While verifying a fourplex sale, an appraiser learns that the buyer paid $900,000 cash equivalent. Potential gross income over the prior year was $100,000, but an above-market lease on one unit was ending, and the buyer projected potential gross income of $90,000 less a 5% vacancy allowance. The subject fourplex has market potential gross income of $110,000. What value does a potential gross income multiplier from this sale indicate?
Correct Answer
C) $1,100,000
The multiplier uses the income the buyer anticipated, processed only to the potential gross level: $900,000 ÷ $90,000 = 10.0, and 10.0 × $110,000 = $1,100,000. Using trailing income gives a 9.0 multiplier and $990,000, averaging the two multipliers gives $1,045,000, and deducting the vacancy allowance before deriving the multiplier gives $1,157,895.
Why This Is the Correct Answer
Option C is correct because the buyer anticipated $90,000 of potential gross income, which gives $900,000 ÷ $90,000 = 10.0. Applying 10.0 to the subject's $110,000 market potential gross income gives $1,100,000.
Why the Other Options Are Wrong
Option A: $990,000
Option A, $990,000, derives the multiplier from trailing income: $900,000 ÷ $100,000 × $110,000. The buyer priced the income expected after the lease ended, so the correct figure is 10.0 × $110,000 = $1,100,000.
Option B: $1,045,000
Option B, $1,045,000, averages the trailing and anticipated multipliers: (9.0 + 10.0) ÷ 2 × $110,000. The trailing figure did not reflect what the buyer expected, so the correct figure is 10.0 × $110,000 = $1,100,000.
Option D: $1,157,895
Option D, $1,157,895, deducts vacancy before deriving the multiplier: $900,000 ÷ ($90,000 × 0.95) × $110,000. A gross income multiplier uses potential income, so the correct figure is $900,000 ÷ $90,000 × $110,000 = $1,100,000.
Buyers price tomorrow's gross
The numerator is what the buyer paid; the denominator is the potential income that buyer expected, not last year's figure and not a net of vacancy.
How to use: Use this phrase when a sale reports both a trailing income and a buyer's expected income.
Exam Tip
Look for words such as anticipated, underwrote or expected when deriving a multiplier from a verified sale. Then confirm the income level named by the multiplier.
Common Mistakes to Avoid
- -Deriving a multiplier from trailing income when the buyer expected something different
- -Deducting vacancy before computing a potential-income multiplier
- -Averaging historic and anticipated multipliers without support
Concept Deep Dive
Analysis
The problem tests two choices about the multiplier's denominator: which period's income and which income level. A buyer prices what the property is expected to earn, so anticipated income governs when it differs from history. A gross income multiplier stops at potential gross income, before any vacancy allowance.
Background Knowledge
Market participants pay for expected future benefits, so a multiplier derived from a sale reflects the income the buyer anticipated. That income may differ from the property's actual current income, and verifying the buyer's expectations helps reveal the difference.
Real-World Application
During sale verification, a buyer explains that a tenant's above-market lease was about to expire and that the price reflected lower expected rent. The appraiser derives the multiplier from that expected income, since trailing income would understate the multiplier the market actually paid.
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?
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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?
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A cash-equivalent price is $480,000 and monthly gross rent is $2,000. What is the monthly-basis multiplier? The matching annual multiplier would use twelve equal monthly rents.
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Market data show a sale at a cash-equivalent price of $2,625,000, with stabilized annual NOI of $210,000. What overall rate does the sale indicate?