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Calculating a Relative Position in a Range

 
 
CDobyns
 
Reply Sun 18 Dec, 2005 09:54 am
Saw this described set of steps as a method to calculate and maintain a person's salary position when the salary range changes. This is different from what I thought was the way to make the calculation. Would invite the collective audience to review both methods and weigh in editorially.

Step 1: Subtract the minimum rate of the range of the employee's position in effect on the day immediately preceding the pay adjustment from the employee's rate of basic pay on the day immediately preceding the pay adjustment.

$137,214 - $107,550= $29,664

Step 2: Subtract the minimum rate of the range in effect immediately preceding the pay adjustment from the maximum rate of that rate range.

$162,100 - $107,550 = $54,550

Step 3: Divide the result of step 1 by the result of step 2. Carry the result to the seventh decimal place and truncate.

$29,664/$54,550 = 0.5437946

Step 4: Subtract the minimum rate of the new rate range from the maximum rate of the new rate range.

$165,200 - $109,808= $55,392

Step 5: Multiply the result of step 3 by the result in step 4. Round to the closest whole dollar amount.

0.5437946 x $55,392 = $30,122

Step 6: Add the result of step 5 to the minimum rate of the new rate range.

$109,808 + $30,122 = $139,930


This is the method that I thought would have been proposed and is the approach I would have used and had been taught in the past.

Step 1: Calculate a relative referent value within the current range, which is typically referred to as a midpoint.

$162,100 + $107,550 = $269,650/2 = $134,825

Step 2: Use the referent value in step 1 to calculate a ratio using the current salary.

$137,214/$134,825 = 1.017719266

Step 3: Calculate a relative referent value within the new range.

$165,200 + $109,808 = $275,008/2 = $137,504

Step 4: Apply the ratio in step 2 to the value in step 3.

1.017719266 * $137,504 = $139,940

So, $139,940 versus $139,930. Not a big deal unless you're the one making (or not making) the extra $10. What says the audience on the more appropriate method to calculate and adjust a salary in order to maintain its relative position in the range?

Thanks
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Type: Discussion • Score: 1 • Views: 581 • Replies: 7
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markr
 
  1  
Reply Sun 18 Dec, 2005 02:05 pm
The first method will maintain the employee's fraction of penetration into the salary range.

Your method will produce numbers outside of the new range. For example, set the employee's salary to the min or the max of the old range.
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engineer
 
  1  
Reply Mon 19 Dec, 2005 08:09 am
The reason you have a discrepancy is that the upper and lower bounds changed by different percentages. If the salary range had been bumped by 2% across the board, the two methods would have produced the same answer.
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CDobyns
 
  1  
Reply Mon 19 Dec, 2005 01:59 pm
I agree with Engineer and his comment, and that's exactly what I would have said. Also, mostly see the perspective presented by Makr.

I'm still conflicted about which of these approaches does the better job maintaining the "relative" position in the range, but my sense is that it's the latter approach?
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markr
 
  1  
Reply Mon 19 Dec, 2005 02:21 pm
I would use the first method. I would consider the second method flawed for the general case.
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engineer
 
  1  
Reply Mon 19 Dec, 2005 02:33 pm
But it really doesn't matter. Just because the entire band moved 2%, that doesn't mean that an employee is entitled to a 2% raise. Hopefully performance and skill growth would allow a bigger raise. If there was no growth, why would there be any raise? If the bottom end of the band moved because of changes to the minimal wage law (for example), why would someone in the middle of the band expect a pay raise?

That said, I agree with Mark that the first approach is better.
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CDobyns
 
  1  
Reply Mon 19 Dec, 2005 08:02 pm
For Engineer, I agree that the general philosophy of maintaining someone's position in the range just because the range moves by a certain percentage is preposterous on a number of different levels.

I'm still uncertain about the most appropriate method to use. It still seems like the first method only accurately accounts for the position in the range relative to the minimum of the range. I've tossed this problem to the PhD mathematician in our office to see what wisdom he can spread on this issue.
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CDobyns
 
  1  
Reply Thu 22 Dec, 2005 09:27 am
Okay, this just in from our internal PhD mathematician. She suggests that the first method is indeed the better approach to calculating the relative position in the range.

She mostly alluded to the fact that using that calculation of the mean of the range as the basis for applying the resulting ratio to the current salary, would result in a "lack of sensitivity". I'm assuming she was referring to numerical sensitivity, and not some other emotional charateristic. In any event, I'm glad I didn't bet the farm on my initial inclination as to the more appropriate approach.

Thanks for all the input.
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