Indications are $410,000 (sales comparison), $432,000 (cost) and $395,000 (income). The appraiser assigns weights of 50%, 30% and 20%. What is the weighted indication?
Correct Answer
A) $413,600
Weighted average: $410,000 × 0.50 + $432,000 × 0.30 + $395,000 × 0.20 = $205,000 + $129,600 + $79,000 = $413,600. $412,333 is the simple average; $418,000 swaps the sales and cost weights; $409,900 swaps the cost and income weights.
Why This Is the Correct Answer
Option A is correct because 410,000 x 0.50 + 432,000 x 0.30 + 395,000 x 0.20 = 205,000 + 129,600 + 79,000 = $413,600. Each indication is multiplied by its own weight and the products are added. The weights total 100%, so no further division is needed.
Why the Other Options Are Wrong
Option B: $412,333
Option B's $412,333 is the simple average: (410,000 + 432,000 + 395,000) / 3 = $412,333. It ignores the stated 50%, 30% and 20% weights, which produce $413,600.
Option C: $418,000
Option C's $418,000 swaps the sales and cost weights: 410,000 x 0.30 + 432,000 x 0.50 + 395,000 x 0.20 = 123,000 + 216,000 + 79,000 = $418,000. The correct pairing gives $413,600.
Option D: $409,900
Option D's $409,900 swaps the cost and income weights: 410,000 x 0.50 + 432,000 x 0.20 + 395,000 x 0.30 = 205,000 + 86,400 + 118,500 = $409,900. The correct pairing gives $413,600.
Pair, multiply, add
Pair each indication with its own weight, multiply, then add the products.
How to use: Use this on any weighted reconciliation calculation.
Exam Tip
Write each indication next to its weight before multiplying to avoid swapped-weight distractors.
Common Mistakes to Avoid
- -Using a simple average instead of the assigned weights
- -Applying a weight to the wrong approach
- -Dividing the weighted sum by the number of approaches
Concept Deep Dive
Analysis
This question tests computing a weighted average correctly. Multiply each indication by its assigned weight and add the products. Distractors come from a simple average or from applying weights to the wrong approaches.
Background Knowledge
A weighted average multiplies each component by a factor representing its relative importance and adds the products. In reconciliation, the weights reflect the appraiser's supported judgment of each approach's reliability. The weights should be explained in the report.
Real-World Application
An appraiser reconciles a small rental property's indications, giving sales comparison 50%, cost 30% and income 20% based on data quality. The weighted result is $413,600. The report explains why each approach received its weight.
More Reconciliation Questions
In a cost approach for an improved property, an appraiser estimates site value by sales comparison, allocation and extraction, then settles on one site-value figure before final reconciliation. How is this step best described?
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An otherwise applicable valuation approach cannot be developed reliably from the available data. The remaining scope can produce credible assignment results. What should the appraiser do?
May an appraiser use a hypothetical condition in any assignment?
An appraisal has a current effective date and permits an extraordinary assumption if its requirements are met. Which situation involves uncertain information rather than a fact known to be contrary to reality on that date?
Why must a report identify any real property interest that is being excluded from the value opinion?
Which review best helps explain divergent cost, sales-comparison and income indications?
Two value indications are $340,000 and $392,000. What is the difference as a percentage of the lower indication, rounded to one decimal place?
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An appraiser proposes to assume there are no hidden defects. Which fact would characterize that assumption as extraordinary under the USPAP 2024 definition, rather than justify dismissing it as routine boilerplate?
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