1) According to our understanding that............
2) As far as we know,John should be responsible for the travelling expenses;
3) In our opinion,John should bear in mind that he ought to pay the travelling expenses.
To bapolaioi,
Correct:-As far as we know,John should bear the travelling expenses.
The word understand=
We understand(verb)
It is understandable(adj)
To know or realize what John do=Do you understand the instruction
Do you understand that John is responsible for the whole travelling cost?
It is understood that John is responsible for the whole travelling cost.