The equity interest in a property is known to be worth $300,000, and its annual equity dividend rate is 10%. Annual NOI is $72,000 and the mortgage constant is 7%. What total property value does the mortgage residual technique indicate?
Correct Answer
C) $900,000
Equity income=300000×0.10=30000; mortgage value=(72000−30000)÷0.07=600000; total=900000. Common errors: leaving out the known equity value gives $600,000; not allocating income to equity before capitalizing gives $1,328,571; capitalizing the remaining income at the equity rate gives $720,000.
Why This Is the Correct Answer
Option C is correct because equity income is $300,000 × 0.10 = $30,000, leaving $72,000 − $30,000 = $42,000 for the mortgage. Capitalizing that at the 7% mortgage constant gives $600,000, and adding the $300,000 equity gives a total of $900,000.
Why the Other Options Are Wrong
Option A: $600,000
Option A, $600,000, is only the mortgage value: ($72,000 − $30,000) ÷ 0.07 = $600,000. The question asks for the total, so the $300,000 equity value must be added, giving $900,000.
Option B: $720,000
Option B, $720,000, capitalizes the remaining income at the equity rate instead of the mortgage constant: ($72,000 − $30,000) ÷ 0.10 + $300,000 = $720,000. The residual belongs to the mortgage and uses 7%, giving $600,000 + $300,000 = $900,000.
Option D: $1,328,571
Option D, $1,328,571, capitalizes all of the NOI at the mortgage constant without first allocating income to equity: $72,000 ÷ 0.07 + $300,000 ≈ $1,328,571. Equity's $30,000 must come off first, giving $42,000 ÷ 0.07 + $300,000 = $900,000.
Known first, then add back
Take off the known part's income, capitalize the rest at the unknown part's rate, then add the known part's value to get the total.
How to use: Use this three-step routine on any residual question that asks for total property value.
Exam Tip
Read whether the question asks for the residual component alone or the total; a common trap stops one step short.
Common Mistakes to Avoid
- -Forgetting to add the known component's value
- -Capitalizing the residual at the wrong component's rate
- -Skipping the income allocation to the known component
Concept Deep Dive
Analysis
This question tests a mortgage residual technique using financial components. The known equity value's income is deducted first, the remaining income is capitalized at the mortgage constant to find the mortgage value, and the equity value is added back. $72,000 − $30,000 = $42,000; $42,000 ÷ 0.07 = $600,000; plus $300,000 equals $900,000.
Background Knowledge
Residual techniques can be applied to financial components, debt and equity, as well as to land and building. The mortgage constant is the ratio of annual debt service to the loan principal, and the equity dividend rate is cash flow to equity divided by equity. Each component's income is capitalized at its own rate.
Real-World Application
An investor knows how much equity a buyer will contribute and the return that equity requires. An appraiser uses the remaining NOI and the lender's mortgage constant to estimate supportable debt, then adds the equity to indicate total value.
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