An appraiser is extracting an overall rate for a fourplex. A comparable fourplex sold for a cash equivalent $600,000, with annual PGI of $72,000, vacancy and credit loss of 5%, operating expenses of $20,400 and buyer's mortgage payments of $31,000. The subject property has annual PGI of $84,000, the same 5% loss and operating expenses of $25,000. Neither property has other income. What is the indicated value of the subject property?
Correct Answer
A) $685,000
Comparable NOI is $68,400 − $20,400 = $48,000, so its overall rate is $48,000 ÷ $600,000 = 8%. Subject NOI is $79,800 − $25,000 = $54,800, and $54,800 ÷ 0.08 = $685,000. Scaling the price by PGI gives $700,000, a gross multiplier result rather than an overall-rate result. Omitting the subject's vacancy loss gives $737,500, and deducting the comparable's expenses gives $742,500.
Why This Is the Correct Answer
Option A is correct because the comparable's NOI of $48,000 over $600,000 gives an 8% overall rate. The subject's NOI, on the same basis, is $54,800, and $54,800 ÷ 0.08 = $685,000.
Why the Other Options Are Wrong
Option B: $700,000
Option B, $700,000, scales the price by gross income: ($600,000 ÷ $72,000) × $84,000 = $700,000. That ignores the expense difference between the properties; the overall-rate result is $54,800 ÷ 0.08 = $685,000.
Option C: $737,500
Option C, $737,500, capitalizes income without the subject's vacancy loss: ($84,000 − $25,000) ÷ 0.08 = $737,500. The rate was extracted after vacancy, so subject NOI must be $54,800, giving $685,000.
Option D: $742,500
Option D, $742,500, deducts the comparable's expenses from subject EGI: ($79,800 − $20,400) ÷ 0.08 = $742,500. The subject's own $25,000 of expenses applies, giving $54,800 and $685,000.
Same statement, both properties
Run the comparable and the subject through identical lines from PGI to NOI. Take the rate from one and apply it to the other.
How to use: Use this approach when a problem gives full income data on both a comparable and the subject.
Exam Tip
Label each figure as comparable or subject before you begin. Mixing the two sets of expenses is an easy error when the numbers look alike.
Common Mistakes to Avoid
- -Mixing comparable and subject expense figures
- -Capitalizing income before vacancy with a rate extracted after vacancy
- -Deducting mortgage payments when extracting an overall rate
Concept Deep Dive
Analysis
This item combines rate extraction with rate application, so each property needs its own income statement. The rate comes from the comparable's NOI and price, and the buyer's mortgage payments stay out because NOI is measured before financing. The rate then goes on subject NOI calculated the same way, which is the matching-basis requirement.
Background Knowledge
An overall rate from a sale expresses the relationship between one year's net income and price. It is meaningful for the subject only when the subject's income has been processed to the same level as the comparable's.
Real-World Application
An appraiser verifies the sale of a similar fourplex and rebuilds its income statement before financing. The rate extracted from that sale is then applied to a subject income statement prepared with the same line items.
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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The subject property has stabilized annual real property NOI of $148,000 after operating expenses and property taxes. The overall capitalization rate is 8%. What value is indicated by direct capitalization, to the nearest dollar?