For whom it may concern,
Consider the following situation, a parent company "P" holds two subsidiaries (i) A1 which in turn has a subsidiary, A2, and a sub-subsidiary A3 (lets call these the A-chain) and (ii) B1, which in turn has a subsidiary B2 (lets call these the B-chain. A network of payables and receivables exists between A1, A2, A3, B1, and B2. The purpose of this exercise is to single out the payables between A1, A2 and A3 excluding payables between A1-A2 & A1-A3 (lets call this the "desired sum") while balances only contain 'group debt' entries which cover payables/receivables to/from all possible group companies. Below follows an image with a numeric example (balances show individual receivables/payables for simplicity).
Considering the fact that group payables and receivables (assume no write-offs) correspond with each other on the balances of all the group companies, I figure the following equation would always return "the desired result"(no matter the amount of payables/receivables/group entities):
-1* (Difference between ALL group payables & Receivables minus the Sum of group payables of A2 & A3)
Translated to the numeric example this results in the following equation: 790 - (1390 - 1290 + 790 - 290) = Desired sum of payables, put simplified: -1*(100-290) = Desired sum of payables Desired sum of payables = 190 190 corresponds with the sum of Payable A1 (170) and Payable A2 (190) from the example (see uploaded image). The elements of the function can be broken up as follows:
1390 = 170 + 50 + 20 + 150 + 400 + 200 + 100 + 200 (I.e. all group receivables found on all balances)
1290 = 150 + 100 + 170 + 100 + 20 + 400 + 100 + 50 + 200 (I.e. all group payables found on all balances)
290 = 170 (payable A1) + 100 (Payable B1) + 20 (payable A2) (I.e all group payables found on the balances of the (sub-)subsidiaries of A-chain)
The question is, whether or not it can be mathematically proved that this method will return the 'desired sum' in all situations (I.e. situations where there are more/less group companies and with more/less complex 'webs' of payables/receivables). Any help would be greatly appreciated.
Kind regards,
Moljka