Indications are sales comparison $480,000, cost $500,000 and income $460,000. The appraiser gave the income approach 10% weight and reconciled to $484,000 with a weighted average. What weight did the sales comparison approach receive?
Correct Answer
C) 60%
With w as the sales comparison weight, cost gets 90% - w, so 480,000w + 500,000(0.90 - w) + 46,000 = 484,000, which gives 496,000 - 20,000w = 484,000 and w = 60% (cost 30%). 30% is the cost weight, 45% splits the remaining 90% evenly, and 80% solves as if only sales comparison and cost had been weighted, ignoring the income share.
Why This Is the Correct Answer
Option C is correct because, with income fixed at 10%, the sales and cost weights share the remaining 90%. Solving 480,000w + 500,000(0.90 - w) + 46,000 = 484,000 gives w = 0.60, so sales comparison received 60% and cost 30%. The check 288,000 + 150,000 + 46,000 = $484,000 confirms it.
Why the Other Options Are Wrong
Option A: 30%
Option A, 30%, is the weight left for the cost approach (90% - 60%), not the sales comparison weight. Giving sales only 30% would leave cost at 60% and push the result to 144,000 + 300,000 + 46,000 = $490,000.
Option B: 45%
Option B, 45%, splits the remaining 90% evenly between sales and cost without solving the equation. That blend gives 216,000 + 225,000 + 46,000 = $487,000, not the $484,000 reported.
Option D: 80%
Option D, 80%, solves 480,000w + 500,000(1 - w) = 484,000 as if only two approaches were weighted, ignoring the 10% income share. With income included, the equation gives 60%.
Weights must total one hundred
Fix the known weight first, give the unknown weight w and the last one the remainder, then solve the single equation.
How to use: Use this when a question gives a final value and asks what weight produced it.
Exam Tip
Always check your answer by plugging the weights back in; a correct solve reproduces the final value exactly.
Common Mistakes to Avoid
- -Reporting the other approach's weight
- -Dropping the known weight and solving a two-approach blend
- -Splitting remaining weight evenly instead of solving
Concept Deep Dive
Analysis
The question reverses a weighted reconciliation: given the indications, one weight and the final value, the candidate solves for an unknown weight. It requires setting up the weighted-average equation with all three approaches and remembering that the weights total 100%.
Background Knowledge
A weighted average multiplies each indication by its weight and adds the products, with weights totalling 100%. Because the relationship is linear, any one missing weight can be solved for when the result and the other inputs are known, which is a useful way to test whether a reported weighting is internally consistent.
Real-World Application
A reviewer sees a report concluding at $484,000 with income weighted 10% but no stated split between sales and cost. Solving the weighted-average equation shows the appraiser must have used 60% and 30%, and the reviewer asks for that weighting to be stated and explained.
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?
An extraordinary assumption was reasonably supported, properly used and disclosed in an appraisal report. Later, the assumed information is found to be false. Which conclusion is best supported?
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?
An unauthorized third party requests a lender-client’s report. No due-process or other permitted disclosure exception applies. How should the appraiser respond?
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?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam