S. Pinfield et al. have self-archived "The 'Total Cost of Publication' in a Hybrid Open-Access Environment: Institutional Approaches to Funding Journal Article-Processing Charges in Combination with Subscriptions."
Here's an excerpt:
This study analyses data from 23 UK institutions covering the period 2007 to 2014 modelling the total cost of publication (TCP). It shows a clear rise in centrally-managed APC payments from 2012 onwards, with payments projected to increase further. As well as evidencing the growing availability and acceptance of OA publishing, these trends reflect particular UK policy developments and funding arrangements intended to accelerate the move towards OA publishing ('Gold' OA). Whilst the mean value of APCs has been relatively stable, there was considerable variation in APC prices paid by institutions since 2007. In particular, 'hybrid' subscription/OA journals were consistently more expensive than fully-OA journals. Most APCs were paid to large 'traditional' commercial publishers who also received considerable subscription income. New administrative costs reported by institutions varied considerably. The total cost of publication modelling shows that APCs are now a significant part of the TCP for academic institutions, in 2013 already constituting an average of 10% of the TCP (excluding administrative costs).