I am an accountant with a university mathematics degree. Although its been some years since I became heavily involved in Mathematics, I should be able to understand most things, however I can't get my head around this problem.
At work I have encountered a problem with fractions. I have to explain this to my Chief Financial Officer and to the board so I need to come up with a credible explanation that is say less than 30 seconds long and is in leyman's term's. I can't simply say the "The maths doesn't work" or go through on a whiteboard the proof. So any references to Math theory would be appreciated so that I can add credibility to my answer.
(e.g. the fraction rule - Fraction addition with different denominators - If one denominator divides evenly into the other, change to the higher denominator and add)
The problem - (I have used simple numbers below but the actual problem is in thousands of dollars and holds more sets of customers)
I have two sets of customers,
'Customer A' had expected revenue of 10 but has only renewed 8, therefore we have a renewal fraction of 4/5
'Cusotomer B' had expected revenue of 20 but has only renewed 10, therefore we have a renewal fraction of 1/2
The summarized renewal fraction is therefore 3/5 (e.g 18 / 30)
We then have this other Key performance indicator called ACV (Annual contract value) I won't explain further what this is but it is independently derived from the renewed dollars.
For this we have the following result
'Customer A' ACV = 5 and 'Customer B' ACV = 15, total ACV therefore equals 20.
So for my purposes we are going to apply the above fractions to these results.
'Customer A' renewal fraction X ACV = 5 x 4/5 = 4 'Customer B' renewal fraction x ACV = 15 x 1/2 = 7.50 4 + 7.50 = 11.50
But if we take summarized renewal fraction and multiply it by the total ACV we reach a different result of 12 ( 20 x 3/5 = 12)
Does anyone know of any theory of why we get different results? I've tried to explain to my CFO that the Maths doesn't work and you can't apply fractions to different sets of data, but he has asked for a more credible answer.
Thanks for your help in advance.