Commission Calculation - Who is Right?

Hi All,

Just a quick one that's baffling me slightly!

We have a commision in place which is based on the total value of stock expiring divided by total purchases for that month. This is paid quarterly and is based on a specific quarterly target.

My manager has based it by getting an average of the percentage each month, e.g. Apr (€14,643 / €508,537) = 2.9%, May (€4,535 / €561,735) = 0.8% Jun (€6,072 / €780,033) = 0.8% and the average is (2.9%+0.8%+0.8%)/3 = 1.49%.

However, as the target is Quarterly and not Monthly, I think it should be based on a total for the quarter, which in this case would be €25,250 / €1,850,305 = 1.36%.

Can anyone throw any light on why the figures are so different? I know it's probably completely obvious but I don't want to point out any issue without knowing all the facts first.

Thanks!

The second calculation is the correct one.
It doesn't make sense to add percentages like in the first example.

umop3p!sdn said:

The second calculation is the correct one.
It doesn't make sense to add percentages like in the first example.

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Thanks for that! Can you explain to my poor confused mind why the difference?

Try it with a simple sum. Im not great at explaining these things, but here goes.
Hopefully this is clear.

(14/200) + (6/100) + (9/250) is not the same calculation and therefore not the same answer as (14+6+9)/(200+100+250)

Multiplication /division are commutative, which means that it doesn't matter what order you do the calculation. ( 14 * 15 * 2) = ( 2 * 15 * 14)

Addition is also commutative.( 14 + 15 + 2 ) = (2 + 15 + 14)

BUT, you cant mix multiplication and addition ( 14 * 15 + 2) is not equal to (2 + 15 * 14)

huskerdu said:

Try it with a simple sum. Im not great at explaining these things, but here goes.
Hopefully this is clear.

(14/200) + (6/100) + (9/250) is not the same calculation and therefore not the same answer as (14+6+9)/(200+100+250)

Multiplication /division are commutative, which means that it doesn't matter what order you do the calculation. ( 14 * 15 * 2) = ( 2 * 15 * 14)

Addition is also commutative.( 14 + 15 + 2 ) = (2 + 15 + 14)

BUT, you cant mix multiplication and addition ( 14 * 15 + 2) is not equal to (2 + 15 * 14)

Click to expand...

Ok that's great, thanks for your help!!

When I went to school I learnt that you multiply out before you add so therefore the two sums ( 14 * 15 + 2) and (2 + 15 * 14) give identical answers.

I think either method could be considered correct.

I know that the first method, getting the quarterly average from the monthly averages, might seem wrong but that's not really the case.. using the first method you're getting an average of an average, and when using the second method you're just getting an overall average, by summing the monthly values first... there is nothing inherently wrong with either method.

It seems your objective is to minimise the amount of 'expired stock', so you want a lower average overall, yes?

I think either method could be correct, but the same method should be used all the time, there shouldn't be a choice made each quarter as to how to calculate the amounts. Once the same method is used all the time then either is ok.

Do you have the exact wording relating to how this should be calculated?

Willowchase said:

When I went to school I learnt that you multiply out before you add so therefore the two sums ( 14 * 15 + 2) and (2 + 15 * 14) give identical answers.

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Yes, you are correct, in each case the answer is (14*15) + 2, as multiplication takes precedence over addition, like you said. But this was just a simple error, and the point was made despite it.

It should have read
(14 * 15) + 2 is not equal to 14 * (15 + 2)... where the brackets override the precedence because brackets have the highest precedence.

The original would also be correct (i.e not equal) if you ignored precedence and operated from left to right.

willowchase said:

when i went to school i learnt that you multiply out before you add so therefore the two sums ( 14 * 15 + 2) and (2 + 15 * 14) give identical answers.

Click to expand...

+1

JoeBallantin said:

It seems your objective is to minimise the amount of 'expired stock', so you want a lower average overall, yes?

Click to expand...

Given that the objective is to minimise the expired stock, it makes more sense (from a logical pov) to use the weighted average (the latter system which applies more weight to a month with a higher total purchases/expired stock figure) than to just average out the monthly averages (which gives/can give an unrealistic weighting to some figures, by giving an equal weight to a high/low performing month which had a very low total purchases figure).

It's certainly the system I'd use to monitor it, personally. That said, it all depends on what system the company have in place.


To give an illustration.... (using terribly simplistic figures)
Apr (€10/€1,000) = 1%
May (€20/€1,500) = 1.33%
Jun (€900/€2,000) = 45%

There, the average of the %'s is (1%+1.33%+45%)/3 = 15.78%.

However, by weighting them relative to the total value for the quarter, it gives (10+20+900)/(1000+1500+2000) = 20.67%.

In the first calculation, the 1% and 1.33% figures carry the same 'value' or weight as the high 45%, dragging the average down much further. In the latter, the high value 45% month carries more weight, rising the total losses as a percentage of the quarterly losses/purchases.