An appraiser finds a comparable that sold for a cash-equivalent price of $1,350,000 with annual PGI of $150,000. The subject has annual PGI of $128,000. Sales in the market area indicate the subject would sell at the same price-to-income ratio, and no other adjustments are needed. What is the indicated value of the subject, to the nearest dollar?
Correct Answer
A) $1,152,000
1350000÷150000×128000 = 1152000. Common errors: inverting the income ratio (comparable income ÷ subject income) gives $1,582,031; using the comparable price without adjusting for the income difference gives $1,350,000; adding the income difference dollar-for-dollar to the comparable price gives $1,328,000.
Why This Is the Correct Answer
Option A is correct because $1,350,000 ÷ $150,000 × $128,000 = 9 × $128,000 = $1,152,000. The subject's lower PGI produces a proportionally lower value under the same ratio.
Why the Other Options Are Wrong
Option B: $1,328,000
Option B, $1,328,000, comes from adding the income difference dollar for dollar: $1,350,000 + ($128,000 − $150,000) = $1,328,000. The difference must be scaled by the ratio, giving $1,350,000 ÷ $150,000 × $128,000 = $1,152,000.
Option C: $1,350,000
Option C, $1,350,000, is the comparable's price with no adjustment for the subject's lower PGI of $128,000. Applying the ratio gives 9 × $128,000 = $1,152,000.
Option D: $1,582,031
Option D, $1,582,031, results from inverting the income ratio: $1,350,000 × $150,000 ÷ $128,000 = $1,582,031. The correct value is $1,350,000 × $128,000 ÷ $150,000 = $1,152,000.
Lower income, lower value
Under the same multiplier, a subject earning less than the comp must be worth less than the comp sold for.
How to use: Use this direction check after any ratio calculation.
Exam Tip
Compute the multiplier as a whole number when possible (here 9) to make the final step simple and reduce errors.
Common Mistakes to Avoid
- -Inverting the income ratio
- -Adding the raw income difference to the comparable price
- -Using the comparable price without adjustment
Concept Deep Dive
Analysis
This question tests applying a comparable's price-to-PGI ratio to the subject's PGI. The comparable sold at $1,350,000 ÷ $150,000 = 9 times PGI. Multiplying the subject's $128,000 PGI by 9 gives value, which should be lower than the comparable's price.
Background Knowledge
A gross income multiplier extracted from a comparable sale must be applied to the subject's income at the same level, here PGI. Under a constant multiplier, value is proportional to income. Comparable prices should be adjusted to cash equivalency before the multiplier is extracted.
Real-World Application
An appraiser valuing a fourplex finds a nearby sale at 9 times PGI. After confirming both properties' PGI is measured alike, the appraiser applies that multiplier to the subject's PGI.
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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