An appraiser's value indications are $520,000, $480,000 and $500,000, initially weighted 50%, 30% and 20%, respectively. If the weights change to 70%, 20% and 10%, respectively, what is the new weighted indication?
Correct Answer
B) $510,000
The initial result is $520,000×0.50 + $480,000×0.30 + $500,000×0.20 = $504,000. The new result is $520,000×0.70 + $480,000×0.20 + $500,000×0.10 = $510,000, an increase of $6,000. Both sets of weights are stated in the facts.
Why This Is the Correct Answer
Option B is correct because the new weights give $520,000 × 0.70 = $364,000, $480,000 × 0.20 = $96,000, and $500,000 × 0.10 = $50,000, for a total of $510,000. The original weights produced $504,000, so the change in weights raises the result by $6,000.
Why the Other Options Are Wrong
Option A: $504,000
Option A, $504,000, is the result using the initial weights: $520,000 × 0.50 + $480,000 × 0.30 + $500,000 × 0.20 = $260,000 + $144,000 + $100,000 = $504,000. The question asks for the result with the new 70%, 20% and 10% weights, which is $510,000.
Option C: $500,000
Option C, $500,000, is the simple unweighted average: ($520,000 + $480,000 + $500,000) ÷ 3 = $500,000. It ignores both weight sets; applying the new weights gives $364,000 + $96,000 + $50,000 = $510,000.
Option D: $516,000
Option D, $516,000, results from adding the $6,000 change to the new result ($510,000 + $6,000 = $516,000), counting the increase twice. The new weighted indication itself is $510,000.
New weights, fresh calculation
When the weights change, redo the full calculation with the new weights rather than adjusting the old answer.
How to use: Use this when a question changes the weights and asks for the new weighted result.
Exam Tip
Read carefully whether the question asks for the new result or the change. Here the new result is $510,000 and the change is $6,000.
Common Mistakes to Avoid
- -Reporting the result from the original weights
- -Adding the change to the new result
- -Averaging the indications without applying any weights
Concept Deep Dive
Analysis
This question tests whether you can recompute a weighted indication after the weights change. Apply the new weights, not the original ones, to the same three indications. Comparing the two results shows how sensitive the conclusion is to the weighting choice.
Background Knowledge
Sensitivity analysis shows how much a conclusion moves when assumptions change. In reconciliation, comparing results under different weightings helps an appraiser understand how much the final opinion depends on the relative reliance placed on each approach.
Real-World Application
After a review comment, an appraiser decides the sales comparison approach deserves more reliance and shifts its weight from 50% to 70%. The appraiser recalculates the weighted indication and notes in the report how the conclusion changed and why.
More Reconciliation Questions
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