An appraiser is verifying the sale of a 24-unit apartment building that was listed at $2,187,500 and sold for $2,050,000 cash. Several units were vacant at the time of sale while the seller finished a renovation at the seller's expense, and NOI over the prior 12 months was $150,000. The buyer confirms the purchase was underwritten on anticipated NOI of $164,000 for the coming year. What is the market-extracted overall rate?
Correct Answer
D) 8.00%
A market-derived rate uses the income anticipated by the buyer divided by the cash-equivalent sale price: $164,000 ÷ $2,050,000 = 8.00%. In-place NOI gives 7.32%, which understates the rate because the temporary vacancy is not the income the buyer priced. Dividing by the list price gives 7.50%, but a list price is not a sale. Averaging the two incomes gives 7.66%, a figure no market participant used.
Why This Is the Correct Answer
Option D is correct because the overall rate is the buyer's anticipated net income divided by the cash-equivalent sale price. That is $164,000 ÷ $2,050,000 = 8.00%. The buyer confirmed the anticipated income, and the price was all cash.
Why the Other Options Are Wrong
Option A: 7.32%
Option A, 7.32%, uses in-place NOI: $150,000 ÷ $2,050,000 = 7.32%. That income reflects temporary renovation vacancy rather than what the buyer was paying for; the correct rate is $164,000 ÷ $2,050,000 = 8.00%.
Option B: 7.50%
Option B, 7.50%, divides by the list price: $164,000 ÷ $2,187,500 = 7.50%. A list price is an asking figure rather than a completed sale; the correct rate is $164,000 ÷ $2,050,000 = 8.00%.
Option C: 7.66%
Option C, 7.66%, averages the two incomes: ($150,000 + $164,000) ÷ 2 = $157,000, and $157,000 ÷ $2,050,000 = 7.66%. An average is not the income either figure describes; the correct rate is $164,000 ÷ $2,050,000 = 8.00%.
Price Pairs With Expectation
A sale price is paid for expected income, so the top of the rate fraction is what the buyer expected and the bottom is what the buyer paid.
How to use: Use this pairing when a sale shows both current income and buyer-anticipated income.
Exam Tip
Separate list price from sale price and current income from anticipated income before dividing. Each wrong pairing produces a believable rate.
Common Mistakes to Avoid
- -Pairing a sale price with temporarily depressed income
- -Using the list price in the denominator
- -Averaging current and anticipated income
Concept Deep Dive
Analysis
When a property sells during a temporary disruption, current income can be well below what the price reflects. The rate should pair the price with the income that motivated it. The denominator must also be the actual sale price, not the list price.
Background Knowledge
A price reflects what the buyer expects a property to earn, which may differ from its income on the sale date. Rates and multipliers derived from sales should therefore be matched to the income anticipated in that transaction, verified where possible.
Real-World Application
An appraiser sees a low rate in a data service for a building that sold mid-renovation. A call to the buyer reveals underwriting based on stabilized income, so the appraiser recalculates the rate on that figure before using the sale.
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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