You don’t have to be a chartered accountant in order to understand and manage project budgets, however it is important that you have a firm grasp of accounting principles. You’ll need to understand that project financials are made up of:
ACTUAL costs to date + remaining FORECAST costs = estimate at complete. (EAC)
All Control boards whether it be program or project will expect you as the project manager to have a firm understanding of your projects current financial position and be able to report on it usually monthly. If you have costs that were due this month but were not invoiced then you will need to create an accrual that will allow you to balance the monthly forecast. Once the accrued costs land then these will need to be reversed.
Do expect that any variation to your forecast will require clear justification and in the case of overspends may well require the sponsor to seek additional funding from investment sources.
The budget should track all costs whether they be project related or from the business in order to run the initiative from an operational perspective. The business case would also contain all project and operational costs plus the associated benefits that would arise from the initiative. Your finance areas should be able to help calculate net present value and internal rate of return that helps measure the profitability of the initiative.