The mortgage interest in a property is valued at $1,050,000, and annual debt service is $96,000. Annual NOI is $142,000. The equity dividend rate is 10%. Using the equity residual technique, what is the total property value?
Correct Answer
C) $1,510,000
1050000+(142000−96000)÷0.1 = 1510000. Common errors: leaving out the mortgage value gives $460,000; not deducting debt service before capitalizing equity income gives $2,470,000; adding the equity cash flow without capitalizing it gives $1,096,000.
Why This Is the Correct Answer
Option C is correct because equity cash flow is $142,000 - $96,000 = $46,000, equity value is $46,000 / 0.10 = $460,000, and adding the $1,050,000 mortgage value gives $1,510,000. Residual techniques can be applied to the financial components of a property, debt and equity, and this calculation combines them.
Why the Other Options Are Wrong
Option A: $460,000
Option A, $460,000, comes from ($142,000 - $96,000) / 0.10 = $460,000, which leaves out the mortgage value. The total is $460,000 + $1,050,000 = $1,510,000.
Option B: $1,096,000
Option B, $1,096,000, comes from $1,050,000 + $142,000 - $96,000 = $1,096,000, which adds the equity cash flow without capitalizing it. The $46,000 must be divided by 0.10 to give $460,000 of equity value, for a total of $1,510,000.
Option D: $2,470,000
Option D, $2,470,000, comes from $142,000 / 0.10 + $1,050,000 = $2,470,000, which does not deduct debt service before capitalizing equity income. Only the $46,000 left after debt service belongs to equity, giving $1,510,000.
NOI minus debt, then capitalize
Subtract debt service from NOI, capitalize what is left at the equity dividend rate, then add the mortgage value. Debt plus equity equals the whole.
How to use: Use it for equity residual problems that give NOI, debt service and a mortgage value.
Exam Tip
Match each income stream to its own rate: equity cash flow goes with the equity dividend rate. Do not capitalize total NOI at an equity rate.
Common Mistakes to Avoid
- -Forgetting to add the mortgage value
- -Capitalizing NOI instead of equity cash flow at the equity rate
- -Adding annual cash flow without capitalizing it
Concept Deep Dive
Analysis
This calculation tests a financial-component (mortgage and equity) residual analysis. The cash flow left for equity is NOI minus debt service, which is capitalized at the equity dividend rate to estimate the equity value, and the given mortgage value is added. The distractors omit the mortgage, skip deducting debt service, or add the equity cash flow without capitalizing it.
Background Knowledge
The equity capitalization (dividend) rate relates annual pre-tax cash flow to equity to the equity investment, so equity value can be estimated as equity cash flow divided by that rate. Residual techniques split a property into physical components (land and improvements) or financial components (debt and equity). The equity dividend rate is a current-income rate, not a total yield rate.
Real-World Application
An investor considering an apartment purchase knows the loan amount and payment and wants to test the price from the equity investor's perspective. The appraiser subtracts annual debt service from NOI, capitalizes the remaining cash flow at a market equity dividend rate, and adds the loan amount. The result is compared with other income and sales indications.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
Annual PGI is $250,000 and combined vacancy and collection loss is explicitly 12% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
Annual NOI is $165,000, and the building value is known to be $1,100,000. Capitalization rates are 5% for land and 11% for the building. Using the land residual technique, what is the total property value?
Next Question
A GRM derived from comparables is most reliable when those comparables: