An appraiser is verifying the sale of a fourplex. The buyer paid the seller $600,000 in cash, using a $450,000 market-rate bank loan and $150,000 of equity. Stabilized annual NOI is $42,000, annual debt service is $30,000 and annual pre-tax cash flow to equity is $12,000. What overall capitalization rate does this sale indicate?
Correct Answer
B) 7.00%
The overall rate relates total property net income to total property value: $42,000 ÷ $600,000 = 7.00%. The 6.67% figure is the mortgage constant, $30,000 ÷ $450,000, and 8.00% is the equity dividend rate, $12,000 ÷ $150,000. The 9.33% figure divides NOI by the loan amount, which mixes property income with one part of the capital.
Why This Is the Correct Answer
Option B is correct because the overall rate compares one year's total property net income with total property value: $42,000 ÷ $600,000 = 7.00%. The seller received all cash, so the $600,000 price needs no financing adjustment. The other percentages describe the loan or the equity rather than the whole property.
Why the Other Options Are Wrong
Option A: 6.67%
Option A, 6.67%, is the mortgage constant: $30,000 ÷ $450,000 = 6.67%. It relates debt service to the loan rather than property income to value. The overall rate is $42,000 ÷ $600,000 = 7.00%.
Option C: 8.00%
Option C, 8.00%, is the equity dividend rate: $12,000 ÷ $150,000 = 8.00%. It measures cash flow to the equity position after debt service. The overall rate is $42,000 ÷ $600,000 = 7.00%.
Option D: 9.33%
Option D, 9.33%, divides total NOI by the loan: $42,000 ÷ $450,000 = 9.33%. That sets whole-property income against only part of the capital and is not a rate used in this analysis. The overall rate is $42,000 ÷ $600,000 = 7.00%.
Match income to its owner
Whole income over whole value, lender's income over the loan, and owner's cash over the equity. Each rate stays with its own slice of the deal.
How to use: Use this matching rule when a problem gives several dollar figures and asks for one named rate.
Exam Tip
Identify the named rate before you touch the numbers. When a sale file holds several figures, a wrong pairing can still give a realistic percentage.
Common Mistakes to Avoid
- -Reporting a buyer's cash-on-cash return as the overall rate
- -Confusing the mortgage constant with the overall rate
- -Dividing NOI by the loan amount or by equity alone
Concept Deep Dive
Analysis
The skill tested is whether you can identify which income goes with which capital. Each rate is a pairing: total property income with total value, debt service with the loan, and equity cash flow with equity. Once you match income to the same interest, the answer follows from one division.
Background Knowledge
Income rates express one year's income as a percentage of the value of the matching interest. The overall rate covers the whole property, the mortgage constant covers the loan, and the equity capitalization rate covers the equity. In this file the weighted result ties together: 75% × 6.67% + 25% × 8.00% = 7.00%.
Real-World Application
A buyer tells an appraiser the deal earned 8%, while the broker's flyer shows a different figure. The appraiser finds that the buyer was quoting cash-on-cash return on equity. For rate extraction, the appraiser uses NOI over the cash-equivalent price and records the buyer's figure separately as an equity dividend rate.
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?
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