to indicate total value.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
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