Otherwise-matched cash-equivalent sales are $478,000 with a supported view amenity and $412,000 without it. Express the observed difference as a percentage of the price without the view, to one decimal place. What results?
Correct Answer
B) 16.0%
(478000 − 412000) / 412000 × 100 = 16.02%. Using the higher price as denominator gives a different percentage. This observed pair does not establish a universal view premium.
Why This Is the Correct Answer
Option B is correct because the difference is $478,000 - $412,000 = $66,000, and dividing by the price without the view gives $66,000 / $412,000 = 16.02%, or 16.0% to one decimal place. This measures the premium relative to the property without the amenity, as the stem requires.
Why the Other Options Are Wrong
Option A: 13.8%
Option A, 13.8%, divides by the wrong base: $66,000 / $478,000 = 13.8%. The stem asks for the percentage of the price without the view, so the correct result is $66,000 / $412,000 = 16.0%.
Option C: 116.0%
Option C, 116.0%, is the ratio of the two prices, $478,000 / $412,000, rather than the difference. Subtracting 100% from that ratio gives the correct premium of 16.0%.
Option D: 86.2%
Option D, 86.2%, is the inverse ratio of the prices, $412,000 / $478,000. It is not the percentage difference at all; the correct result is $66,000 / $412,000 = 16.0%.
Divide by the base named
Percentage difference equals the dollar difference divided by whichever price the question names as the base.
How to use: Use this to choose the correct denominator in percentage adjustment questions.
Exam Tip
Underline the words that name the base, such as percentage of the price without the view, before dividing.
Common Mistakes to Avoid
- -Dividing by the higher price when the lower price is the stated base
- -Reporting the price ratio instead of the percentage difference
- -Treating one paired sale as proof of a universal premium
Concept Deep Dive
Analysis
This question tests expressing a paired sales difference as a percentage of the correct base. The stem specifies the price without the view as the denominator, so the difference of $66,000 is divided by $412,000. The distractors use the wrong denominator or report a price ratio instead of a difference.
Background Knowledge
Paired sales differences can be expressed in dollars or as percentages, and the percentage depends on which price is used as the base. Using the lower price gives a larger percentage than using the higher price for the same dollar difference. A single pair indicates a market reaction but does not establish a universal premium for that feature.
Real-World Application
Two matched condos in the same building sold, one facing the bay at $478,000 and one facing the parking lot at $412,000. The appraiser expresses the view premium as about 16% of the no-view price. That percentage can then be applied, if supported, to a comparable lacking the view.
More Sales Comparison Questions
Which stated cause of supported value loss is external?
Improvement cost new is $450,000. Separately supported improvement depreciation deductions of $45,000, $25,000, $15,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $125,000, already reflecting any site losses. What total indicated value results?
Which two depreciation categories may each be classified as curable or incurable by comparing the cost to remedy a deficiency with the value gained?
Improvement cost new is $800,000. Separately supported improvement depreciation deductions of $120,000, $80,000, $40,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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Which highest-and-best-use criterion addresses whether a proposed use is allowed by zoning and applicable legal restrictions?
Three comparables produce adjusted indications of $312,000, $309,000 and $315,000, requiring gross adjustments of 9%, 14% and 22% respectively. Verification also establishes that the first sale is the closest competitive substitute and its adjustments are better supported than the other two. Which indication deserves the most weight on those facts?
When reconciling value indications from the three approaches to value, an appraiser should:
A property sold at a cash-equivalent price of $1,062,500. Its stabilized annual NOI is $85,000. What is the indicated overall rate?
In reconciliation, an appraiser should:
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