As part of our contributor series, Steven W. Vehmeier, Appraisal Educator Emeritus, shares an easy-to-understand appraisal reconciliation technique called Weighted Mean.
In my experience reviewing appraisal reports, it has been common to see a brief, obviously canned, reconciliation, such as: “The sales comparison approach yields the strongest indication of the subject property’s value because it best replicates the actions of buyers and sellers in the market area. The cost approach is supportive. The income approach is not applicable due to a lack of annual rental data from which to develop a gross rent multiplier.”
While everything in that statement may be true, does it logically inform the reader as to how the appraiser arrived at the conclusions? What are the steps in the process, what is the rationale for that process, and what was the actual thought process behind the conclusions? In contrast to the above example, sometimes appraisal reconciliation involves a detailed explanation of facts and reasoning, especially in non-residential and litigation work. Although sometimes warranted, going to that extreme is not always necessary for the reader to reach the reported conclusion.
There is a technique called Weighted Mean that can be used in most assignments to reconcile data, such as reconciling comparables and site values, reconciling indicators for adjustments, determining multipliers and rates, or for final reconciliation.
Using Weighted Mean to reconcile comparables
In theory, if every detail of each comparable sale were known and perfectly accounted for, they could yield the same indicated value; or the mean (average) of their indicated values in the sales comparison grid could be the subject property’s value. In reality, even as adjusted, there are stronger and weaker indicators of value, and it is necessary to allocate greater or less weight to each comparable.
Let’s say you have a residential assignment with three comparables showing the following adjusted indicated values for the subject. Sale #1 is $223,000, Sale #2 is $239,000, and Sale #3 is $249,000. Sale #1 is the furthest away and requires the most adjustment. Sale #2 has the same floor plan as the subject and is located across the street. Sale #3 also has the same floor plan and is located one block away.
In this case, the appraiser needs to apply weight to each comparable. Without using Weighted Mean, making those weight percentage decisions is often done purely mentally without any explanation to the reader.
We can instead use Weighted Mean and allocate percentages to each comparable. The percentages chosen are part of the “art” of appraising, and make it easier to explain the rationale of how you arrived at your conclusion to the reader.
Example #1
It would be appropriate to allocate percentages to the above comparables in this case: Sales #2 and #3 are the most similar, require minimal adjustment, have the same floor plan, and are geographically closest to the subject. Therefore, equal weight of 40% is given to each. Sale #1 is least similar overall, especially in proximity, and is given only 20% weight. Make sure the weights total 100%.
HP-12C keystrokes
223,000 [ENTER] .20 [∑+]
239,000 [ENTER] .40 [∑+]
249,000 [ENTER] .40 [∑+]
[g] [x̄ w] Solution 239,800
Value for subject property (rounded) is $240,000.
Note: The [∑+] key is bottom row right side, and [x̄ w] is found in the bottom of the 6 key in blue.
Manual calculation
Alternatively, you can calculate the solution manually as follows:
223,000 X .20 = 44,600
239,000 X .40 = 95,600
249,000 X .40 = 99,600
Weight Mean = 239,800
Example #2
Another example would be to reconcile site values for the cost approach. Vacant lot sales in the vicinity range from $20,000 to $36,000 depending on size, shape, and view. Four lots have recently sold. The adjusted values are: #1 = $28,000, #2 = $25,000, #3 = $34,000, and #4 = $30,000.
Just as in Example #1, state the percentages allocated and why. Let’s assume #1 received 20% from that allocation. A 10% weight is assigned to #2. Sales #3 and #4 receive 40% and 30% weight, respectively.
HP-12C keystrokes
28,000 [ENTER] .20 [∑+]
25,000 [ENTER] .10 [∑+]
34,000 [ENTER] .40 [∑+]
30,000 [ENTER] .30 [∑+]
[g] [x̄ w] Solution 30,700
Manual calculation
Alternatively, you can calculate the solution manually as follows:
28,000 X .20 = 5,600
25,000 X .10 = 2,500
34,000 X .40 = 13,600
30,000 X .30 = 9,000
Weight Mean = 30,700
As a result of presenting it this way, a reviewer can replicate your steps, understand the logic, and come to the same conclusion.
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What about reconciling adjustment amounts?
The same steps and explanation logic can be applied in reconciling the amount to adjust a comparable.
Let’s say three sales indicate the adjustment for an additional garage bay at $15,000, $17,000, and $20,000. Reconcile those figures in the same manner, giving a weight to each one, say 50%, 40%, and 10% in that order. Then explain the rationale, and show the reader how we calculated the solution with the HP-12C keystrokes or the manual calculations. Just always make sure the percentages add up to 100%.
HP-12C keystrokes
15,000 [ENTER] .50 [∑+]
17,000 [ENTER] .40 [∑+]
20,000 [ENTER] .10 [∑+]
[g] [x̄ w] Solution 16,300
Manual calculation
15,000 X .50 = 7,500
17,000 X .40 = 6,800
20,000 X .10 = 2,000
Weight Mean = 16,300
Can you use the Weighted Mean in the Income Approach?
Yes, you can use the same appraisal reconciliation technique in the Income Approach. There is a very low likelihood that several sales of rental properties will yield the same indicated gross rent multiplier (GRM). To determine and support the GRM used, enter the GRM figure for each comparable used, then press ENTER followed by the allocated percentage and press ∑+.
Finally, press [g] and [x̄ w] to find the solution.
HP-12C keystrokes
135 [ENTER] .30 [∑+]
125 [ENTER] .40 [∑+]
120 [ENTER] .20 [∑+]
118 [ENTER] .10 [∑+]
[g] [x̄ w] Solution 126.30
Manual calculation
135 X .30 = 40.5
125 X .40 = 50.0
120 X .20 = 24.0
118 X .10 = 11.8
Weight Mean = 126.3
Capitalization rates can also be reconciled in the same way. Reconcile the indicated rates from the varied sources by assigning weights to each indicator and entering them into an HP-12C (or calculating the Weighted Mean manually), as shown above for the GRM.
What about the final appraisal reconciliation?
The process is the same with the final reconciliation. Present the indicated values of the three approaches to value (sales, cost, and income), then apply the weighting percentages, expressing the rationale and demonstrating how it was calculated using the Weighted Mean.
Let’s say we have a new construction house in a new development with some verifiable rental activity in the area. The sales comparison approach value is $320,000, the cost approach is $323,000, and the income approach is $300,000. The weighted percentages are determined as 50% for the sales comparison approach, 45% for the cost approach, and 5% for the income approach.
HP-12C keystrokes
320,000 [ENTER] .50 [∑+]
323,000 [ENTER] .45 [∑+]
300,000 [ENTER] .05 [∑+]
[g] [x̄ w] Solution 320,350
Manual calculation
320,000 X .50 = 160,000
323,000 X .45 = 145,350
300,000 X .05 = 15,000
Weight Mean = 320,350
Final thoughts
Weighted Mean is a basic tool in an appraiser’s skill set. Because seldom do all indicators yield the exact same indication of value, adjustment amount, or final conclusion, Weighted Mean is a simple, easily understood appraisal reconciliation technique that can be replicated by the reviewer at their desk.
Weighted Mean essentially quantifies the mental reconciliation appraisers undergo when reconciling numbers in their minds. The trained appraiser mentally allocates weight to each number and arrives at a solution. The Weighted Mean effectively illustrates that process.
Is it applicable in every case? There are certainly times when different skills are warranted, but overall Weighted Mean works very well to develop, as well as support, many conclusions in an appraisal report.
Written by Steven W. Vehmeier, Appraisal Educator Emeritus. Steve retired from his appraisal and appraisal education practices after a long career specializing in writing and teaching pre-license and continuing education courses, including twenty-two years doing so for McKissock. He continues to write articles and blogs to share his knowledge and experience.
