Profit Sharing without a Cap

Laura Milhouse
Laura Milhouse used Ask the Experts™
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Hi,  I am looking to design a profit sharing scheme that would take into account the job level of the employee, the performance of the geographic region, and the individual performance level.  The first can be a number between 1 and 7 or a dollar amount, the second will be the achievement of projected profit, and the third will be a number between 1 and 5.  Is there anyway to calculate a final contribution without making it the percentage of a cap?  The total pool for each geographic regional will be a straight percentage of profits.

i.e. 15% of profits might be 10 million for ease of calculation.  For thirty employees, is there some formula that will reward each employee a portion of that 10 million based on their job level, achievement of projected profit, and ind. performance???

Thank you!
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I am not sure what you mean by "a cap"
It seem to me that the amount to be distributed must not total more than the 15%, thus a "cap" seems to be inevitable

Author

Commented:
There is a cap to the pool of money, but not to the individual. Usuall ypu wpuld have a target incentive per person - say 20%. So the most a person making 100 grand could get is around 20 grand. Often in plans it would look like this:

(100,000 × 20% cap) x 0 - 120% for group performance x 0 - 120% for individual performance.

If I don't have that 20% target incentive, is there a mathematical way to do the above calculation?
"There is a cap to the pool of money, but not to the individual"
-

If there is a cap to the pool there MUST be a cap to the individual. Furthermore if, for example, there are 30 people and
and 4 of them earn 25% of the pool, there is nothing left for the other 26 no matter how deserving they are.
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You probably have some heuristics and concrete use case scenarios that you would like to model. If you could post a few examples of how you would distribute the pool , then we could try to help you come up with a model that formulates your ideas .

Author

Commented:
Each employee's share should be established by taking into account their job level (the more they earn the more they are entitled to), the performance of their area (the better their area does the more they are entitled to) and their individual performance (the better they do the more they are entitled to).

Employee 1:
Makes 75,000
Her area achieved 100 of target so is entitled to full area portion profit sharing
Her individual performance was a 2 out of 5, so she is entitled to less profit sharing

Employee 2:
Makes 40, 000 so is entitled to less profit sharing than Employee 1
His area exceeded projections so is entitled to more profit sharing for area portion.
His individual performance is a 4 put of 5 so is entitled to more of the individual portion of profit sharing

Employee 3:
Makes 100,000 so is entitled to more profit sharing than 1 or 2
His area missed it's target so he receives a lower share of the area portion
His individual performance is 3 out of 5 which is average so he receives an average portion of the individual profit sharing share

This all needs to fit into the enveloped of 15% of profits before tax on all profit after the first 0.5% profit.

Thank you!
Kevin CrossChief Technology Officer
Most Valuable Expert 2011

Commented:
If initial entitlement is based on salary as the indication of higher job level, then you could do what we did.  You start with a max percentage say 15%.  If these person is upper management, it could be 30%.  In other words, you can use a flat percentage that automatically increases those with a higher base but then make higher targets for executives, et cetera to further segment high performers.

We then took each of the buckets and assigned their max.  Taking 15%, it would be 5% per bucket.
You then align each number of their target with a percent payout (e.g., 1 - 7, must hit a 3 before you get 1% and increase by 1% as you go up)
If employee hits 7, they get 5%.
If company profits exceeds target levels, employee gets appropriate percentage of that 5%.
If employee performs high, they get 5%.

You can make all three contingent on a base profit of the company to make sure you are not paying out at the detriment of staying in business (they would rather have a job than a bonus if they are honest with themselves) but as you can see it creates a natural spread of benefits based on performance.

Now same results for a manager whose maxes are 7.5% or 10% can earn up to 30% bonus versus another employee who earns 15% total.

I hope that makes sense.
Kevin CrossChief Technology Officer
Most Valuable Expert 2011

Commented:
Based on the way you laid it out above, you could just do your number system but just have a multiplier for employees that should get more like my solution above where you increased percent for some individuals, so you could have number go 1 to 7 but then 4 to 10 for others.  At the end you will have the total number earned by all employees.  Take this sum and divide $10M to get award per point, then multiply that number times each individual's points to get their portion of the $10M.
Kevin CrossChief Technology Officer
Most Valuable Expert 2011

Commented:
This is a crude spreadsheet but hopefully it helps clarify the solution suggestion with the point system you have (at least as I understood it).  I used 1-7 in first bucket to represent you first measure, 4's in second bucket to represent company performance but could be different if you assign different value by region, third bucket is the individual performance review then I added fourth bucket to break tie between two employees who both do well but one is paid more per your examples.  Kept this fourth bucket a simple divide salary by $10K to get an integer.  Taking the sum of all the results, I find a dollar amount something like $17K that I then multiply for each employee.  As you see there is no cap on an employee based on percentage of their salary but ensures it is within your $10M available.
EE-Profit-Share.xlsx
It seems to me that a fairly simple equation that includes all the parts would be feasible.  Let's see:

State the given information:

Each geographic area is treated separately.  The total pool for each geographic regional will be a straight percentage of profits.  So, I will assume that this means: "The total pool of dollars for each geographic regional will be a percentage of profits for that geographic region.
Call the profit rate for the geographic region "P%" of the Revenue "R".
The dollar amount of profit is "C":
C = P*R
The pool of dollars for bonuses is "M":
M  = 0.15*C - 0.005*C = 0.145*C = 0.145*P*R
This amount of money M is to be split amongst the employees according to some sharing formula:

First: Job level distribution factor
Job level of employees goes from 1 to 7.
Add up the total job level points for all the employees:  
Level 1 = a1
Level 2 = a2
.
Level 7 = a7
Where the aNs are the number of employees at each level.
Total points = sum over n=1 to 7 fir k=n of k*ak
Then divide each employee's level by that sum.
Example: if there is one employee at each level then the sum is 28.
Level 1 factor is 1/28 = 3.57% for this employee distribution amongst levels.
Level 2 factor is 2/28 = 7.14%  for this employee distribution amongst levels.
.
Level 7 factor is 7/28 = 25%  for this employee distribution amongst levels.
Total is 100%

Next: Achievement of projected profit

Presumably you will pay less if the actual profit is less than the projected profit.  So that can be done but it seems like double-dipping because the amount M is already weighed by the level of profit.  
And, if the actual profit is greater than the projected profit the M is greater as well.
So it seems like this is covered.
That said, one could make it nonlinear so that smaller profits are penalized even more and larger profits are rewarded even more EXCEPT you have already tied M to a percentage of total profits.  That seems to leave out the possibility of nonlinearly greater rewards as you are already at the maximum you'll allow.
So, maybe you'd be happy to penalize more heavily for lower profits and leave the higher profits alone.
Example:
Profit projection for P is 10% and that projection of 10% profit is $10M.  So, revenue of $10M/0.1 = $100M and the projected M is 0.145*P*R-0.075*R
so projected M is 0.145*0.1*$100M = $1.45M

Now, let's look at a lower actual profit of 5%:
Profit rate realized P is 5% and that 5% profit is $5M.  So, revenue of $5MM/0.05 = $100M (still)  so M is 0.145*0.05*$100M = $0.725M
This could be weighed so that the bonus would be zero at profit = half of projected:
Call "Pp" the projected profit and call "Pa" the actual profit.
So, in this case we'd call the bonus profit:
Pp-2*Pa
And the bonus pool might be M = 0.145*(Pp-2*(Pp - Pa)*R
So with an actual profit of 5% vs. projected profit of 10%, it would be:
M = 0.145*(0.1-2*0.05)*$100M = $0
There are any number of ways to reduce the bonuses, including zero if the goal isn't met.

Now, what if the profit is above the projected 10% at 20%?
From above we'd get M = 0.145*20%*$100M or $2.9M out of a profit of $20M or 14.5%.
Any increase from this amount would exceed the 14.5% limit.
So that was my point earlier.

Last: Individual achievement level

Here you might start with M which is the maximum bonus pool and then award a bonus to each employee according to their own score.  However, this would effectively reduce the bonus pool.  And, that may be OK with you.
So, let's first calculate the bonus per employee as if they got the maximum score of 5:

Start with M and distribute it according to the job level distribution factor.
Then calculate the individual bonuses by weighting by their individual score "S" by multiplying their bonus maximum by S/5.

Alternately you could redistribute the bonus pool as follows:
Calculate the sum of all the employee achievement points Ss
Award a bonus that is the maximum individual bonus amount multiplied by S/Ss.
This is likely going to cause a very big swing in the bonuses but maybe that's what you want?

Overall example:

Revenue: R = $100M
Profit rate projected: Pp=15%
Profit rate actual: Pa=10% (and I will use a straight line discount here)
Profit:
Total levels: 28
M = 0.145*(0.15-0.05)*$100M = $1.45M

Job level maximum bonus = $1.45/28 = $51,786.

Assuming a Level 1 with an individual score of 1: 1*$51,768*(1/5) = $10,357
Assuming a Level 7 with an individual score of 5: 7*$51,768*(5/5) = $362,502

Assuming a Level 1 with an individual score of 5: 1*$51786*(5/5) = $51,786
Assuming a Level 7 with an individual score of 3: 7*($51786)*3/5) = $217,501

Now, I'm sure I must have made some mistakes here but I hope the approaches are clear enough.
It can be cleaned up and tailored to your objectives - as I probably misinterpreted them all perfectly.
Kevin CrossChief Technology Officer
Most Valuable Expert 2011
Commented:
It can be cleaned up and tailored to your objectives - as I probably misinterpreted them all perfectly.
*laughing* Such is business, though.  I thing somehow I got to the same answer as you in my spreadsheet but I did not interpret the 1-7 as already being a representation of salary; therefore, I redid the spreadsheet.
EE-Profit-Share-v2.xlsx

This version has two columns.  The first Share All is how I interpreted your request first as you want to share the entire $10M and individual scores determines the balance, so if one region does better than the other (used flat number before but think your middle calc on how region did to target is to determine if they get a bigger piece of the pie) but other two calcs the same then you would get a bigger bump.  Still simple math of summing all the numbers (i.e., all 90 scores - 3 each per 30 employees) which we will call "S" and use that to divide profit "P" to get a profit per score then multiply that by individual's personal score which is "s".

Share All $$ = P / S * s

The second column does not distribute all profits.  It figures if you have 30 employees "E", each has 1/30 of the pie up for grabs.  Their score divided by total possible is percent they earn.
Share Earned $$ = P / E * s/17
I would say that the real problem is solved and that any modifications are due to differing objectives / definitions.
Kevin CrossChief Technology Officer
Most Valuable Expert 2011

Commented:
Agree.  Love your quote by the way.  Hope my post came across that way.  I misinterpret perfectly requirements all the time, coming up with really cool solutions and proud of myself only to be told no we want X even though we said Y.  The claim is IT people speak a different language, so it always is good start out with a good working definition.

Take care, Fred, Laura, et al!

Author

Commented:
I can't tell you how helpful the two of you have been. Thank you so much!!
Kevin CrossChief Technology Officer
Most Valuable Expert 2011

Commented:
You are very welcome!  We get very excited about getting bonuses. *laughing*
Thank you!  Now and then even a typo becomes a quoted phrase.  So I get no credit, just my "all thumbs" fingers!!

Author

Commented:
Ha! Yes! Of course. And I will obviously put you in at the top level for individual performance!

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