The cheapest way to do accounting is to do it yourself, but that can be time consuming and difficult. The costs for outsourcing it varies greatly between companies and how much work they have to do. Firms like PwC, KPMG, Ernst&Young, and Deloitte are fantastic to work with but tend to cost a fortune, compared to smaller accounting firms, where the service may not be the best.
You need to better estimate the number of invoices, payments, and receipts your company will generate in a fiscal year and contact accounting firms to get an estimate.