A comparable sold for a cash-equivalent price of $1,000,000 and has annual NOI of $80,000. The subject property has annual NOI of $88,000. Sales in the market area indicate the subject would sell at the same price-to-income ratio, with no other adjustments. What is the indicated value of the subject, to the nearest dollar?
Correct Answer
D) $1,100,000
1000000÷80000×88000 = 1100000. Common errors: inverting the income ratio (comparable income ÷ subject income) gives $909,091; using the comparable price without adjusting for the income difference gives $1,000,000; adding the income difference dollar-for-dollar to the comparable price gives $1,008,000.
Why This Is the Correct Answer
Option D is correct because $1,000,000 ÷ $80,000 = 12.5, and 12.5 × $88,000 = $1,100,000. Equivalently, the comparable's overall rate is 8%, and $88,000 ÷ 0.08 = $1,100,000, using the same income basis.
Why the Other Options Are Wrong
Option A: $909,091
Option A, $909,091, inverts the income ratio: $1,000,000 × $80,000 ÷ $88,000 = $909,091. That gives the higher-income subject a lower value; the correct calculation is $1,000,000 ÷ $80,000 × $88,000 = $1,100,000.
Option B: $1,000,000
Option B, $1,000,000, uses the comparable's price without adjusting for the subject's higher NOI. With NOI of $88,000 rather than $80,000, the ratio of 12.5 gives $1,100,000.
Option C: $1,008,000
Option C, $1,008,000, adds the income difference dollar-for-dollar to the comparable price: $1,000,000 + ($88,000 − $80,000) = $1,008,000. The income difference must be converted through the ratio, giving $1,100,000.
Same Ratio, Scaled Income
When the same price-to-income ratio applies, value rises in proportion to income. A subject with 10% more NOI gets 10% more value.
How to use: Use this proportion check after applying a comparable's ratio to a subject.
Exam Tip
Compare the percentage change in income with the percentage change in value; they should match when the same ratio applies.
Common Mistakes to Avoid
- -Inverting the income ratio
- -Adding the NOI difference in dollars to the comparable price
- -Using the comparable price unchanged
Concept Deep Dive
Analysis
This question tests applying a comparable's price-to-NOI ratio to a subject with different NOI. The comparable's price divided by its NOI gives the multiplier, which is then applied to the subject's NOI. Since the subject earns more, its indicated value should exceed the comparable price.
Background Knowledge
A market-derived overall rate is NOI divided by a cash-equivalent sale price. Applying that rate, or its reciprocal multiplier, to the subject's NOI converts the subject's income into value when the income conventions match.
Real-World Application
An appraiser valuing a rented duplex finds a similar property that sold on a cash-equivalent basis. The appraiser extracts its price-to-NOI ratio and applies it to the subject's stabilized NOI.
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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